ChemWiki - User contributions [en]

Rep:Mod:db9127physical

2008-11-20T21:31:19Z

Db406: /* '''Diels-Alder Cycloaddition''' */

== '''Optimising the Reactants and Products''' ==

This project was done to model the Cope rearrangment. In order to do this, we must first model the reactants and products of the reaction. The reaction scheme is shown here:
[[Image:CopeReaction.gif]]

This reaction can occur via either a boat or a chair transition state. These resemble the conformers of cyclohexane with the same names. The boat transition state is generally accepted to be much higher in energy and therefore less favourable.

For this reaction the reactant is 1,5-hexadiene. This can occur in many conformers. Firstly, it was optimised for an anti-linkage between the central four carbon atoms. This was done using a HF/3-21G calculation. This created this molecule:

<jmol><jmolApplet><title>1,5-Hexadiene</title><color>white</color>
<size>150</size><script>zoom 150; cpk -20;</script>
<uploadedFileContents>REACT_ANTI.mol</uploadedFileContents>
</jmolApplet></jmol>

The calculation summary is shown here:

[[Image:Anti_HF.JPG]]

The point group of the molecule is actually Ci.

This molecule was then optimised again with a "gauche" linkage in the central four carbon atoms:

<jmol><jmolApplet><title>1,5-Hexadiene</title><color>white</color>
<size>150</size><script>zoom 150; cpk -20;</script>
<uploadedFileContents>REACT_GAUCHE.mol</uploadedFileContents>
</jmolApplet></jmol>
[[Image:Gauche_HF.JPG]]

Here the summary point group is correct. This conformer has a much greater energy than the anti-conformer optimised before. This is due to greater repulsions between non-bonding atoms in the gauche conformer, due to the larger groups being placed closer together.
The "anti" conformer already shown should therefore be close to the conformer with the lowest energy, as it has the largest possible dihedral angles between carbon atoms. The alkene group is rotated 60 degrees. This is ''all anti''-1,5-hexadiene, which is the anti2 conformer shown in the appendix of the instructions.
This conformer was optimised and found to have an energy of -231.69253529 Hartree. This is the same as the conformer in the appendix.

The anti1 conformer (the first one optimised in this project) was then re-optimised using a higher level of theory, the B3LYP with a 6-31G basis set. This should provide more accurate results. The geometry of the molecule changed very little, implying that for this compound a high level of accuracy is not necessary.
The changes that were noted were that the B3LYP model had an energy of -234.55970439 Hartree, ~3 Hartree greater than the HF calculated model. This is a very large difference (~7500kJmol-1).
Also, the HF calculated model had a dipole moment of 0.0003 Debye. This is incorrect, as the molecule should be symmetrical (Ci) and should have no dipole moment. This illustrates well the inaccuracy of the Hartree-Fock level of calculation.

The B3LYP/6-31G level optimised model was then submitted for frequency calculation. This was done using the same level of theory and the same basis set to ensure the correct vibrations were calculated. The calculated IR spectrum for 1,5-hexadiene is shown here:

[[Image:Hexadiene_IR.JPG]]

The peaks at ~3000cm-1 are all relating to C-H stretches. The large peak at 948cm-1 is H-C=C bending. The peak at 679cm-1 is due to C-C=C bending, as are the two peaks at ~1050cm-1. The peak at 1728cm-1 is due to C=C stretching.

'''Thermochemistry'''
The optimised frequency calculation also includes some thermochemical data in the results file. This is recorded here:
Sum of electronic and zero-point energies = -234.416245 Hartree
Sum of electronic and thermal energies = -234.408955 Hartree
Sum of electronic and thermal enthalpies = -234.408010 Hartree
Sum of electronic and thermal free energies = -234.447848 Hartree

== '''Optimising the "Chair" and "Boat" transition structures''' ==

Firstly, this allyl structure was optimised using HF/3-21G for use as a building block for the transition states:

<jmol><jmolApplet><title>Allyl</title><color>white</color>
<size>150</size><script>zoom 150; cpk -20;</script>
<uploadedFileContents>ALLYL.mol</uploadedFileContents>
</jmolApplet></jmol>

All further optimisations were also done using a HF/3-21G level unless stated otherwise.
This optimised allyl was used to create a guess for the "chair" transition state, as shown:

<jmol><jmolApplet><title>ChairGuess</title><color>white</color>
<size>150</size><script>zoom 150; cpk -20;</script>
<uploadedFileContents>Chair_ts_guess.mol</uploadedFileContents>
</jmolApplet></jmol>

The distance between the two atoms that were expected to form a bond on the near side was set to 2.2Å. The same was done with the other two atoms expected to form a bond. This structure was then optimised to a transition state. The calculation stopped halfway through so the initial guess transition state was edited slightly to make the calculation easier. This was done by rotating one of the allyl groups to be better aligned with the other. The optimisation process is very sensitive and requires a structure quite close to the final transition state or the calculation will stop. After three changes to the original input, the calculation produced this optimisation of the transition state:

<jmol><jmolApplet><title>ChairOpt1</title><color>white</color>
<size>150</size><script>zoom 150; cpk -20;</script>
<uploadedFileContents>Chair_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The vibrational frequencies were also calculated as part of the same calculation. An imaginary frequency (one with a negative wavenumber) of magnitude 817.929cm-1 was found. This corresponds to the formation of the bonds in this reaction, as shown here:

[[Image:Chair_Vibration.JPG]]

This image clearly shows one bond breaking (the relevant atoms moving apart) as the other bond forms (the atoms moving closer together).

The Chair transition state was then optimised again using a different technique. This technique involves fixing the two bond lengths that are being changed during the reaction, optimising the rest of the molecules, unfixing the bonds and then optimising again. This reduces the amount of computational power required to run the calculations and should also improve the accuracy of the transition state structure.
This creates a structure that looks exactly the same as the transitions state first calculated. The reaction bond lengths are the same between the two calculated transition states to 0.0002Å and the dihedral angles across the reaction bonds are the same to within 0.005 degrees. This implies that either method is quite accurate but the second method produced dihedral angles that were 0.009 degrees different from each other, whereas the first method produced dihedral angles that were 0.003 degrees apart. This would imply that the first method was more accurate, as the transition state should be symmetrical and both dihedral angles across the reactive bonds should be the same.

== '''Optimising the "Boat" transition structure''' ==

The boat transition structure was optimised using a third method. This involved optimising the reactant and product and using the QST2 method to optimise a transition state from them. The labelling of all atoms has to be the same on the reactant and product for this method to work.
The reactant and product used for the calculation are shown here:

[[Image:Boat_R+P_Guess.JPG]]

This calculation failed. This was due to the limitations of this method, in that it will only work for conformers of the reactant and product that are closer to the reacting conformers.
Hence, this reactant and product isomer were submitted to the same technique:

[[Image:Boat_R+P_2.JPG]]

This produced the boat transition state. However, the scan did not complete the frequency calculation due to an error. After this error was fruitlessly searched for, a separate frequency calculation was run on the optimised boat transition state shown:

<jmol><jmolApplet><title>Boat</title><color>white</color>
<size>150</size><script>zoom 150; cpk -20;</script>
<uploadedFileContents>BOAT_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

This gave an imaginary vibration of magnitude 1016cm-1, which follows the vectors of the reaction bond formation and breaking in the same way as the chair formation. This greater magnitude implies a greater energy is required for this "vibration" to take place. This is concurrent with the boat transition state being of greater energy.

