ChemWiki - User contributions [en]

Rep:Mod:JYC214

2017-02-24T11:59:52Z

Jyc214:

'''Introduction to Molecular Dynamics Simulation'''

An error-time graph is plotted and the maxima is identified. The values of the maxima appear to be in good fit to a linear model with equation y=0.0004x.
[[File:Graph 1.png]]

[[File:Picture2.png]]

[[File:Screen_Shot_2017-02-24_at_11.12.57_AM.png]]

Under standard conditions, ie 298 K and 1atm,

Number of moles of 1 mL of water, n = 1/18 = 0.056 moles

Number of molecules, N = n x NA = 0.056 x 6.022e23 = 3.346e22

Number of moles of 10000 water molecules = 10000/6.022E23 = 1.66e-20 moles

Volume of 10000 water molecules = 1.66e-20 x 18 = 3e-19 mL

As a point (0.5, 0.5, 0.5) moves along the vector (0.7, 0.6, 0.2), with periodic boundary conditions applied, it will end up at (0.2, 0.1, 0.7).

[[File:Screen_Shot_2017-02-24_at_11.17.50_AM.png]]

Giving atoms random starting coordinates causes problems in simulations as when two atoms happen to be generated close together, repulsion between the 2 atoms will cause potential energy to increase dramatically and hence causing discrepancies in simulation calculations.

As a simple cubic lattice has only one lattice point per unit cell,

[[File:Screen_Shot_2017-02-24_at_11.23.09_AM.png]]

ie [[File:Screen_Shot_2017-02-24_at_11.24.36_AM.png]]

A face centred cubic has 4 lattice points per unit cell,

[[File:Screen_Shot_2017-02-24_at_11.25.38_AM.png]]

As a box of simple cubic lattice contains 1000 (10x10x10) unit cells, and so contains 1000 lattice points; A face centred cubic lattice would result in 4000 atoms.

When we are specifying [[File:SimulationX.png]] and [[File:SimulationY.png]], we use the velocity Verlet algorithm.

Plots of the energy, temperature, and pressure, against time for the 0.001 timestep experiment:

[[File:Energy-time.png]]

[[File:Pressure-time.png]]

[[File:Temp-time.png]]

'''Running Simulations under Specific Conditions'''

To solve [[File:Simulationsymbol1.png]]:

[[File:Screen_Shot_2017-02-24_at_11.42.44_AM.png]]

'''Plotting the Equations of State'''

Density against temperature for pressures at 2.5 and 3.0:

[[File:P2.5.png]]

[[File:P3.0.png]]

RDFs for simulations of the Lennard-Jones system in the three phases:
[[File:G(r)gas.png]]

[[File:G(r)liq.png]]

[[File:G(r)solid.png]]

[[File:G(r)all.png]]

There is essentially zero probability of finding particles at distances less than about 1.0Å from each other. This is due to the presence of very strong repulsive forces at short distances.

Rep:Mod:JYC214

2017-02-24T11:59:35Z

Jyc214:

'''Introduction to Molecular Dynamics Simulation'''

An error-time graph is plotted and the maxima is identified. The values of the maxima appear to be in good fit to a linear model with equation y=0.0004x.
[[File:Graph 1.png]]

[[File:Picture2.png]]

[[File:Screen_Shot_2017-02-24_at_11.12.57_AM.png]]

Under standard conditions, ie 298 K and 1atm,

Number of moles of 1 mL of water, n = 1/18 = 0.056 moles

Number of molecules, N = n x NA = 0.056 x 6.022e23 = 3.346e22

Number of moles of 10000 water molecules = 10000/6.022E23 = 1.66e-20 moles

Volume of 10000 water molecules = 1.66e-20 x 18 = 3e-19 mL

As a point (0.5, 0.5, 0.5) moves along the vector (0.7, 0.6, 0.2), with periodic boundary conditions applied, it will end up at (0.2, 0.1, 0.7).

[[File:Screen_Shot_2017-02-24_at_11.17.50_AM.png]]

Giving atoms random starting coordinates causes problems in simulations as when two atoms happen to be generated close together, repulsion between the 2 atoms will cause potential energy to increase dramatically and hence causing discrepancies in simulation calculations.

As a simple cubic lattice has only one lattice point per unit cell,

[[File:Screen_Shot_2017-02-24_at_11.23.09_AM.png]]

ie [[File:Screen_Shot_2017-02-24_at_11.24.36_AM.png]]

A face centred cubic has 4 lattice points per unit cell,

[[File:Screen_Shot_2017-02-24_at_11.25.38_AM.png]]

As a box of simple cubic lattice contains 1000 (10x10x10) unit cells, and so contains 1000 lattice points; A face centred cubic lattice would result in 4000 atoms.

When we are specifying [[File:SimulationX.png]] and [[File:SimulationY.png]], we use the velocity Verlet algorithm.

