ChemWiki - User contributions [en]

Third year simulation experiment

2023-09-20T07:01:03Z

Fbresme:

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

The best approach to get help is to attend the Teams sessions. The demonstrators will be available to answer questions between 10-12 and 3-4 on Mon, Tue, Thu and Fri. Please feel free to contact the demonstrators via Teams, and ask for help during the lab sessions. Questions can also be asked via email.

'''The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). ''Please feel free to contact Prof. Bresme via email if you have questions about the molecular dynamics method, the theoretical background behind molecular dynamics (statistical thermodynamics) or questions about the exercises. '''''

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials. What additional elements would you need to add to the interaction potential to model a molecule, e.g. water? [6]
#What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? (''Hint: consider here the balance of computational cost vs accuracy in describing the properties of a system''.) [3]
#In this lab you have investigated the properties of solids, liquids and gases. Would you observe a liquid phase (and by extension a critical point) if the LJ interaction strength,<math>\varepsilon</math>, is very weak? What interaction strength is required to generate a liquid phase? (''Hint: to address this question you may want to revise the 2nd year Solids, Liquid and Interfaces lecture notes - see "Phase transitions of pure substances"'') [4]
#What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE are widely used to model molecular systems as they allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [4] ''(Hint: think about the timestep.)''

Third year simulation experiment

2023-01-25T10:54:20Z

Fbresme:

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

The best approach to get help is to attend the Teams sessions. The demonstrators will be available to answer questions between 10-12 and 3-4 on Mon, Tue, Thu and Fri. Please feel free to contact the demonstrators via Teams, and ask for help during the lab sessions. Questions can also be asked via email.

'''The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). ''Please feel free to contact Prof. Bresme via email if you have questions about the molecular dynamics method, the theoretical background behind molecular dynamics (statistical thermodynamics) or questions about the exercises. You can also contact Prof F. Bresme via email the week after you have completed your session, and before you submit your report.'''''

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials. What additional elements would you need to add to the interaction potential to model a molecule, e.g. water? [6]
#What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? (''Hint: consider here the balance of computational cost vs accuracy in describing the properties of a system''.) [3]
#In this lab you have investigated the properties of solids, liquids and gases. Would you observe a liquid phase (and by extension a critical point) if the LJ interaction strength,<math>\varepsilon</math>, is very weak? What interaction strength is required to generate a liquid phase? (''Hint: to address this question you may want to revise the 2nd year Solids, Liquid and Interfaces lecture notes - see "Phase transitions of pure substances"'') [4]
#What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE are widely used to model molecular systems as they allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [4] ''(Hint: think about the timestep.)''

Third year simulation experiment/Files to download

2022-11-19T19:08:02Z

Fbresme: /* Getting the files for the experiment */

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

All of the simulations that you run in this experiment are going to be performed in Virtual Machines (VM). Before the beginning of your lab session, you should have received an invitation email to register/connect to the VM.


In each section of the exercise, we have tried to provide a number of mathematical and/or research exercises that you should attempt while you are waiting for the simulations in that section to be completed. Each simulation should take a few minutes. You can also use this time to write your report on the previous sections!

In this first section, we will teach you how to login to the Virtual Machines and submit an example simulation. While you wait for that example to complete, you can move on to the next section and read about the theory of molecular dynamics simulations

==Connecting to the Virtual Machine==

You will be using a Microsoft Azure Lab Virtual Machine (VM) to access the software needed for the lab.

: 1. You will receive an invitation email, before your session starts, with the subject Register for Lab - IC_Chemistry_UK_LS.
: 2. Follow the link to 'Register for the lab' in the email which will direct you to the Azure Lab Services page.
: 3. On the web page, you should see a box corresponding to the VM shared with you. In the bottom left, slide the toggle from left to right to start the VM (It may take some time to start running).
: 4. Once running, at the bottom right of the box, click the computer-style icon next to the three vertical dots.
A file with the extension rdp will be downloaded: IC_Chemistry_UK_LS.rdp. Follow the instructions for your operating service below to use the file:

'''Windows'''

:: a. Navigate to where the file has downloaded and double click on the file to open.

'''Linux'''

:: a. Open a terminal window and through the terminal, go to the location where the file has downloaded.
:: b. Type the command: <pre> remmina IC_Chemistry_UK_LS.rdp </pre> to run the file.

'''Mac'''

:: a. Download and install the Microsoft Remote Desktop app for Mac OS.
:: b. Open the Microsoft Remote Desktop app
:: c. On the top toolbar bar, click on the cog icon and then select Import from RDP file..
:: d. Navigate and select the downloaded rdp file.
:: e. There should now be an 'IC_Chemistry_UK_LS' PC showing, double click on this to initialise.

: 5. You should be asked to Accept Certificate?, select Yes.
: 6. You will be asked to Enter authentication credentials:
:: a. Change the username into "chemistry" by removing "~/".
:: b. Enter the password provided in the invitation email to 'Register for the Lab'.
The VM should now launch and you will be taken to a Windows desktop where you should be able to see the LAMMPS icon on the desktop. Double click this to launch.

If you have any problems with accessing the VM then let a demonstrator know.



== How to run lammps==

Once connected to the Microsoft Azure Window virtual machine, click on Lammps-shell (bottom left icon) to open a special lammps terminal, 
then click on the yellow folder as indicated by the arrow and drag-and-drop it in the terminal after "cd "

 
[[File:ThirdYearSimulationExpt-lammps-vm.png|600px|center|'''Lammps''': How to run lammps]]
 

To run, type:
source melt_crystal.in

Remember to open a new Lammps-shell for each calculation

In your windows folder, edit the input file with Notepad or Code

VMD is available as an icon on the desktop (and anaconda is installed).

==Getting the files for the experiment==

You can download all of the files that you will need for this experiment [https://imperialcollegelondon.box.com/s/mjxn9zxl67y10pgn8wkwlin05hmyqdsn from this address] or from this [https://imperiallondon-my.sharepoint.com/:u:/g/personal/fbresme_ic_ac_uk/EcxHpQ9p09BIs81A7vnpYSIBOIaxGzTVp9aj_kDjKYqCMw address] [[this address .|.]] You should copy the folder '''ImperialChem-Year3SimExpt1415-master''' to a location of your choice. It contains a number of subfolders — one for each section of the experiment. Every subsequent page of this lab manual will begin with a line telling you which folder contains the necessary files, like this one:

<big>'''THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "Intro" SUBFOLDER'''.</big>

Have a look in the '''"Intro"''' folder now. It contains a file called '''melt_crystal.in''', which you should open with a text editor (like Notepad++ or VSCode which you can find on Software Hub. VSCode is also on the Virtual Machines). This file is called an "input script", and it controls how the simulation software operates. We will perform all of our simulations with a software package called [http://lammps.sandia.gov LAMMPS]. Over the course of the experiment, you will learn what all of the commands in this file mean. The [https://lammps.sandia.gov/doc/Commands.html LAMMPS manual] contains a lot of valuable information about each of the commands, if you don't understand one of them or want to look up what some parameter means you can look it up there. To make life easier, we put "further info" links in the wiki. For now, we are going to use this file to run a few trial simulations.

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

Third year simulation experiment

2022-11-16T08:52:12Z

Fbresme:

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

The best approach to get help is to attend the Teams sessions. The demonstrators will be available to answer questions between 10-12 and 3-4 on Mon, Tue, Thu and Fri. Please feel free to contact the demonstrators via Teams, and ask for help during the lab sessions. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). ''Please feel free to contact Prof. Bresme via email if you have questions about the molecular dynamics method, the theoretical background behind molecular dynamics (statistical thermodynamics) or questions about the exercises. You can also contact Prof F. Bresme via email the week after you have completed your session, and before you submit your report.''

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials. What additional elements would you need to add to the interaction potential to model a molecule, e.g. water? [6]
#What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? (''Hint: consider here the balance of computational cost vs accuracy in describing the properties of a system''.) [3]
#In this lab you have investigated the properties of solids, liquids and gases. Would you observe a liquid phase (and by extension a critical point) if the LJ interaction strength,<math>\varepsilon</math>, is very weak? What interaction strength is required to generate a liquid phase? (''Hint: to address this question you may want to revise the 2nd year Solids, Liquid and Interfaces lecture notes - see "Phase transitions of pure substances"'') [4]
#What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE are widely used to model molecular systems as they allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [4] ''(Hint: think about the timestep.)''

Third year simulation experiment

2022-11-16T08:50:43Z

Fbresme:

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

The best approach to get help is to attend the Teams sessions. The demonstrators will be available to answer questions between 10-12 and 3-4 on Mon, Tue, Thu and Fri. Please feel free to contact the demonstrators via Teams, and ask for help during the lab sessions. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). ''Please feel free to contact Prof. Bresme via email if you have questions about the molecular dynamics method and the theoretical background behind molecular dynamics (statistical thermodynamics). You can also contact Prof F. Bresme via email the week after your session, before you submit your report.''

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials. What additional elements would you need to add to the interaction potential to model a molecule, e.g. water? [6]
#What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? (''Hint: consider here the balance of computational cost vs accuracy in describing the properties of a system''.) [3]
#In this lab you have investigated the properties of solids, liquids and gases. Would you observe a liquid phase (and by extension a critical point) if the LJ interaction strength,<math>\varepsilon</math>, is very weak? What interaction strength is required to generate a liquid phase? (''Hint: to address this question you may want to revise the 2nd year Solids, Liquid and Interfaces lecture notes - see "Phase transitions of pure substances"'') [4]
#What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE are widely used to model molecular systems as they allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [4] ''(Hint: think about the timestep.)''

Third year simulation experiment/Running simulations under specific conditions

2022-10-10T17:09:36Z

Fbresme: /* Temperature and Pressure Control */

'''<big>This is the fourth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Equilibration|Equilibration]], or jump ahead to the next section, [[Third_year_simulation_experiment/Structural_properties_and_the_radial_distribution_function| Structural Properties and the Radial Distribution Functions]].</big>'''

'''<big>THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "NpT" SUBFOLDER.</big>'''

==Changing Ensemble==

So far, we have been able to do some simulations in which the number of particles and the volume of the simulation cell are held constant. The energy is also constant (within a certain degree of error, which is introduced by the approximations that we make to do the simulation). If the simulation is a working properly, then the pressure and temperature of the system should also reach a constant ''average'' value (although there will again be fluctuations). As mentioned in the introductory questions in this lab ensembles are used in statistical thermodynamics to represent different sorts of experimental conditions. The simulations we have done so far are described by the ''microcanonical'', or NVE ensemble (the letters represent those thermodynamic quantities which are constant).

As chemists, we often want to understand what happens under particular experimental conditions — at 298K under 1 atmosphere of pressure, for example. These sorts of conditions are described by different ensembles in statistical thermodynamics, such as the NVT (''canonical'') or NpT (''isobaric-isothermal'') ensembles.

In this section, we are going to modify our simulations from the previous section to run under NpT conditions, and sketch an equation of state for our model fluid at atmospheric pressure.

==Temperature and Pressure Control==

The file npt.in can be used to perform a constant temperature/pressure simulation of our model fluid. It starts by melting a simple cubic crystal, just as before, so much of this file will look familiar to you. You will notice a new section near the top, however, called '''### SPECIFY THE REQUIRED THERMODYNAMIC STATE ###'''. It contains three ''variables'' — these are used by the script later on to define the desired temperature, pressure, and timestep. The ellipses need to be replaced by the actual temperature, pressure and timestep that you want to use, so

<pre>
variable T equal 0.5
variable p equal 1.0
variable timestep equal 0.75
</pre>

would run a simulation at <math>T=0.5,\ p=1.0,\ \delta t=0.75</math>. You should remember from the [[Third_year_simulation_experiment/Equilibration|Equilibration]] section that this is a poor choice of timestep!

'''<big>TASK 8: Choose 5 temperatures (above the critical temperature, e.g. <math>T^* \ge 1.5</math>), and two pressures (you can get a good idea of what a reasonable pressure is in Lennard-Jones units by looking at the average pressure of your simulations from the last section). This gives ten phase points — five temperatures at each pressure. Create 10 copies of npt.in, and modify each to run a simulation at one of your chosen <math>\left(p, T\right)</math> points. You should be able to use the results of the previous section to choose a timestep. Run these 10 scripts on the virtual machine. When your simulations have finished, download the log files as before. At the end of the log file, LAMMPS will output the values and errors for the pressure, temperature, and density <math>\left(\frac{N}{V}\right)</math>. </big>'''

=== Plot the density as a function of temperature for both pressures that you simulated. Include a line corresponding to the predictions made by the ideal gas law. [3] ===

=== How do your results compare to the ideal gas law? Do deviations increase/decrease with temperature and pressure? Explain. [7] ===

=== Do you expect your simulation results to be in better or worse agreement with the Van der Waals equation of state? Why? [3] ===

===Thermostats and Barostats - controlling the thermodynamic properties===
The 2nd year Solids, Liquid and Interfaces lectures will have introduced you to the ''equipartition theorem'', which states that, on average, every degree of freedom in a system at equilibrium will have <math>\frac{1}{2}k_B T</math> of energy. In our system with <math>N</math> atoms, each with 3 degrees of freedom, we can write
<math>E_K = \frac{3}{2} N k_B T</math>

<math>\frac{1}{2}\sum_i m_i v_i^2 = \frac{3}{2} N k_B T</math>

At the end of every timestep, we use the left hand side of this equation to calculate the kinetic energy, then divide by <math>\frac{3}{2}Nk_B</math> to get the ''instantaneous'' temperature <math>T</math>. In general, <math>T</math> will fluctuate, and will be different to our ''target'' temperature, <math>\mathfrak{T}</math> (this is whatever value we specify in the input script). We can change the temperature by multiplying every velocity by a constant factor, <math>\gamma</math>.

* If <math> T > \mathfrak{T} </math>, then the kinetic energy of the system is too high, and we need to reduce it. <math>\gamma < 1</math>
* If <math> T < \mathfrak{T} </math>, then the kinetic energy of the system is too low, and we need to increase it. <math>\gamma > 1</math>

We need to choose a scaling parameter <math>\gamma</math> so that the temperature is correct <math>T = \mathfrak{T}</math> if we multiply every velocity <math>\gamma</math>. We can write two equations:'''
<math>\frac{1}{2}\sum_i m_i v_i^2 = \frac{3}{2} N k_B T</math>

<math>\frac{1}{2}\sum_i m_i \left(\gamma v_i\right)^2 = \frac{3}{2} N k_B \mathfrak{T}</math>

By combining these equations, one can see that <math> \gamma = \sqrt{\frac{\mathfrak{T}}{T}} </math> (satisfy yourself that this is true!). A target value of <math> \gamma </math> of 1 is required and thus, dependent on whether it's larger or smaller than 1 the simulation can target the desired temperature.

Controlling the pressure is a little more involved, but the principle is largely the same: at each timestep, the pressure of the system is calculated; if the pressure is too high, then the simulation box is made a little larger, while if the pressure is too low the box is made smaller. Simulations in which the pressure is controlled are thus in the NpT ensemble — the volume of the simulation box is not constant!

===Examining the Input Script===

Open one of your input scripts (it doesn't matter which), and look at the section '''### BRING SYSTEM TO REQUIRED STATE ###'''. The line <pre>fix npt all npt temp ${T} ${T} ${tdamp} iso ${p} ${p} ${pdamp}</pre> is the one responsible for switching on the temperature and pressure control. LAMMPS actually allows us to heat or cool the system over the course of a simulation, if we want to — this is the reason that the temperature appears twice in this line. The first ${T} is the desired starting temperature, and the second is the desired temperature at the end of the simulation. We want a constant average temperature, so we specify the same value twice. The same goes for the pressure.

Now look at the lines near the end of the file:

<pre>
### MEASURE SYSTEM STATE ###
thermo_style custom step etotal temp press density
variable dens equal density
variable dens2 equal density*density
variable temp equal temp
variable temp2 equal temp*temp
variable press equal press
variable press2 equal press*press
fix aves all ave/time 100 1000 30000 v_dens v_temp v_press v_dens2 v_temp2 v_press2
run 30000
</pre>

The first command, ''thermo_style'', controls which thermodynamic properties are recorded, as before. The next lines are used to measure ''average'' thermodynamic properties for the system. To draw our equations of state, we need to know the average temperature, pressure, and density, and the statistical errors in those quantities. The six variable lines link those quantities (and their squared values, needed for the errors), to variable names that we can use in the averaging command, which is the line starting ''fix aves...''. This command takes a number of input values and averages them every so many timesteps. Exactly how often this happens depends in the values of the three numbers which follow ''ave/time''.

'''<big>This is the fourth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Equilibration|Equilibration]], or jump ahead to the next section, [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]].</big>'''

Programming a 2D Ising Model/Locating the Curie temperature

2022-03-09T16:51:43Z

Fbresme:

'''<big>This is the eighth (and final) section of the third year CMP experiment. You can return to the previous page, [[Third_year_CMP_compulsory_experiment/Determining the heat capacity|Determining the heat capacity]], or go back to the [[Third year CMP compulsory experiment|Introduction]].</big>'''

You should have seen in the previous section that the heat capacity becomes strongly peaked in the vicinity of the critical temperature and that the peak became increasingly sharply peaked as the system size was increased — in fact, Onsager proved that in an infinite system the heat capacity should diverge at <math>T = T_C</math>. In our finite systems, however, not only does the heat capacity not diverge, the Curie temperature changes with system size! This is known as a ''finite size effect''.

It can be shown, however, that the temperature at which the heat capacity has its maximum must scale according to <math>T_{C, L} = \frac{A}{L} + T_{C,\infty}</math>, where <math>T_{C, L}</math> is the Curie temperature of an <math>L\times L</math>lattice, <math>T_{C,\infty}</math> is the Curie temperature of an infinite lattice, and <math>A</math> is a constant in which we are not especially interested.

'''<big>TASK 8a</big>: A C++ program has been used to run some much longer simulations than would be possible on the college computers in Python. Each file contains six columns: <math>T, E, E^2, M, M^2, C</math> (the final five quantities are per spin), and you can read them with the NumPy loadtxt function as before. For each lattice size, plot the C++ data against your data. For ''one'' lattice size, save a PNG of this comparison and add it to your report — add a legend to the graph to label which is which. To do this, you will need to pass the label="..." keyword to the plot function, then call the legend() function of the axis object (documentation [http://matplotlib.org/api/axes_api.html#matplotlib.axes.Axes.legend here]).'''

==Polynomial fitting==

To find the temperature at which the heat capacity has its maximum, we are going to fit a polynomial to the data in the critical region. NumPy provides the useful [http://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html polyfit] and [http://docs.scipy.org/doc/numpy/reference/generated/numpy.polyval.html#numpy.polyval polyval] functions for this purpose. The usage is as follows:

<pre>
data = np.loadtxt("...") #assume data is now a 2D array containing two columns, T and C
T = data[:,0] #get the first column
C = data[:,1] # get the second column

#first we fit the polynomial to the data
fit = np.polyfit(T, C, 3) # fit a third order polynomial

#now we generate interpolated values of the fitted polynomial over the range of our function
T_min = np.min(T)
T_max = np.max(T)
T_range = np.linspace(T_min, T_max, 1000) #generate 1000 evenly spaced points between T_min and T_max
fitted_C_values = np.polyval(fit, T_range) # use the fit object to generate the corresponding values of C
</pre>

'''<big>TASK 8b</big>: write a script to read the data from a particular file, and plot C vs T, as well as a fitted polynomial. Try changing the degree of the polynomial to improve the fit — in general, it might be difficult to get a good fit! Attach a PNG of an example fit to your report.'''

===Fitting in a particular temperature range===

Rather than fit to all of the data, we might want to fit in only a particular range. NumPy provides a very powerful way to index arrays based on certain conditions. For example, if we want to extract only those data points which are between a particular <math>T_{\mathrm{min}}</math> and <math>T_{\mathrm{max}}</math>, we can use the following syntax:

<pre>
data = np.loadtxt("...") #assume data is now a 2D array containing two columns, T and C
T = data[:,0] #get the first column
C = data[:,1] # get the second column

Tmin = 0.5 #for example
Tmax = 2.0 #for example

selection = np.logical_and(T > Tmin, T < Tmax) #choose only those rows where both conditions are true
peak_T_values = T[selection]
peak_C_values = C[selection]
</pre>

'''<big>TASK 8c</big>: Modify your script from the previous section. You should still plot the whole temperature range, but fit the polynomial only to the peak of the heat capacity! You should find it easier to get a good fit when restricted to this region.'''

===Finding the peak in C===

Your fitting script should now generate two variables: peak_T_range, containing 1000 equally spaced temperature values between <math>T_{\mathrm{min}}</math> and <math>T_{\mathrm{max}}</math> (whatever you chose those values to be), and fitted_C_values, containing the fitted heat capacity at each of those points. Use the NumPy max function to find the maximum in C. If you store the maximum value of C in the variable Cmax, you can use the following notation to find the corresponding temperature:

<pre>
Cmax = np.max(...)
Tmax = peak_T_range[fitted_C_values == Cmax]
</pre>

'''<big>TASK 8d</big>: find the temperature at which the maximum in C occurs for each datafile that you were given or generated with Python. Make a text file containing two colums: the lattice side length (2,4,8, etc.), and the temperature at which C is a maximum. This is your estimate of <math>T_C</math> for that side length. Make a plot that uses the scaling relation given above to determine <math>T_{C,\infty}</math>. By doing a little research online, you should be able to find the theoretical exact Curie temperature for the infinite 2D Ising lattice. How does your value compare to this? Are you surprised by how good/bad the agreement is? Attach a PNG of this final graph to your report, and discuss briefly what you think the major sources of error are in your estimate.'''

'''<big>This is the eighth (and final) section of the third year CMP experiment. You can return to the previous page, [[Third_year_CMP_compulsory_experiment/Determining the heat capacity|Determining the heat capacity]], or go back to the [[Third year CMP compulsory experiment|Introduction]].</big>'''

Programming a 2D Ising Model/The effect of system size

2022-03-09T16:48:52Z

Fbresme: /* Scaling the System Size */

'''<big>This is the sixth section of the third year CMP experiment. You can return to the previous page, [[Third_year_CMP_compulsory_experiment/The effect of temperature|The effect of temperature]], or jump ahead to the next section, [[Third year CMP compulsory experiment/Determining the heat capacity|Determining the heat capacity]].</big>'''

==Scaling the System Size==

Your plots from the previous section showed how the magnetisation and energy vary with temperature, and you should be able to see the onset of the phase transition. In this region, the energetic and entropic driving forces are of almost equal importance, and large fluctuations in the state of the system can take place. In fact, it is a characteristic of phase transitions that fluctuations within a system start to take place over very long ranges. This is a big problem in our simulation — so far, we only have 64 spins (or "atoms", if you prefer), so our system may not be big enough for these long ranged fluctuations to be correctly modelled.

'''<big>TASK 6</big>: Repeat the final task of the previous section for the following lattice sizes: 2x2, 4x4, 8x8, 16x16, 32x32. Make sure that you name each datafile that your produce after the corresponding lattice size! Write a Python script to make a plot showing the energy ''per spin'' versus temperature for each of your lattice sizes. Hint: the NumPy loadtxt function is the reverse of the savetxt function, and can be used to read your previously saved files into the script. Repeat this for the magnetisation. As before, use the plot controls to save your a PNG image of your plot and attach this to the report. How big a lattice do you think is big enough to capture the long range correlations?'''

'''<big>This is the sixth section of the third year CMP experiment. You can return to the previous page, [[Third_year_CMP_compulsory_experiment/The effect of temperature|The effect of temperature]], or jump ahead to the next section, [[Third year CMP compulsory experiment/Determining the heat capacity|Determining the heat capacity]].</big>'''

Third year simulation experiment

2021-10-24T11:04:28Z

Fbresme: /* Conclusion Questions */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials. What additional elements would you need to add to the interaction potential to model a molecule, e.g. water? [6]
#What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? (''Hint: consider here the balance of computational cost vs accuracy in describing the properties of a system''.) [3]
#In this lab you have investigated the properties of solids, liquids and gases. Would you observe a liquid phase (and by extension a critical point) if the LJ interaction strength,<math>\varepsilon</math>, is very weak? What interaction strength is required to generate a liquid phase? (''Hint: to address this question you may want to revise the 2nd year Solids, Liquid and Interfaces lecture notes - see "Phase transitions of pure substances"'') [4]
#What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE are widely used to model molecular systems as they allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [4] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T11:03:01Z

Fbresme: /* Conclusion Questions */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials. What additional elements would you need to add to the interaction potential to model a molecule, e.g. water? [6]
#What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? (''Hint: consider here the balance of computational cost vs accuracy in describing the properties of a system''.) [3]
#In this lab you have investigated the properties of solids, liquids and gases. Would you observe a liquid phase (and by extension a critical point) if the LJ interaction strength,<math>\varepsilon</math>, is very weak? What interaction strength is required to generate a liquid phase? (''Hint: to address this question you may want to revise the 2nd year Solids, Liquid and Interfaces lecture notes - see "Phase transitions of pure substances"'') [4]
#What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE are widely used to model molecular systems as they allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [4] ''(Hint: think about the timestep.)''
# In the simulations you have performed ergodicity has not been an issue. Describe a system in which "brute force" MD struggles to achieve ergodic sampling. Describe one "enhanced sampling" technique that can be used to overcome this. [7]

Third year simulation experiment

2021-10-24T11:02:16Z

Fbresme: /* Conclusion Questions */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials. What additional elements would you need to add to the interaction potential to model a molecule, e.g. water? [6]
#What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? (''Hint: consider here the balance of computational cost vs accuracy in describing the properties of a system''.) [3]
#In this lab you have investigated the properties of solids, liquids and gases. Would you observe a liquid phase (and by extension a critical point) if the LJ interaction strength,<math>\varepsilon</math>, is very weak? What interaction strength is required to generate a liquid phase? (''Hint: to address this question you may want to revise the 2nd year Solids, Liquid and Interfaces lecture notes - see "Phase transitions of pure substances"'') [3]
#What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE are widely used to model molecular systems as they allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''
# In the simulations you have performed ergodicity has not been an issue. Describe a system in which "brute force" MD struggles to achieve ergodic sampling. Describe one "enhanced sampling" technique that can be used to overcome this. [7]

Third year simulation experiment

2021-10-24T10:59:59Z

Fbresme: /* Conclusion Questions */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials. What additional elements would you need to add to the interaction potential to model a molecule, e.g. water? [6]
#What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? (''Hint: consider here the balance of computational cost vs accuracy in describing the properties of a system''.) [3]
#In this lab you have investigated the properties of solids, liquids and gases. Would you observe a liquid phase if the LJ interaction strength,<math>\varepsilon</math>, is very weak? (''Hint: to address this question you may want to revise the 2nd year Solids, Liquid and Interfaces lecture notes - Phase transitions of pure substances'') [3]
#What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE are widely used to model molecular systems as they allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''
# In the simulations you have performed ergodicity has not been an issue. Describe a system in which "brute force" MD struggles to achieve ergodic sampling. Describe one "enhanced sampling" technique that can be used to overcome this. [7]

Third year simulation experiment

2021-10-24T10:57:30Z

Fbresme: /* Conclusion Questions */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials. What additional elements would you need to add to the interaction potential to model a molecule, e.g. water? [6]
#What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? (''Hint: consider here the balance of computational cost vs accuracy in describing the properties of a system''.) [3]
#In this lab you have investigated the properties of solids, liquids and gases. Would you observe a liquid phase if the LJ interaction strength is very weak? (''Hint: to address this question you may want to revise the 2nd year Solids, Liquid and Interfaces lecture notes - Phase transitions of pure substances'') [3]
#What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE are widely used to model molecular systems as they allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''
# In the simulations you have performed ergodicity has not been an issue. Describe a system in which "brute force" MD struggles to achieve ergodic sampling. Describe one "enhanced sampling" technique that can be used to overcome this. [7]

Third year simulation experiment/Structural properties and the radial distribution function

2021-10-24T10:41:16Z

Fbresme:

'''<big>This is the fifth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]], or jump ahead to the next section, [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]].</big>'''

We can characterise the structure of systems that we simulate using [http://en.wikipedia.org/wiki/Radial_distribution_function radial distribution functions], which we denote <math>g(r)</math>. Calculating the RDF for a simulation is very useful — it can tell us the distances from an atom at which it is more likely to find it's nearest neighbour, second nearest neighbour, and so on; it is also a quantity that can be accessed [[experimentally]], and so provides a good check that the forcefield in our simulation is correctly reproducing the structural features.

In this section, you are going to use VMD to calculate the radial distribution function for the solid, liquid, and vapour phases of the Lennard-Jones fluid.

===Simulations in this section===

The '''RDF''' subfolder contains an example input script that you can use to record an atomic trajectory to generate RDFs for the solid, liquid, and vapour phase Lennard Jones systems. Make three copies of that script (one for each phase), and modify the density and temperature parameters to give the phase that you want (a phase diagram for the Lennard-Jones system can be found [http://journals.aps.org/pr/abstract/10.1103/PhysRev.184.151 here]). <big>'''Note: when simulating the solid, you will need to change the lattice type in the lattice command to fcc, rather than sc. '''</big>

'''<big>TASK 9: perform simulations of the Lennard-Jones system in the three phases (solid, liquid and vapour). When each is complete, open the trajectories (.dump files) and calculate <math>g(r)</math> and <math>4\pi \int g(r) r^{2}\mathrm{d}r</math>. See instructions at the end of this page.</big>'''

=== Briefly explain what a Radial Distribution Function is. What is the relationship between the coordination number and RDF? [2] ===

=== Plot the RDFs for the three systems. [2] ===

=== Discuss qualitatively the differences between the three RDFs, and what this tells you about the structure of the system in each phase. [5] ===

=== In the solid case, illustrate which lattice sites the first three peaks correspond to [2]. What is the lattice spacing [1]? What are the coordination number for each of the first three peaks [1]? ===
'''<big>This is the sixth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Running simulations under specific conditions|Running simulations under specific conditions]], or jump ahead to the next section, [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]].</big>'''

===Calculating <math>g(r)</math> in VMD===

# Start VMD as before and load the trajectory that you want to analyse.
# Select '''Extensions''' -> '''Analysis''' -> '''Radial Pair Distribution Function g(r)'''
# Set '''Selection 1''' to '''all''' and '''Selection 2''' to '''all'''
# Change '''delta r''' to '''0.05''' — this is the distance between points in the generated RDF.
# Ensure that '''Use PBC''', '''Display g(r)''', '''Display Int(g(r))''', and '''Save to File''' are checked
# Click '''Compute g(r)'''

After a short pause while it performs the calculation, VMD will display both the RDF, and its running integral. You will then be prompted to save this data — choose a location for the file that you will be able to find easily later.

Third year simulation experiment/Structural properties and the radial distribution function

2021-10-24T10:39:54Z

Fbresme:

'''<big>This is the fifth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]], or jump ahead to the next section, [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]].</big>'''

We can characterise the structure of systems that we simulate using [http://en.wikipedia.org/wiki/Radial_distribution_function radial distribution functions], which we denote <math>g(r)</math>. Calculating the RDF for a simulation is very useful — it can tell us the distances from an atom at which it is more likely to find it's nearest neighbour, second nearest neighbour, and so on; it is also a quantity that can be accessed [[experimentally]], and so provides a good check that the forcefield in our simulation is correctly reproducing the structural features.

In this section, you are going to use VMD to calculate the radial distribution function for the solid, liquid, and vapour phases of the Lennard-Jones fluid.

===Simulations in this section===

The '''RDF''' subfolder contains an example input script that you can use to record an atomic trajectory to generate RDFs for the solid, liquid, and vapour phase Lennard Jones systems. Make three copies of that script (one for each phase), and modify the density and temperature parameters to give the phase that you want (a phase diagram for the Lennard-Jones system can be found [http://journals.aps.org/pr/abstract/10.1103/PhysRev.184.151 here]). <big>'''Note: when simulating the solid, you will need to change the lattice type in the lattice command to fcc, rather than sc. '''</big>

'''<big>TASK 9: perform simulations of the Lennard-Jones system in the three phases. When each is complete, open the trajectories (.dump files) and calculate <math>g(r)</math> and <math>4\pi \int g(r) r^{2}\mathrm{d}r</math>. See instructions at the end of this page.</big>'''

=== Briefly explain what a Radial Distribution Function is. What is the relationship between the coordination number and RDF? [2] ===

=== Plot the RDFs for the three systems. [2] ===

=== Discuss qualitatively the differences between the three RDFs, and what this tells you about the structure of the system in each phase. [5] ===

=== In the solid case, illustrate which lattice sites the first three peaks correspond to [2]. What is the lattice spacing [1]? What are the coordination number for each of the first three peaks [1]? ===
'''<big>This is the sixth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Running simulations under specific conditions|Running simulations under specific conditions]], or jump ahead to the next section, [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]].</big>'''

===Calculating <math>g(r)</math> in VMD===

# Start VMD as before and load the trajectory that you want to analyse.
# Select '''Extensions''' -> '''Analysis''' -> '''Radial Pair Distribution Function g(r)'''
# Set '''Selection 1''' to '''all''' and '''Selection 2''' to '''all'''
# Change '''delta r''' to '''0.05''' — this is the distance between points in the generated RDF.
# Ensure that '''Use PBC''', '''Display g(r)''', '''Display Int(g(r))''', and '''Save to File''' are checked
# Click '''Compute g(r)'''

After a short pause while it performs the calculation, VMD will display both the RDF, and its running integral. You will then be prompted to save this data — choose a location for the file that you will be able to find easily later.

Third year simulation experiment/Running simulations under specific conditions

2021-10-24T08:53:05Z

Fbresme:

'''<big>This is the fourth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Equilibration|Equilibration]], or jump ahead to the next section, [[Third_year_simulation_experiment/Structural_properties_and_the_radial_distribution_function| Structural Properties and the Radial Distribution Functions]].</big>'''

'''<big>THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "NpT" SUBFOLDER.</big>'''

==Changing Ensemble==

So far, we have been able to do some simulations in which the number of particles and the volume of the simulation cell are held constant. The energy is also constant (within a certain degree of error, which is introduced by the approximations that we make to do the simulation). If the simulation is a working properly, then the pressure and temperature of the system should also reach a constant ''average'' value (although there will again be fluctuations). As mentioned in the introductory questions in this lab ensembles are used in statistical thermodynamics to represent different sorts of experimental conditions. The simulations we have done so far are described by the ''microcanonical'', or NVE ensemble (the letters represent those thermodynamic quantities which are constant).

As chemists, we often want to understand what happens under particular experimental conditions — at 298K under 1 atmosphere of pressure, for example. These sorts of conditions are described by different ensembles in statistical thermodynamics, such as the NVT (''canonical'') or NpT (''isobaric-isothermal'') ensembles.

In this section, we are going to modify our simulations from the previous section to run under NpT conditions, and sketch an equation of state for our model fluid at atmospheric pressure.

==Temperature and Pressure Control==

The file npt.in can be used to perform a constant temperature/pressure simulation of our model fluid. It starts by melting a simple cubic crystal, just as before, so much of this file will look familiar to you. You will notice a new section near the top, however, called '''### SPECIFY THE REQUIRED THERMODYNAMIC STATE ###'''. It contains three ''variables'' — these are used by the script later on to define the desired temperature, pressure, and timestep. The ellipses need to be replaced by the actual temperature, pressure and timestep that you want to use, so

<pre>
variable T equal 0.5
variable p equal 1.0
variable timestep equal 0.75
</pre>

would run a simulation at <math>T=0.5,\ p=1.0,\ \delta t=0.75</math>. You should remember from the [[Third_year_simulation_experiment/Equilibration|Equilibration]] section that this is a poor choice of timestep!

'''<big>TASK 8: Choose 5 temperatures (above the critical temperature <math>T^* = 1.5</math>), and two pressures (you can get a good idea of what a reasonable pressure is in Lennard-Jones units by looking at the average pressure of your simulations from the last section). This gives ten phase points — five temperatures at each pressure. Create 10 copies of npt.in, and modify each to run a simulation at one of your chosen <math>\left(p, T\right)</math> points. You should be able to use the results of the previous section to choose a timestep. Run these 10 scripts on the virtual machine. When your simulations have finished, download the log files as before. At the end of the log file, LAMMPS will output the values and errors for the pressure, temperature, and density <math>\left(\frac{N}{V}\right)</math>. </big>'''

=== Plot the density as a function of temperature for both pressures that you simulated. Include a line corresponding to the predictions made by the ideal gas law. [3] ===

=== How do your results compare to the ideal gas law? Do deviations increase/decrease with temperature and pressure? Explain. [7] ===

=== Do you expect your simulation results to be in better or worse agreement with the Van der Waals equation of state? Why? [3] ===

===Thermostats and Barostats - controlling the thermodynamic properties===
The 2nd year Solids, Liquid and Interfaces lectures will have introduced you to the ''equipartition theorem'', which states that, on average, every degree of freedom in a system at equilibrium will have <math>\frac{1}{2}k_B T</math> of energy. In our system with <math>N</math> atoms, each with 3 degrees of freedom, we can write
<math>E_K = \frac{3}{2} N k_B T</math>

<math>\frac{1}{2}\sum_i m_i v_i^2 = \frac{3}{2} N k_B T</math>

At the end of every timestep, we use the left hand side of this equation to calculate the kinetic energy, then divide by <math>\frac{3}{2}Nk_B</math> to get the ''instantaneous'' temperature <math>T</math>. In general, <math>T</math> will fluctuate, and will be different to our ''target'' temperature, <math>\mathfrak{T}</math> (this is whatever value we specify in the input script). We can change the temperature by multiplying every velocity by a constant factor, <math>\gamma</math>.

* If <math> T > \mathfrak{T} </math>, then the kinetic energy of the system is too high, and we need to reduce it. <math>\gamma < 1</math>
* If <math> T < \mathfrak{T} </math>, then the kinetic energy of the system is too low, and we need to increase it. <math>\gamma > 1</math>

We need to choose a scaling parameter <math>\gamma</math> so that the temperature is correct <math>T = \mathfrak{T}</math> if we multiply every velocity <math>\gamma</math>. We can write two equations:'''
<math>\frac{1}{2}\sum_i m_i v_i^2 = \frac{3}{2} N k_B T</math>

<math>\frac{1}{2}\sum_i m_i \left(\gamma v_i\right)^2 = \frac{3}{2} N k_B \mathfrak{T}</math>

By combining these equations, one can see that <math> \gamma = \sqrt{\frac{\mathfrak{T}}{T}} </math> (satisfy yourself that this is true!). A target value of <math> \gamma </math> of 1 is required and thus, dependent on whether it's larger or smaller than 1 the simulation can target the desired temperature.

Controlling the pressure is a little more involved, but the principle is largely the same: at each timestep, the pressure of the system is calculated; if the pressure is too high, then the simulation box is made a little larger, while if the pressure is too low the box is made smaller. Simulations in which the pressure is controlled are thus in the NpT ensemble — the volume of the simulation box is not constant!

===Examining the Input Script===

Open one of your input scripts (it doesn't matter which), and look at the section '''### BRING SYSTEM TO REQUIRED STATE ###'''. The line <pre>fix npt all npt temp ${T} ${T} ${tdamp} iso ${p} ${p} ${pdamp}</pre> is the one responsible for switching on the temperature and pressure control. LAMMPS actually allows us to heat or cool the system over the course of a simulation, if we want to — this is the reason that the temperature appears twice in this line. The first ${T} is the desired starting temperature, and the second is the desired temperature at the end of the simulation. We want a constant average temperature, so we specify the same value twice. The same goes for the pressure.

Now look at the lines near the end of the file:

<pre>
### MEASURE SYSTEM STATE ###
thermo_style custom step etotal temp press density
variable dens equal density
variable dens2 equal density*density
variable temp equal temp
variable temp2 equal temp*temp
variable press equal press
variable press2 equal press*press
fix aves all ave/time 100 1000 30000 v_dens v_temp v_press v_dens2 v_temp2 v_press2
run 30000
</pre>

The first command, ''thermo_style'', controls which thermodynamic properties are recorded, as before. The next lines are used to measure ''average'' thermodynamic properties for the system. To draw our equations of state, we need to know the average temperature, pressure, and density, and the statistical errors in those quantities. The six variable lines link those quantities (and their squared values, needed for the errors), to variable names that we can use in the averaging command, which is the line starting ''fix aves...''. This command takes a number of input values and averages them every so many timesteps. Exactly how often this happens depends in the values of the three numbers which follow ''ave/time''.

'''<big>This is the fourth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Equilibration|Equilibration]], or jump ahead to the next section, [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]].</big>'''

Third year simulation experiment/Running simulations under specific conditions

2021-10-24T08:52:41Z

Fbresme:

'''<big>This is the fourth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Equilibration|Equilibration]], or jump ahead to the next section, [[Third_year_simulation_experiment/Structural_properties_and_the_radial_distribution_function| Structural Properties and the Radial Distribution Functions]].</big>'''

'''<big>THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "NpT" SUBFOLDER.</big>'''

==Changing Ensemble==

So far, we have been able to do some simulations in which the number of particles and the volume of the simulation cell are held constant. The energy is also constant (within a certain degree of error, which is introduced by the approximations that we make to do the simulation). If the simulation is a working properly, then the pressure and temperature of the system should also reach a constant ''average'' value (although there will again be fluctuations). As mentioned in the introductory questions in this lab ensembles are used in statistical thermodynamics to represent different sorts of experimental conditions. The simulations we have done so far are described by the ''microcanonical'', or NVE ensemble (the letters represent those thermodynamic quantities which are constant).

As chemists, we often want to understand what happens under particular experimental conditions — at 298K under 1 atmosphere of pressure, for example. These sorts of conditions are described by different ensembles in statistical mechanics, such as the NVT (''canonical'') or NpT (''isobaric-isothermal'') ensembles.

In this section, we are going to modify our simulations from the previous section to run under NpT conditions, and sketch an equation of state for our model fluid at atmospheric pressure.

==Temperature and Pressure Control==

The file npt.in can be used to perform a constant temperature/pressure simulation of our model fluid. It starts by melting a simple cubic crystal, just as before, so much of this file will look familiar to you. You will notice a new section near the top, however, called '''### SPECIFY THE REQUIRED THERMODYNAMIC STATE ###'''. It contains three ''variables'' — these are used by the script later on to define the desired temperature, pressure, and timestep. The ellipses need to be replaced by the actual temperature, pressure and timestep that you want to use, so

<pre>
variable T equal 0.5
variable p equal 1.0
variable timestep equal 0.75
</pre>

would run a simulation at <math>T=0.5,\ p=1.0,\ \delta t=0.75</math>. You should remember from the [[Third_year_simulation_experiment/Equilibration|Equilibration]] section that this is a poor choice of timestep!

'''<big>TASK 8: Choose 5 temperatures (above the critical temperature <math>T^* = 1.5</math>), and two pressures (you can get a good idea of what a reasonable pressure is in Lennard-Jones units by looking at the average pressure of your simulations from the last section). This gives ten phase points — five temperatures at each pressure. Create 10 copies of npt.in, and modify each to run a simulation at one of your chosen <math>\left(p, T\right)</math> points. You should be able to use the results of the previous section to choose a timestep. Run these 10 scripts on the virtual machine. When your simulations have finished, download the log files as before. At the end of the log file, LAMMPS will output the values and errors for the pressure, temperature, and density <math>\left(\frac{N}{V}\right)</math>. </big>'''

=== Plot the density as a function of temperature for both pressures that you simulated. Include a line corresponding to the predictions made by the ideal gas law. [3] ===

=== How do your results compare to the ideal gas law? Do deviations increase/decrease with temperature and pressure? Explain. [7] ===

=== Do you expect your simulation results to be in better or worse agreement with the Van der Waals equation of state? Why? [3] ===

===Thermostats and Barostats - controlling the thermodynamic properties===
The 2nd year Solids, Liquid and Interfaces lectures will have introduced you to the ''equipartition theorem'', which states that, on average, every degree of freedom in a system at equilibrium will have <math>\frac{1}{2}k_B T</math> of energy. In our system with <math>N</math> atoms, each with 3 degrees of freedom, we can write
<math>E_K = \frac{3}{2} N k_B T</math>

<math>\frac{1}{2}\sum_i m_i v_i^2 = \frac{3}{2} N k_B T</math>

At the end of every timestep, we use the left hand side of this equation to calculate the kinetic energy, then divide by <math>\frac{3}{2}Nk_B</math> to get the ''instantaneous'' temperature <math>T</math>. In general, <math>T</math> will fluctuate, and will be different to our ''target'' temperature, <math>\mathfrak{T}</math> (this is whatever value we specify in the input script). We can change the temperature by multiplying every velocity by a constant factor, <math>\gamma</math>.

* If <math> T > \mathfrak{T} </math>, then the kinetic energy of the system is too high, and we need to reduce it. <math>\gamma < 1</math>
* If <math> T < \mathfrak{T} </math>, then the kinetic energy of the system is too low, and we need to increase it. <math>\gamma > 1</math>

We need to choose a scaling parameter <math>\gamma</math> so that the temperature is correct <math>T = \mathfrak{T}</math> if we multiply every velocity <math>\gamma</math>. We can write two equations:'''
<math>\frac{1}{2}\sum_i m_i v_i^2 = \frac{3}{2} N k_B T</math>

<math>\frac{1}{2}\sum_i m_i \left(\gamma v_i\right)^2 = \frac{3}{2} N k_B \mathfrak{T}</math>

By combining these equations, one can see that <math> \gamma = \sqrt{\frac{\mathfrak{T}}{T}} </math> (satisfy yourself that this is true!). A target value of <math> \gamma </math> of 1 is required and thus, dependent on whether it's larger or smaller than 1 the simulation can target the desired temperature.

Controlling the pressure is a little more involved, but the principle is largely the same: at each timestep, the pressure of the system is calculated; if the pressure is too high, then the simulation box is made a little larger, while if the pressure is too low the box is made smaller. Simulations in which the pressure is controlled are thus in the NpT ensemble — the volume of the simulation box is not constant!

===Examining the Input Script===

Open one of your input scripts (it doesn't matter which), and look at the section '''### BRING SYSTEM TO REQUIRED STATE ###'''. The line <pre>fix npt all npt temp ${T} ${T} ${tdamp} iso ${p} ${p} ${pdamp}</pre> is the one responsible for switching on the temperature and pressure control. LAMMPS actually allows us to heat or cool the system over the course of a simulation, if we want to — this is the reason that the temperature appears twice in this line. The first ${T} is the desired starting temperature, and the second is the desired temperature at the end of the simulation. We want a constant average temperature, so we specify the same value twice. The same goes for the pressure.

Now look at the lines near the end of the file:

<pre>
### MEASURE SYSTEM STATE ###
thermo_style custom step etotal temp press density
variable dens equal density
variable dens2 equal density*density
variable temp equal temp
variable temp2 equal temp*temp
variable press equal press
variable press2 equal press*press
fix aves all ave/time 100 1000 30000 v_dens v_temp v_press v_dens2 v_temp2 v_press2
run 30000
</pre>

The first command, ''thermo_style'', controls which thermodynamic properties are recorded, as before. The next lines are used to measure ''average'' thermodynamic properties for the system. To draw our equations of state, we need to know the average temperature, pressure, and density, and the statistical errors in those quantities. The six variable lines link those quantities (and their squared values, needed for the errors), to variable names that we can use in the averaging command, which is the line starting ''fix aves...''. This command takes a number of input values and averages them every so many timesteps. Exactly how often this happens depends in the values of the three numbers which follow ''ave/time''.

'''<big>This is the fourth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Equilibration|Equilibration]], or jump ahead to the next section, [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]].</big>'''

Third year simulation experiment/Equilibration

2021-10-24T08:49:19Z

Fbresme:

'''<big>This is the third section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Introduction_to_molecular_dynamics_simulation|Introduction to molecular dynamics simulation]], or jump ahead to the next section, [[Third year simulation experiment/Running simulations under specific conditions|Running simulations under specific conditions]].</big>'''
 
We will be using the LAMMPS program to carry out our molecular dynamics simulations.
'''In several places in this section, we will ask you to consult the LAMMPS manual to find out things about how the software works. You can find the manual [https://lammps.sandia.gov/doc/Manual.html here].''' We appreciate that the format of this document can make it a little hard to navigate, but it is the definitive resource on how different commands in LAMMPS work, and is therefore invaluable. The files you will need for this section can be found in the intro folder downloaded previously.

===Creating the simulation box===
In the previous section, it was pointed out that before we can start a simulation, we need to know the initial states of all of the atoms in the system. Exactly what information we need about each atom depends on which method of numerical integration we need, but at the very least we need to specify the starting position of each atom. If we wanted to simulate a crystal, this information would be quite easy to come by — we could just look up the crystal structure, and use that to generate coordinates for however many unit cells we wanted. For this purpose, LAMMPS includes a command which generates crystal lattice structures.

Generating coordinates for atoms in a liquid is more difficult. There is no long range order, so we can't use a single point of reference to work out the positions of every other atom like we can in a solid. We could generate a random position for each atom. This would certainly create a disordered structure, but causes larger problems when we try to run the simulation.

Instead, we are going to place the atoms on the lattice points of a simple cubic lattice. This, of course, is not a situation in which the system is likely to be found physically. It turns out, though, that if we simulate for enough time we will find that the atoms rearrange themselves into more realistic configurations. We will discuss towards the end of this section exactly what is meant by "enough time"!

Consider the line in the input file <pre>lattice sc 0.8</pre> This command [https://lammps.sandia.gov/doc/lattice.html (further info)] creates a grid of points forming a simple cubic lattice (one lattice point per unit cell). The parameter <math>0.8</math> specifies the number density (number of lattice points per unit volume). In a corresponding output file, you will see the line <pre>Lattice spacing in x,y,z = 1.07722 1.07722 1.07722</pre> This indicates that the distance between the points of this lattice is <math>1.07722</math> (in reduced units, remember!).

The next lines in the input file are
<pre>
region box block 0 5 0 5 0 5
create_box 1 box
</pre>
The corresponding log file output is
<pre>
Created orthogonal box = (0.0000000 0.0000000 0.0000000) to (5.3860867 5.3860867 5.3860867)
</pre>

The region command [https://lammps.sandia.gov/doc/region.html (further info)] simply defines a geometrical region in space, which we call "box". In this case, "box" is a cube extending ten lattice spacings from the origin in all three dimensions. The subsequent create_box command [https://lammps.sandia.gov/doc/create_box.html (further info)] tells LAMMPS to use the geometrical region called "box" as a template for the simulation box. The number 1 between "create_box" and "box" indicates that our simulation will contain only one type (species) of atom.

So far we have defined a simulation box which is based around a virtual simple cubic lattice. Our box contains 125 (5x5x5) unit cells of this lattice, and so contains 125 lattice points. We now need to fill our simulation box with atoms. The input command is <pre>create_atoms 1 box</pre> [https://lammps.sandia.gov/doc/create_atoms.html (further info)] while the log file simply contains an acknowledgement of this <pre>Created 125 atoms</pre>

The create_atoms command has two arguments; the first tells LAMMPS that all of the atoms that we create will be of type 1. Every atom in the simulation has a type — because we will be simulating a pure fluid, containing only one chemical species, every atom will have the same type. The actual type that we assign to each atom is arbitrary — type 1 does not, for example, need to correspond to the element with atomic number 1 (hydrogen). If we wanted to simulate water, we might make the hydrogen atoms type 1 and the oxygen atoms type 2. We will specify the physical and chemical properties of each atom type later in the input script.

The remaining data in the log file isn't very instructive as it stands — it simply contains a list of the thermodynamic properties of the simulation at certain intervals. In a few sections time, we will plot this data, but for now you can close the log file. Keep the input script open.

===Setting the properties of the atoms===

In addition to their positions, we also need the physical properties of the atoms to be able to perform the simulation. We set these properties on a 'per-type' basis, so that every atom of the same type has the same mass and the same interactions.

So far we have created 125 atoms, and we know the starting (<math>t = 0</math>) position for each of them. We have also set their masses, and told LAMMPS what sort of forces to calculate between them. The final thing we need to specify to completely specify the initial conditions is the velocity of each atom.

Choosing initial velocities for the atoms is a little easier than choosing initial positions. From the 1st year lectures, you should know that, at equilibrium, the velocities of atoms in any system must be distributed according to the [http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution Maxwell-Boltzmann (MB) distribution]. If we know the masses of the atoms, and we know what temperature we want to simulate, then we can determine the relevant MB distribution function. LAMMPS is able to give every atom a random velocity whilst ensuring that overall the MB distribution is followed. This is the purpose of the line

<pre>
velocity all create 1.5 12345 dist gaussian rot yes mom yes
</pre>

You can see the manual page for this command [http://lammps.sandia.gov/doc/velocity.html here], but the key sections are:

* '''all''': the ''group'' of atoms on which the command acts. '''all''' simply specifies that we want every atom to have a velocity assigned to it.
* '''1.5''': the temperature, <math>T</math>, needed to calculate the MB distribution(in reduced units, as always)

===Monitoring thermodynamic properties===

We need to be sure that our simulation is correctly modelling whatever physical system we want to study. It is relatively easy to set up simulations, but how can we be sure that the "results" we get make sense? One of the best ways is to calculate from the simulation things that we can measure in experiment, and see if they agree. For example, we might want to simulate our system at a particular temperature and pressure, and measure the resulting density. If we repeat this over a range of temperatures at the same pressure, we will be able to plot an ''equation of state'', which we could compare to experimental measurements.

LAMMPS is able to calculate a great deal of thermodynamic information for us (you can see a full list of the properties it is able to calculate [http://lammps.sandia.gov/doc/thermo_style.html here]), but in these first simulations we are only interested in those properties specified in these commands:

<pre>
thermo_style custom time etotal temp press
thermo 10
</pre>

The first controls which properties will be printed out in the log file. In this case, we print how much time we have simulated so far (which is ''not'' the same as how long it has taken us to simulate it!), the total energy of the atoms, their temperature, and their pressure. The second line tells LAMMPS to print this information on every 10th timestep.

===Running the simulation===

'''Look at the lines below.'''
<pre>
### SPECIFY TIMESTEP ###
variable timestep equal 0.001
variable n_steps equal floor(50/${timestep})
timestep ${timestep}

### RUN SIMULATION ###
run ${n_steps}
</pre>
'''The second line (starting "variable timestep...") tells LAMMPS that if it encounters the text ${timestep} on a subsequent line, it should replace it by the value given. In this case, the value ${timestep} is always replaced by 0.001.'''
 

'''<big> It is now time to run your first simulation, submit the input script with the data file in the intro folder of the files you have downloaded Try changing the timestep - what happens when you make the timestep larger?. </big>'''

===Visualising the trajectory===

The '''trajectory files''' contain the positions of all the atoms in the simulation, recorded at a set interval (for all of these simulations, this was every ten timesteps — this is controlled by the '''dump''' command in the input scripts). We use a programme called [http://www.ks.uiuc.edu/Research/vmd/ '''VMD'''] to view these trajectories, which you should find is already installed on both the desktop and laptop computers. You can run VMD from the start menu with '''Start''' -> '''All Programs''' -> '''University of Illinois''' -> '''VMD'''.

====Loading a Trajectory====

We'll start by looking at the output of the 0.02 timestep simulation. In the '''VMD Main''' window, select the menu option '''File''' -> '''New Molecule'''. Click the '''Browse''' button, then select the relevant trajectory file. In the '''Determine file type''' dropdown, select '''LAMMPS Trajectory'''. Then click '''Load'''.

You will see that the '''VMD 1.9.1 OpenGL Display''' window now shows a horrible mess. VMD's default behaviour is to draw lines between atoms which it thinks might be chemically bonded. Our system doesn't model chemical bonds, so we want to turn this off. In the '''VMD Main''' window, select the menu option '''Graphics''' -> '''Representations'''. This shows a list of "representations" of our atoms. You will see that at the moment, there is a single representation listed, and it is selected. It will have the ''Lines'' style, the ''Name'' colour, and the selection ''all''. "Selection" simply tells VMD which atoms we want it to draw. We want to show every atom, so the current selection is fine. The ''name'' colouring method just makes VMD give atoms colours according to their specified type. The colour isn't important to us, so we can leave this be too. The "style" tells VMD what we want it to display for each atom. Change the '''Drawing Method''' from ''Lines'' to ''VDW''. You will see that the mess of lines is replaced by a mess of low resolution, overlapping spheres. Change the '''Sphere Scale''' to 0.3, and the '''Sphere Resolution''' to 17. The result should look a little smoother. Close the '''Graphical Representations''' window. You will notice that in the bottom right of the '''VMD Main''' window, there is a small play button. Click this, and you will see the animated version of your simulation trajectory.

By clicking and dragging with the mouse, you can rotate the simulation box (though this may be sluggish). At any time, you can reset the view by pressing the equals key.

====Tracking a Single Particle====
To illustrate the periodic boundary conditions that we are using, we are going to draw almost all of the atoms as points, but we will pick a single atom at random to draw as a sphere. This will make it easy to see how a single atom moves through the box. Reset the display using the equals key, then use the '''VMD Main''' window controls to pause the trajectory and reset it to the first trajectory (play with the different buttons until you find the one that does this). You should see the perfect cubic lattice. Use the option '''Display''' -> '''Orthographic''' to change the drawing mode, then rotate the displayed crystal so that you are looking at one vertex (looking down the 111 direction, in crystallographic terms).

Open the '''Graphical Representations''' window again. Change the representation style from '''VDW''' to points, then click the '''Create Rep''' button. This creates a second representation, allowing a subset of the atoms to be drawn in a different way. The '''Selected Atoms''' box allows us to choose which atoms this representation applies to. We just want to pick two of them at random — VMD assigns every atom an index, from 0 to N-1. In our case, there are 125 atoms, so choose two numbers between 0 and 124. Changed the '''Selected Atoms''' field to <pre>index i or index j</pre> where i and j are your chosen numbers, press return, then change the '''Drawing Method''' to '''VDW'''. You should now see only two atoms represented by spheres, with the rest shown as small points. In the '''VMD Main''' window, click play. Try rotating the box, and changing the playback speed.

You will see that sometimes one of the spheres seems to change position across the box very rapidly — this occurs when it reaches one periodic boundary, and is reflected back across the other face. Try playing with some of the other representation types in VMD — it is a very powerful package, which is often used to render images of simulated proteins, so many of its options aren't relevant to our simple system!

===Checking equilibration===

When we first set up a simulation, it is very important to make sure that our system reaches an equilibrium state. We characterise equilibrium by the average values of thermodynamic quantities becoming constant (due to the approximations that we have made, there will always be fluctuations, but the average values will become constant).

In this section, we are going to plot the thermodynamic output of the simulation to see how long it takes to reach the equilibrium state (and indeed, whether this happens at all). Instructions are given below to import data from the LAMMPS log file into Microsoft Excel. Once you have the data in a spreadsheet, you can plot it. If you know how to use some of the other plotting software available on the chemistry computers (like Origin), you are welcome to use it.

# Open a blank Excel workbook
# Copy the data in the textfile into the first cell
# With these data highlighted, click the Data tab and "Text to Columns"
# Click "Delimited", continue and let it be space delimited
# Click finish
You can then export this and data as a .csv and analyse in Python or Excel, as you wish.

Challenge: Can you write a python script or function that extracts this data for a given file automatically?

'''<big>TASK 7: </big>'''

=== What does it mean for a simulation to "reach equilibrium"? Why is this important in terms of sampling from an ensemble using molecular dynamics? [2] ===

=== Plot the energy (potential, kinetic and total), temperature and pressure, against time for the 0.001 timestep experiment [2] ===

=== Does the simulation reach equilibrium? How can you tell? [2] ===

=== Make a single plot which shows the energy vs. time for the timesteps you have simulated [2]. ===

=== Of the timesteps that you used, which timestep will you use for subsequent simulations and why? [6] ===
''(Think about what is happening "physically" as you increase/decrease the timestep. Also, what features of each timeseries are indicative of the simulation's "health"?)''

'''<big>This is the third section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Introduction_to_molecular_dynamics_simulation|Introduction to molecular dynamics simulation]], or jump ahead to the next section, [[Third year simulation experiment/Running simulations under specific conditions|Running simulations under specific conditions]].</big>'''

Third year simulation experiment/Introduction to molecular dynamics simulation

2021-10-24T08:40:45Z

Fbresme:

'''<big>This is the second section of the third year simulation experiment. You can return to the previous section, [[Third year simulation experiment/Files to download|Downloading Files]], or jump ahead to the next section, [[Third year simulation experiment/Equilibration|Equilibration]].</big>'''

'''<big>This section contains background information about the theory of molecular dynamics simulations. It contains a number of relatively short exercises that you must complete as part of your lab write-up. These are labelled in bold and preceded by the word TASK in large print. It is recommended that you read the information on this page before carrying on with the rest of the experiment, but you are encouraged to save the TASKS for later; you can attempt them while you wait for long simulations to finish.</big>'''

In this section, we briefly discuss the theory behind molecular dynamics (MD) simulations. When we perform MD, we calculate how a particular set of atoms move over time. Using statistical physics, we can use the positions, velocities, and forces, of the atoms to calculate thermodynamic quantities like temperature and pressure.

==Theory==

===The Classical Particle Approximation===

As you may remember from your quantum chemistry lectures, it is very straightforward to write down the Schroedinger equation that describes the behaviour of any particular chemical system. For anything more complicated than a hydrogen atom, however, it is impossible to solve exactly. Even approximate solutions can be extremely computationally demanding. To be able to simulate a real system, we have to make some approximations.

It turns out that, to a very good approximation, we can assume that atoms behave as classical particles. Imagine a collection of <math>N</math> atoms. Each one of them will interact with all of the others, and so each atom will feel a force. Newton's second law tell us that that force causes the atom to accelerate.

Throughout this section, we are going to use the following notation:

* <math>\mathbf{F}_i</math> is the force acting on atom i.
* <math>m_i</math> is the mass of atom i.
* <math>\mathbf{a}_i</math> is the acceleration of atom i, the rate of change of its velocity.
* <math>\mathbf{v}_i</math> is the velocity of atom i.
* <math>\mathbf{x}_i</math> is the position of atom i.

<center><math>\mathbf{F}_i = m_i \mathbf{a}_i = m_i \frac{\mathrm{d}\mathbf{v}_i}{\mathrm{d}t} = m_i \frac{\mathrm{d}^2 \mathbf{x}_i}{\mathrm{d}t^2} \ \ (1)</math></center>

This is a second order differential equation for the positions of the atoms — if we know how the force, <math>\mathbf{F}_i</math>, behaves as a function of time, then we can determine the atomic positions and velocities at any time we like. Our system of <math>N</math> atoms has <math>N</math> of these equations, one for each atom. This is one of the reasons that computer simulations are needed — if we want to model the behaviour of a liquid, we can hardly solve the necessary number of equations by hand.

===Numerical Integration===

'''Numerical integration is a rather complex topic. In particular, the notation used below can be quite intimidating. Remember that you are encouraged to ask for help from the demonstrator if you want to discuss any part of this experiment!'''
 

There are a number of numerical algorithms to perform a molecular dynamics simulation, two are presented here- The Classical Verlet algorithm and The Velocity-Verlet algorithm.

====Verlet Algorithm====

To solve these equations numerically we have to ''discretise'' the problem: rather than treating the atomic positions, velocities, and forces as continuous functions of time, we break our simulation up into a sequence of '''timesteps''', each of length <math>\delta t</math>. This process is illustrated for a simple function in '''figure 1'''. The method that we are going to use to solve Newton's law for our atoms is usually called the Verlet algorithm (although it is an old method, and has been 'rediscovered' many times!). To understand its origin, we will begin with a brief derivation.

 
[[File:ThirdYearSimulationExpt-Intro-Discretisation.png|300px|thumb|center|'''Figure 1''': Discretisation of sin(x) between 0 and <math>2\pi</math>]]
 

We denote the position of an atom, <math>i</math>, at time <math>t</math> by <math>\mathbf{x}_i \left(t\right)</math>. Similarly, <math>\mathbf{v}_i \left(t\right)</math> is the velocity of that atom at the same time. What we want to know is the position of the atoms at the next timestep, <math>t + \delta t</math>. The basic Verlet algorithm is shown in '''figure 2''' - knowing a set of initial conditions the algorithm calculates forces and by Newton's second law, we can update the positions of a set of particles are a time <math>t + \delta t</math>.

 
[[File:ThirdYearSimulationExpt-Intro-Verlet-flowchart.svg|300px|thumb|center|'''Figure 2''': Steps to implement the classic Verlet algorithm.]]
 
'''<big> TASK 1: By taking Taylor expansions of <math>x(t + \delta t)</math> and <math>x(t - \delta t)</math>, write general expressions for them up to the fourth order <math>\mathcal{O}\left(\delta t^4\right)</math> </big>'''

 
'''<big> Having written these expressions, derive the formula in figure 2 to update positions as used in the classical Verlet algorithm <math> x(t + \delta t) \approx 2x_{i}(t) - x_{i}(t-\delta t) + \frac{F_{i}(t)}{m} \delta t^{2}</math> by using Newton's second law to replace <math>\frac{\mathrm{d}^2\mathbf{x}_i\left(t\right)}{\mathrm{d}t^2}</math> [4 marks] </big>'''

Using this last equation, we can use a sequence of steps like those shown in '''figure 2''' to get the positions. At no point are the velocities calculated in this method!

====Velocity Verlet Algorithm====

If we assume that the acceleration of an atom depends only on its position and not its velocity, then we are able to come up with a new algorithm that lets us calculate atomic velocities explicitly as shown in '''figure 3'''.

 

[[File:ThirdYearSimulationExpt-Intro-VelocityVerlet-flowchart.svg|300px|thumb|center|'''Figure 3''': Steps to implement the velocity Verlet algorithm.]]

 

We start by noting that
<center><math>\mathbf{v}_i\left(t + \delta t\right) = \mathbf{v}_i\left(t\right) + \frac{\mathbf{a}_i\left(t\right) + \mathbf{a}_i\left(t + \delta t\right)}{2}\delta t \ \ (6)</math></center>

We can Taylor expand the velocity by half a step, instead of a full step.

<center><math>\mathbf{v}_i\left(t + \frac{1}{2}\delta t\right) = \mathbf{v}_i\left(t\right) + \frac{1}{2} \mathbf{a}_i\left(t\right)\delta t \ \ (7)</math></center>

We then substitute this into your expansion for <math> x_{i} (t + \delta t) </math> to obtain an accuracy up to <math> \delta t ^{2} </math>. Notice that terms up to <math> \delta t ^{2} </math> in your expansion can be written:

<center><math> \mathbf{x}_{i} (t + \delta t) = \mathbf{x}_{i} (t) + \mathbf{v}(t) \delta t + \frac{1}{2} \mathbf{a}(t) \delta t ^{2} </math></center>

<center><math>\mathbf{x}_i\left(t + \delta t\right) = \mathbf{x}_i\left(t\right) + \mathbf{v}_i\left(t + \frac{1}{2}\delta t\right)\delta t \ \ (8)</math></center>

When we know the updated atomic positions, we can calculate new forces, <math>\mathbf{a}_i\left(t + \delta t\right)</math>. Finally, we substitute equation (7) into equation (6) to get the new velocities <math>\mathbf{v}_i\left(t + \delta t\right)</math>.

<center><math>\mathbf{v}_i\left(t + \delta t\right) = \mathbf{v}_i\left(t + \frac{1}{2}\delta t\right) + \frac{1}{2}\mathbf{a}_i\left(t + \delta t\right)\delta t \ \ (9)</math></center>

Notice that for both numerical integration algorithms, the first step is "specify initial conditions". When using the Verlet algorithm, we need to know the starting positions of the atoms (<math>\mathbf{x}_i\left(0\right)</math>), and their positions one timestep in the past (<math>\mathbf{x}_i\left(-\delta t\right)</math>). If the velocity-Verlet algorithm is used, then we have to know the the starting positions of the atoms (<math>\mathbf{x}_i\left(0\right)</math>) and their velocities at the same time (<math>\mathbf{v}_i\left(0\right)</math>). For this reason, we often start new simulations by using the output of older ones. If, however, you are performing your first simulations of a system (as we are now), then you must choose your initial conditions. The simulation software that we will use is able to do this for us, and this will be explained in the next section.

 
'''<big> TASK 2: What could be an advantage of the Velocity-Verlet algorithm over the classical Verlet algorithm? [2 marks]</big>'''
 

===Atomic Forces===

Since we can't reasonably solve the exact equations from quantum mechanics necessary to determine the forces acting on a given configuration of N atoms, we have to make approximations. We know from classical physics that the force acting on an object is determined by the potential that it experiences:

<center><math>\mathbf{F}_i = - \frac{\mathrm{d}U\left(\mathbf{r}^N\right)}{\mathrm{d}\mathbf{r}_i}</math></center>

The shorthand notation <math>\mathbf{r}^N</math> stands for the position vectors of '''every''' atom in system. In principle, the force that a single atom feels is determined by the position of every other atom in the simulation. All we then need to do is to find a function <math>U</math>, the potential energy, that captures all the key physics of the interatomic interactions in the system. For many simple liquids, it turns out that we can model the interactions between each pair of atoms extremely well using the Lennard-Jones potential. Overall, U takes the form:

<center><math>U\left(\mathbf{r}^N\right) = \sum_{i=1}^{N-1} \sum_{j > i}^{N} \left\{ 4\epsilon \left( \frac{\sigma^{12}}{r_{ij}^{12}} - \frac{\sigma^6}{r_{ij}^6} \right) \right\} \ \ (10)</math></center>

=== TASK 3: Consider the Lennard-Jones pair potential. What physical interaction(s) does it describe? What is the physical significance for the r^(-6) and r^(-12) terms? [3 marks] ===

'''<big>TASK 4: For a single Lennard-Jones interaction, <math>\phi\left(r\right) = 4\epsilon \left( \frac{\sigma^{12}}{r^{12}} - \frac{\sigma^6}{r^6} \right)</math>, find the separation, <math>r_0</math>, at which the potential energy is zero. What is the force at this separation? Find the equilibrium separation, <math>r_{eq}</math>, and work out the well depth (<math>\phi\left(r_{eq}\right)</math>). Evaluate the integrals <math>\int_{2\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math>, <math>\int_{2.5\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math>, and <math>\int_{3\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math> when <math>\sigma = \epsilon = 1.0</math> [4 marks]</big>.'''

====Periodic Boundary Conditions====

[[File:ThirdYearSimulationExpt-Intro-Box.png|200px|thumb|right|'''Figure 4''': Diagram of a simulation box containing 2139 atoms. The blue lines indicate the boundaries of the box.]]
[[File:ThirdYearSimulationExpt-Intro-Periodic.svg|300px|thumb|left|'''Figure 5''': Periodic boundary conditions in two dimensions.]]

We cannot simulate realistic volumes of liquid. In fact, in our simulations, <math>N</math> will be between <math>1000</math> and <math>10000</math>. The following task should illustrate why this must be so.

In order for our simulations to approximate a bulk liquid, we have to use a computational trick. The atoms in the simulation are enclosed in a simulation box, of fixed dimensions ('''figure 4'''). This box is very often a cuboid, but parallelepipeds can also be used (and this can be very useful when simulating crystal structures). We pretend that we have repeated our box infinitely in all directions, so that the atoms at the very edges are not exposed to a vacuum. This is illustrated in two dimensions in '''figure 5'''. The darker coloured atoms in the central box are the "real" atoms. The faded atoms in the outer four boxes are the replicas. When an atom crosses the boundary of the box, one of its replicas enters the box through the opposite face. In this way, the number of atoms inside the box is always constant.

'''<big>TASK 5: Consider an atom at position <math>\left(0.5, 0.5, 0.5\right)</math> in a cubic simulation box which runs from <math>\left(0, 0, 0\right)</math> to <math>\left(1, 1, 1\right)</math>. In a single timestep, it moves along the vector <math>\left(0.7, 0.6, 0.2\right)</math>. At what point does it end up, ''after the periodic boundary conditions have been applied''? [1 marks]''' </big>.

====Truncation====

Periodic boundary conditions introduce their own problems. When we defined our potential function (equation 10), we specified that it depended on all possible pairs of atoms. If we have an infinite number of replicas of our system, how can we avoid calculating an infinite number of pair interactions?

Think about the three integrals you calculated for the Lennard-Jones potential task. They represent the area under the Lennard-Jones potential curve between some specified distance (<math>2\sigma</math>, <math>2.5\sigma</math>, and <math>3\sigma</math>), and infinite separation (where there is no interaction). You should find that this value becomes rather small as the near distance is increased! The attractive <math>\frac{1}{r^6}</math> part of the potential dominates here, and this decays rapidly with <math>r</math>. We assume that this means that there is a distance beyond which the interaction is so small that we can safely ignore it. In fact, in most simulations this is chosen to be something close to <math>2.5\sigma</math> or <math>3\sigma</math>. When the forces are calculated, we only calculate interactions between a pair of atoms if their separation is less than this cutoff.

====Reduced Units====

It is typical when using Lennard-Jones interactions to work in reduced units. By this, we mean that all quantities in our simulation are divided by scaling factors — for example, distances are divided by <math>\sigma</math>. The result of this is that the values become more manageable: all values that we might work out are typically around 1, rather than <math>1\times 10^{-10}</math> (in the case of distance), <math>300</math> (in the case of temperature), or <math>1\times 10^{-19}</math> (in the case of energy).

We denote these reduced quantities by a star, and they take the following conversion factors:

* distance <math>r^* = \frac{r}{\sigma}</math>
* energy <math>E^* = \frac{E}{\epsilon}</math>
* temperature <math>T^* = \frac{k_BT}{\epsilon}</math>

'''<big>TASK 6: The Lennard-Jones parameters for argon are <math>\sigma = 0.34\mathrm{nm}, \epsilon\ /\ k_B= 120 \mathrm{K}</math>. If the LJ cutoff is <math>r^* = 3.2</math>, what is it in real units? What is the well depth in <math>\mathrm{kJ\ mol}^{-1}</math>? What is the reduced temperature <math>T^* = 1.5</math> in real units? [1 marks]</big> '''

'''<big>This is the second section of the third year simulation experiment. You can return to the previous section, [[Third year simulation experiment/Running your first simulation|Files to Download]], or jump ahead to the next section, [[Third year simulation experiment/Equilibration|Equilibration]].</big>'''

Third year simulation experiment/Introduction to molecular dynamics simulation

2021-10-24T08:40:06Z

Fbresme:

'''<big>This is the second section of the third year simulation experiment. You can return to the previous section, [[Third year simulation experiment/Files to download|Downloading Files]], or jump ahead to the next section, [[Third year simulation experiment/Equilibration|Equilibration]].</big>'''

'''<big>This section contains background information about the theory of molecular dynamics simulations. It contains a number of relatively short exercises that you must complete as part of your lab write-up. These are labelled in bold and preceded by the word TASK in large print. It is recommended that you read the information on this page before carrying on with the rest of the experiment, but you are encouraged to save the TASKS for later; you can attempt them while you wait for long simulations to finish.</big>'''

In this section, we briefly discuss the theory behind molecular dynamics (MD) simulations. When we perform MD, we calculate how a particular set of atoms move over time. Using statistical physics, we can use the positions, velocities, and forces, of the atoms to calculate thermodynamic quantities like temperature and pressure.

==Theory==

===The Classical Particle Approximation===

As you may remember from your quantum chemistry lectures, it is very straightforward to write down the Schroedinger equation that describes the behaviour of any particular chemical system. For anything more complicated than a hydrogen atom, however, it is impossible to solve exactly. Even approximate solutions can be extremely computationally demanding. To be able to simulate a real system, we have to make some approximations.

It turns out that, to a very good approximation, we can assume that atoms behave as classical particles. Imagine a collection of <math>N</math> atoms. Each one of them will interact with all of the others, and so each atom will feel a force. Newton's second law tell us that that force causes the atom to accelerate.

Throughout this section, we are going to use the following notation:

* <math>\mathbf{F}_i</math> is the force acting on atom i.
* <math>m_i</math> is the mass of atom i.
* <math>\mathbf{a}_i</math> is the acceleration of atom i, the rate of change of its velocity.
* <math>\mathbf{v}_i</math> is the velocity of atom i.
* <math>\mathbf{x}_i</math> is the position of atom i.

<center><math>\mathbf{F}_i = m_i \mathbf{a}_i = m_i \frac{\mathrm{d}\mathbf{v}_i}{\mathrm{d}t} = m_i \frac{\mathrm{d}^2 \mathbf{x}_i}{\mathrm{d}t^2} \ \ (1)</math></center>

This is a second order differential equation for the positions of the atoms — if we know how the force, <math>\mathbf{F}_i</math>, behaves as a function of time, then we can determine the atomic positions and velocities at any time we like. Our system of <math>N</math> atoms has <math>N</math> of these equations, one for each atom. This is one of the reasons that computer simulations are needed — if we want to model the behaviour of a liquid, we can hardly solve the necessary number of equations by hand.

===Numerical Integration===

'''Numerical integration is a rather complex topic. In particular, the notation used below can be quite intimidating. Remember that you are encouraged to ask for help from the demonstrator if you want to discuss any part of this experiment!'''
 

There are a number of numerical algorithms to perform a molecular dynamics simulation, two are presented here- The Classical Verlet algorithm and The Velocity-Verlet algorithm.

====Verlet Algorithm====

To solve these equations numerically we have to ''discretise'' the problem: rather than treating the atomic positions, velocities, and forces as continuous functions of time, we break our simulation up into a sequence of '''timesteps''', each of length <math>\delta t</math>. This process is illustrated for a simple function in '''figure 1'''. The method that we are going to use to solve Newton's law for our atoms is usually called the Verlet algorithm (although it is an old method, and has been 'rediscovered' many times!). To understand its origin, we will begin with a brief derivation.

 
[[File:ThirdYearSimulationExpt-Intro-Discretisation.png|300px|thumb|center|'''Figure 1''': Discretisation of sin(x) between 0 and <math>2\pi</math>]]
 

We denote the position of an atom, <math>i</math>, at time <math>t</math> by <math>\mathbf{x}_i \left(t\right)</math>. Similarly, <math>\mathbf{v}_i \left(t\right)</math> is the velocity of that atom at the same time. What we want to know is the position of the atoms at the next timestep, <math>t + \delta t</math>. The basic Verlet algorithm is shown in '''figure 2''' - knowing a set of initial conditions the algorithm calculates forces and by Newton's second law, we can update the positions of a set of particles are a time <math>t + \delta t</math>.

 
[[File:ThirdYearSimulationExpt-Intro-Verlet-flowchart.svg|300px|thumb|center|'''Figure 2''': Steps to implement the classic Verlet algorithm.]]
 
'''<big> TASK 1: By taking Taylor expansions of <math>x(t + \delta t)</math> and <math>x(t - \delta t)</math>, write general expressions for them up to the fourth order <math>\mathcal{O}\left(\delta t^4\right)</math> </big>'''

 
'''<big> Having written these expressions, derive the formula in figure 2 to update positions as used in the classical Verlet algorithm <math> x(t + \delta t) \approx 2x_{i}(t) - x_{i}(t-\delta t) + \frac{F_{i}(t)}{m} \delta t^{2}</math> by using Newton's second law to replace <math>\frac{\mathrm{d}^2\mathbf{x}_i\left(t\right)}{\mathrm{d}t^2}</math> [4 marks] </big>'''

Using this last equation, we can use a sequence of steps like those shown in '''figure 2''' to get the positions. At no point are the velocities calculated in this method!

====Velocity Verlet Algorithm====

If we assume that the acceleration of an atom depends only on its position and not its velocity, then we are able to come up with a new algorithm that lets us calculate atomic velocities explicitly as shown in '''figure 3'''.

 

[[File:ThirdYearSimulationExpt-Intro-VelocityVerlet-flowchart.svg|300px|thumb|center|'''Figure 3''': Steps to implement the velocity Verlet algorithm.]]

 

We start by noting that
<center><math>\mathbf{v}_i\left(t + \delta t\right) = \mathbf{v}_i\left(t\right) + \frac{\mathbf{a}_i\left(t\right) + \mathbf{a}_i\left(t + \delta t\right)}{2}\delta t \ \ (6)</math></center>

We can Taylor expand the velocity by half a step, instead of a full step.

<center><math>\mathbf{v}_i\left(t + \frac{1}{2}\delta t\right) = \mathbf{v}_i\left(t\right) + \frac{1}{2} \mathbf{a}_i\left(t\right)\delta t \ \ (7)</math></center>

We then substitute this into your expansion for <math> x_{i} (t + \delta t) </math> to obtain an accuracy up to <math> \delta t ^{2} </math>. Notice that terms up to <math> \delta t ^{2} </math> in your expansion can be written:

<center><math> \mathbf{x}_{i} (t + \delta t) = \mathbf{x}_{i} (t) + \mathbf{v}(t) \delta t + \frac{1}{2} \mathbf{a}(t) \delta t ^{2} </math></center>

<center><math>\mathbf{x}_i\left(t + \delta t\right) = \mathbf{x}_i\left(t\right) + \mathbf{v}_i\left(t + \frac{1}{2}\delta t\right)\delta t \ \ (8)</math></center>

When we know the updated atomic positions, we can calculate new forces, <math>\mathbf{a}_i\left(t + \delta t\right)</math>. Finally, we substitute equation (7) into equation (6) to get the new velocities <math>\mathbf{v}_i\left(t + \delta t\right)</math>.

<center><math>\mathbf{v}_i\left(t + \delta t\right) = \mathbf{v}_i\left(t + \frac{1}{2}\delta t\right) + \frac{1}{2}\mathbf{a}_i\left(t + \delta t\right)\delta t \ \ (9)</math></center>

Notice that for both numerical integration algorithms, the first step is "specify initial conditions". When using the Verlet algorithm, we need to know the starting positions of the atoms (<math>\mathbf{x}_i\left(0\right)</math>), and their positions one timestep in the past (<math>\mathbf{x}_i\left(-\delta t\right)</math>). If the velocity-Verlet algorithm is used, then we have to know the the starting positions of the atoms (<math>\mathbf{x}_i\left(0\right)</math>) and their velocities at the same time (<math>\mathbf{v}_i\left(0\right)</math>). For this reason, we often start new simulations by using the output of older ones. If, however, you are performing your first simulations of a system (as we are now), then you must choose your initial conditions. The simulation software that we will use is able to do this for us, and this will be explained in the next section.

 
'''<big> TASK 2: What could be an advantage of the Velocity-Verlet algorithm over the classical Verlet algorithm? [2 marks]</big>'''
 

===Atomic Forces===

Since we can't reasonably solve the exact equations from quantum mechanics necessary to determine the forces acting on a given configuration of N atoms, we have to make approximations. We know from classical physics that the force acting on an object is determined by the potential that it experiences:

<center><math>\mathbf{F}_i = - \frac{\mathrm{d}U\left(\mathbf{r}^N\right)}{\mathrm{d}\mathbf{r}_i}</math></center>

The shorthand notation <math>\mathbf{r}^N</math> stands for the position vectors of '''every''' atom in system. In principle, the force that a single atom feels is determined by the position of every other atom in the simulation. All we then need to do is to find a function <math>U</math>, the potential energy, that captures all the key physics of the interatomic interactions in the system. For many simple liquids, it turns out that we can model the interactions between each pair of atoms extremely well using the Lennard-Jones potential. Overall, U takes the form:

<center><math>U\left(\mathbf{r}^N\right) = \sum_i^{N-1} \sum_{j > j}^{N} \left\{ 4\epsilon \left( \frac{\sigma^{12}}{r_{ij}^{12}} - \frac{\sigma^6}{r_{ij}^6} \right) \right\} \ \ (10)</math></center>

=== TASK 3: Consider the Lennard-Jones pair potential. What physical interaction(s) does it describe? What is the physical significance for the r^(-6) and r^(-12) terms? [3 marks] ===

'''<big>TASK 4: For a single Lennard-Jones interaction, <math>\phi\left(r\right) = 4\epsilon \left( \frac{\sigma^{12}}{r^{12}} - \frac{\sigma^6}{r^6} \right)</math>, find the separation, <math>r_0</math>, at which the potential energy is zero. What is the force at this separation? Find the equilibrium separation, <math>r_{eq}</math>, and work out the well depth (<math>\phi\left(r_{eq}\right)</math>). Evaluate the integrals <math>\int_{2\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math>, <math>\int_{2.5\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math>, and <math>\int_{3\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math> when <math>\sigma = \epsilon = 1.0</math> [4 marks]</big>.'''

====Periodic Boundary Conditions====

[[File:ThirdYearSimulationExpt-Intro-Box.png|200px|thumb|right|'''Figure 4''': Diagram of a simulation box containing 2139 atoms. The blue lines indicate the boundaries of the box.]]
[[File:ThirdYearSimulationExpt-Intro-Periodic.svg|300px|thumb|left|'''Figure 5''': Periodic boundary conditions in two dimensions.]]

We cannot simulate realistic volumes of liquid. In fact, in our simulations, <math>N</math> will be between <math>1000</math> and <math>10000</math>. The following task should illustrate why this must be so.

In order for our simulations to approximate a bulk liquid, we have to use a computational trick. The atoms in the simulation are enclosed in a simulation box, of fixed dimensions ('''figure 4'''). This box is very often a cuboid, but parallelepipeds can also be used (and this can be very useful when simulating crystal structures). We pretend that we have repeated our box infinitely in all directions, so that the atoms at the very edges are not exposed to a vacuum. This is illustrated in two dimensions in '''figure 5'''. The darker coloured atoms in the central box are the "real" atoms. The faded atoms in the outer four boxes are the replicas. When an atom crosses the boundary of the box, one of its replicas enters the box through the opposite face. In this way, the number of atoms inside the box is always constant.

'''<big>TASK 5: Consider an atom at position <math>\left(0.5, 0.5, 0.5\right)</math> in a cubic simulation box which runs from <math>\left(0, 0, 0\right)</math> to <math>\left(1, 1, 1\right)</math>. In a single timestep, it moves along the vector <math>\left(0.7, 0.6, 0.2\right)</math>. At what point does it end up, ''after the periodic boundary conditions have been applied''? [1 marks]''' </big>.

====Truncation====

Periodic boundary conditions introduce their own problems. When we defined our potential function (equation 10), we specified that it depended on all possible pairs of atoms. If we have an infinite number of replicas of our system, how can we avoid calculating an infinite number of pair interactions?

Think about the three integrals you calculated for the Lennard-Jones potential task. They represent the area under the Lennard-Jones potential curve between some specified distance (<math>2\sigma</math>, <math>2.5\sigma</math>, and <math>3\sigma</math>), and infinite separation (where there is no interaction). You should find that this value becomes rather small as the near distance is increased! The attractive <math>\frac{1}{r^6}</math> part of the potential dominates here, and this decays rapidly with <math>r</math>. We assume that this means that there is a distance beyond which the interaction is so small that we can safely ignore it. In fact, in most simulations this is chosen to be something close to <math>2.5\sigma</math> or <math>3\sigma</math>. When the forces are calculated, we only calculate interactions between a pair of atoms if their separation is less than this cutoff.

====Reduced Units====

It is typical when using Lennard-Jones interactions to work in reduced units. By this, we mean that all quantities in our simulation are divided by scaling factors — for example, distances are divided by <math>\sigma</math>. The result of this is that the values become more manageable: all values that we might work out are typically around 1, rather than <math>1\times 10^{-10}</math> (in the case of distance), <math>300</math> (in the case of temperature), or <math>1\times 10^{-19}</math> (in the case of energy).

We denote these reduced quantities by a star, and they take the following conversion factors:

* distance <math>r^* = \frac{r}{\sigma}</math>
* energy <math>E^* = \frac{E}{\epsilon}</math>
* temperature <math>T^* = \frac{k_BT}{\epsilon}</math>

'''<big>TASK 6: The Lennard-Jones parameters for argon are <math>\sigma = 0.34\mathrm{nm}, \epsilon\ /\ k_B= 120 \mathrm{K}</math>. If the LJ cutoff is <math>r^* = 3.2</math>, what is it in real units? What is the well depth in <math>\mathrm{kJ\ mol}^{-1}</math>? What is the reduced temperature <math>T^* = 1.5</math> in real units? [1 marks]</big> '''

'''<big>This is the second section of the third year simulation experiment. You can return to the previous section, [[Third year simulation experiment/Running your first simulation|Files to Download]], or jump ahead to the next section, [[Third year simulation experiment/Equilibration|Equilibration]].</big>'''

Third year simulation experiment/Introduction to molecular dynamics simulation

2021-10-24T08:39:16Z

Fbresme:

'''<big>This is the second section of the third year simulation experiment. You can return to the previous section, [[Third year simulation experiment/Files to download|Downloading Files]], or jump ahead to the next section, [[Third year simulation experiment/Equilibration|Equilibration]].</big>'''

'''<big>This section contains background information about the theory of molecular dynamics simulations. It contains a number of relatively short exercises that you must complete as part of your lab write-up. These are labelled in bold and preceded by the word TASK in large print. It is recommended that you read the information on this page before carrying on with the rest of the experiment, but you are encouraged to save the TASKS for later; you can attempt them while you wait for long simulations to finish.</big>'''

In this section, we briefly discuss the theory behind molecular dynamics (MD) simulations. When we perform MD, we calculate how a particular set of atoms move over time. Using statistical physics, we can use the positions, velocities, and forces, of the atoms to calculate thermodynamic quantities like temperature and pressure.

==Theory==

===The Classical Particle Approximation===

As you may remember from your quantum chemistry lectures, it is very straightforward to write down the Schroedinger equation that describes the behaviour of any particular chemical system. For anything more complicated than a hydrogen atom, however, it is impossible to solve exactly. Even approximate solutions can be extremely computationally demanding. To be able to simulate a real system, we have to make some approximations.

It turns out that, to a very good approximation, we can assume that atoms behave as classical particles. Imagine a collection of <math>N</math> atoms. Each one of them will interact with all of the others, and so each atom will feel a force. Newton's second law tell us that that force causes the atom to accelerate.

Throughout this section, we are going to use the following notation:

* <math>\mathbf{F}_i</math> is the force acting on atom i.
* <math>m_i</math> is the mass of atom i.
* <math>\mathbf{a}_i</math> is the acceleration of atom i, the rate of change of its velocity.
* <math>\mathbf{v}_i</math> is the velocity of atom i.
* <math>\mathbf{x}_i</math> is the position of atom i.

<center><math>\mathbf{F}_i = m_i \mathbf{a}_i = m_i \frac{\mathrm{d}\mathbf{v}_i}{\mathrm{d}t} = m_i \frac{\mathrm{d}^2 \mathbf{x}_i}{\mathrm{d}t^2} \ \ (1)</math></center>

This is a second order differential equation for the positions of the atoms — if we know how the force, <math>\mathbf{F}_i</math>, behaves as a function of time, then we can determine the atomic positions and velocities at any time we like. Our system of <math>N</math> atoms has <math>N</math> of these equations, one for each atom. This is one of the reasons that computer simulations are needed — if we want to model the behaviour of a liquid, we can hardly solve the necessary number of equations by hand.

===Numerical Integration===

'''Numerical integration is a rather complex topic. In particular, the notation used below can be quite intimidating. Remember that you are encouraged to ask for help from the demonstrator if you want to discuss any part of this experiment!'''
 

There are a number of numerical algorithms to perform a molecular dynamics simulation, two are presented here- The Classical Verlet algorithm and The Velocity-Verlet algorithm.

====Verlet Algorithm====

To solve these equations numerically we have to ''discretise'' the problem: rather than treating the atomic positions, velocities, and forces as continuous functions of time, we break our simulation up into a sequence of '''timesteps''', each of length <math>\delta t</math>. This process is illustrated for a simple function in '''figure 1'''. The method that we are going to use to solve Newton's law for our atoms is usually called the Verlet algorithm (although it is an old method, and has been 'rediscovered' many times!). To understand its origin, we will begin with a brief derivation.

 
[[File:ThirdYearSimulationExpt-Intro-Discretisation.png|300px|thumb|center|'''Figure 1''': Discretisation of sin(x) between 0 and <math>2\pi</math>]]
 

We denote the position of an atom, <math>i</math>, at time <math>t</math> by <math>\mathbf{x}_i \left(t\right)</math>. Similarly, <math>\mathbf{v}_i \left(t\right)</math> is the velocity of that atom at the same time. What we want to know is the position of the atoms at the next timestep, <math>t + \delta t</math>. The basic Verlet algorithm is shown in '''figure 2''' - knowing a set of initial conditions the algorithm calculates forces and by Newton's second law, we can update the positions of a set of particles are a time <math>t + \delta t</math>.

 
[[File:ThirdYearSimulationExpt-Intro-Verlet-flowchart.svg|300px|thumb|center|'''Figure 2''': Steps to implement the classic Verlet algorithm.]]
 
'''<big> TASK 1: By taking Taylor expansions of <math>x(t + \delta t)</math> and <math>x(t - \delta t)</math>, write general expressions for them up to the fourth order <math>\mathcal{O}\left(\delta t^4\right)</math> </big>'''

 
'''<big> Having written these expressions, derive the formula in figure 2 to update positions as used in the classical Verlet algorithm <math> x(t + \delta t) \approx 2x_{i}(t) - x_{i}(t-\delta t) + \frac{F_{i}(t)}{m} \delta t^{2}</math> by using Newton's second law to replace <math>\frac{\mathrm{d}^2\mathbf{x}_i\left(t\right)}{\mathrm{d}t^2}</math> [4 marks] </big>'''

Using this last equation, we can use a sequence of steps like those shown in '''figure 2''' to get the positions. At no point are the velocities calculated in this method!

====Velocity Verlet Algorithm====

If we assume that the acceleration of an atom depends only on its position and not its velocity, then we are able to come up with a new algorithm that lets us calculate atomic velocities explicitly as shown in '''figure 3'''.

 

[[File:ThirdYearSimulationExpt-Intro-VelocityVerlet-flowchart.svg|300px|thumb|center|'''Figure 3''': Steps to implement the velocity Verlet algorithm.]]

 

We start by noting that
<center><math>\mathbf{v}_i\left(t + \delta t\right) = \mathbf{v}_i\left(t\right) + \frac{\mathbf{a}_i\left(t\right) + \mathbf{a}_i\left(t + \delta t\right)}{2}\delta t \ \ (6)</math></center>

We can Taylor expand the velocity by half a step, instead of a full step.

<center><math>\mathbf{v}_i\left(t + \frac{1}{2}\delta t\right) = \mathbf{v}_i\left(t\right) + \frac{1}{2} \mathbf{a}_i\left(t\right)\delta t \ \ (7)</math></center>

We then substitute this into your expansion for <math> x_{i} (t + \delta t) </math> to obtain an accuracy up to <math> \delta t ^{2} </math>. Notice that terms up to <math> \delta t ^{2} </math> in your expansion can be written:

<center><math> \mathbf{x}_{i} (t + \delta t) = \mathbf{x}_{i} (t) + \mathbf{v}(t) \delta t + \frac{1}{2} \mathbf{a}(t) \delta t ^{2} </math></center>

<center><math>\mathbf{x}_i\left(t + \delta t\right) = \mathbf{x}_i\left(t\right) + \mathbf{v}_i\left(t + \frac{1}{2}\delta t\right)\delta t \ \ (8)</math></center>

When we know the updated atomic positions, we can calculate new forces, <math>\mathbf{a}_i\left(t + \delta t\right)</math>. Finally, we substitute equation (7) into equation (6) to get the new velocities <math>\mathbf{v}_i\left(t + \delta t\right)</math>.

<center><math>\mathbf{v}_i\left(t + \delta t\right) = \mathbf{v}_i\left(t + \frac{1}{2}\delta t\right) + \frac{1}{2}\mathbf{a}_i\left(t + \delta t\right)\delta t \ \ (9)</math></center>

Notice that for both numerical integration algorithms, the first step is "specify initial conditions". When using the Verlet algorithm, we need to know the starting positions of the atoms (<math>\mathbf{x}_i\left(0\right)</math>), and their positions one timestep in the past (<math>\mathbf{x}_i\left(-\delta t\right)</math>). If the velocity-Verlet algorithm is used, then we have to know the the starting positions of the atoms (<math>\mathbf{x}_i\left(0\right)</math>) and their velocities at the same time (<math>\mathbf{v}_i\left(0\right)</math>). For this reason, we often start new simulations by using the output of older ones. If, however, you are performing your first simulations of a system (as we are now), then you must choose your initial conditions. The simulation software that we will use is able to do this for us, and this will be explained in the next section.

 
'''<big> TASK 2: What could be an advantage of the Velocity-Verlet algorithm over the classical Verlet algorithm? [2 marks]</big>'''
 

===Atomic Forces===

Since we can't reasonably solve the exact equations from quantum mechanics necessary to determine the forces acting on a given configuration of N atoms, we have to make approximations. We know from classical physics that the force acting on an object is determined by the potential that it experiences:

<center><math>\mathbf{F}_i = - \frac{\mathrm{d}U\left(\mathbf{r}^N\right)}{\mathrm{d}\mathbf{r}_i}</math></center>

The shorthand notation <math>\mathbf{r}^N</math> stands for the position vectors of '''every''' atom in system. In principle, the force that a single atom feels is determined by the position of every other atom in the simulation. All we then need to do is to find a function <math>U</math>, the potential energy, that captures all the key physics of the interatomic interactions in the system. For many simple liquids, it turns out that we can model the interactions between each pair of atoms extremely well using the Lennard-Jones potential. Overall, U takes the form:

<center><math>U\left(\mathbf{r}^N\right) = \sum_i^N \sum_{j > j}^{N} \left\{ 4\epsilon \left( \frac{\sigma^{12}}{r_{ij}^{12}} - \frac{\sigma^6}{r_{ij}^6} \right) \right\} \ \ (10)</math></center>

=== TASK 3: Consider the Lennard-Jones pair potential. What physical interaction(s) does it describe? What is the physical significance for the r^(-6) and r^(-12) terms? [3 marks] ===

'''<big>TASK 4: For a single Lennard-Jones interaction, <math>\phi\left(r\right) = 4\epsilon \left( \frac{\sigma^{12}}{r^{12}} - \frac{\sigma^6}{r^6} \right)</math>, find the separation, <math>r_0</math>, at which the potential energy is zero. What is the force at this separation? Find the equilibrium separation, <math>r_{eq}</math>, and work out the well depth (<math>\phi\left(r_{eq}\right)</math>). Evaluate the integrals <math>\int_{2\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math>, <math>\int_{2.5\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math>, and <math>\int_{3\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math> when <math>\sigma = \epsilon = 1.0</math> [4 marks]</big>.'''

====Periodic Boundary Conditions====

[[File:ThirdYearSimulationExpt-Intro-Box.png|200px|thumb|right|'''Figure 4''': Diagram of a simulation box containing 2139 atoms. The blue lines indicate the boundaries of the box.]]
[[File:ThirdYearSimulationExpt-Intro-Periodic.svg|300px|thumb|left|'''Figure 5''': Periodic boundary conditions in two dimensions.]]

We cannot simulate realistic volumes of liquid. In fact, in our simulations, <math>N</math> will be between <math>1000</math> and <math>10000</math>. The following task should illustrate why this must be so.

In order for our simulations to approximate a bulk liquid, we have to use a computational trick. The atoms in the simulation are enclosed in a simulation box, of fixed dimensions ('''figure 4'''). This box is very often a cuboid, but parallelepipeds can also be used (and this can be very useful when simulating crystal structures). We pretend that we have repeated our box infinitely in all directions, so that the atoms at the very edges are not exposed to a vacuum. This is illustrated in two dimensions in '''figure 5'''. The darker coloured atoms in the central box are the "real" atoms. The faded atoms in the outer four boxes are the replicas. When an atom crosses the boundary of the box, one of its replicas enters the box through the opposite face. In this way, the number of atoms inside the box is always constant.

'''<big>TASK 5: Consider an atom at position <math>\left(0.5, 0.5, 0.5\right)</math> in a cubic simulation box which runs from <math>\left(0, 0, 0\right)</math> to <math>\left(1, 1, 1\right)</math>. In a single timestep, it moves along the vector <math>\left(0.7, 0.6, 0.2\right)</math>. At what point does it end up, ''after the periodic boundary conditions have been applied''? [1 marks]''' </big>.

====Truncation====

Periodic boundary conditions introduce their own problems. When we defined our potential function (equation 10), we specified that it depended on all possible pairs of atoms. If we have an infinite number of replicas of our system, how can we avoid calculating an infinite number of pair interactions?

Think about the three integrals you calculated for the Lennard-Jones potential task. They represent the area under the Lennard-Jones potential curve between some specified distance (<math>2\sigma</math>, <math>2.5\sigma</math>, and <math>3\sigma</math>), and infinite separation (where there is no interaction). You should find that this value becomes rather small as the near distance is increased! The attractive <math>\frac{1}{r^6}</math> part of the potential dominates here, and this decays rapidly with <math>r</math>. We assume that this means that there is a distance beyond which the interaction is so small that we can safely ignore it. In fact, in most simulations this is chosen to be something close to <math>2.5\sigma</math> or <math>3\sigma</math>. When the forces are calculated, we only calculate interactions between a pair of atoms if their separation is less than this cutoff.

====Reduced Units====

It is typical when using Lennard-Jones interactions to work in reduced units. By this, we mean that all quantities in our simulation are divided by scaling factors — for example, distances are divided by <math>\sigma</math>. The result of this is that the values become more manageable: all values that we might work out are typically around 1, rather than <math>1\times 10^{-10}</math> (in the case of distance), <math>300</math> (in the case of temperature), or <math>1\times 10^{-19}</math> (in the case of energy).

We denote these reduced quantities by a star, and they take the following conversion factors:

* distance <math>r^* = \frac{r}{\sigma}</math>
* energy <math>E^* = \frac{E}{\epsilon}</math>
* temperature <math>T^* = \frac{k_BT}{\epsilon}</math>

'''<big>TASK 6: The Lennard-Jones parameters for argon are <math>\sigma = 0.34\mathrm{nm}, \epsilon\ /\ k_B= 120 \mathrm{K}</math>. If the LJ cutoff is <math>r^* = 3.2</math>, what is it in real units? What is the well depth in <math>\mathrm{kJ\ mol}^{-1}</math>? What is the reduced temperature <math>T^* = 1.5</math> in real units? [1 marks]</big> '''

'''<big>This is the second section of the third year simulation experiment. You can return to the previous section, [[Third year simulation experiment/Running your first simulation|Files to Download]], or jump ahead to the next section, [[Third year simulation experiment/Equilibration|Equilibration]].</big>'''

Third year simulation experiment/Introduction to molecular dynamics simulation

2021-10-24T08:36:35Z

Fbresme:

'''<big>This is the second section of the third year simulation experiment. You can return to the previous section, [[Third year simulation experiment/Files to download|Downloading Files]], or jump ahead to the next section, [[Third year simulation experiment/Equilibration|Equilibration]].</big>'''

'''<big>This section contains background information about the theory of molecular dynamics simulations. It contains a number of relatively short exercises that you must complete as part of your lab write-up. These are labelled in bold and preceded by the word TASK in large print. It is recommended that you read the information on this page before carrying on with the rest of the experiment, but you are encouraged to save the TASKS for later; you can attempt them while you wait for long simulations to finish.</big>'''

In this section, we briefly discuss the theory behind molecular dynamics (MD) simulations. When we perform MD, we calculate how a particular set of atoms move over time. Using statistical physics, we can use the positions, velocities, and forces, of the atoms to calculate thermodynamic quantities like temperature and pressure.

==Theory==

===The Classical Particle Approximation===

As you may remember from your quantum chemistry lectures, it is very straightforward to write down the Schroedinger equation that describes the behaviour of any particular chemical system. For anything more complicated than a hydrogen atom, however, it is impossible to solve exactly. Even approximate solutions can be extremely computationally demanding. To be able to simulate a real system, we have to make some approximations.

It turns out that, to a very good approximation, we can assume that atoms behave as classical particles. Imagine a collection of <math>N</math> atoms. Each one of them will interact with all of the others, and so each atom will feel a force. Newton's second law tell us that that force causes the atom to accelerate.

Throughout this section, we are going to use the following notation:

* <math>\mathbf{F}_i</math> is the force acting on atom i.
* <math>m_i</math> is the mass of atom i.
* <math>\mathbf{a}_i</math> is the acceleration of atom i, the rate of change of its velocity.
* <math>\mathbf{v}_i</math> is the velocity of atom i.
* <math>\mathbf{x}_i</math> is the position of atom i.

<center><math>\mathbf{F}_i = m_i \mathbf{a}_i = m_i \frac{\mathrm{d}\mathbf{v}_i}{\mathrm{d}t} = m_i \frac{\mathrm{d}^2 \mathbf{x}_i}{\mathrm{d}t^2} \ \ (1)</math></center>

This is a second order differential equation for the positions of the atoms — if we know how the force, <math>\mathbf{F}_i</math>, behaves as a function of time, then we can determine the atomic positions and velocities at any time we like. Our system of <math>N</math> atoms has <math>N</math> of these equations, one for each atom. This is one of the reasons that computer simulations are needed — if we want to model the behaviour of a liquid, we can hardly solve the necessary number of equations by hand.

===Numerical Integration===

'''Numerical integration is a rather complex topic. In particular, the notation used below can be quite intimidating. Remember that you are encouraged to ask for help from the demonstrator if you want to discuss any part of this experiment!'''
 

There are a number of numerical algorithms to perform a molecular dynamics simulation, two are presented here- The Classical Verlet algorithm and The Velocity-Verlet algorithm.

====Verlet Algorithm====

To solve these equations numerically we have to ''discretise'' the problem: rather than treating the atomic positions, velocities, and forces as continuous functions of time, we break our simulation up into a sequence of '''timesteps''', each of length <math>\delta t</math>. This process is illustrated for a simple function in '''figure 1'''. The method that we are going to use to solve Newton's law for our atoms is usually called the Verlet algorithm (although it is an old method, and has been 'rediscovered' many times!). To understand its origin, we will begin with a brief derivation.

 
[[File:ThirdYearSimulationExpt-Intro-Discretisation.png|300px|thumb|center|'''Figure 1''': Discretisation of sin(x) between 0 and <math>2\pi</math>]]
 

We denote the position of an atom, <math>i</math>, at time <math>t</math> by <math>\mathbf{x}_i \left(t\right)</math>. Similarly, <math>\mathbf{v}_i \left(t\right)</math> is the velocity of that atom at the same time. What we want to know is the position of the atoms at the next timestep, <math>t + \delta t</math>. The basic Verlet algorithm is shown in '''figure 2''' - knowing a set of initial conditions the algorithm calculates forces and by Newton's second law, we can update the positions of a set of particles are a time <math>t + \delta t</math>.

 
[[File:ThirdYearSimulationExpt-Intro-Verlet-flowchart.svg|300px|thumb|center|'''Figure 2''': Steps to implement the classic Verlet algorithm.]]
 
'''<big> TASK 1: By taking Taylor expansions of <math>x(t + \delta t)</math> and <math>x(t - \delta t)</math>, write general expressions for them up to the fourth order <math>\mathcal{O}\left(\delta t^4\right)</math> </big>'''

 
'''<big> Having written these expressions, derive the formula in figure 2 to update positions as used in the classical Verlet algorithm <math> x(t + \delta t) \approx 2x_{i}(t) - x_{i}(t-\delta t) + \frac{F_{i}(t)}{m} \delta t^{2}</math> by using Newton's second law to replace <math>\frac{\mathrm{d}^2\mathbf{x}_i\left(t\right)}{\mathrm{d}t^2}</math> [4 marks] </big>'''

Using this last equation, we can use a sequence of steps like those shown in '''figure 2''' to get the positions. At no point are the velocities calculated in this method!

====Velocity Verlet Algorithm====

If we assume that the acceleration of an atom depends only on its position and not its velocity, then we are able to come up with a new algorithm that lets us calculate atomic velocities explicitly as shown in '''figure 3'''.

 

[[File:ThirdYearSimulationExpt-Intro-VelocityVerlet-flowchart.svg|300px|thumb|center|'''Figure 3''': Steps to implement the velocity Verlet algorithm.]]

 

We start by noting that
<center><math>\mathbf{v}_i\left(t + \delta t\right) = \mathbf{v}_i\left(t\right) + \frac{\mathbf{a}_i\left(t\right) + \mathbf{a}_i\left(t + \delta t\right)}{2}\delta t \ \ (6)</math></center>

We can Taylor expand the velocity by half a step, instead of a full step.

<center><math>\mathbf{v}_i\left(t + \frac{1}{2}\delta t\right) = \mathbf{v}_i\left(t\right) + \frac{1}{2} \mathbf{a}_i\left(t\right)\delta t \ \ (7)</math></center>

We then substitute this into your expansion for <math> x_{i} (t + \delta t) </math> to obtain an accuracy up to <math> \delta t ^{2} </math>. Notice that terms up to <math> \delta t ^{2} </math> in your expansion can be written:

<center><math> \mathbf{x}_{i} (t + \delta t) = \mathbf{x}_{i} (t) + \mathbf{v}(t) \delta t + \frac{1}{2} \mathbf{a}(t) \delta t ^{2} </math></center>

<center><math>\mathbf{x}_i\left(t + \delta t\right) = \mathbf{x}_i\left(t\right) + \mathbf{v}_i\left(t + \frac{1}{2}\delta t\right)\delta t \ \ (8)</math></center>

When we know the updated atomic positions, we can calculate new forces, <math>\mathbf{a}_i\left(t + \delta t\right)</math>. Finally, we substitute equation (7) into equation (6) to get the new velocities <math>\mathbf{v}_i\left(t + \delta t\right)</math>.

<center><math>\mathbf{v}_i\left(t + \delta t\right) = \mathbf{v}_i\left(t + \frac{1}{2}\delta t\right) + \frac{1}{2}\mathbf{a}_i\left(t + \delta t\right)\delta t \ \ (9)</math></center>

Notice that for both numerical integration algorithms, the first step is "specify initial conditions". When using the Verlet algorithm, we need to know the starting positions of the atoms (<math>\mathbf{x}_i\left(0\right)</math>), and their positions one timestep in the past (<math>\mathbf{x}_i\left(-\delta t\right)</math>). If the velocity-Verlet algorithm is used, then we have to know the the starting positions of the atoms (<math>\mathbf{x}_i\left(0\right)</math>) and their velocities at the same time (<math>\mathbf{v}_i\left(0\right)</math>). For this reason, we often start new simulations by using the output of older ones. If, however, you are performing your first simulations of a system (as we are now), then you must choose your initial conditions. The simulation software that we will use is able to do this for us, and this will be explained in the next section.

 
'''<big> TASK 2: What could be an advantage of the Velocity-Verlet algorithm over the classical Verlet algorithm? [2 marks]</big>'''
 

===Atomic Forces===

Since we can't reasonably solve the exact equations from quantum mechanics necessary to determine the forces acting on a given configuration of N atoms, we have to make approximations. We know from classical physics that the force acting on an object is determined by the potential that it experiences:

<center><math>\mathbf{F}_i = - \frac{\mathrm{d}U\left(\mathbf{r}^N\right)}{\mathrm{d}\mathbf{r}_i}</math></center>

The shorthand notation <math>\mathbf{r}^N</math> stands for the position vectors of '''every''' atom in system. In principle, the force that a single atom feels is determined by the position of every other atom in the simulation. All we then need to do is to find a function <math>U</math> that captures all the key physics of the interatomic interactions in the system. For many simple liquids, it turns out that we can model the interactions between each pair of atoms extremely well using the Lennard-Jones potential. Overall, U takes the form:

<center><math>U\left(\mathbf{r}^N\right) = \sum_i^N \sum_{i \neq j}^{N} \left\{ 4\epsilon \left( \frac{\sigma^{12}}{r_{ij}^{12}} - \frac{\sigma^6}{r_{ij}^6} \right) \right\} \ \ (10)</math></center>

=== TASK 3: Consider the Lennard-Jones pair potential. What physical interaction(s) does it describe? What is the physical significance for the r^(-6) and r^(-12) terms? [3 marks] ===

'''<big>TASK 4: For a single Lennard-Jones interaction, <math>\phi\left(r\right) = 4\epsilon \left( \frac{\sigma^{12}}{r^{12}} - \frac{\sigma^6}{r^6} \right)</math>, find the separation, <math>r_0</math>, at which the potential energy is zero. What is the force at this separation? Find the equilibrium separation, <math>r_{eq}</math>, and work out the well depth (<math>\phi\left(r_{eq}\right)</math>). Evaluate the integrals <math>\int_{2\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math>, <math>\int_{2.5\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math>, and <math>\int_{3\sigma}^\infty \phi\left(r\right)\mathrm{d}r</math> when <math>\sigma = \epsilon = 1.0</math> [4 marks]</big>.'''

====Periodic Boundary Conditions====

[[File:ThirdYearSimulationExpt-Intro-Box.png|200px|thumb|right|'''Figure 4''': Diagram of a simulation box containing 2139 atoms. The blue lines indicate the boundaries of the box.]]
[[File:ThirdYearSimulationExpt-Intro-Periodic.svg|300px|thumb|left|'''Figure 5''': Periodic boundary conditions in two dimensions.]]

We cannot simulate realistic volumes of liquid. In fact, in our simulations, <math>N</math> will be between <math>1000</math> and <math>10000</math>. The following task should illustrate why this must be so.

In order for our simulations to approximate a bulk liquid, we have to use a computational trick. The atoms in the simulation are enclosed in a simulation box, of fixed dimensions ('''figure 4'''). This box is very often a cuboid, but parallelepipeds can also be used (and this can be very useful when simulating crystal structures). We pretend that we have repeated our box infinitely in all directions, so that the atoms at the very edges are not exposed to a vacuum. This is illustrated in two dimensions in '''figure 5'''. The darker coloured atoms in the central box are the "real" atoms. The faded atoms in the outer four boxes are the replicas. When an atom crosses the boundary of the box, one of its replicas enters the box through the opposite face. In this way, the number of atoms inside the box is always constant.

'''<big>TASK 5: Consider an atom at position <math>\left(0.5, 0.5, 0.5\right)</math> in a cubic simulation box which runs from <math>\left(0, 0, 0\right)</math> to <math>\left(1, 1, 1\right)</math>. In a single timestep, it moves along the vector <math>\left(0.7, 0.6, 0.2\right)</math>. At what point does it end up, ''after the periodic boundary conditions have been applied''? [1 marks]''' </big>.

====Truncation====

Periodic boundary conditions introduce their own problems. When we defined our potential function (equation 10), we specified that it depended on all possible pairs of atoms. If we have an infinite number of replicas of our system, how can we avoid calculating an infinite number of pair interactions?

Think about the three integrals you calculated for the Lennard-Jones potential task. They represent the area under the Lennard-Jones potential curve between some specified distance (<math>2\sigma</math>, <math>2.5\sigma</math>, and <math>3\sigma</math>), and infinite separation (where there is no interaction). You should find that this value becomes rather small as the near distance is increased! The attractive <math>\frac{1}{r^6}</math> part of the potential dominates here, and this decays rapidly with <math>r</math>. We assume that this means that there is a distance beyond which the interaction is so small that we can safely ignore it. In fact, in most simulations this is chosen to be something close to <math>2.5\sigma</math> or <math>3\sigma</math>. When the forces are calculated, we only calculate interactions between a pair of atoms if their separation is less than this cutoff.

====Reduced Units====

It is typical when using Lennard-Jones interactions to work in reduced units. By this, we mean that all quantities in our simulation are divided by scaling factors — for example, distances are divided by <math>\sigma</math>. The result of this is that the values become more manageable: all values that we might work out are typically around 1, rather than <math>1\times 10^{-10}</math> (in the case of distance), <math>300</math> (in the case of temperature), or <math>1\times 10^{-19}</math> (in the case of energy).

We denote these reduced quantities by a star, and they take the following conversion factors:

* distance <math>r^* = \frac{r}{\sigma}</math>
* energy <math>E^* = \frac{E}{\epsilon}</math>
* temperature <math>T^* = \frac{k_BT}{\epsilon}</math>

'''<big>TASK 6: The Lennard-Jones parameters for argon are <math>\sigma = 0.34\mathrm{nm}, \epsilon\ /\ k_B= 120 \mathrm{K}</math>. If the LJ cutoff is <math>r^* = 3.2</math>, what is it in real units? What is the well depth in <math>\mathrm{kJ\ mol}^{-1}</math>? What is the reduced temperature <math>T^* = 1.5</math> in real units? [1 marks]</big> '''

'''<big>This is the second section of the third year simulation experiment. You can return to the previous section, [[Third year simulation experiment/Running your first simulation|Files to Download]], or jump ahead to the next section, [[Third year simulation experiment/Equilibration|Equilibration]].</big>'''

Third year simulation experiment/Files to download

2021-10-24T08:31:15Z

Fbresme:

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

All of the simulations that you run in this experiment are going to be performed in Virtual Machines (VM). Before the beginning of your lab session, you should have received an invitation email to register/connect to the VM.


In each section of the exercise, we have tried to provide a number of mathematical and/or research exercises that you should attempt while you are waiting for the simulations in that section to be completed. Each simulation should take a few minutes. You can also use this time to write your report on the previous sections!

In this first section, we will teach you how to login to the Virtual Machines and submit an example simulation. While you wait for that example to complete, you can move on to the next section and read about the theory of molecular dynamics simulations

==Connecting to the Virtual Machine==

You will be using a Microsoft Azure Lab Virtual Machine (VM) to access the software needed for the lab.