== '''Optimising the reactant to find the activation energies''' ==

The activation energies for the Cope rearrangement via each transition state can be calculated using our transition state models but the reactant is also needed (the activation energy for a reaction is the difference between the transition state and the reactant). However, it is almost impossible to tell which conformation of 1,5-hexadiene is the reactant from the transition states. So a further calculation must be run. This is known as the IRC (Intrinsic Reaction Coordinate) method. The transition state is taken as a starting point and the molecule is changed slightly to a lower energy many times until a minimum energy is reached. This should be the reactant conformer, as energy would be required to change conformation and so, if the calculation stops at the first minimum, it should hit the conformation of the reactant that is closest to the transition states.
This was run using the chair transition state calculated with the second method. This produced 50 steps towards the reactant molecule. 50 steps was set as the maximum number of steps so this final step would not have produced the reactant, but it was close enough to optimise the structure from there and avoid using too much computational power and time. This produced this reactant:

<jmol><jmolApplet><title>Reactant</title><color>white</color>
<size>150</size><script>zoom 150; cpk -20;</script>
<uploadedFileContents>Reactant.mol</uploadedFileContents>
</jmolApplet></jmol>

This is the same as the gauche3 conformer in appendix 1 of the instructions.
The reactant energy was -231.69166702 a.u.
The chair transition state (as calculated by the first method) energy was -231.61932247 a.u.
The chair transition state (as calculated by the second method) energy was -231.61932241 a.u.
The boat transition state energy was -230.06026147 a.u.
This makes the activation energy for the "chair" mechanism 45.397kcal mol-1.
The activation energy for the "boat" mechanism is 1023kcal mol-1. This is clearly incorrect, as the experimental value is 44.7kcal mol-1. Clearly, the gauche3 conformer is not applicable as the reactant for the boat transition state. However, the calculated activation energy for the chair conformation is very close to the value above (46.9kcal mol-1). This implies that the method has worked correctly and the optimisation of the reactant instead of continuing the IRC method made a minimal difference. Indeed, the energy obtained here is closer to the experimental activation energy of 33.5kcal mol-1.

== '''Diels-Alder Cycloaddition''' ==

''cis'' butadiene was optimised and the HOMO and LUMO were calculated. They are shown here:

[[Image:Butadiene_HOMO.JPG]]

[[Image:Butadiene_LUMO2.JPG]]

The HOMO is clearly antisymmetric to the plane, whereas the LUMO is symmetric to the plane.

The addition of ''cis'' butadiene to ethylene was then studied and the transition state optimised using the method that was used to create the "boat" transition state. This was the transition state formed:

<jmol><jmolApplet><title>Cyclohexene</title><color>white</color>
<size>150</size><script>zoom 150; cpk -20;</script>
<uploadedFileContents>Ethylene3.mol</uploadedFileContents>
</jmolApplet></jmol>

This is formed from the ethylene molecule on the left bonding with the ''cis'' butadiene molecule on the right. The two very long single bonds are the bonds being formed. These bonds are longer than the others (2.2095Å compared with 1.370Å) because they were set to be 2.2Å apart when the optimisation was started. However, the bond lengths were not restricted during the calculation. These bonds should be longer than any other bonds in the transition state, as they are single bonds being formed, whereas all the other bonds in the transition state are double bonds being formed or broken. Double bonds are much shorter than single bonds, due to the greater number of electrons present between the two carbon atoms causing an attractive force and screening repulsion. The LUMO of the transition state is shown here:

[[Image:TransitionMO.JPG]]

This clearly shows the HOMO of the ethylene overlapping with the LUMO of the ''cis'' butadiene. This is the reaction pathway and it is symmetric. This reaction is allowed because the HOMO of one reactant is overlapping with the LUMO of another. There is significant overlap because the two MOs have the same symmetry. To further illustrate the symmetry of the transition state and the reaction pathway, the imaginary vibration frequency (818cm-1) is shown here:

[[Image:TransitionVib.JPG]]

It can be seen that the two bonds are formed synchronously. The lowest positive frequency shows the asynchronous movement along these vectors.

File:TransitionVib.JPG

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Db406: /* '''Diels-Alder Cycloaddition''' */

File:Butadiene LUMO2.JPG

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File:Butadiene HOMO.JPG

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Db406: /* '''Optimising the reactant to find the activation energies''' */

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Db406: /* '''Optimising the reactant to find the activation energies''' */

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Db406: /* '''Optimising the "Boat" transition structure''' */

File:BOAT TS OPT.mol

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Db406: /* '''Optimising the "Boat" transition structure''' */

File:Boat R+P 2.JPG

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Db406: /* '''Optimising the "Chair" transition structure''' */

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Db406: /* '''Optimising the "Chair" and "Boat" transition structures''' */

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Db406: /* '''Optimising the "Chair" and "Boat" transition structures''' */

File:Chair Vibration.JPG

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Db406: /* '''Optimising the Reactants and Products''' */

File:Hexadiene IR.JPG

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Db406: /* '''Optimising the Reactants and Products''' */

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Db406: /* '''Optimising the Reactants and Products''' */

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== '''Optimising the Reactants and Products''' ==

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Db406: /* '''Mini Project: Fuels of the Future''' */

== '''BH3 Introduction Molecule''' ==

BH3 was optimised using an FOPT calculation type with the RB3LYP method with a basis set of 3-21G. This method means that the molecule is calculated using the Schrődinger equation. This calculates the energy of different geometries and minimises the energy. This geometry with the smallest energy value should be the most stable conformation of the molecule. The basis set 3-21G is a very simple basis set so the calculation will not be extremely accurate but will run quickly. This calculation created a .log file, which gave the optimised geometry and the following information about the optimised molecule:

[[Image:BH3_data.JPG]][[Image:BH3.JPG]]

The molecule is trigonal planar, hence the D3h point group. This gives the bond angle of 120 degrees. BH3 is trigonal planar due to the pz orbital being non-bonding and unoccupied. This is because boron only has 3 electrons and is clearly shown by the molecular orbitals in the later section.

== '''BCl3''' ==

BCl3 was optimised using the same method as BH3. However, the basis set used was LANL2MB. This is a more complex basis set than 3-21G so should give a more accurate optimisation. This gave the following data:

[[Image:BCl3_data.JPG]][[Image:BCl3.JPG]]

BCl3 has a longer bond length than BH3. This is primarily because chlorine is a larger molecule than hydrogen. It also means that the calculation took less time (12s as opposed to 24s). This is because the optimisation works by moving the atoms from far apart to closer together and the BCl3 took less steps to find the optimised geometry because the final molecule was closer to the starting point of the calculation.

BCl3 also has a much lower energy than BH3. This implies that BCl3 is more stable. This is correct as the energy calculation for a chlorine atom is also far lower than that of a hydrogen atom. This is because chlorine contains more electrons and protons so has greater attractive forces acting on the molecule. The BCl bond is also stronger than the BH bond. This is due to secondary overlap from the lower lying orbitals in the chlorine atoms.

BCl3 has the same geometry as BH3. This is again due to the low number of valence electrons present in a boron atom.

== '''PCl5''' ==

PCl5 was optimised using the same method as for BCl3 with the same basis set. The calculation took 34 seconds. This time is because the molecule is more complex than the previous molecules and the Schrõdinger equation takes longer to solve. This gave the following data:

[[Image:PCl5_data.JPG]][[Image:PCl5.JPG]]

GaussView does not show the P-Cl bonds because the atoms are too far apart. This is merely a graphical issue - the bonds are still there as far as the calculations are concerned. In fact, it is somewhat difficult to define a bond, given that a bond is the overlap of molecular orbitals with the same symmetry to create a lower energy orbital and so-called "non-bonding" orbitals still have some overlap effects with others. Since the gaussian calculation takes into account the molecular orbitals, the definition of a bond does not affect the optimised geometry.

PCl5 is trigonal bipyramidal. The co-ordinates of the atoms are shown here:
[[Image:PCl5_coords.JPG]]

The slightly shorter bond length is for the P-Cl bonds parallel to the y-axis, as denoted by the co-ordinate values. This is because these chlorine atoms are 90 degrees from 3 other chlorine atoms. The equatorial chlorine atoms are 90 degrees from the two axial chlorine atoms and 120 degrees from the other equatorial chlorine atoms so suffer a slightly greater repulsion from them. Hence, they are slightly further from the phosphorus atom and have a slightly weaker bond. This makes the equatorial chlorine atoms more susceptible to substitution reactions.

== '''Vibrational analysis of BH3''' ==

The vibrational frequencies of BH3 were calculated. They are shown here:

[[Image:BH3_vibrations1.JPG]][[Image:BH3_vibrations2.JPG]]

The IR Spectrum for BH3 is shown here:

[[Image:BH3_IR.JPG]]

Only 3 peaks are shown on this spectrum, despite there clearly being 6 vibrations for BH3. This is because the two B-H stretching vibrations occur at the same frequency, as do two of the bending vibrations. The symmetric bending stretch is also not present in the IR spectrum, as it does not change the symmetry of the molecule.

== '''Molecular Orbitals of BH3''' ==

The MOs for BH3 were also calculated using Gaussian and compared to qualitative molecular orbitals. The qualitative MO diagram for BH3 is shown here:

[[Image:BH3_MO.gif]]

The occupied MOs and LUMO were calculated and are shown here. The other unoccupied orbitals were not calculated as they become more diffuse and therefore have odd forms.

[[Image:BH3_MO1.JPG]][[Image:BH3_MO2.JPG]]

The first calculated MO does not exist. It is there to help the Gaussian calculation by making the molecule BH3-. This is because BH3 has only 6 electrons in the system.
The other MOs are analogous with the qualitative MOs shown. These correlate very well, which implies that in the absence of computational software, qualitative MOs are an accurate description of occupied and reactive orbitals.
The HOMO orbital can be either orbital 3 or 4 as they both have the same energy (-0.356 a.u.).

All of the occupied MOs are in the same plane as the B-H bonds. This is why BH3 is trigonal planar; the atomic orbitals of boron must have the same symmetry as the atomic orbitals of the hydrogen atoms to form bonds. The first non-planar MO is the LUMO, which is why BH4- is not a planar molecule; the last hydrogen atom bonds with the LUMO which is perpendicular to the plane.

== '''''cis''- and ''trans''- isomerism of molybdenum complexes''' ==

Mo(CO)4L2 complexes were optimised, first loosely using a low level basis set (LANL2MB) and then further using a higher level basis set (LANL2DZ). This was done to make the calculation faster than using a high level basis set immediately. L=piperidine or P(CH3)3. Both the ''cis'' and ''trans'' isomers were optimised.
Unfortunately, the Mo-L bond lengths were too long for GaussView to show them.

The cis-isomers both have slightly increased angles between the L ligands and the CO ligands (91 degrees). This decreases the other inter-ligand angles in the molecule accordingly.
The trans-isomers both have all angles at 90 degrees. This difference in angles for the cis-isomers is due to a steric effect from the large CH3 or piperidine groups, repelling the CO ligands.

Literature values for the angles and bond distances in cis-Mo(CO)4(PPh3)2 are shown here compared with the computational values for cis-Mo(CO)4(P(CH3)3)2. The comparison is valid, as we have been using P(CH3)3 as a simplified model for PPh3. This was to lower calculation time and the two ligands should behave similarly.

[[Image:Bonds_Mo.JPG]][[Image:Bonds_Mo_Labels.JPG]]

The literature values were taken from "Steric contributions to the solid-state structures of bis(phosphine) derivatives of molybdenum carbonyl. X-ray structural studies of cis-Mo(CO)4[PPh3-nMen]2 (n = 0, 1, 2)", F. Albert Cotton, Donald J. Darensbourg, Simonetta Klein, and Brian W. S. Kolthammer, Inorg. Chem., 21, (1982), p294-299 {{DOI|101.1021/ic00131a055}}

The bond lengths are all very similar. The only major difference is that the PPh3 ligands lie closer to the molybdenum atom. This is because the phenyl rings donate electron density to the phosphorus atom, making it more electron rich and therefore more strongly attracted to the metal centre.
The P-Mo-P bond angle for the PPh3 complex is 104.62 degrees. This is far greater than the P-Mo-P bond angle for the P(CH3)3 complex which was 90.93 degrees. The remainder of the bond angles within the computed complex are all ~90 degrees. This shows a large discrepancy from the literature. This is probably due to the simplification of our model, as it removes a large part of the steric effects from the phenyl groups. It may also be because we have not taken into account the presence of d-orbitals in our model. If d-orbitals are taken into account, the calculated P-Mo-P bond angle becomes 92.73 degrees. This is closer to the literature value but implies that the majority of the difference is due to the change in ligand.

The vibrational frequencies of the cis- and trans- isomers were then calculated. These are shown here:

cis-Mo(CO)4(pip)2

[[Image:Cis_Mo(CO)4(pip)2_IR.JPG]]

cis-Mo(CO)4(P(CH3)3)2

[[Image:Cis_Mo(CO)4(P(CH3)3)2_IR.JPG]]

trans-Mo(CO)4(pip)2

[[Image:Trans_Mo(CO)4(pip)2_IR.JPG]]

trans-Mo(CO)4(P(CH3)3)2

[[Image:Trans_Mo(CO)4(P(CH3)3)2_IR.JPG]]

As can be seen, there are two major comparisons that can be drawn. The first is that the piperidine complexes exhibit four different stretches in the 3000-3300cm-1 region to the two exhibited by the methylphosphine complexes. That is because these vibrations are due to C-H bonds and these are in different environments between these two ligands.

The second comparison to be drawn is that the cis- complexes exhibit a peak at ~1850cm-1 that is not exhibited by the trans- complexes. This stretch is shown below:

[[Image:Mo_C_stretch.JPG]]

In the trans- complexes, this vibration does occur. However, here it is a symmetrical stretch so does not change the dipole moment of the molecule. This means that it is not present on the IR spectrum.
The remaining vibrations are assigned in the table below:

[[Image:1MoVib.JPG]][[Image:2MoVib.JPG]][[Image:3MoVib.JPG]]

Any further peaks were due to various C-H bending vibrations within the ligands.

== '''Following a Reaction Path: The Quantum Nature of Ammonia''' ==

Ammonia is an interesting molecule because it readily inverts its structure. This is also true of most trivalent nitrogen atoms but ammonia is easiest to calculate results for and it provides a model for all nitrogen inversion. Ammonia can invert because the activation energy required to reach a trigonal planar transition state is very low. The inversion reaction occurs as shown:

[[Image:Inversion.jpg]]

In this section, three isomers of ammonia were optimised and the energies compared. The three isomers were: ammonia in its usually accepted tetrahedral shape; the same shape with one N-H bond length changed to 1.01Å; a trigonal planar ammonia molecule. These isomers will be referred to as 1, 2 and 3 respectively. The summaries of their optimisations are shown here:
_____________1____________________________________________2_______________________________________3____________________________

[[Image:NH3_1.JPG]][[Image:NH3_nosymm.JPG]][[Image:NH3_highsymm.JPG]]

The calculations were then redone using the MP2 method. The same basis set was used to make direct comparison possible.
___________________1____________________________________________2_______________________________________3___________________________

[[Image:NH3_MP2.JPG]][[Image:NH3_MP2_nosymm.JPG]][[Image:NH3_MP2_highsymm.JPG]]

The energy difference between isomers 1 and 2 (the normal geometric state of ammonia and the transition state for inversion) was calculated as ΔE= 16.8595kJmol-1 for the DFT method and ΔE= 20.8252kJmol-1 for the MP2 method of calculation. The literature value for the energy barrier of inversion is 24.3kJmol-1. This implies that the MP2 method is more accurate, as it gives an energy closer to the literature value. However, it should be noted that the basis set chosen makes a very large difference to the energy values (~2000kJmol-1 when changing from 6-31G to 6-311G). The energy also changes slightly each time the optimisation is re-run. Hence, the calculated energy values can never be fully accurate when using either of these methods. A much more complex and time-consuming basis set would be required to achieve a high level of accuracy.

It should be noted also that both of these methods give the energy barrier for inversion as lower than the literature value. This may be due to contributions from neighbouring molecules which the calculations do not take into account.

== '''Vibrational analysis of NH3 isomers''' ==

The C3v and D3h models were used to calculate the vibrational frequencies of these conformations for NH3. These vibrations are shown below:

'''D3h'''

[[Image:NH3_vibrations1.JPG]][[Image:NH3_vibrations2.JPG]]

'''C3v'''

[[Image:HS_NH3_vibrations1.JPG]][[Image:HS_NH3_vibrations2.JPG]]

The main differences are the first vibration and the 4th vibration. The first vibration has a greatly different frequency because the D3h isomer vibration changes the dipole moment slightly because the H atoms do not move far from the plane. Because the C3v isomer is already bent, this vibration pushes the H atoms even further from the plane, greatly changing the dipole moment and requiring a greater frequency of vibration.
The 4th vibration is different because for the D3h isomer it is a symmetric stretch. This means that it does not show up on IR spectra, as it does not change the dipole moment of the molecule.

The first vibration follows the reaction path (the vectors that the atoms move are the same as those for forming the transition state). This gives it a negative frequency in the transition state, as it requires energy to keep the molecule as it is, rather than to change the molecule.

The IR Spectra of both isomers are shown below:
________________________1_________________________________________________________________2_____________________________________

[[Image:NH3_IR.JPG]][[Image:HS_NH3_IR.JPG]]

== '''Mini Project: Fuels of the Future''' ==

Ammonia borane was optimised in both the eclipsed and staggered conformers. The staggered conformer was found to be more stable by 8.74kJmol-1. This was compared to optimisations of the conformers of ethane, which is-1 isoelectric with ammonia borane. Ethane was found to have a staggered conformer that was more stable by 11.83kJmol-1. This difference is probably due to the increased bond length in ammonia borane. The N-B bond was found to be 1.685Å, while the C-C bond in ethane is 1.544Å. This means that the hydrogen atoms are further apart in ammonia borane than in ethane. Hence, they repel each other less and affect the conformation of the molecule less. Since the orbitals of the hydrogen atoms are the only restraint on the conformation (through repulsion with each other and gauche effects), this makes it easier for ammonia borane to adopt the eclipsed conformation than ethane.
The staggered structure of ammonia borane is shown here:

[[Image:NH3BH3.JPG]]

Borane has similar bonding to its isoelectric analog, as the atoms are all bonded via the same number of electrons. They should not have any difference to other molecular orbitals either as the electrons are all the same. However, ammonia borane has a dipole moment of 1.844 Debye, due to the greater electronegativity of nitrogen and the lower electronegativity of boron. This distorts the MOs of ammonia borane, creating greater electron density over the nitrogen atom.

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Db406: /* '''Mini Project: Fuels of the Future''' */

File:NH3BH3.JPG

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Db406:

File:NH3BH3staggered.mol

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Db406:

Rep:Mod:db9127inorganic

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Db406: /* '''Mini Project: Fuels of the Future''' */

Rep:Mod:db9127inorganic

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Db406: /* '''Mini Project: Fuels of the Future''' */

== '''BH3 Introduction Molecule''' ==

BH3 was optimised using an FOPT calculation type with the RB3LYP method with a basis set of 3-21G. This method means that the molecule is calculated using the Schrődinger equation. This calculates the energy of different geometries and minimises the energy. This geometry with the smallest energy value should be the most stable conformation of the molecule. The basis set 3-21G is a very simple basis set so the calculation will not be extremely accurate but will run quickly. This calculation created a .log file, which gave the optimised geometry and the following information about the optimised molecule:

[[Image:BH3_data.JPG]][[Image:BH3.JPG]]

The molecule is trigonal planar, hence the D3h point group. This gives the bond angle of 120 degrees. BH3 is trigonal planar due to the pz orbital being non-bonding and unoccupied. This is because boron only has 3 electrons and is clearly shown by the molecular orbitals in the later section.

== '''BCl3''' ==

BCl3 was optimised using the same method as BH3. However, the basis set used was LANL2MB. This is a more complex basis set than 3-21G so should give a more accurate optimisation. This gave the following data:

[[Image:BCl3_data.JPG]][[Image:BCl3.JPG]]

BCl3 has a longer bond length than BH3. This is primarily because chlorine is a larger molecule than hydrogen. It also means that the calculation took less time (12s as opposed to 24s). This is because the optimisation works by moving the atoms from far apart to closer together and the BCl3 took less steps to find the optimised geometry because the final molecule was closer to the starting point of the calculation.

BCl3 also has a much lower energy than BH3. This implies that BCl3 is more stable. This is correct as the energy calculation for a chlorine atom is also far lower than that of a hydrogen atom. This is because chlorine contains more electrons and protons so has greater attractive forces acting on the molecule. The BCl bond is also stronger than the BH bond. This is due to secondary overlap from the lower lying orbitals in the chlorine atoms.

BCl3 has the same geometry as BH3. This is again due to the low number of valence electrons present in a boron atom.

== '''PCl5''' ==

PCl5 was optimised using the same method as for BCl3 with the same basis set. The calculation took 34 seconds. This time is because the molecule is more complex than the previous molecules and the Schrõdinger equation takes longer to solve. This gave the following data:

[[Image:PCl5_data.JPG]][[Image:PCl5.JPG]]

GaussView does not show the P-Cl bonds because the atoms are too far apart. This is merely a graphical issue - the bonds are still there as far as the calculations are concerned. In fact, it is somewhat difficult to define a bond, given that a bond is the overlap of molecular orbitals with the same symmetry to create a lower energy orbital and so-called "non-bonding" orbitals still have some overlap effects with others. Since the gaussian calculation takes into account the molecular orbitals, the definition of a bond does not affect the optimised geometry.

PCl5 is trigonal bipyramidal. The co-ordinates of the atoms are shown here:
[[Image:PCl5_coords.JPG]]

The slightly shorter bond length is for the P-Cl bonds parallel to the y-axis, as denoted by the co-ordinate values. This is because these chlorine atoms are 90 degrees from 3 other chlorine atoms. The equatorial chlorine atoms are 90 degrees from the two axial chlorine atoms and 120 degrees from the other equatorial chlorine atoms so suffer a slightly greater repulsion from them. Hence, they are slightly further from the phosphorus atom and have a slightly weaker bond. This makes the equatorial chlorine atoms more susceptible to substitution reactions.

== '''Vibrational analysis of BH3''' ==

The vibrational frequencies of BH3 were calculated. They are shown here:

[[Image:BH3_vibrations1.JPG]][[Image:BH3_vibrations2.JPG]]

The IR Spectrum for BH3 is shown here:

[[Image:BH3_IR.JPG]]

Only 3 peaks are shown on this spectrum, despite there clearly being 6 vibrations for BH3. This is because the two B-H stretching vibrations occur at the same frequency, as do two of the bending vibrations. The symmetric bending stretch is also not present in the IR spectrum, as it does not change the symmetry of the molecule.

== '''Molecular Orbitals of BH3''' ==

The MOs for BH3 were also calculated using Gaussian and compared to qualitative molecular orbitals. The qualitative MO diagram for BH3 is shown here:

[[Image:BH3_MO.gif]]

The occupied MOs and LUMO were calculated and are shown here. The other unoccupied orbitals were not calculated as they become more diffuse and therefore have odd forms.

[[Image:BH3_MO1.JPG]][[Image:BH3_MO2.JPG]]

The first calculated MO does not exist. It is there to help the Gaussian calculation by making the molecule BH3-. This is because BH3 has only 6 electrons in the system.
The other MOs are analogous with the qualitative MOs shown. These correlate very well, which implies that in the absence of computational software, qualitative MOs are an accurate description of occupied and reactive orbitals.
The HOMO orbital can be either orbital 3 or 4 as they both have the same energy (-0.356 a.u.).

All of the occupied MOs are in the same plane as the B-H bonds. This is why BH3 is trigonal planar; the atomic orbitals of boron must have the same symmetry as the atomic orbitals of the hydrogen atoms to form bonds. The first non-planar MO is the LUMO, which is why BH4- is not a planar molecule; the last hydrogen atom bonds with the LUMO which is perpendicular to the plane.

== '''''cis''- and ''trans''- isomerism of molybdenum complexes''' ==

Mo(CO)4L2 complexes were optimised, first loosely using a low level basis set (LANL2MB) and then further using a higher level basis set (LANL2DZ). This was done to make the calculation faster than using a high level basis set immediately. L=piperidine or P(CH3)3. Both the ''cis'' and ''trans'' isomers were optimised.
Unfortunately, the Mo-L bond lengths were too long for GaussView to show them.

The cis-isomers both have slightly increased angles between the L ligands and the CO ligands (91 degrees). This decreases the other inter-ligand angles in the molecule accordingly.
The trans-isomers both have all angles at 90 degrees. This difference in angles for the cis-isomers is due to a steric effect from the large CH3 or piperidine groups, repelling the CO ligands.

Literature values for the angles and bond distances in cis-Mo(CO)4(PPh3)2 are shown here compared with the computational values for cis-Mo(CO)4(P(CH3)3)2. The comparison is valid, as we have been using P(CH3)3 as a simplified model for PPh3. This was to lower calculation time and the two ligands should behave similarly.

[[Image:Bonds_Mo.JPG]][[Image:Bonds_Mo_Labels.JPG]]

The literature values were taken from "Steric contributions to the solid-state structures of bis(phosphine) derivatives of molybdenum carbonyl. X-ray structural studies of cis-Mo(CO)4[PPh3-nMen]2 (n = 0, 1, 2)", F. Albert Cotton, Donald J. Darensbourg, Simonetta Klein, and Brian W. S. Kolthammer, Inorg. Chem., 21, (1982), p294-299 {{DOI|101.1021/ic00131a055}}

The bond lengths are all very similar. The only major difference is that the PPh3 ligands lie closer to the molybdenum atom. This is because the phenyl rings donate electron density to the phosphorus atom, making it more electron rich and therefore more strongly attracted to the metal centre.
The P-Mo-P bond angle for the PPh3 complex is 104.62 degrees. This is far greater than the P-Mo-P bond angle for the P(CH3)3 complex which was 90.93 degrees. The remainder of the bond angles within the computed complex are all ~90 degrees. This shows a large discrepancy from the literature. This is probably due to the simplification of our model, as it removes a large part of the steric effects from the phenyl groups. It may also be because we have not taken into account the presence of d-orbitals in our model. If d-orbitals are taken into account, the calculated P-Mo-P bond angle becomes 92.73 degrees. This is closer to the literature value but implies that the majority of the difference is due to the change in ligand.

The vibrational frequencies of the cis- and trans- isomers were then calculated. These are shown here:

cis-Mo(CO)4(pip)2

[[Image:Cis_Mo(CO)4(pip)2_IR.JPG]]

cis-Mo(CO)4(P(CH3)3)2

[[Image:Cis_Mo(CO)4(P(CH3)3)2_IR.JPG]]

trans-Mo(CO)4(pip)2

[[Image:Trans_Mo(CO)4(pip)2_IR.JPG]]

trans-Mo(CO)4(P(CH3)3)2

[[Image:Trans_Mo(CO)4(P(CH3)3)2_IR.JPG]]

As can be seen, there are two major comparisons that can be drawn. The first is that the piperidine complexes exhibit four different stretches in the 3000-3300cm-1 region to the two exhibited by the methylphosphine complexes. That is because these vibrations are due to C-H bonds and these are in different environments between these two ligands.

The second comparison to be drawn is that the cis- complexes exhibit a peak at ~1850cm-1 that is not exhibited by the trans- complexes. This stretch is shown below:

[[Image:Mo_C_stretch.JPG]]

In the trans- complexes, this vibration does occur. However, here it is a symmetrical stretch so does not change the dipole moment of the molecule. This means that it is not present on the IR spectrum.
The remaining vibrations are assigned in the table below:

[[Image:1MoVib.JPG]][[Image:2MoVib.JPG]][[Image:3MoVib.JPG]]

Any further peaks were due to various C-H bending vibrations within the ligands.

== '''Following a Reaction Path: The Quantum Nature of Ammonia''' ==

Ammonia is an interesting molecule because it readily inverts its structure. This is also true of most trivalent nitrogen atoms but ammonia is easiest to calculate results for and it provides a model for all nitrogen inversion. Ammonia can invert because the activation energy required to reach a trigonal planar transition state is very low. The inversion reaction occurs as shown:

[[Image:Inversion.jpg]]

In this section, three isomers of ammonia were optimised and the energies compared. The three isomers were: ammonia in its usually accepted tetrahedral shape; the same shape with one N-H bond length changed to 1.01Å; a trigonal planar ammonia molecule. These isomers will be referred to as 1, 2 and 3 respectively. The summaries of their optimisations are shown here:
_____________1____________________________________________2_______________________________________3____________________________

[[Image:NH3_1.JPG]][[Image:NH3_nosymm.JPG]][[Image:NH3_highsymm.JPG]]

The calculations were then redone using the MP2 method. The same basis set was used to make direct comparison possible.
___________________1____________________________________________2_______________________________________3___________________________

[[Image:NH3_MP2.JPG]][[Image:NH3_MP2_nosymm.JPG]][[Image:NH3_MP2_highsymm.JPG]]

The energy difference between isomers 1 and 2 (the normal geometric state of ammonia and the transition state for inversion) was calculated as ΔE= 16.8595kJmol-1 for the DFT method and ΔE= 20.8252kJmol-1 for the MP2 method of calculation. The literature value for the energy barrier of inversion is 24.3kJmol-1. This implies that the MP2 method is more accurate, as it gives an energy closer to the literature value. However, it should be noted that the basis set chosen makes a very large difference to the energy values (~2000kJmol-1 when changing from 6-31G to 6-311G). The energy also changes slightly each time the optimisation is re-run. Hence, the calculated energy values can never be fully accurate when using either of these methods. A much more complex and time-consuming basis set would be required to achieve a high level of accuracy.

It should be noted also that both of these methods give the energy barrier for inversion as lower than the literature value. This may be due to contributions from neighbouring molecules which the calculations do not take into account.

== '''Vibrational analysis of NH3 isomers''' ==

The C3v and D3h models were used to calculate the vibrational frequencies of these conformations for NH3. These vibrations are shown below:

'''D3h'''

[[Image:NH3_vibrations1.JPG]][[Image:NH3_vibrations2.JPG]]

'''C3v'''

[[Image:HS_NH3_vibrations1.JPG]][[Image:HS_NH3_vibrations2.JPG]]

The main differences are the first vibration and the 4th vibration. The first vibration has a greatly different frequency because the D3h isomer vibration changes the dipole moment slightly because the H atoms do not move far from the plane. Because the C3v isomer is already bent, this vibration pushes the H atoms even further from the plane, greatly changing the dipole moment and requiring a greater frequency of vibration.
The 4th vibration is different because for the D3h isomer it is a symmetric stretch. This means that it does not show up on IR spectra, as it does not change the dipole moment of the molecule.

The first vibration follows the reaction path (the vectors that the atoms move are the same as those for forming the transition state). This gives it a negative frequency in the transition state, as it requires energy to keep the molecule as it is, rather than to change the molecule.

The IR Spectra of both isomers are shown below:
________________________1_________________________________________________________________2_____________________________________

[[Image:NH3_IR.JPG]][[Image:HS_NH3_IR.JPG]]

== '''Mini Project: Fuels of the Future''' ==

Ammonia borane was optimised in both the eclipsed and staggered conformers. The staggered conformer was found to be more stable by 8.74kJmol-1. This was compared to optimisations of the conformers of ethane, which is isoelectric with ammonia borane. Ethane was found to have a staggered conformer that was more stable by 11.83kJmol-1. This difference is probably due to the increased bond length in ammonia borane. The N-B bond was found to be 1.685Å, while the C-C bond in ethane is 1.544Å. This means that the hydrogen atoms are further apart in ammonia borane than in ethane. Hence, they repel each other less and affect the conformation of the molecule less. Since the orbitals of the hydrogen atoms are the only restraint on the conformation (through repulsion with each other and gauche effects), this makes it easier for ammonia borane to adopt the eclipsed conformation than ethane.

Rep:Mod:db9127inorganic

2008-11-09T21:38:27Z

Db406: /* '''Mini Project: Fuels of the Future''' */

== '''BH3 Introduction Molecule''' ==

BH3 was optimised using an FOPT calculation type with the RB3LYP method with a basis set of 3-21G. This method means that the molecule is calculated using the Schrődinger equation. This calculates the energy of different geometries and minimises the energy. This geometry with the smallest energy value should be the most stable conformation of the molecule. The basis set 3-21G is a very simple basis set so the calculation will not be extremely accurate but will run quickly. This calculation created a .log file, which gave the optimised geometry and the following information about the optimised molecule:

[[Image:BH3_data.JPG]][[Image:BH3.JPG]]

The molecule is trigonal planar, hence the D3h point group. This gives the bond angle of 120 degrees. BH3 is trigonal planar due to the pz orbital being non-bonding and unoccupied. This is because boron only has 3 electrons and is clearly shown by the molecular orbitals in the later section.

== '''BCl3''' ==

BCl3 was optimised using the same method as BH3. However, the basis set used was LANL2MB. This is a more complex basis set than 3-21G so should give a more accurate optimisation. This gave the following data:

[[Image:BCl3_data.JPG]][[Image:BCl3.JPG]]

BCl3 has a longer bond length than BH3. This is primarily because chlorine is a larger molecule than hydrogen. It also means that the calculation took less time (12s as opposed to 24s). This is because the optimisation works by moving the atoms from far apart to closer together and the BCl3 took less steps to find the optimised geometry because the final molecule was closer to the starting point of the calculation.

BCl3 also has a much lower energy than BH3. This implies that BCl3 is more stable. This is correct as the energy calculation for a chlorine atom is also far lower than that of a hydrogen atom. This is because chlorine contains more electrons and protons so has greater attractive forces acting on the molecule. The BCl bond is also stronger than the BH bond. This is due to secondary overlap from the lower lying orbitals in the chlorine atoms.

BCl3 has the same geometry as BH3. This is again due to the low number of valence electrons present in a boron atom.

== '''PCl5''' ==

PCl5 was optimised using the same method as for BCl3 with the same basis set. The calculation took 34 seconds. This time is because the molecule is more complex than the previous molecules and the Schrõdinger equation takes longer to solve. This gave the following data:

[[Image:PCl5_data.JPG]][[Image:PCl5.JPG]]

GaussView does not show the P-Cl bonds because the atoms are too far apart. This is merely a graphical issue - the bonds are still there as far as the calculations are concerned. In fact, it is somewhat difficult to define a bond, given that a bond is the overlap of molecular orbitals with the same symmetry to create a lower energy orbital and so-called "non-bonding" orbitals still have some overlap effects with others. Since the gaussian calculation takes into account the molecular orbitals, the definition of a bond does not affect the optimised geometry.

PCl5 is trigonal bipyramidal. The co-ordinates of the atoms are shown here:
[[Image:PCl5_coords.JPG]]

The slightly shorter bond length is for the P-Cl bonds parallel to the y-axis, as denoted by the co-ordinate values. This is because these chlorine atoms are 90 degrees from 3 other chlorine atoms. The equatorial chlorine atoms are 90 degrees from the two axial chlorine atoms and 120 degrees from the other equatorial chlorine atoms so suffer a slightly greater repulsion from them. Hence, they are slightly further from the phosphorus atom and have a slightly weaker bond. This makes the equatorial chlorine atoms more susceptible to substitution reactions.

== '''Vibrational analysis of BH3''' ==

The vibrational frequencies of BH3 were calculated. They are shown here:

[[Image:BH3_vibrations1.JPG]][[Image:BH3_vibrations2.JPG]]

The IR Spectrum for BH3 is shown here:

[[Image:BH3_IR.JPG]]

Only 3 peaks are shown on this spectrum, despite there clearly being 6 vibrations for BH3. This is because the two B-H stretching vibrations occur at the same frequency, as do two of the bending vibrations. The symmetric bending stretch is also not present in the IR spectrum, as it does not change the symmetry of the molecule.

== '''Molecular Orbitals of BH3''' ==

The MOs for BH3 were also calculated using Gaussian and compared to qualitative molecular orbitals. The qualitative MO diagram for BH3 is shown here:

[[Image:BH3_MO.gif]]

The occupied MOs and LUMO were calculated and are shown here. The other unoccupied orbitals were not calculated as they become more diffuse and therefore have odd forms.

[[Image:BH3_MO1.JPG]][[Image:BH3_MO2.JPG]]

The first calculated MO does not exist. It is there to help the Gaussian calculation by making the molecule BH3-. This is because BH3 has only 6 electrons in the system.
The other MOs are analogous with the qualitative MOs shown. These correlate very well, which implies that in the absence of computational software, qualitative MOs are an accurate description of occupied and reactive orbitals.
The HOMO orbital can be either orbital 3 or 4 as they both have the same energy (-0.356 a.u.).

All of the occupied MOs are in the same plane as the B-H bonds. This is why BH3 is trigonal planar; the atomic orbitals of boron must have the same symmetry as the atomic orbitals of the hydrogen atoms to form bonds. The first non-planar MO is the LUMO, which is why BH4- is not a planar molecule; the last hydrogen atom bonds with the LUMO which is perpendicular to the plane.

== '''''cis''- and ''trans''- isomerism of molybdenum complexes''' ==

Mo(CO)4L2 complexes were optimised, first loosely using a low level basis set (LANL2MB) and then further using a higher level basis set (LANL2DZ). This was done to make the calculation faster than using a high level basis set immediately. L=piperidine or P(CH3)3. Both the ''cis'' and ''trans'' isomers were optimised.
Unfortunately, the Mo-L bond lengths were too long for GaussView to show them.

The cis-isomers both have slightly increased angles between the L ligands and the CO ligands (91 degrees). This decreases the other inter-ligand angles in the molecule accordingly.
The trans-isomers both have all angles at 90 degrees. This difference in angles for the cis-isomers is due to a steric effect from the large CH3 or piperidine groups, repelling the CO ligands.

Literature values for the angles and bond distances in cis-Mo(CO)4(PPh3)2 are shown here compared with the computational values for cis-Mo(CO)4(P(CH3)3)2. The comparison is valid, as we have been using P(CH3)3 as a simplified model for PPh3. This was to lower calculation time and the two ligands should behave similarly.

[[Image:Bonds_Mo.JPG]][[Image:Bonds_Mo_Labels.JPG]]

The literature values were taken from "Steric contributions to the solid-state structures of bis(phosphine) derivatives of molybdenum carbonyl. X-ray structural studies of cis-Mo(CO)4[PPh3-nMen]2 (n = 0, 1, 2)", F. Albert Cotton, Donald J. Darensbourg, Simonetta Klein, and Brian W. S. Kolthammer, Inorg. Chem., 21, (1982), p294-299 {{DOI|101.1021/ic00131a055}}

The bond lengths are all very similar. The only major difference is that the PPh3 ligands lie closer to the molybdenum atom. This is because the phenyl rings donate electron density to the phosphorus atom, making it more electron rich and therefore more strongly attracted to the metal centre.
The P-Mo-P bond angle for the PPh3 complex is 104.62 degrees. This is far greater than the P-Mo-P bond angle for the P(CH3)3 complex which was 90.93 degrees. The remainder of the bond angles within the computed complex are all ~90 degrees. This shows a large discrepancy from the literature. This is probably due to the simplification of our model, as it removes a large part of the steric effects from the phenyl groups. It may also be because we have not taken into account the presence of d-orbitals in our model. If d-orbitals are taken into account, the calculated P-Mo-P bond angle becomes 92.73 degrees. This is closer to the literature value but implies that the majority of the difference is due to the change in ligand.

The vibrational frequencies of the cis- and trans- isomers were then calculated. These are shown here:

cis-Mo(CO)4(pip)2

[[Image:Cis_Mo(CO)4(pip)2_IR.JPG]]

cis-Mo(CO)4(P(CH3)3)2

[[Image:Cis_Mo(CO)4(P(CH3)3)2_IR.JPG]]

trans-Mo(CO)4(pip)2

[[Image:Trans_Mo(CO)4(pip)2_IR.JPG]]

trans-Mo(CO)4(P(CH3)3)2

[[Image:Trans_Mo(CO)4(P(CH3)3)2_IR.JPG]]

As can be seen, there are two major comparisons that can be drawn. The first is that the piperidine complexes exhibit four different stretches in the 3000-3300cm-1 region to the two exhibited by the methylphosphine complexes. That is because these vibrations are due to C-H bonds and these are in different environments between these two ligands.

The second comparison to be drawn is that the cis- complexes exhibit a peak at ~1850cm-1 that is not exhibited by the trans- complexes. This stretch is shown below:

[[Image:Mo_C_stretch.JPG]]

In the trans- complexes, this vibration does occur. However, here it is a symmetrical stretch so does not change the dipole moment of the molecule. This means that it is not present on the IR spectrum.
The remaining vibrations are assigned in the table below:

[[Image:1MoVib.JPG]][[Image:2MoVib.JPG]][[Image:3MoVib.JPG]]

Any further peaks were due to various C-H bending vibrations within the ligands.

== '''Following a Reaction Path: The Quantum Nature of Ammonia''' ==

Ammonia is an interesting molecule because it readily inverts its structure. This is also true of most trivalent nitrogen atoms but ammonia is easiest to calculate results for and it provides a model for all nitrogen inversion. Ammonia can invert because the activation energy required to reach a trigonal planar transition state is very low. The inversion reaction occurs as shown:

[[Image:Inversion.jpg]]

In this section, three isomers of ammonia were optimised and the energies compared. The three isomers were: ammonia in its usually accepted tetrahedral shape; the same shape with one N-H bond length changed to 1.01Å; a trigonal planar ammonia molecule. These isomers will be referred to as 1, 2 and 3 respectively. The summaries of their optimisations are shown here:
_____________1____________________________________________2_______________________________________3____________________________

[[Image:NH3_1.JPG]][[Image:NH3_nosymm.JPG]][[Image:NH3_highsymm.JPG]]

The calculations were then redone using the MP2 method. The same basis set was used to make direct comparison possible.
___________________1____________________________________________2_______________________________________3___________________________

[[Image:NH3_MP2.JPG]][[Image:NH3_MP2_nosymm.JPG]][[Image:NH3_MP2_highsymm.JPG]]

The energy difference between isomers 1 and 2 (the normal geometric state of ammonia and the transition state for inversion) was calculated as ΔE= 16.8595kJmol-1 for the DFT method and ΔE= 20.8252kJmol-1 for the MP2 method of calculation. The literature value for the energy barrier of inversion is 24.3kJmol-1. This implies that the MP2 method is more accurate, as it gives an energy closer to the literature value. However, it should be noted that the basis set chosen makes a very large difference to the energy values (~2000kJmol-1 when changing from 6-31G to 6-311G). The energy also changes slightly each time the optimisation is re-run. Hence, the calculated energy values can never be fully accurate when using either of these methods. A much more complex and time-consuming basis set would be required to achieve a high level of accuracy.

It should be noted also that both of these methods give the energy barrier for inversion as lower than the literature value. This may be due to contributions from neighbouring molecules which the calculations do not take into account.

== '''Vibrational analysis of NH3 isomers''' ==

The C3v and D3h models were used to calculate the vibrational frequencies of these conformations for NH3. These vibrations are shown below:

'''D3h'''

[[Image:NH3_vibrations1.JPG]][[Image:NH3_vibrations2.JPG]]

'''C3v'''

[[Image:HS_NH3_vibrations1.JPG]][[Image:HS_NH3_vibrations2.JPG]]

The main differences are the first vibration and the 4th vibration. The first vibration has a greatly different frequency because the D3h isomer vibration changes the dipole moment slightly because the H atoms do not move far from the plane. Because the C3v isomer is already bent, this vibration pushes the H atoms even further from the plane, greatly changing the dipole moment and requiring a greater frequency of vibration.
The 4th vibration is different because for the D3h isomer it is a symmetric stretch. This means that it does not show up on IR spectra, as it does not change the dipole moment of the molecule.

The first vibration follows the reaction path (the vectors that the atoms move are the same as those for forming the transition state). This gives it a negative frequency in the transition state, as it requires energy to keep the molecule as it is, rather than to change the molecule.

The IR Spectra of both isomers are shown below:
________________________1_________________________________________________________________2_____________________________________

[[Image:NH3_IR.JPG]][[Image:HS_NH3_IR.JPG]]

== '''Mini Project: Fuels of the Future''' ==

Ammonia borane was optimised in both the eclipsed and staggered conformers. The staggered conformer was found to be more stable by 8.74kJmol-1. This was compared to optimisations of the conformers of ethane, which is isoelectric with ammonia borane. Ethane was found to have a staggered conformer that was more stable by 11.83kJmol-1. This difference is probably due to the increased bond length in ammonia borane. The N-B bond was found to be 1.685Å, while the C-C bond in ethane is 1.544Å. This means that the hydrogen atoms are further apart in ammonia borane than in ethane. Hence, they repel each other less and affect the conformation of the molecule less. Since the orbitals of the hydrogen atoms are the only restraint on the conformation (through repulsion with each other and gauche effects), this makes it easier for ammonia borane to adopt the eclipsed conformation than ethane.

Rep:Mod:db9127inorganic

2008-11-09T20:45:25Z

Db406: /* '''Vibrational analysis of NH3 isomers''' */

Rep:Mod:db9127inorganic

2008-11-09T20:44:35Z

Db406: /* '''Mini Project: Fuels of the Future''' */

Rep:Mod:db9127inorganic

2008-11-09T20:44:10Z

Db406: /* '''Following a Reaction Path: The Quantum Nature of Ammonia''' */

== '''BH3 Introduction Molecule''' ==

BH3 was optimised using an FOPT calculation type with the RB3LYP method with a basis set of 3-21G. This method means that the molecule is calculated using the Schrődinger equation. This calculates the energy of different geometries and minimises the energy. This geometry with the smallest energy value should be the most stable conformation of the molecule. The basis set 3-21G is a very simple basis set so the calculation will not be extremely accurate but will run quickly. This calculation created a .log file, which gave the optimised geometry and the following information about the optimised molecule:

[[Image:BH3_data.JPG]][[Image:BH3.JPG]]

The molecule is trigonal planar, hence the D3h point group. This gives the bond angle of 120 degrees. BH3 is trigonal planar due to the pz orbital being non-bonding and unoccupied. This is because boron only has 3 electrons and is clearly shown by the molecular orbitals in the later section.

== '''BCl3''' ==

BCl3 was optimised using the same method as BH3. However, the basis set used was LANL2MB. This is a more complex basis set than 3-21G so should give a more accurate optimisation. This gave the following data:

[[Image:BCl3_data.JPG]][[Image:BCl3.JPG]]

BCl3 has a longer bond length than BH3. This is primarily because chlorine is a larger molecule than hydrogen. It also means that the calculation took less time (12s as opposed to 24s). This is because the optimisation works by moving the atoms from far apart to closer together and the BCl3 took less steps to find the optimised geometry because the final molecule was closer to the starting point of the calculation.

BCl3 also has a much lower energy than BH3. This implies that BCl3 is more stable. This is correct as the energy calculation for a chlorine atom is also far lower than that of a hydrogen atom. This is because chlorine contains more electrons and protons so has greater attractive forces acting on the molecule. The BCl bond is also stronger than the BH bond. This is due to secondary overlap from the lower lying orbitals in the chlorine atoms.

BCl3 has the same geometry as BH3. This is again due to the low number of valence electrons present in a boron atom.

== '''PCl5''' ==

PCl5 was optimised using the same method as for BCl3 with the same basis set. The calculation took 34 seconds. This time is because the molecule is more complex than the previous molecules and the Schrõdinger equation takes longer to solve. This gave the following data:

[[Image:PCl5_data.JPG]][[Image:PCl5.JPG]]

GaussView does not show the P-Cl bonds because the atoms are too far apart. This is merely a graphical issue - the bonds are still there as far as the calculations are concerned. In fact, it is somewhat difficult to define a bond, given that a bond is the overlap of molecular orbitals with the same symmetry to create a lower energy orbital and so-called "non-bonding" orbitals still have some overlap effects with others. Since the gaussian calculation takes into account the molecular orbitals, the definition of a bond does not affect the optimised geometry.

PCl5 is trigonal bipyramidal. The co-ordinates of the atoms are shown here:
[[Image:PCl5_coords.JPG]]

The slightly shorter bond length is for the P-Cl bonds parallel to the y-axis, as denoted by the co-ordinate values. This is because these chlorine atoms are 90 degrees from 3 other chlorine atoms. The equatorial chlorine atoms are 90 degrees from the two axial chlorine atoms and 120 degrees from the other equatorial chlorine atoms so suffer a slightly greater repulsion from them. Hence, they are slightly further from the phosphorus atom and have a slightly weaker bond. This makes the equatorial chlorine atoms more susceptible to substitution reactions.

== '''Vibrational analysis of BH3''' ==

The vibrational frequencies of BH3 were calculated. They are shown here:

[[Image:BH3_vibrations1.JPG]][[Image:BH3_vibrations2.JPG]]

The IR Spectrum for BH3 is shown here:

[[Image:BH3_IR.JPG]]

Only 3 peaks are shown on this spectrum, despite there clearly being 6 vibrations for BH3. This is because the two B-H stretching vibrations occur at the same frequency, as do two of the bending vibrations. The symmetric bending stretch is also not present in the IR spectrum, as it does not change the symmetry of the molecule.

== '''Molecular Orbitals of BH3''' ==

The MOs for BH3 were also calculated using Gaussian and compared to qualitative molecular orbitals. The qualitative MO diagram for BH3 is shown here:

[[Image:BH3_MO.gif]]

The occupied MOs and LUMO were calculated and are shown here. The other unoccupied orbitals were not calculated as they become more diffuse and therefore have odd forms.

[[Image:BH3_MO1.JPG]][[Image:BH3_MO2.JPG]]

The first calculated MO does not exist. It is there to help the Gaussian calculation by making the molecule BH3-. This is because BH3 has only 6 electrons in the system.
The other MOs are analogous with the qualitative MOs shown. These correlate very well, which implies that in the absence of computational software, qualitative MOs are an accurate description of occupied and reactive orbitals.
The HOMO orbital can be either orbital 3 or 4 as they both have the same energy (-0.356 a.u.).

All of the occupied MOs are in the same plane as the B-H bonds. This is why BH3 is trigonal planar; the atomic orbitals of boron must have the same symmetry as the atomic orbitals of the hydrogen atoms to form bonds. The first non-planar MO is the LUMO, which is why BH4- is not a planar molecule; the last hydrogen atom bonds with the LUMO which is perpendicular to the plane.

== '''''cis''- and ''trans''- isomerism of molybdenum complexes''' ==

Mo(CO)4L2 complexes were optimised, first loosely using a low level basis set (LANL2MB) and then further using a higher level basis set (LANL2DZ). This was done to make the calculation faster than using a high level basis set immediately. L=piperidine or P(CH3)3. Both the ''cis'' and ''trans'' isomers were optimised.
Unfortunately, the Mo-L bond lengths were too long for GaussView to show them.

The cis-isomers both have slightly increased angles between the L ligands and the CO ligands (91 degrees). This decreases the other inter-ligand angles in the molecule accordingly.
The trans-isomers both have all angles at 90 degrees. This difference in angles for the cis-isomers is due to a steric effect from the large CH3 or piperidine groups, repelling the CO ligands.

Literature values for the angles and bond distances in cis-Mo(CO)4(PPh3)2 are shown here compared with the computational values for cis-Mo(CO)4(P(CH3)3)2. The comparison is valid, as we have been using P(CH3)3 as a simplified model for PPh3. This was to lower calculation time and the two ligands should behave similarly.

[[Image:Bonds_Mo.JPG]][[Image:Bonds_Mo_Labels.JPG]]

The literature values were taken from "Steric contributions to the solid-state structures of bis(phosphine) derivatives of molybdenum carbonyl. X-ray structural studies of cis-Mo(CO)4[PPh3-nMen]2 (n = 0, 1, 2)", F. Albert Cotton, Donald J. Darensbourg, Simonetta Klein, and Brian W. S. Kolthammer, Inorg. Chem., 21, (1982), p294-299 {{DOI|101.1021/ic00131a055}}

The bond lengths are all very similar. The only major difference is that the PPh3 ligands lie closer to the molybdenum atom. This is because the phenyl rings donate electron density to the phosphorus atom, making it more electron rich and therefore more strongly attracted to the metal centre.
The P-Mo-P bond angle for the PPh3 complex is 104.62 degrees. This is far greater than the P-Mo-P bond angle for the P(CH3)3 complex which was 90.93 degrees. The remainder of the bond angles within the computed complex are all ~90 degrees. This shows a large discrepancy from the literature. This is probably due to the simplification of our model, as it removes a large part of the steric effects from the phenyl groups. It may also be because we have not taken into account the presence of d-orbitals in our model. If d-orbitals are taken into account, the calculated P-Mo-P bond angle becomes 92.73 degrees. This is closer to the literature value but implies that the majority of the difference is due to the change in ligand.

The vibrational frequencies of the cis- and trans- isomers were then calculated. These are shown here:

cis-Mo(CO)4(pip)2

[[Image:Cis_Mo(CO)4(pip)2_IR.JPG]]

cis-Mo(CO)4(P(CH3)3)2

[[Image:Cis_Mo(CO)4(P(CH3)3)2_IR.JPG]]

trans-Mo(CO)4(pip)2

[[Image:Trans_Mo(CO)4(pip)2_IR.JPG]]

trans-Mo(CO)4(P(CH3)3)2

[[Image:Trans_Mo(CO)4(P(CH3)3)2_IR.JPG]]

As can be seen, there are two major comparisons that can be drawn. The first is that the piperidine complexes exhibit four different stretches in the 3000-3300cm-1 region to the two exhibited by the methylphosphine complexes. That is because these vibrations are due to C-H bonds and these are in different environments between these two ligands.

The second comparison to be drawn is that the cis- complexes exhibit a peak at ~1850cm-1 that is not exhibited by the trans- complexes. This stretch is shown below:

[[Image:Mo_C_stretch.JPG]]

In the trans- complexes, this vibration does occur. However, here it is a symmetrical stretch so does not change the dipole moment of the molecule. This means that it is not present on the IR spectrum.
The remaining vibrations are assigned in the table below:

[[Image:1MoVib.JPG]][[Image:2MoVib.JPG]][[Image:3MoVib.JPG]]

Any further peaks were due to various C-H bending vibrations within the ligands.

== '''Following a Reaction Path: The Quantum Nature of Ammonia''' ==

Ammonia is an interesting molecule because it readily inverts its structure. This is also true of most trivalent nitrogen atoms but ammonia is easiest to calculate results for and it provides a model for all nitrogen inversion. Ammonia can invert because the activation energy required to reach a trigonal planar transition state is very low. The inversion reaction occurs as shown:

[[Image:Inversion.jpg]]

In this section, three isomers of ammonia were optimised and the energies compared. The three isomers were: ammonia in its usually accepted tetrahedral shape; the same shape with one N-H bond length changed to 1.01Å; a trigonal planar ammonia molecule. These isomers will be referred to as 1, 2 and 3 respectively. The summaries of their optimisations are shown here:
_____________1____________________________________________2_______________________________________3____________________________

[[Image:NH3_1.JPG]][[Image:NH3_nosymm.JPG]][[Image:NH3_highsymm.JPG]]

The calculations were then redone using the MP2 method. The same basis set was used to make direct comparison possible.
___________________1____________________________________________2_______________________________________3___________________________

[[Image:NH3_MP2.JPG]][[Image:NH3_MP2_nosymm.JPG]][[Image:NH3_MP2_highsymm.JPG]]

The energy difference between isomers 1 and 2 (the normal geometric state of ammonia and the transition state for inversion) was calculated as ΔE= 16.8595kJmol-1 for the DFT method and ΔE= 20.8252kJmol-1 for the MP2 method of calculation. The literature value for the energy barrier of inversion is 24.3kJmol-1. This implies that the MP2 method is more accurate, as it gives an energy closer to the literature value. However, it should be noted that the basis set chosen makes a very large difference to the energy values (~2000kJmol-1 when changing from 6-31G to 6-311G). The energy also changes slightly each time the optimisation is re-run. Hence, the calculated energy values can never be fully accurate when using either of these methods. A much more complex and time-consuming basis set would be required to achieve a high level of accuracy.

It should be noted also that both of these methods give the energy barrier for inversion as lower than the literature value. This may be due to contributions from neighbouring molecules which the calculations do not take into account.

== '''Mini Project: Fuels of the Future''' ==

== '''Vibrational analysis of NH3 isomers''' ==

The C3v and D3h models were used to calculate the vibrational frequencies of these conformations for NH3. These vibrations are shown below:

'''D3h'''

[[Image:NH3_vibrations1.JPG]][[Image:NH3_vibrations2.JPG]]

'''C3v'''

[[Image:HS_NH3_vibrations1.JPG]][[Image:HS_NH3_vibrations2.JPG]]

The main differences are the first vibration and the 4th vibration. The first vibration has a greatly different frequency because the D3h isomer vibration changes the dipole moment slightly because the H atoms do not move far from the plane. Because the C3v isomer is already bent, this vibration pushes the H atoms even further from the plane, greatly changing the dipole moment and requiring a greater frequency of vibration.
The 4th vibration is different because for the D3h isomer it is a symmetric stretch. This means that it does not show up on IR spectra, as it does not change the dipole moment of the molecule.

The first vibration follows the reaction path (the vectors that the atoms move are the same as those for forming the transition state). This gives it a negative frequency in the transition state, as it requires energy to keep the molecule as it is, rather than to change the molecule.

The IR Spectra of both isomers are shown below:
________________________1_________________________________________________________________2_____________________________________

[[Image:NH3_IR.JPG]][[Image:HS_NH3_IR.JPG]]

Rep:Mod:db9127inorganic

2008-11-09T20:42:36Z

Db406: /* '''''cis''- and ''trans''- isomerism of molybdenum complexes''' */