Plots of the energy, temperature, and pressure, against time for the 0.001 timestep experiment:

[[File:Energy-time.png]]

[[File:Pressure-time.png]]

[[File:Temp-time.png]]

'''Running Simulations under Specific Conditions'''

To solve [[File:Simulationsymbol1.png]]:

[[File:Screen_Shot_2017-02-24_at_11.42.44_AM.png]]

'''Plotting the Equations of State'''

Density against temperature for pressures at 2.5 and 3.0:

[[File:P2.5.png]]

[[File:P3.0.png]]

RDFs for simulations of the Lennard-Jones system in the three phases:
[[File:G(r)gas.png]]

[[File:G(r)liq.png]]

[[File:G(r)solid.png]]

[[File:G(r)all.png]]

here is essentially zero probability of finding particles at distances less than about 1.0Å from each other. This is due to the presence of very strong repulsive forces at short distances.

Rep:Mod:JYC214

2017-02-24T11:57:05Z

Jyc214:

File:G(r)all.png

2017-02-24T11:55:29Z

Jyc214:

File:G(r)solid.png

2017-02-24T11:55:17Z

Jyc214:

File:G(r)liq.png

2017-02-24T11:55:05Z

Jyc214:

File:G(r)gas.png

2017-02-24T11:54:53Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:52:17Z

Jyc214:

File:P3.0.png

2017-02-24T11:50:06Z

Jyc214:

File:P2.5.png

2017-02-24T11:49:56Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:49:41Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:45:55Z

Jyc214:

File:Simulationsymbol1.png

2017-02-24T11:45:12Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:44:56Z

Jyc214:

File:Screen Shot 2017-02-24 at 11.42.44 AM.png

2017-02-24T11:43:11Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:42:58Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:35:30Z

Jyc214:

File:Temp-time.png

2017-02-24T11:34:01Z

Jyc214:

File:Pressure-time.png

2017-02-24T11:33:36Z

Jyc214:

File:Energy-time.png

2017-02-24T11:33:23Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:33:03Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:30:23Z

Jyc214:

File:SimulationY.png

2017-02-24T11:29:37Z

Jyc214:

File:SimulationX.png

2017-02-24T11:29:08Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:28:38Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:27:49Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:26:53Z

Jyc214:

File:Screen Shot 2017-02-24 at 11.25.38 AM.png

2017-02-24T11:26:07Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:25:47Z

Jyc214:

File:Screen Shot 2017-02-24 at 11.24.36 AM.png

2017-02-24T11:25:01Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:24:21Z

Jyc214:

File:Screen Shot 2017-02-24 at 11.23.09 AM.png

2017-02-24T11:23:48Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:23:21Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:19:37Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:18:49Z

Jyc214:

File:Screen Shot 2017-02-24 at 11.17.50 AM.png

2017-02-24T11:18:26Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:17:57Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:14:04Z

Jyc214:

File:Screen Shot 2017-02-24 at 11.12.57 AM.png

2017-02-24T11:13:31Z

Jyc214:

Rep:Mod:JYC214

2017-02-24T11:10:27Z

Jyc214:

File:Picture2.png

2017-02-24T11:10:02Z

Jyc214: Jyc214 uploaded a new version of File:Picture2.png

Rep:Mod:JYC214

2017-02-24T11:08:45Z

Jyc214:

File:Picture1.png

2017-02-24T11:07:26Z

Jyc214: Jyc214 uploaded a new version of File:Picture1.png

Preparation of Schwartz Reagent

Rep:Mod:JYC214

2017-02-24T11:06:59Z

Jyc214:

'''Introduction to Molecular Dynamics Simulation'''

An error-time graph is plotted and the maxima is identified. The values of the maxima appear to be in good fit to a linear model with equation y=0.0004x.
[[File:Graph 1.png]]

is the intermolecular potential between two atoms
is the well depth, ie how strongly the two particles attract each other
is the distance at which intermolecular potential between two particles is zero
r is the distance of separation between both particles

When potential energy is zero, .

At equilibrium,
4[-1212r-13 + 66r-7] = 0
0.51/6 r

Rep:Mod:JYC214

2017-02-24T11:05:30Z

Jyc214:

An error-time graph is plotted and the maxima is identified. The values of the maxima appear to be in good fit to a linear model with equation y=0.0004x.
[[File:Graph 1.png]]

Rep:Mod:JYC214

2017-02-24T11:03:17Z

Jyc214: Created page with "An error-time graph is plotted and the maxima is identified. The values of the maxima appear to be in good fit to a linear model with equation y=0.0004x. ["

An error-time graph is plotted and the maxima is identified. The values of the maxima appear to be in good fit to a linear model with equation y=0.0004x.
[

File:Graph 1.png

2017-02-24T11:02:10Z

Jyc214: