ChemWiki - User contributions [en]

Rep:Mod:hezmana

2009-02-25T22:04:52Z

Reb06: /* The Cope Rearrangement: modelling the transition state */

=Physical Computational Chemistry Experiment 3 - The Transition State=

==The Cope Rearrangement: modelling the dimer==

A molecule of 1,5-hexadiene was modelled with an anti linkage about the central bond and optimisted using the HF/3-21G method and basis set. The resulting model has energy -231.69260 a.u., point group C2 and corresponds to conformer anti1 in [[Mod:phys3|appendix 1]].

The gauche form is expected to be higher in energy in general due to increaced 1,4 strain but this depends upon the specific conformers.

A molecule of 1,5-hexadiene was then modelled with an gauche linkage about the central bond and optimisted using the HF/3-21G method and basis set. The resulting model has energy -231.69153 a.u., point group C2 and corresponds to conformer gauche4 in [[Mod:phys3|appendix 1]].

A molecule of 1,5-hexadiene was then modelled with an anti linkage about the central bond which corresponded to conformer anti2 in [[Mod:phys3|appendix 1]] and optimisted using the HF/3-21G method and basis set. The resulting model has energy -231.68279 a.u. and point group Ci. This is lower than the energy given in [[Mod:phys3|appendix 1]] which, assuming the other energies are correct, makes it the lowest energy conformer.

This model was then reoptimised using the B3LYP/6-31G* method and basis set. The energy of the new model is -234.60056 a.u. and point group Ci is retained. The geometry appears to be unchanged. The vibrations were then calculated. The results showed three negative frequencies demonstrating that there was a problem with the geometry of this model. The calculations were repeated with the model reconstructed from scratch.

For the HF/3-21G calculation the new result was an energy of -231.69254 a.u. which does match that given in [[Mod:phys3|appendix 1]]. The point group was Ci. For the B3LYP/6-31G* calculation the new result was an energy of -234.61172 a.u. and point group Ci. Relative to the HF/3-21G calculated model the B3LYP/6-31G* has lengthed c=c double bonds and shortened c-c single bonds suggesting a degree of increaced delocalisation.

[[Image:React_anti2_spec.JPG|thumb|left|200|Dihydro Calculated IR spectrum]] A vibrational analysis of this second model was performed and all frequencies produced were positive as demonstrated in the calculated IR spectrum (left). The sum of electronic and zero point energies was -234.469182. The sum of electronic and thermal energies was -234.461844. The sum of electronic and thermal enthalpies was -234.460900. The sum of electronic and thermal free energies was -234.500730.

==The Cope Rearrangement: modelling the transition state==

A model of the chair transition state was created by placing two delocallised allyl fragments CH2CHCH2 so that the terminal carbons were at a distance of 2.2A from each other. The model was then optimised to a berny transition state and the frequencies calculated using HF/3-21G. The resulting transition state (shown below) had energy -231.61932 a.u. and one imaginary frequency at -837 cm-1 which corresponds to the cope rearrangement.

<jmol>
<jmolApplet>
<title>chair ts</title>
<color>yellow</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>CHAIR_TS_OPT1.mol</uploadedFileContents>
</jmolApplet>
</jmol>

The model was then reoptimised using the frozen coordinate method. First freezing the terminal atom spacing at 2.2 angstroms and then allowing it to vary. This new model had an energy of -231.61932 a.u. with the imaginary vibration now lying at -818 cm-1 and the terminal atom spacing down to 2.02 angstroms from 2.14.

The boat transition structure was optimised using the QST2 method. This method generates the transition state automatically when given the reactat and product structures. The B3LYP/6-31G* anti2 model produced earlier was used for both reactant and product with atom labelling adjusted accordingly. This calculation failed since this method does not take into account the rotation around the central bond necessary to enter the transition state. The reactant and product were therefore manually manipulated to create a syn central linkage and the calculation was run again.

The resulting model had energy -231.60280 with a single imaginary frequency at -840 cm-1.