: 1. You will receive an invitation email, before your session starts, with the subject Register for Lab - IC_Chemistry_UK_LS.
: 2. Follow the link to 'Register for the lab' in the email which will direct you to the Azure Lab Services page.
: 3. On the web page, you should see a box corresponding to the VM shared with you. In the bottom left, slide the toggle from left to right to start the VM (It may take some time to start running).
: 4. Once running, at the bottom right of the box, click the computer-style icon next to the three vertical dots.
A file with the extension rdp will be downloaded: IC_Chemistry_UK_LS.rdp. Follow the instructions for your operating service below to use the file:

'''Windows'''

:: a. Navigate to where the file has downloaded and double click on the file to open.

'''Linux'''

:: a. Open a terminal window and through the terminal, go to the location where the file has downloaded.
:: b. Type the command: <pre> remmina IC_Chemistry_UK_LS.rdp </pre> to run the file.

'''Mac'''

:: a. Download and install the Microsoft Remote Desktop app for Mac OS.
:: b. Open the Microsoft Remote Desktop app
:: c. On the top toolbar bar, click on the cog icon and then select Import from RDP file..
:: d. Navigate and select the downloaded rdp file.
:: e. There should now be an 'IC_Chemistry_UK_LS' PC showing, double click on this to initialise.

: 5. You should be asked to Accept Certificate?, select Yes.
: 6. You will be asked to Enter authentication credentials:
:: a. Change the username into "chemistry" by removing "~/".
:: b. Enter the password provided in the invitation email to 'Register for the Lab'.
The VM should now launch and you will be taken to a Windows desktop where you should be able to see the LAMMPS icon on the desktop. Double click this to launch.

If you have any problems with accessing the VM then let a demonstrator know.



==Getting the files for the experiment==

You can download all of the files that you will need for this experiment [https://imperialcollegelondon.box.com/s/mjxn9zxl67y10pgn8wkwlin05hmyqdsn from this address]. You should copy the folder '''ImperialChem-Year3SimExpt1415-master''' to a location of your choice. It contains a number of subfolders — one for each section of the experiment. Every subsequent page of this lab manual will begin with a line telling you which folder contains the necessary files, like this one:

<big>'''THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "Intro" SUBFOLDER'''.</big>

Have a look in the '''"Intro"''' folder now. It contains a file called '''melt_crystal.in''', which you should open with a text editor (like Notepad++ or VSCode which you can find on Software Hub. VSCode is also on the Virtual Machines). This file is called an "input script", and it controls how the simulation software operates. We will perform all of our simulations with a software package called [http://lammps.sandia.gov LAMMPS]. Over the course of the experiment, you will learn what all of the commands in this file mean. The [https://lammps.sandia.gov/doc/Commands.html LAMMPS manual] contains a lot of valuable information about each of the commands, if you don't understand one of them or want to look up what some parameter means you can look it up there. To make life easier, we put "further info" links in the wiki. For now, we are going to use this file to run a few trial simulations.

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

Third year simulation experiment

2021-10-24T08:28:25Z

Fbresme: /* Conclusion Questions */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. [4]
#What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? [3]
#What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''
# In the simulations you have performed ergodicity has not been an issue. Describe a system in which "brute force" MD struggles to achieve ergodic sampling. Describe one "enhanced sampling" technique that can be used to overcome this. [7]

Third year simulation experiment

2021-10-24T08:24:08Z

Fbresme: /* Introduction Questions */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. The thermodynamic ensemble defines these conditions. Explain what is meant by the thermodynamic ensemble. Your answer should also provide three ensemble examples and briefly discuss what quantities are conserved in each ensemble. You may want to consult Atkins' Physical Chemistry 11th edition (Focus 13D) to address this question. [5] 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T08:12:11Z

Fbresme: /* Introduction Questions */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Computer simulations are performed under specific "experimental" conditions. These conditions are defined by the ensemble. Explain what is meant by a thermodynamic ensemble, and what thermodynamic quantities are conserved quantity". 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T08:09:12Z

Fbresme: /* Introduction Questions */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore difficult to study experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T08:07:28Z

Fbresme: /* Introduction Questions */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T08:06:52Z

Fbresme:

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed. 



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. 
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T07:56:53Z

Fbresme:

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed.



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk). Please feel free to contact Prof. Bresme if you have general questions about the molecular dynamics method and/or the theoretical background behind molecular dynamics (statistical thermodynamics).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. 
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T07:55:01Z

Fbresme:

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed.



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations - ''as noted above this exercise is not compulsory''

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. 
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T07:52:26Z

Fbresme: /* Introduction */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed.



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of an atomistic liquid.

At the end of this experiment, you will have performed your own simulations with state of the art software packages used by researchers all around the world, and used those simulations to investigate thermophysical and structural properties of liquids, solids and gases. You will learn to compute thermodynamic quantities such as temperature and pressure.

All the information that you need to complete the experiment is provided in these wiki pages. We have provided links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (2nd year lectures by Prof. Fernando Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism. If you copy paste text, this will be flagged up as plagiarised. Think carefully what you write, and use your own words and conclusions.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab.''' That section provides information on calculations of dynamic properties. If you are interested in learning more about simulations, please give it a go. However, you should NOT submit this material as part of your lab report, as it will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. 
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T07:44:26Z

Fbresme:

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need the molecular dynamics code [[LAMMPS]]. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed.



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of a simple liquid using the virtual machines.

At the end of this experiment, you will have performed your own simulations using state of the art software packages used by researchers all around the world, and used those simulations to calculate both structural and dynamic properties of a simple liquid. You will learn to calculate thermodynamic quantities such as temperature and pressure in computer simulations.

All of the information that you need to complete the experiment is provided in these wiki pages. We have also tried to provide links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject. You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (lectures by Prof. Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab this year.''' The section has been left on the wiki for any interested student to give it a go. However, it should NOT be submitted as part of your lab report, and will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. 
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T07:43:48Z

Fbresme:

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 To run this experiment, you will need molecular dynamics code LAMMPS. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed.



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of a simple liquid using the virtual machines.

At the end of this experiment, you will have performed your own simulations using state of the art software packages used by researchers all around the world, and used those simulations to calculate both structural and dynamic properties of a simple liquid. You will learn to calculate thermodynamic quantities such as temperature and pressure in computer simulations.

All of the information that you need to complete the experiment is provided in these wiki pages. We have also tried to provide links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject. You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (lectures by Prof. Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab this year.''' The section has been left on the wiki for any interested student to give it a go. However, it should NOT be submitted as part of your lab report, and will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. 
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment

2021-10-24T07:43:27Z

Fbresme:

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 '''To run this experiment, you will need molecular dynamics code LAMMPS. LAMMPS runs on laptops, desktop computers and supercomputers.
You will be provided with access to a Microsoft Azure Lab Virtual Machines (VM), which has LAMMPS pre-installed.



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of a simple liquid using the virtual machines.

At the end of this experiment, you will have performed your own simulations using state of the art software packages used by researchers all around the world, and used those simulations to calculate both structural and dynamic properties of a simple liquid. You will learn to calculate thermodynamic quantities such as temperature and pressure in computer simulations.

All of the information that you need to complete the experiment is provided in these wiki pages. We have also tried to provide links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject. You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (lectures by Prof. Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab this year.''' The section has been left on the wiki for any interested student to give it a go. However, it should NOT be submitted as part of your lab report, and will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. 
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". 


== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. 
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? 
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? 
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''

Third year simulation experiment/Equilibration

2021-10-20T10:44:32Z

Fbresme:

'''<big>This is the third section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Introduction_to_molecular_dynamics_simulation|Introduction to molecular dynamics simulation]], or jump ahead to the next section, [[Third year simulation experiment/Running simulations under specific conditions|Running simulations under specific conditions]].</big>'''
 
We will be using the LAMMPS program to carry out our molecular dynamics simulations.
'''In several places in this section, we will ask you to consult the LAMMPS manual to find out things about how the software works. You can find the manual [https://lammps.sandia.gov/doc/Manual.html here].''' We appreciate that the format of this document can make it a little hard to navigate, but it is the definitive resource on how different commands in LAMMPS work, and is therefore invaluable. The files you will need for this section can be found in the intro folder downloaded previously.

===Creating the simulation box===
In the previous section, it was pointed out that before we can start a simulation, we need to know the initial states of all of the atoms in the system. Exactly what information we need about each atom depends on which method of numerical integration we need, but at the very least we need to specify the starting position of each atom. If we wanted to simulate a crystal, this information would be quite easy to come by — we could just look up the crystal structure, and use that to generate coordinates for however many unit cells we wanted. For this purpose, LAMMPS includes a command which generates crystal lattice structures.

Generating coordinates for atoms in a liquid is more difficult. There is no long range order, so we can't use a single point of reference to work out the positions of every other atom like we can in a solid. We could generate a random position for each atom. This would certainly create a disordered structure, but causes larger problems when we try to run the simulation.

Instead, we are going to place the atoms on the lattice points of a simple cubic lattice. This, of course, is not a situation in which the system is likely to be found physically. It turns out, though, that if we simulate for enough time we will find that the atoms rearrange themselves into more realistic configurations. We will discuss towards the end of this section exactly what is meant by "enough time"!

Consider the line in the input file <pre>lattice sc 0.8</pre> This command [https://lammps.sandia.gov/doc/lattice.html (further info)] creates a grid of points forming a simple cubic lattice (one lattice point per unit cell). The parameter <math>0.8</math> specifies the number density (number of lattice points per unit volume). In a corresponding output file, you will see the line <pre>Lattice spacing in x,y,z = 1.07722 1.07722 1.07722</pre> This indicates that the distance between the points of this lattice is <math>1.07722</math> (in reduced units, remember!).

The next lines in the input file are
<pre>
region box block 0 5 0 5 0 5
create_box 1 box
</pre>
The corresponding log file output is
<pre>
Created orthogonal box = (0 0 0) to (5.3861 5.3861 5.3861)
</pre>

The region command [https://lammps.sandia.gov/doc/region.html (further info)] simply defines a geometrical region in space, which we call "box". In this case, "box" is a cube extending ten lattice spacings from the origin in all three dimensions. The subsequent create_box command [https://lammps.sandia.gov/doc/create_box.html (further info)] tells LAMMPS to use the geometrical region called "box" as a template for the simulation box. The number 1 between "create_box" and "box" indicates that our simulation will contain only one type (species) of atom.

So far we have defined a simulation box which is based around a virtual simple cubic lattice. Our box contains 125 (5x5x5) unit cells of this lattice, and so contains 125 lattice points. We now need to fill our simulation box with atoms. The input command is <pre>create_atoms 1 box</pre> [https://lammps.sandia.gov/doc/create_atoms.html (further info)] while the log file simply contains an acknowledgement of this <pre>Created 125 atoms</pre>

The create_atoms command has two arguments; the first tells LAMMPS that all of the atoms that we create will be of type 1. Every atom in the simulation has a type — because we will be simulating a pure fluid, containing only one chemical species, every atom will have the same type. The actual type that we assign to each atom is arbitrary — type 1 does not, for example, need to correspond to the element with atomic number 1 (hydrogen). If we wanted to simulate water, we might make the hydrogen atoms type 1 and the oxygen atoms type 2. We will specify the physical and chemical properties of each atom type later in the input script.

The remaining data in the log file isn't very instructive as it stands — it simply contains a list of the thermodynamic properties of the simulation at certain intervals. In a few sections time, we will plot this data, but for now you can close the log file. Keep the input script open.

===Setting the properties of the atoms===

In addition to their positions, we also need the physical properties of the atoms to be able to perform the simulation. We set these properties on a 'per-type' basis, so that every atom of the same type has the same mass and the same interactions.

So far we have created 125 atoms, and we know the starting (<math>t = 0</math>) position for each of them. We have also set their masses, and told LAMMPS what sort of forces to calculate between them. The final thing we need to specify to completely specify the initial conditions is the velocity of each atom.

Choosing initial velocities for the atoms is a little easier than choosing initial positions. From the statistical thermodynamics lectures, you should know that, at equilibrium, the velocities of atoms in any system must be distributed according to the [http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution Maxwell-Boltzmann (MB) distribution]. If we know the masses of the atoms, and we know what temperature we want to simulate, then we can determine the relevant MB distribution function. LAMMPS is able to give every atom a random velocity whilst ensuring that overall the MB distribution is followed. This is the purpose of the line

<pre>
velocity all create 1.5 12345 dist gaussian rot yes mom yes
</pre>

You can see the manual page for this command [http://lammps.sandia.gov/doc/velocity.html here], but the key sections are:

* '''all''': the ''group'' of atoms on which the command acts. '''all''' simply specifies that we want every atom to have a velocity assigned to it.
* '''1.5''': the temperature, <math>T</math>, needed to calculate the MB distribution(in reduced units, as always)

===Monitoring thermodynamic properties===

We need to be sure that our simulation is correctly modelling whatever physical system we want to study. It is relatively easy to set up simulations, but how can we be sure that the "results" we get make sense? One of the best ways is to calculate from the simulation things that we can measure in experiment, and see if they agree. For example, we might want to simulate our system at a particular temperature and pressure, and measure the resulting density. If we repeat this over a range of temperatures at the same pressure, we will be able to plot an ''equation of state'', which we could compare to experimental measurements.

LAMMPS is able to calculate a great deal of thermodynamic information for us (you can see a full list of the properties it is able to calculate [http://lammps.sandia.gov/doc/thermo_style.html here]), but in these first simulations we are only interested in those properties specified in these commands:

<pre>
thermo_style custom time etotal temp press
thermo 10
</pre>

The first controls which properties will be printed out in the log file. In this case, we print how much time we have simulated so far (which is ''not'' the same as how long it has taken us to simulate it!), the total energy of the atoms, their temperature, and their pressure. The second line tells LAMMPS to print this information on every 10th timestep.

===Running the simulation===

'''Look at the lines below.'''
<pre>
### SPECIFY TIMESTEP ###
variable timestep equal 0.001
variable n_steps equal floor(100/${timestep})
timestep ${timestep}

### RUN SIMULATION ###
run ${n_steps}
</pre>
'''The second line (starting "variable timestep...") tells LAMMPS that if it encounters the text ${timestep} on a subsequent line, it should replace it by the value given. In this case, the value ${timestep} is always replaced by 0.001.'''
 

'''<big> It is now time to run your first simulation, submit the input script with the data file in the intro folder of the files you have downloaded Try changing the timestep - what happens when you make the timestep larger?. </big>'''

===Visualising the trajectory===

The '''trajectory files''' contain the positions of all the atoms in the simulation, recorded at a set interval (for all of these simulations, this was every ten timesteps — this is controlled by the '''dump''' command in the input scripts). We use a programme called [http://www.ks.uiuc.edu/Research/vmd/ '''VMD'''] to view these trajectories, which you should find is already installed on both the desktop and laptop computers. You can run VMD from the start menu with '''Start''' -> '''All Programs''' -> '''University of Illinois''' -> '''VMD'''.

====Loading a Trajectory====

We'll start by looking at the output of the 0.02 timestep simulation. In the '''VMD Main''' window, select the menu option '''File''' -> '''New Molecule'''. Click the '''Browse''' button, then select the relevant trajectory file. In the '''Determine file type''' dropdown, select '''LAMMPS Trajectory'''. Then click '''Load'''.

You will see that the '''VMD 1.9.1 OpenGL Display''' window now shows a horrible mess. VMD's default behaviour is to draw lines between atoms which it thinks might be chemically bonded. Our system doesn't model chemical bonds, so we want to turn this off. In the '''VMD Main''' window, select the menu option '''Graphics''' -> '''Representations'''. This shows a list of "representations" of our atoms. You will see that at the moment, there is a single representation listed, and it is selected. It will have the ''Lines'' style, the ''Name'' colour, and the selection ''all''. "Selection" simply tells VMD which atoms we want it to draw. We want to show every atom, so the current selection is fine. The ''name'' colouring method just makes VMD give atoms colours according to their specified type. The colour isn't important to us, so we can leave this be too. The "style" tells VMD what we want it to display for each atom. Change the '''Drawing Method''' from ''Lines'' to ''VDW''. You will see that the mess of lines is replaced by a mess of low resolution, overlapping spheres. Change the '''Sphere Scale''' to 0.3, and the '''Sphere Resolution''' to 17. The result should look a little smoother. Close the '''Graphical Representations''' window. You will notice that in the bottom right of the '''VMD Main''' window, there is a small play button. Click this, and you will see the animated version of your simulation trajectory.

By clicking and dragging with the mouse, you can rotate the simulation box (though this may be sluggish). At any time, you can reset the view by pressing the equals key.

====Tracking a Single Particle====
To illustrate the periodic boundary conditions that we are using, we are going to draw almost all of the atoms as points, but we will pick a single atom at random to draw as a sphere. This will make it easy to see how a single atom moves through the box. Reset the display using the equals key, then use the '''VMD Main''' window controls to pause the trajectory and reset it to the first trajectory (play with the different buttons until you find the one that does this). You should see the perfect cubic lattice. Use the option '''Display''' -> '''Orthographic''' to change the drawing mode, then rotate the displayed crystal so that you are looking at one vertex (looking down the 111 direction, in crystallographic terms).

Open the '''Graphical Representations''' window again. Change the representation style from '''VDW''' to points, then click the '''Create Rep''' button. This creates a second representation, allowing a subset of the atoms to be drawn in a different way. The '''Selected Atoms''' box allows us to choose which atoms this representation applies to. We just want to pick two of them at random — VMD assigns every atom an index, from 0 to N-1. In our case, there are 125 atoms, so choose two numbers between 0 and 124. Changed the '''Selected Atoms''' field to <pre>index i or index j</pre> where i and j are your chosen numbers, press return, then change the '''Drawing Method''' to '''VDW'''. You should now see only two atoms represented by spheres, with the rest shown as small points. In the '''VMD Main''' window, click play. Try rotating the box, and changing the playback speed.

You will see that sometimes one of the spheres seems to change position across the box very rapidly — this occurs when it reaches one periodic boundary, and is reflected back across the other face. Try playing with some of the other representation types in VMD — it is a very powerful package, which is often used to render images of simulated proteins, so many of its options aren't relevant to our simple system!

===Checking equilibration===

When we first set up a simulation, it is very important to make sure that our system reaches an equilibrium state. We characterise equilibrium by the average values of thermodynamic quantities becoming constant (due to the approximations that we have made, there will always be fluctuations, but the average values will become constant).

In this section, we are going to plot the thermodynamic output of the simulation to see how long it takes to reach the equilibrium state (and indeed, whether this happens at all). Instructions are given below to import data from the LAMMPS log file into Microsoft Excel. Once you have the data in a spreadsheet, you can plot it. If you know how to use some of the other plotting software available on the chemistry computers (like Origin), you are welcome to use it.

# Open a blank Excel workbook
# Copy the data in the textfile into the first cell
# With these data highlighted, click the Data tab and "Text to Columns"
# Click "Delimited", continue and let it be space delimited
# Click finish

'''<big>TASK 7: </big>'''

=== What does it mean for a simulation to "reach equilibrium"? Why is this important in terms of sampling from an ensemble using molecular dynamics? [2] ===

=== Plot the energy (potential, kinetic and total), temperature and pressure, against time for the 0,001 timestep experiment [2] ===

=== Does the simulation reach equilibrium? How can you tell? [2] ===

=== Make a single plot which shows the energy vs. time for the timesteps you have simulated [2]. ===

=== Of the timesteps that you used, which timestep will you use for subsequent simulations and why? [6] ===
''(Think about what is happening "physically" as you increase/decrease the timestep. Also, what features of each timeseries are indicative of the simulation's "health"?)''

'''<big>This is the third section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Introduction_to_molecular_dynamics_simulation|Introduction to molecular dynamics simulation]], or jump ahead to the next section, [[Third year simulation experiment/Running simulations under specific conditions|Running simulations under specific conditions]].</big>'''

Third year simulation experiment/Running simulations under specific conditions

2021-10-20T10:40:16Z

Fbresme:

'''<big>This is the fourth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Equilibration|Equilibration]], or jump ahead to the next section, [[Third_year_simulation_experiment/Structural_properties_and_the_radial_distribution_function| Structural Properties and the Radial Distribution Functions]].</big>'''

'''<big>THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "NpT" SUBFOLDER.</big>'''

==Changing Ensemble==

So far, we have been able to do some simulations in which the number of particles and the volume of the simulation cell are held constant. The energy is also constant (within a certain degree of error, which is introduced by the approximations that we make to do the simulation). If the simulation is a working properly, then the pressure and temperature of the system should also reach a constant ''average'' value (although there will again be fluctuations). In the statistical thermodynamics lectures, you met the concept of ensembles, which are used in statistical mechanics to represent different sorts of experimental conditions. The simulations we have done so far are described by the ''microcanonical'', or NVE ensemble (the letters represent those thermodynamic quantities which are constant).

As chemists, we often want to understand what happens under particular experimental conditions — at 298K under 1 atmosphere of pressure, for example. These sorts of conditions are described by different ensembles in statistical mechanics, such as the NVT (''canonical'') or NpT (''isobaric-isothermal'') ensembles.

In this section, we are going to modify our simulations from the previous section to run under NpT conditions, and sketch an equation of state for our model fluid at atmospheric pressure.

==Temperature and Pressure Control==

The file npt.in can be used to perform a constant temperature/pressure simulation of our model fluid. It starts by melting a simple cubic crystal, just as before, so much of this file will look familiar to you. You will notice a new section near the top, however, called '''### SPECIFY THE REQUIRED THERMODYNAMIC STATE ###'''. It contains three ''variables'' — these are used by the script later on to define the desired temperature, pressure, and timestep. The ellipses need to be replaced by the actual temperature, pressure and timestep that you want to use, so

<pre>
variable T equal 0.5
variable p equal 1.0
variable timestep equal 0.75
</pre>

would run a simulation at <math>T=0.5,\ p=1.0,\ \delta t=0.75</math>. You should remember from the [[Third_year_simulation_experiment/Equilibration|Equilibration]] section that this is a poor choice of timestep!

'''<big>TASK 8: Choose 5 temperatures (above the critical temperature <math>T^* = 1.5</math>), and two pressures (you can get a good idea of what a reasonable pressure is in Lennard-Jones units by looking at the average pressure of your simulations from the last section). This gives ten phase points — five temperatures at each pressure. Create 10 copies of npt.in, and modify each to run a simulation at one of your chosen <math>\left(p, T\right)</math> points. You should be able to use the results of the previous section to choose a timestep. Submit these ten jobs to the HPC portal. When your simulations have finished, download the log files as before. At the end of the log file, LAMMPS will output the values and errors for the pressure, temperature, and density <math>\left(\frac{N}{V}\right)</math>. </big>'''

=== Plot the density as a function of temperature for both pressures that you simulated. Include a line corresponding to the predictions made by the ideal gas law. [3] ===

=== How do your results compare to the ideal gas law? Do deviations increase/decrease with temperature and pressure? Explain. [7] ===

=== Do you expect your simulation results to be in better or worse agreement with the Van der Waals equation of state? Why? [3] ===

===Thermostats and Barostats - controlling the thermodynamic properties===
The statistical thermodynamics lectures will have introduced you to the ''equipartition theorem'', which states that, on average, every degree of freedom in a system at equilibrium will have <math>\frac{1}{2}k_B T</math> of energy. In our system with <math>N</math> atoms, each with 3 degrees of freedom, we can write
<math>E_K = \frac{3}{2} N k_B T</math>

<math>\frac{1}{2}\sum_i m_i v_i^2 = \frac{3}{2} N k_B T</math>

At the end of every timestep, we use the left hand side of this equation to calculate the kinetic energy, then divide by <math>\frac{3}{2}Nk_B</math> to get the ''instantaneous'' temperature <math>T</math>. In general, <math>T</math> will fluctuate, and will be different to our ''target'' temperature, <math>\mathfrak{T}</math> (this is whatever value we specify in the input script). We can change the temperature by multiplying every velocity by a constant factor, <math>\gamma</math>.

* If <math> T > \mathfrak{T} </math>, then the kinetic energy of the system is too high, and we need to reduce it. <math>\gamma < 1</math>
* If <math> T < \mathfrak{T} </math>, then the kinetic energy of the system is too low, and we need to increase it. <math>\gamma > 1</math>

We need to choose a scaling parameter <math>\gamma</math> so that the temperature is correct <math>T = \mathfrak{T}</math> if we multiply every velocity <math>\gamma</math>. We can write two equations:'''
<math>\frac{1}{2}\sum_i m_i v_i^2 = \frac{3}{2} N k_B T</math>

<math>\frac{1}{2}\sum_i m_i \left(\gamma v_i\right)^2 = \frac{3}{2} N k_B \mathfrak{T}</math>

By combining these equations, one can see that <math> \gamma = \sqrt{\frac{\mathfrak{T}}{T}} </math> (satisfy yourself that this is true!). A target value of <math> \gamma </math> of 1 is required and thus, dependent on whether it's larger or smaller than 1 the simulation can target the desired temperature.

Controlling the pressure is a little more involved, but the principle is largely the same: at each timestep, the pressure of the system is calculated; if the pressure is too high, then the simulation box is made a little larger, while if the pressure is too low the box is made smaller. Simulations in which the pressure is controlled are thus in the NpT ensemble — the volume of the simulation box is not constant!

===Examining the Input Script===

Open one of your input scripts (it doesn't matter which), and look at the section '''### BRING SYSTEM TO REQUIRED STATE ###'''. The line <pre>fix npt all npt temp ${T} ${T} ${tdamp} iso ${p} ${p} ${pdamp}</pre> is the one responsible for switching on the temperature and pressure control. LAMMPS actually allows us to heat or cool the system over the course of a simulation, if we want to — this is the reason that the temperature appears twice in this line. The first ${T} is the desired starting temperature, and the second is the desired temperature at the end of the simulation. We want a constant average temperature, so we specify the same value twice. The same goes for the pressure.

Now look at the lines near the end of the file:

<pre>
### MEASURE SYSTEM STATE ###
thermo_style custom step etotal temp press density
variable dens equal density
variable dens2 equal density*density
variable temp equal temp
variable temp2 equal temp*temp
variable press equal press
variable press2 equal press*press
fix aves all ave/time 100 1000 30000 v_dens v_temp v_press v_dens2 v_temp2 v_press2
run 30000
</pre>

The first command, ''thermo_style'', controls which thermodynamic properties are recorded, as before. The next lines are used to measure ''average'' thermodynamic properties for the system. To draw our equations of state, we need to know the average temperature, pressure, and density, and the statistical errors in those quantities. The six variable lines link those quantities (and their squared values, needed for the errors), to variable names that we can use in the averaging command, which is the line starting ''fix aves...''. This command takes a number of input values and averages them every so many timesteps. Exactly how often this happens depends in the values of the three numbers which follow ''ave/time''.

'''<big>This is the fourth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Equilibration|Equilibration]], or jump ahead to the next section, [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]].</big>'''

Third year simulation experiment/Files to download

2021-10-20T10:38:10Z

Fbresme:

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

All of the simulations that you run in this experiment are going to be performed in Virtual Machines (VM). Before the beginning of your lab session, you should have received an invitation email to register/connect to the VM.

'''The small-scale simulations that we will perform in this experiment should not be too long a few minutes. '''

In each section of the exercise, we have tried to provide a number of mathematical and/or research exercises that you should attempt while you are waiting for the simulations in that section to be completed. You can also use this time to write your report on the previous sections!

In this first section, we will teach you how to login to the Virtual Machines and submit an example simulation. While you wait for that example to complete, you can move on to the next section and read about the theory of molecular dynamics simulations

==Connecting to the Virtual Machine==

You will be using a Microsoft Azure Lab Virtual Machine (VM) to access the software needed for the lab.

: 1. You will receive an invitation email, before your session starts, with the subject Register for Lab - IC_Chemistry_UK.
: 2. Follow the link to 'Register for the lab' in the email which will direct you to the Azure Lab Services page.
: 3. On the web page, you should see a box corresponding to the VM shared with you. In the bottom left, slide the toggle from left to right to start the VM (It may take some time to start running).
: 4. Once running, at the bottom right of the box, click the computer-style icon next to the three vertical dots.
A file with the extension rdp will be downloaded: IC_Chemistry_UK.rdp. Follow the instructions for your operating service below to use the file:

'''Windows'''

:: a. Navigate to where the file has downloaded and double click on the file to open.

'''Linux'''

:: a. Open a terminal window and through the terminal, go to the location where the file has downloaded.
:: b. Type the command: <pre> remmina IC_Chemistry_UK.rdp </pre> to run the file.

'''Mac'''

:: a. Download and install the Microsoft Remote Desktop app for Mac OS.
:: b. Open the Microsoft Remote Desktop app
:: c. On the top toolbar bar, click on the cog icon and then select Import from RDP file..
:: d. Navigate and select the downloaded rdp file.
:: e. There should now be an 'IC_Chemistry_UK' PC showing, double click on this to initialise.

: 5. You should be asked to Accept Certificate?, select Yes.
: 6. You will be asked to Enter authentication credentials:
:: a. Change the username into "chemistry" by removing "~/".
:: b. Enter Imperial2021 as the password.
The VM should now launch and you will be taken to a Windows desktop where you should be able to see the LAMMPS icon on the desktop. Double click this to launch.

If you have any problems with accessing the VM then let a demonstrator know.



==Getting the files for the experiment==

You can download all of the files that you will need for this experiment [https://imperialcollegelondon.box.com/s/4jseyj0r7hkxpxcd8u175afwketbhkjj from this address]. You should copy the folder '''ImperialChem-Year3SimExpt1415-master''' to a location of your choice. It contains a number of subfolders — one for each section of the experiment. Every subsequent page of this lab manual will begin with a line telling you which folder contains the necessary files, like this one:

<big>'''THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "Intro" SUBFOLDER'''.</big>

Have a look in the '''"Intro"''' folder now. It contains a file called '''melt_crystal.in''', which you should open with a text editor (like Notepad++ which you can find on your Desktop). This file is called an "input script", and it controls how the simulation software operates. We will perform all of our simulations with a software package called [http://lammps.sandia.gov LAMMPS]. Over the course of the experiment, you will learn what all of the commands in this file mean. The [https://lammps.sandia.gov/doc/Commands.html LAMMPS manual] contains a lot of valuable information about each of the commands, if you don't understand one of them or want to look up what some parameter means you can look it up there. To make life easier, we put "further info" links in the wiki. For now, we are going to use this file to run a few trial simulations.

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

Third year simulation experiment/Equilibration

2021-10-20T10:36:27Z

Fbresme:

'''<big>This is the third section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Introduction_to_molecular_dynamics_simulation|Introduction to molecular dynamics simulation]], or jump ahead to the next section, [[Third year simulation experiment/Running simulations under specific conditions|Running simulations under specific conditions]].</big>'''
 
We will be using the LAMMPS program to carry out our molecular dynamics simulations.
'''In several places in this section, we will ask you to consult the LAMMPS manual to find out things about how the software works. You can find the manual [https://lammps.sandia.gov/doc/Manual.html here].''' We appreciate that the format of this document can make it a little hard to navigate, but it is the definitive resource on how different commands in LAMMPS work, and is therefore invaluable. The files you will need for this section can be found in the intro folder downloaded previously.

===Creating the simulation box===
In the previous section, it was pointed out that before we can start a simulation, we need to know the initial states of all of the atoms in the system. Exactly what information we need about each atom depends on which method of numerical integration we need, but at the very least we need to specify the starting position of each atom. If we wanted to simulate a crystal, this information would be quite easy to come by — we could just look up the crystal structure, and use that to generate coordinates for however many unit cells we wanted. For this purpose, LAMMPS includes a command which generates crystal lattice structures.

Generating coordinates for atoms in a liquid is more difficult. There is no long range order, so we can't use a single point of reference to work out the positions of every other atom like we can in a solid. We could generate a random position for each atom. This would certainly create a disordered structure, but causes larger problems when we try to run the simulation.

Instead, we are going to place the atoms on the lattice points of a simple cubic lattice. This, of course, is not a situation in which the system is likely to be found physically. It turns out, though, that if we simulate for enough time we will find that the atoms rearrange themselves into more realistic configurations. We will discuss towards the end of this section exactly what is meant by "enough time"!

Consider the line in the input file <pre>lattice sc 0.8</pre> This command [https://lammps.sandia.gov/doc/lattice.html (further info)] creates a grid of points forming a simple cubic lattice (one lattice point per unit cell). The parameter <math>0.8</math> specifies the number density (number of lattice points per unit volume). In a corresponding output file, you will see the line <pre>Lattice spacing in x,y,z = 1.07722 1.07722 1.07722</pre> This indicates that the distance between the points of this lattice is <math>1.07722</math> (in reduced units, remember!).

The next lines in the input file are
<pre>
region box block 0 5 0 5 0 5
create_box 1 box
</pre>
The corresponding log file output is
<pre>
Created orthogonal box = (0 0 0) to (10.7722 10.7722 10.7722)
</pre>

The region command [https://lammps.sandia.gov/doc/region.html (further info)] simply defines a geometrical region in space, which we call "box". In this case, "box" is a cube extending ten lattice spacings from the origin in all three dimensions. The subsequent create_box command [https://lammps.sandia.gov/doc/create_box.html (further info)] tells LAMMPS to use the geometrical region called "box" as a template for the simulation box. The number 1 between "create_box" and "box" indicates that our simulation will contain only one type (species) of atom.

So far we have defined a simulation box which is based around a virtual simple cubic lattice. Our box contains 125 (5x5x5) unit cells of this lattice, and so contains 125 lattice points. We now need to fill our simulation box with atoms. The input command is <pre>create_atoms 1 box</pre> [https://lammps.sandia.gov/doc/create_atoms.html (further info)] while the log file simply contains an acknowledgement of this <pre>Created 125 atoms</pre>

The create_atoms command has two arguments; the first tells LAMMPS that all of the atoms that we create will be of type 1. Every atom in the simulation has a type — because we will be simulating a pure fluid, containing only one chemical species, every atom will have the same type. The actual type that we assign to each atom is arbitrary — type 1 does not, for example, need to correspond to the element with atomic number 1 (hydrogen). If we wanted to simulate water, we might make the hydrogen atoms type 1 and the oxygen atoms type 2. We will specify the physical and chemical properties of each atom type later in the input script.

The remaining data in the log file isn't very instructive as it stands — it simply contains a list of the thermodynamic properties of the simulation at certain intervals. In a few sections time, we will plot this data, but for now you can close the log file. Keep the input script open.

===Setting the properties of the atoms===

In addition to their positions, we also need the physical properties of the atoms to be able to perform the simulation. We set these properties on a 'per-type' basis, so that every atom of the same type has the same mass and the same interactions.

So far we have created 125 atoms, and we know the starting (<math>t = 0</math>) position for each of them. We have also set their masses, and told LAMMPS what sort of forces to calculate between them. The final thing we need to specify to completely specify the initial conditions is the velocity of each atom.

Choosing initial velocities for the atoms is a little easier than choosing initial positions. From the statistical thermodynamics lectures, you should know that, at equilibrium, the velocities of atoms in any system must be distributed according to the [http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution Maxwell-Boltzmann (MB) distribution]. If we know the masses of the atoms, and we know what temperature we want to simulate, then we can determine the relevant MB distribution function. LAMMPS is able to give every atom a random velocity whilst ensuring that overall the MB distribution is followed. This is the purpose of the line

<pre>
velocity all create 1.5 12345 dist gaussian rot yes mom yes
</pre>

You can see the manual page for this command [http://lammps.sandia.gov/doc/velocity.html here], but the key sections are:

* '''all''': the ''group'' of atoms on which the command acts. '''all''' simply specifies that we want every atom to have a velocity assigned to it.
* '''1.5''': the temperature, <math>T</math>, needed to calculate the MB distribution(in reduced units, as always)

===Monitoring thermodynamic properties===

We need to be sure that our simulation is correctly modelling whatever physical system we want to study. It is relatively easy to set up simulations, but how can we be sure that the "results" we get make sense? One of the best ways is to calculate from the simulation things that we can measure in experiment, and see if they agree. For example, we might want to simulate our system at a particular temperature and pressure, and measure the resulting density. If we repeat this over a range of temperatures at the same pressure, we will be able to plot an ''equation of state'', which we could compare to experimental measurements.

LAMMPS is able to calculate a great deal of thermodynamic information for us (you can see a full list of the properties it is able to calculate [http://lammps.sandia.gov/doc/thermo_style.html here]), but in these first simulations we are only interested in those properties specified in these commands:

<pre>
thermo_style custom time etotal temp press
thermo 10
</pre>

The first controls which properties will be printed out in the log file. In this case, we print how much time we have simulated so far (which is ''not'' the same as how long it has taken us to simulate it!), the total energy of the atoms, their temperature, and their pressure. The second line tells LAMMPS to print this information on every 10th timestep.

===Running the simulation===

'''Look at the lines below.'''
<pre>
### SPECIFY TIMESTEP ###
variable timestep equal 0.001
variable n_steps equal floor(100/${timestep})
timestep ${timestep}

### RUN SIMULATION ###
run ${n_steps}
</pre>
'''The second line (starting "variable timestep...") tells LAMMPS that if it encounters the text ${timestep} on a subsequent line, it should replace it by the value given. In this case, the value ${timestep} is always replaced by 0.001.'''
 

'''<big> It is now time to run your first simulation, submit the input script with the data file in the intro folder of the files you have downloaded Try changing the timestep - what happens when you make the timestep larger?. </big>'''

===Visualising the trajectory===

The '''trajectory files''' contain the positions of all the atoms in the simulation, recorded at a set interval (for all of these simulations, this was every ten timesteps — this is controlled by the '''dump''' command in the input scripts). We use a programme called [http://www.ks.uiuc.edu/Research/vmd/ '''VMD'''] to view these trajectories, which you should find is already installed on both the desktop and laptop computers. You can run VMD from the start menu with '''Start''' -> '''All Programs''' -> '''University of Illinois''' -> '''VMD'''.

====Loading a Trajectory====

We'll start by looking at the output of the 0.02 timestep simulation. In the '''VMD Main''' window, select the menu option '''File''' -> '''New Molecule'''. Click the '''Browse''' button, then select the relevant trajectory file. In the '''Determine file type''' dropdown, select '''LAMMPS Trajectory'''. Then click '''Load'''.

You will see that the '''VMD 1.9.1 OpenGL Display''' window now shows a horrible mess. VMD's default behaviour is to draw lines between atoms which it thinks might be chemically bonded. Our system doesn't model chemical bonds, so we want to turn this off. In the '''VMD Main''' window, select the menu option '''Graphics''' -> '''Representations'''. This shows a list of "representations" of our atoms. You will see that at the moment, there is a single representation listed, and it is selected. It will have the ''Lines'' style, the ''Name'' colour, and the selection ''all''. "Selection" simply tells VMD which atoms we want it to draw. We want to show every atom, so the current selection is fine. The ''name'' colouring method just makes VMD give atoms colours according to their specified type. The colour isn't important to us, so we can leave this be too. The "style" tells VMD what we want it to display for each atom. Change the '''Drawing Method''' from ''Lines'' to ''VDW''. You will see that the mess of lines is replaced by a mess of low resolution, overlapping spheres. Change the '''Sphere Scale''' to 0.3, and the '''Sphere Resolution''' to 17. The result should look a little smoother. Close the '''Graphical Representations''' window. You will notice that in the bottom right of the '''VMD Main''' window, there is a small play button. Click this, and you will see the animated version of your simulation trajectory.

By clicking and dragging with the mouse, you can rotate the simulation box (though this may be sluggish). At any time, you can reset the view by pressing the equals key.

====Tracking a Single Particle====
To illustrate the periodic boundary conditions that we are using, we are going to draw almost all of the atoms as points, but we will pick a single atom at random to draw as a sphere. This will make it easy to see how a single atom moves through the box. Reset the display using the equals key, then use the '''VMD Main''' window controls to pause the trajectory and reset it to the first trajectory (play with the different buttons until you find the one that does this). You should see the perfect cubic lattice. Use the option '''Display''' -> '''Orthographic''' to change the drawing mode, then rotate the displayed crystal so that you are looking at one vertex (looking down the 111 direction, in crystallographic terms).

Open the '''Graphical Representations''' window again. Change the representation style from '''VDW''' to points, then click the '''Create Rep''' button. This creates a second representation, allowing a subset of the atoms to be drawn in a different way. The '''Selected Atoms''' box allows us to choose which atoms this representation applies to. We just want to pick two of them at random — VMD assigns every atom an index, from 0 to N-1. In our case, there are 125 atoms, so choose two numbers between 0 and 124. Changed the '''Selected Atoms''' field to <pre>index i or index j</pre> where i and j are your chosen numbers, press return, then change the '''Drawing Method''' to '''VDW'''. You should now see only two atoms represented by spheres, with the rest shown as small points. In the '''VMD Main''' window, click play. Try rotating the box, and changing the playback speed.

You will see that sometimes one of the spheres seems to change position across the box very rapidly — this occurs when it reaches one periodic boundary, and is reflected back across the other face. Try playing with some of the other representation types in VMD — it is a very powerful package, which is often used to render images of simulated proteins, so many of its options aren't relevant to our simple system!

===Checking equilibration===

When we first set up a simulation, it is very important to make sure that our system reaches an equilibrium state. We characterise equilibrium by the average values of thermodynamic quantities becoming constant (due to the approximations that we have made, there will always be fluctuations, but the average values will become constant).

In this section, we are going to plot the thermodynamic output of the simulation to see how long it takes to reach the equilibrium state (and indeed, whether this happens at all). Instructions are given below to import data from the LAMMPS log file into Microsoft Excel. Once you have the data in a spreadsheet, you can plot it. If you know how to use some of the other plotting software available on the chemistry computers (like Origin), you are welcome to use it.

# Open a blank Excel workbook
# Copy the data in the textfile into the first cell
# With these data highlighted, click the Data tab and "Text to Columns"
# Click "Delimited", continue and let it be space delimited
# Click finish

'''<big>TASK 7: </big>'''

=== What does it mean for a simulation to "reach equilibrium"? Why is this important in terms of sampling from an ensemble using molecular dynamics? [2] ===

=== Plot the energy (potential, kinetic and total), temperature and pressure, against time for the 0,001 timestep experiment [2] ===

=== Does the simulation reach equilibrium? How can you tell? [2] ===

=== Make a single plot which shows the energy vs. time for the timesteps you have simulated [2]. ===

=== Of the timesteps that you used, which timestep will you use for subsequent simulations and why? [6] ===
''(Think about what is happening "physically" as you increase/decrease the timestep. Also, what features of each timeseries are indicative of the simulation's "health"?)''

'''<big>This is the third section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Introduction_to_molecular_dynamics_simulation|Introduction to molecular dynamics simulation]], or jump ahead to the next section, [[Third year simulation experiment/Running simulations under specific conditions|Running simulations under specific conditions]].</big>'''

Third year simulation experiment/Files to download

2021-10-20T10:31:00Z

Fbresme:

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

All of the simulations that you run in this experiment are going to be performed in Virtual Machines (VM). Before the beginning of your lab session, you should have received an invitation email to register/connect to the VM.

'''The small-scale simulations that we will perform in this experiment should not be too long (a few minutes ~ 10min). However, you should expect to have to wait up to several hours for results to be available, particularly in the later stages!'''

In each section of the exercise, we have tried to provide a number of mathematical and/or research exercises that you should attempt while you are waiting for the simulations in that section to be completed. You can also use this time to write your report on the previous sections!

In this first section, we will teach you how to login to the Virtual Machines and submit an example simulation. While you wait for that example to complete, you can move on to the next section and read about the theory of molecular dynamics simulations

==Connecting to the Virtual Machine==

You will be using a Microsoft Azure Lab Virtual Machine (VM) to access the software needed for the lab.

: 1. You will receive an invitation email, before your session starts, with the subject Register for Lab - IC_Chemistry_UK.
: 2. Follow the link to 'Register for the lab' in the email which will direct you to the Azure Lab Services page.
: 3. On the web page, you should see a box corresponding to the VM shared with you. In the bottom left, slide the toggle from left to right to start the VM (It may take some time to start running).
: 4. Once running, at the bottom right of the box, click the computer-style icon next to the three vertical dots.
A file with the extension rdp will be downloaded: IC_Chemistry_UK.rdp. Follow the instructions for your operating service below to use the file:

'''Windows'''

:: a. Navigate to where the file has downloaded and double click on the file to open.

'''Linux'''

:: a. Open a terminal window and through the terminal, go to the location where the file has downloaded.
:: b. Type the command: <pre> remmina IC_Chemistry_UK.rdp </pre> to run the file.

'''Mac'''

:: a. Download and install the Microsoft Remote Desktop app for Mac OS.
:: b. Open the Microsoft Remote Desktop app
:: c. On the top toolbar bar, click on the cog icon and then select Import from RDP file..
:: d. Navigate and select the downloaded rdp file.
:: e. There should now be an 'IC_Chemistry_UK' PC showing, double click on this to initialise.

: 5. You should be asked to Accept Certificate?, select Yes.
: 6. You will be asked to Enter authentication credentials:
:: a. Change the username into "chemistry" by removing "~/".
:: b. Enter Imperial2021 as the password.
The VM should now launch and you will be taken to a Windows desktop where you should be able to see the LAMMPS icon on the desktop. Double click this to launch.

If you have any problems with accessing the VM then let a demonstrator know.



==Getting the files for the experiment==

You can download all of the files that you will need for this experiment [https://imperialcollegelondon.box.com/s/4jseyj0r7hkxpxcd8u175afwketbhkjj from this address]. You should copy the folder '''ImperialChem-Year3SimExpt1415-master''' to a location of your choice. It contains a number of subfolders — one for each section of the experiment. Every subsequent page of this lab manual will begin with a line telling you which folder contains the necessary files, like this one:

<big>'''THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "Intro" SUBFOLDER'''.</big>

Have a look in the '''"Intro"''' folder now. It contains a file called '''melt_crystal.in''', which you should open with a text editor (like Notepad++ which you can find on your Desktop). This file is called an "input script", and it controls how the simulation software operates. We will perform all of our simulations with a software package called [http://lammps.sandia.gov LAMMPS]. Over the course of the experiment, you will learn what all of the commands in this file mean. The [https://lammps.sandia.gov/doc/Commands.html LAMMPS manual] contains a lot of valuable information about each of the commands, if you don't understand one of them or want to look up what some parameter means you can look it up there. To make life easier, we put "further info" links in the wiki. For now, we are going to use this file to run a few trial simulations.

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

Third year simulation experiment/Files to download

2021-10-20T10:28:25Z

Fbresme: /* Getting the files for the experiment */

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

All of the simulations that you run in this experiment are going to be performed in Virtual Machines (VM). Before the beginning of your lab session, you should have received an invitation email to register/connect to the VM.

'''The small-scale simulations that we will perform in this experiment should not be too long (a few minutes ~ 10min). However, you should expect to have to wait up to several hours for results to be available, particularly in the later stages!'''

In each section of the exercise, we have tried to provide a number of mathematical and/or research exercises that you should attempt while you are waiting for the simulations in that section to be completed. You can also use this time to write your report on the previous sections!

In this first section, we will teach you how to login to the Virtual Machines and submit an example simulation. While you wait for that example to complete, you can move on to the next section and read about the theory of molecular dynamics simulations

==Connecting to the Virtual Machine==

You will be using a Microsoft Azure Lab Virtual Machine (VM) to access the software needed for the lab.

: 1. You will receive an invitation email, before your session starts, with the subject Register for Lab - IC_Chemistry_UK.
: 2. Follow the link to 'Register for the lab' in the email which will direct you to the Azure Lab Services page.
: 3. On the web page, you should see a box corresponding to the VM shared with you. In the bottom left, slide the toggle from left to right to start the VM (It may take some time to start running).
: 4. Once running, at the bottom right of the box, click the computer-style icon next to the three vertical dots.
A file with the extension rdp will be downloaded: IC_Chemistry_UK.rdp. Follow the instructions for your operating service below to use the file:

'''Windows'''

:: a. Navigate to where the file has downloaded and double click on the file to open.

'''Linux'''

:: a. Open a terminal window and through the terminal, go to the location where the file has downloaded.
:: b. Type the command: <pre> remmina IC_Chemistry_UK.rdp </pre> to run the file.

'''Mac'''

:: a. Download and install the Microsoft Remote Desktop app for Mac OS.
:: b. Open the Microsoft Remote Desktop app
:: c. On the top toolbar bar, click on the cog icon and then select Import from RDP file..
:: d. Navigate and select the downloaded rdp file.
:: e. There should now be an 'IC_Chemistry_UK' PC showing, double click on this to initialise.

: 5. You should be asked to Accept Certificate?, select Yes.
: 6. You will be asked to Enter authentication credentials:
:: a. Change the username into "chemistry" by removing "~/".
:: b. Enter Imperial2021 as the password.
The VM should now launch and you will be taken to a Windows desktop where you should be able to see the LAMMPS icon on the desktop. Double click this to launch.

If you have any problems with accessing the VM then let a demonstrator know.



==Getting the files for the experiment==

You can download all of the files that you will need for this experiment [https://imperialcollegelondon.box.com/s/4jseyj0r7hkxpxcd8u175afwketbhkjj from this address]. This .zip archive contains a folder called '''ImperialChem-Year3SimExpt1415-master''', which you should extract to a location of your choice. It contains a number of subfolders — one for each section of the experiment. Every subsequent page of this lab manual will begin with a line telling you which folder contains the necessary files, like this one:

<big>'''THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "Intro" SUBFOLDER'''.</big>

Have a look in the '''"Intro"''' folder now. It contains a file called '''melt_crystal.in''', which you should open with a text editor (like Notepad++ which you can find on your Desktop). This file is called an "input script", and it controls how the simulation software operates. We will perform all of our simulations with a software package called [http://lammps.sandia.gov LAMMPS]. Over the course of the experiment, you will learn what all of the commands in this file mean. The [https://lammps.sandia.gov/doc/Commands.html LAMMPS manual] contains a lot of valuable information about each of the commands, if you don't understand one of them or want to look up what some parameter means you can look it up there. To make life easier, we put "further info" links in the wiki. For now, we are going to use this file to run a few trial simulations.

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

Third year simulation experiment/Files to download

2021-10-20T10:27:17Z

Fbresme: /* Getting the files for the experiment */

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

All of the simulations that you run in this experiment are going to be performed in Virtual Machines (VM). Before the beginning of your lab session, you should have received an invitation email to register/connect to the VM.

'''The small-scale simulations that we will perform in this experiment should not be too long (a few minutes ~ 10min). However, you should expect to have to wait up to several hours for results to be available, particularly in the later stages!'''

In each section of the exercise, we have tried to provide a number of mathematical and/or research exercises that you should attempt while you are waiting for the simulations in that section to be completed. You can also use this time to write your report on the previous sections!

In this first section, we will teach you how to login to the Virtual Machines and submit an example simulation. While you wait for that example to complete, you can move on to the next section and read about the theory of molecular dynamics simulations

==Connecting to the Virtual Machine==

You will be using a Microsoft Azure Lab Virtual Machine (VM) to access the software needed for the lab.

: 1. You will receive an invitation email, before your session starts, with the subject Register for Lab - IC_Chemistry_UK.
: 2. Follow the link to 'Register for the lab' in the email which will direct you to the Azure Lab Services page.
: 3. On the web page, you should see a box corresponding to the VM shared with you. In the bottom left, slide the toggle from left to right to start the VM (It may take some time to start running).
: 4. Once running, at the bottom right of the box, click the computer-style icon next to the three vertical dots.
A file with the extension rdp will be downloaded: IC_Chemistry_UK.rdp. Follow the instructions for your operating service below to use the file:

'''Windows'''

:: a. Navigate to where the file has downloaded and double click on the file to open.

'''Linux'''

:: a. Open a terminal window and through the terminal, go to the location where the file has downloaded.
:: b. Type the command: <pre> remmina IC_Chemistry_UK.rdp </pre> to run the file.

'''Mac'''

:: a. Download and install the Microsoft Remote Desktop app for Mac OS.
:: b. Open the Microsoft Remote Desktop app
:: c. On the top toolbar bar, click on the cog icon and then select Import from RDP file..
:: d. Navigate and select the downloaded rdp file.
:: e. There should now be an 'IC_Chemistry_UK' PC showing, double click on this to initialise.

: 5. You should be asked to Accept Certificate?, select Yes.
: 6. You will be asked to Enter authentication credentials:
:: a. Change the username into "chemistry" by removing "~/".
:: b. Enter Imperial2021 as the password.
The VM should now launch and you will be taken to a Windows desktop where you should be able to see the LAMMPS icon on the desktop. Double click this to launch.

If you have any problems with accessing the VM then let a demonstrator know.



==Getting the files for the experiment==

You can download all of the files that you will need for this experiment [https://github.com/niallj/ImperialChem-Year3SimExpt1415/archive/master.zip from this address]. This .zip archive contains a folder called '''ImperialChem-Year3SimExpt1415-master''', which you should extract to a location of your choice. It contains a number of subfolders — one for each section of the experiment. Every subsequent page of this lab manual will begin with a line telling you which folder contains the necessary files, like this one:

<big>'''THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "Intro" SUBFOLDER'''.</big>

Have a look in the '''"Intro"''' folder now. It contains a file called '''melt_crystal.in''', which you should open with a text editor (like Notepad++ which you can find on your Desktop). This file is called an "input script", and it controls how the simulation software operates. We will perform all of our simulations with a software package called [http://lammps.sandia.gov LAMMPS]. Over the course of the experiment, you will learn what all of the commands in this file mean. The [https://lammps.sandia.gov/doc/Commands.html LAMMPS manual] contains a lot of valuable information about each of the commands, if you don't understand one of them or want to look up what some parameter means you can look it up there. To make life easier, we put "further info" links in the wiki. For now, we are going to use this file to run a few trial simulations.

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

Third year simulation experiment

2021-10-16T12:14:50Z

Fbresme: /* Introduction */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 '''To run this experiment, you will need access to the Microsoft Azure Lab Virtual Machines (VM).



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of a simple liquid using the virtual machines.

At the end of this experiment, you will have performed your own simulations using state of the art software packages used by researchers all around the world, and used those simulations to calculate both structural and dynamic properties of a simple liquid. You will learn to calculate thermodynamic quantities such as temperature and pressure in computer simulations.

All of the information that you need to complete the experiment is provided in these wiki pages. We have also tried to provide links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject. You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (lectures by Prof. Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab this year.''' The section has been left on the wiki for any interested student to give it a go. However, it should NOT be submitted as part of your lab report, and will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". [2]
# What is the Ergodic hypothesis? Explain its relevance to molecular dynamics simulations. [3]

== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. [4]
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? [3]
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''
# In the simulations you have performed ergodicity has not been an issue. Describe a system in which "brute force" MD struggles to achieve ergodic sampling. Describe one "enhanced sampling" technique that can be used to overcome this. [7]

Third year simulation experiment

2021-10-16T12:14:24Z

Fbresme: /* Introduction */

'''<big>Liquid simulations: this is the optional experiment which may be chosen by any third year student.</big>'''

'''<big> If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 '''To run this experiment, you will need access to the Microsoft Azure Lab Virtual Machines (VM).



==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of a simple liquid using the virtual machines.

At the end of this experiment, you will have performed your own simulations using state of the art software packages used by researchers all around the world, and used those simulations to calculate both structural and dynamic properties of a simple liquid. You will learn to calculate thermodynamic quantities such as temperature and pressure in computer simulations.

All of the information that you need to complete the experiment is provided in these wiki pages. We have also tried to provide links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject. You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (lectures by Prof. Bresme).

The member of academic staff responsible for this exercise is Prof. Fernando Bresme (f.bresme@imperial.ac.uk).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab this year.''' The section has been left on the wiki for any interested student to give it a go. However, it should NOT be submitted as part of your lab report, and will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". [2]
# What is the Ergodic hypothesis? Explain its relevance to molecular dynamics simulations. [3]

== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. [4]
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? [3]
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''
# In the simulations you have performed ergodicity has not been an issue. Describe a system in which "brute force" MD struggles to achieve ergodic sampling. Describe one "enhanced sampling" technique that can be used to overcome this. [7]

Third year simulation experiment/Files to download

2021-10-02T10:20:30Z

Fbresme: /* Connecting to the Virtual Machine */

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

All of the simulations that you run in this experiment are going to be performed in Virtual Machines (VM). To do this, you must login to one of the VM machines, ('''tba -- instructions to run). '''For the small-scale simulations that we will perform in this experiment the simulations should not be too long '''(tba - a few minutes)'''. (t'''ba However, you should expect to have to wait up to several hours for results to be available, particularly in the later stages!)'''

In each section of the exercise, we have tried to provide a number of mathematical and/or research exercises that you should attempt while you are waiting for the simulations in that section to be completed. You can also use this time to write your report on the previous sections!

In this first section, we will teach you how to login to the Virtual Machines and submit an example simulation. While you wait for that example to complete, you can move on to the next section and read about the theory of molecular dynamics simulations

==Connecting to the Virtual Machine==

You will be using a Virtual Machine (VM) to access the software needed for the lab.

1. You should have received an email with the subject Register for Lab - IC_Chemistry_UK.
2. Follow the link to 'Register for the lab' in the email which will direct you to the Azure Lab Services page.
3. On the web page, you should see a box corresponding to the VM shared with you. In the bottom left, slide the toggle from left to right to start the VM (It may take some time to start running).
4. Once running, at the bottom right of the box, click the computer-style icon next to the three vertical dots.
A file with the extension rdp will be downloaded: IC_Chemistry_UK.rdp. Follow the instructions for your operating service below to use the file:

Windows

a. Navigate to where the file has downloaded and double click on the file to open.
Linux

a. Open a terminal window and through the terminal, go to the location where the file has downloaded.
b. Type the command:
remmina IC_Chemistry_UK.rdp
to run the file.
Mac

a. Download and install the Microsoft Remote Desktop app for Mac OS.
b. Open the Microsoft Remote Desktop app
c. On the top toolbar bar, click on the cog icon and then select Import from RDP file..
d. Navigate and select the downloaded rdp file.
e. There should now be an 'IC_Chemistry_UK' PC showing, double click on this to initialise.

5. You should be asked to Accept Certificate?, select Yes.
6. You will be asked to Enter authentication credentials:
a. Change the username into "chemistry" by removing "~/".
b. Enter Imperial2021 as the password.
The VM should now launch and you will be taken to a Windows desktop where you should be able to see the GaussView icon on the desktop. Double click this to launch.

If you have any problems with accessing the VM then let a demonstrator know.


==Getting the files for the experiment==

You can download all of the files that you will need for this experiment [https://github.com/niallj/ImperialChem-Year3SimExpt1415/archive/master.zip from this address]. This .zip archive contains a folder called '''ImperialChem-Year3SimExpt1415-master''', which you should extract to a location of your choice. It contains a number of subfolders — one for each section of the experiment. Every subsequent page of this lab manual will begin with a line telling you which folder contains the necessary files, like this one:

<big>'''THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "Intro" SUBFOLDER'''.</big>

Have a look in the '''"Intro"''' folder now. It contains a file called '''melt_crystal.in''', which you should open with a text editor (like Notepad++ which you can find in Software Hub on your Desktop). This file is called an "input script", and it controls how the simulation software operates. We will perform all of our simulations with a software package called [http://lammps.sandia.gov LAMMPS]. Over the course of the experiment, you will learn what all of the commands in this file mean. The [https://lammps.sandia.gov/doc/Commands.html LAMMPS manual] contains a lot of valuable information about each of the commands, if you don't understand one of them or want to look up what some parameter means you can look it up there. To make life easier, we put "further info" links in the wiki. For now, we are going to use this file to run a few trial simulations.

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

Third year simulation experiment/Files to download

2021-10-02T10:19:57Z

Fbresme: /* Connecting to the Virtual Machine */

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

All of the simulations that you run in this experiment are going to be performed in Virtual Machines (VM). To do this, you must login to one of the VM machines, ('''tba -- instructions to run). '''For the small-scale simulations that we will perform in this experiment the simulations should not be too long '''(tba - a few minutes)'''. (t'''ba However, you should expect to have to wait up to several hours for results to be available, particularly in the later stages!)'''

In each section of the exercise, we have tried to provide a number of mathematical and/or research exercises that you should attempt while you are waiting for the simulations in that section to be completed. You can also use this time to write your report on the previous sections!

In this first section, we will teach you how to login to the Virtual Machines and submit an example simulation. While you wait for that example to complete, you can move on to the next section and read about the theory of molecular dynamics simulations

==Connecting to the Virtual Machine==

You will be using a Virtual Machine (VM) to access the software needed for the lab.

1. You should have received an email with the subject Register for Lab - IC_Chemistry_UK.
2. Follow the link to 'Register for the lab' in the email which will direct you to the Azure Lab Services page.
3. On the web page, you should see a box corresponding to the VM shared with you. In the bottom left, slide the toggle from left to right to start the VM (It may take some time to start running).
4. Once running, at the bottom right of the box, click the computer-style icon next to the three vertical dots.
A file with the extension rdp will be downloaded: IC_Chemistry_UK.rdp. Follow the instructions for your operating service below to use the file:

Windows

a. Navigate to where the file has downloaded and double click on the file to open.
Linux

a. Open a terminal window and through the terminal, go to the location where the file has downloaded.
b. Type the command:
remmina IC_Chemistry_UK.rdp
to run the file.
Mac

a. Download and install the Microsoft Remote Desktop app for Mac OS.
b. Open the Microsoft Remote Desktop app
c. On the top toolbar bar, click on the cog icon and then select Import from RDP file..
d. Navigate and select the downloaded rdp file.
e. There should now be an 'IC_Chemistry_UK' PC showing, double click on this to initialise.

5. You should be asked to Accept Certificate?, select Yes.
6. You will be asked to Enter authentication credentials:
a. Change the username into "chemistry" by removing "~/".
b. Enter Imperial2021 as the password.
The VM should now launch and you will be taken to a Windows desktop where you should be able to see the GaussView icon on the desktop. Double click this to launch.

If you have any problems with accessing the VM then let a demonstrator know.

'''(tba -- new text explaining connecting to the VMs)'''



==Getting the files for the experiment==

You can download all of the files that you will need for this experiment [https://github.com/niallj/ImperialChem-Year3SimExpt1415/archive/master.zip from this address]. This .zip archive contains a folder called '''ImperialChem-Year3SimExpt1415-master''', which you should extract to a location of your choice. It contains a number of subfolders — one for each section of the experiment. Every subsequent page of this lab manual will begin with a line telling you which folder contains the necessary files, like this one:

<big>'''THE FILES THAT YOU NEED FOR THIS SECTION ARE FOUND IN THE "Intro" SUBFOLDER'''.</big>

Have a look in the '''"Intro"''' folder now. It contains a file called '''melt_crystal.in''', which you should open with a text editor (like Notepad++ which you can find in Software Hub on your Desktop). This file is called an "input script", and it controls how the simulation software operates. We will perform all of our simulations with a software package called [http://lammps.sandia.gov LAMMPS]. Over the course of the experiment, you will learn what all of the commands in this file mean. The [https://lammps.sandia.gov/doc/Commands.html LAMMPS manual] contains a lot of valuable information about each of the commands, if you don't understand one of them or want to look up what some parameter means you can look it up there. To make life easier, we put "further info" links in the wiki. For now, we are going to use this file to run a few trial simulations.

'''<big>This is the first section of the third year simulation experiment. You can return to the introduction page, [[Third year simulation experiment]], or jump ahead to the next section, [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]].</big>'''

Third year simulation experiment/Files to download

2021-10-02T09:49:07Z

Fbresme: /* Connecting to the Virtual Machine */

Third year simulation experiment/Files to download

2021-10-02T09:48:32Z

Fbresme:

Third year simulation experiment

2021-10-02T09:40:14Z

Fbresme:

'''<big>This is the optional experiment which may be chosen by any third year student. If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 '''To run this experiment, you will need access to the Imperial College Virtual Machines (VM). If you have VPN installed, you should be able to access the VM directly.'''

'''If you have not yet installed VPN, you may 1) use Remote Desktop connection (VPN not needed) or 2) install VPN.'''

Please follow the instructions to use one of these two options:

A) [https://www.imperial.ac.uk/admin-services/ict/self-service/connect-communicate/remote-access/remotely-access-my-college-computer/remote-desktop-access-for-students/ Remote Desktop connection]

B) [https://www.imperial.ac.uk/admin-services/ict/self-service/connect-communicate/remote-access/virtual-private-network-vpn/ using VPN]

==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of a simple liquid using the virtual machines.

At the end of this experiment, you will have performed your own simulations using state of the art software packages used by researchers all around the world, and used those simulations to calculate both structural and dynamic properties of a simple liquid. You will learn to calculate thermodynamic quantities such as temperature and pressure in computer simulations.

All of the information that you need to complete the experiment is provided in these wiki pages. We have also tried to provide links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject. You may find helpful revising the thermodynamic concepts in Solids, Liquids and Interfaces (lectures by Prof. Bresme).

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab this year.''' The section has been left on the wiki for any interested student to give it a go. However, it should NOT be submitted as part of your lab report, and will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". [2]
# What is the Ergodic hypothesis? Explain its relevance to molecular dynamics simulations. [3]

== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. [4]
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? [3]
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''
# In the simulations you have performed ergodicity has not been an issue. Describe a system in which "brute force" MD struggles to achieve ergodic sampling. Describe one "enhanced sampling" technique that can be used to overcome this. [7]

Third year simulation experiment

2021-10-02T09:37:59Z

Fbresme:

'''<big>This is the optional experiment which may be chosen by any third year student. If you are looking for the Programming-Ising experiment, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

 '''To run this experiment, you will need access to the Imperial College Virtual Machines (VM). If you have VPN installed, you should be able to access the VM directly.'''

'''If you have not yet installed VPN, you may 1) use Remote Desktop connection (VPN not needed) or 2) install VPN.'''

Please follow the instructions to use one of these two options:

A) [https://www.imperial.ac.uk/admin-services/ict/self-service/connect-communicate/remote-access/remotely-access-my-college-computer/remote-desktop-access-for-students/ Remote Desktop connection]

B) [https://www.imperial.ac.uk/admin-services/ict/self-service/connect-communicate/remote-access/virtual-private-network-vpn/ using VPN]

==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of materials and molecules under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we will give you an introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of a simple liquid using the virtual machines.

At the end of this experiment, you will have performed your own simulations using state of the art software packages used by researchers all around the world, and used those simulations to calculate both structural and dynamic properties of a simple liquid. You will learn to calculate thermodynamic quantities such as temperature and pressure in computer simulations.

All of the information that you need to complete the experiment is provided in these wiki pages. We have also tried to provide links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

==Assessment==

At the end of this experiment you must submit a report (pdf format via turnitin) and a zip file with inputs and outputs. The report should be structured:

* Introduction Questions (20% of the total mark)
* Results and Discussion (60% of total mark)
* Conclusion Questions (20% of total mark)
* References (see note below)

Relevant supplementary material can be added at the end of the report so long as it supports your discussion. Please limit the introduction and conclusion sections (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font). It is certainly possible to answer the introduction and conclusion questions with under this length limit, and as with most scientific writing, shorter concise but well thought out answers are preferable. We have not imposed a hard word limit because, equally, you should spend the majority of this lab learning, not editing and rewriting answers to just satisfy the word limit.

Please note that five "floating" marks have been reserved in the results and discussion section. These can be used to reward particularly insightful comments and/or explanations, on the basis of good/bad presentation, use of scientific language, or for other reasons.

It is important to provide appropriate references. 'Appropriate' refers to both quality (books and peer-reviewed papers are preferred over a link to wikipedia) and quantity (make sure to include references where you used them, but there is no point quoting 10 papers for a statement like 'macroscopic systems consist of a large number of atoms'). Please note that presenting external information as your own counts as plagiarism! As a bare minimum, you will need to reference the information you present in your introduction.

'''Copy&Paste will not be accepted, even if referenced! Every report is automatically checked for plagiarism.'''

'''The final task of the lab (task 10 - MSD diffusion simulations) is NOT part of the lab this year.''' The section has been left on the wiki for any interested student to give it a go. However, it should NOT be submitted as part of your lab report, and will not be marked.

==Getting Help==

Please feel free to ask any demonstrators for help during the lab sessions - that is what we are here for. Questions can also be asked via email.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. To help you plan your time it is suggested you complete the following at these times:

Monday (morning session): Theory - Introduction to molecular dynamics simulations

Monday (afternoon session): Theory + Equilibration (submit your files for running)

Tuesday (morning session): Equilibration (analyse your files)

Tuesday (afternoon session): Running simulations under specific conditions (submit and read)

Thursday (morning session): Checkpoint for progress. Submit your input files for the radial distribution function and analyse your equation of state from the previous section

Thursday (afternoon session).

Friday (morning session): Analyse MSD diffusion simulations

Friday (afternoon session): Analyse MSD diffusion simulations. Report write-up.

Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.
# [[Third year simulation experiment/Files to download|Downloading the Files]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

== Introduction Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# Give a brief account on what molecular dynamics is, and (broadly speaking) what it aims to achieve. [5]
# Give two examples of instances where molecular dynamics simulations have/can be used (in a helpful way) instead of or in synergy with experimental techniques. In each case explain why. [10] (''Please consider only chemically relevant examples. E.g. To study geochemical processes which occur under extreme temperature/pressure conditions, and therefore cannot be studied experimentally.'')
# Explain what is meant by a thermodynamic ensemble, and the term "conserved quantity". [2]
# What is the Ergodic hypothesis? Explain its relevance to molecular dynamics simulations. [3]

== Conclusion Questions ==
Please limit your answers to this section (which are now just answers to questions) to a maximum of ~1.5 pages at size 12 font Times New Roman, or equivalent (e.g. if you are using latex or simply prefer another font).
# In this lab, you have used the Lennard-Jones potential exclusively. Give one example of a system that can be described well using only LJ potentials, and one that cannot. In each case explain why. [4]
# What cut-off have you been using in your simulations? What are the advantages and disadvantages for using a shorter/longer cut-off? [3]
# What are finite size effects? Do you think they are significant in the simulations you have performed? Why? [3]
# Algorithms such as SHAKE and RATTLE (holonomic constraints) allow MD simulations to be performed while fixing bond lengths. Why is this desirable? [3] ''(Hint: think about the timestep.)''
# In the simulations you have performed ergodicity has not been an issue. Describe a system in which "brute force" MD struggles to achieve ergodic sampling. Describe one "enhanced sampling" technique that can be used to overcome this. [7]