Rep:Mod:hezmana

2009-02-25T21:52:16Z

Reb06: /* The Cope Rearrangement: modelling the transition state */

2009-02-25T20:03:23Z

Reb06:

Rep:Mod:hezmana

2009-02-25T17:16:42Z

Reb06: /* The Cope Rearrangement: modelling the transition state */

Rep:Mod:hezmana

2009-02-25T17:10:19Z

Reb06: /* The Cope Rearrangement: modelling the dimer */

Rep:Mod:hezmana

2009-02-25T17:09:47Z

Reb06: /* The Cope Rearrangement */

Rep:Mod:hezmana

2009-02-25T17:09:08Z

Reb06: /* The Cope Rearrangement */

=Physical Computational Chemistry Experiment 3 - The Transition State=

==The Cope Rearrangement==

A molecule of 1,5-hexadiene was modelled with an anti linkage about the central bond and optimisted using the HF/3-21G method and basis set. The resulting model has energy -231.69260 a.u., point group C2 and corresponds to conformer anti1 in [[Mod:phys3|appendix 1]].

The gauche form is expected to be higher in energy in general due to increaced 1,4 strain but this depends upon the specific conformers.

A molecule of 1,5-hexadiene was then modelled with an gauche linkage about the central bond and optimisted using the HF/3-21G method and basis set. The resulting model has energy -231.69153 a.u., point group C2 and corresponds to conformer gauche4 in [[Mod:phys3|appendix 1]].

A molecule of 1,5-hexadiene was then modelled with an anti linkage about the central bond which corresponded to conformer anti2 in [[Mod:phys3|appendix 1]] and optimisted using the HF/3-21G method and basis set. The resulting model has energy -231.68279 a.u. and point group Ci. This is lower than the energy given in [[Mod:phys3|appendix 1]] which, assuming the other energies are correct, makes it the lowest energy conformer.

This model was then reoptimised using the B3LYP/6-31G* method and basis set. The energy of the new model is -234.60056 a.u. and point group Ci is retained. The geometry appears to be unchanged. The vibrations were then calculated. The results showed three negative frequencies demonstrating that there was a problem with the geometry of this model. The calculations were repeated with the model reconstructed from scratch.

For the HF/3-21G calculation the new result was an energy of -231.69254 a.u. which does match that given in [[Mod:phys3|appendix 1]]. The point group was Ci. For the B3LYP/6-31G* calculation the new result was an energy of -234.61172 a.u. and point group Ci. Relative to the HF/3-21G calculated model the B3LYP/6-31G* has lengthed c=c double bonds and shortened c-c single bonds suggesting a degree of increaced delocalisation.

[[Image:React_anti2_spec.JPG|thumb|left|200|Dihydro Calculated IR spectrum]] A vibrational analysis of this second model was performed and all frequencies produced were positive as demonstrated in the calculated IR spectrum (left). The sum of electronic and zero point energies was -234.469182. The sum of electronic and thermal energies was -234.461844. The sum of electronic and thermal enthalpies was -234.460900. The sum of electronic and thermal free energies was -234.500730.

2009-02-18T15:39:17Z

Reb06:

File:Reb Ru-Cp iPr opt1.mol

2009-02-18T15:38:45Z

Reb06:

Rep:Mod:noyjitat

2009-02-18T15:37:10Z

Reb06: /* Dimerisation of the ruthenocenium ion */

=Computational inorganic chemistry=

==BCl3==

A molecule of BCl3 was optimised using the B3LYP/3-21G method with the following results:
{| border="0" cellpadding="0" cellspacing="0"
|-
|Bond distance - 1.87 A
|-
|Bond angle - 120.0
|-
|File type - .log
|-
|Calculation type - FOPT
|-
|Calculation method - RB3LYP
|-
|Basis set - LANL2MB
|-
|Final energy - -69.439 a.u.
|-
|Dipole moment - 0.00 Deby
|-
|Point group - D3H
|-
|Calculation time - 11.0 seconds
|-
|}

==BF3==

This was repeated for BF3 with the following results:

Atomic positions (Angstroms)
{| border="1" cellpadding="3" cellspacing="3"
|-
|Centre Number
|Atomic Type
|X Coordinate
|Y Coordinate
|Z Coordinate
|-
|1
|C
|"0.000"
|"0.000"
|"0.000"
|-
|2
|F
|"0.000"
|"1.334"
|"0.000"
|-
|3
|F
|"1.155"
|"-0.667"
|"0.000"
|-
|4
|F
|"-1.155"
|"-0.667"
|"0.000"
|-
|}

{| border="0" cellpadding="0" cellspacing="0"
|-
|Bond distance - 1.33 A
|-
|Bond angle - 120.0
|-
|File type - .log
|-
|Calculation type - FOPT
|-
|Calculation method - RB3LYP
|-
|Basis set - LANL2MB
|-
|Final energy - -319.872 a.u.
|-
|Dipole moment - 0.00 Deby
|-
|Point group - D3H
|-
|Calculation time - 18.0 seconds
|-
|}

'''Upload log file'''

==BH3 vibrational analysis==

BH3 was optimised in the same manner as above and the vibrations were then calculated:
{| border="1" cellpadding="3" cellspacing="3"
|-
|No
|Form of the vibration
|Frequency
|Intensity
|Symmetry
(Dh3 point group)
|-
|1
|[[Image:Reb_BH3_vib_image1.JPG|thumb|left|200|Hydrogens all move in a concerted motion in the z direction. B atom is stationary.]]
|1145.71
|92.6991
|A'2
|-
|2
|[[Image:Reb BH3 vib image2.JPG|thumb|left|200|Two hydrogens move in a scissoring motion. Third hydrogen and B atom are stationary]]
|1204.66
|12.3789
|A'1
|-
|3
|[[Image:Reb BH3 vib image3.JPG|thumb|left|200|Hydrogen wagging motion. B atom is stationary]]
|1204.66
|12.3814
|E'
|-
|4
|[[Image:Reb_BH3_vib_image4.JPG|thumb|left|200|Hydrogens all move in and out in a concerted motion. B atom is stationary.]]
|2592.79
|0
|A'1
|-
|5
|[[Image:Reb_BH3_vib_image5.JPG|thumb|left|200|Two hydrogens move in and out alternately. Third hydrogen and B atom are stationary.]]
|2731.31
|103.837
|A'2
|-
|6
|[[Image:Reb_BH3_vib_image6.JPG|thumb|left|200|Two hydrogens move in and out in a concerted motion with the third hydrogen moving in and out in alternate motion. B atom is stationary.]]
|2731.31
|103.83
|A'2
|-
|}

[[Image:Reb BH3 vib spec.JPG|thumb|right|800|Computed IR spectrum for BH3]]

Giving the followng IR spectrum

==BH3 molecular orbitals==

[[Image:REB_BH3_MO.GIF|thumb|left|800|Qualitative MO diagram for BH3]] The molecular orbitals for BH3 can now be calculated by the same method as above and compared to the qualitative MO diagram.

{| border="1" cellpadding="3" cellspacing="3"
|-
|[[Image:Reb_BH3_mo_lumo+2.JPG|thumb|left|800|LUMO +2
(energy 0.188)]]
|[[Image:Reb_BH3_mo_lumo+1.JPG|thumb|left|800|LUMO +1
(energy 0.188)]]
|-
|[[Image:Reb_BH3_mo_lumo.JPG|thumb|left|800|LUMO
(energy -0.074)]]
|[[Image:Reb_BH3_mo_homo.JPG|thumb|left|800|HOMO
(energy -0.356)]]
|-
|[[Image:Reb_BH3_mo_homo-1.JPG|thumb|left|800|HOMO -1
(energy -0.356)]]
|[[Image:Reb_BH3_mo_homo-2.JPG|thumb|left|800|HOMO -2
(energy -0.517)]]
|-
|[[Image:Reb_BH3_mo_homo-3.JPG|thumb|left|800|HOMO -3
(energy -6.730)]]
|
|-
|}

There is good agreement between the occupied qualitative MOs and the occupied quantatative calculated MOs. The shapes are reasonable when compared to the linear combination of orbitals and the predicted degeneracies hold. The unoccupied orbitals however, show little agreement. The predicted LUMO for BH3 is a simple Pz orbital on the boron whereas the calculated LUMO is far more complex and presents a different symmetry making the predicted LUMO a very bad model. The quantative LUMO+1 and LUMO+2 levels are also given as degenerate, differing again from prediction.

==NH3==
Three versions of the NH3 molecule restrained to different symmetries were optimised using a 6-31G basis set and the B3LYP method. Summeries of these optisations are given below

{| border="1" cellpadding="3" cellspacing="3"
|-
|[[Image:Reb_nh3_summary2.JPG|thumb|left|200|]]
|[[Image:Reb_nh3_summary1.JPG|thumb|left|200|]]
|[[Image:Reb_nh3_summary3.JPG|thumb|left|200|]]
|-
|This model was optimised after setting one bond to 1.01 angstroms to restrain the molecule to C1 symmetry
|This model was optimised as a standard C3v symmetry NH3
|This model was optimised using a dummy atom to restrain the molecule to Dh3 symmetry
|-
|Bond lengths all 1.006 angstroms
Bond angles all 116 degrees
|Bond lengths 1.000, 1.000, 1.010 angstroms
Bond angles all 109 degrees
|Bond lengths all 0.998 angstroms
Bond angles all 120 degrees
|-
|Relative energy 4.95 kJ/mol
|Relative energy 0 kJ/mol
|Relative energy 4.05 kJ/mol
|-
|}

By changing the symmetry we change the structure of the optimised molecule in terms of both bond lengths and angles.
Time needed to optimise the geometry increaced with increacing degree of symmetry. This is due to the fact that the molecule cannot break symmetry at any stage of the optimization and so each step must be calculated to conform to the correct symmetry. This takes more time for a higher symmetry since it contains more symmetry elements which must be calculated. This indicates that calculations on molecules with very high symmetry (for example Oh) would be very time consuming indeed.
The lowest energy geometry was the C1 geometry, with the energy differences between the diffrent geometries given above. These differences represent the energy barrier to movement between differering geometries. This barrier is clearly small.

The C3V and D3H calculations were then repeated from scratch using the higher level MP2/6-311+G(d,p) method and basis set. These calculations took 33.0 sec and 1 min 35.0 sec respectively, an increace of around 20% on the calulation time for the B3LYP/6-31G calculation. The energy has also been reduced in the order of 0.1 a.u. giving an energy difference between D3H and C3V symmetries of 20.5 kJ/mol. Since the D3H symmetry represents the trasition state for inversion of ammonia this figure represents the barrier height to inversion and is in reasonable agreement with the experimental value of 24.3 kJ/mol.

==NH3 vibrational analysis==
[[Image:Reb_NH3_c3v_vib_spec.JPG|thumb|right|800|Computed IR spectrum for C3v NH3]] [[Image:Reb_NH3_d3h_vib_spec.JPG|thumb|left|800|Computed IR spectrum for Dh3 BH3]]The vibrations for NH3 were then calculated from the B3LYP/6-31G optimised structures of C3v and D3h symmetry. The IR spectra are seen here.

{| border="1" cellpadding="3" cellspacing="3"
|-
|Calculated frequency (D3h)/cm-1
|Calculated frequency (C3v)/cm-1
|Experimental frequency/cm-1
|-
|452
|"-318"
|950
|-
|1680
|1641
|1627
|-
|1680
|1641
|1627
|-
|3575
|3636
|3336
|-
|3776
|3854
|3414
|-
|3776
|3854
|3414
|-
|}

These results show the C3v structure to be the ground state since it has all positive frequencies. The D3h structure has a sigle negative frequency at -318 which shows it to be a transition state. The vibration at this frequency is the a'2 "umberella" like stretch and this is the vibration which follows the inversion reaction path.

==Cis-Trans isomerism of [Mo(CO)4(pip)2]==

Models of both the cis and trans forms of [Mo(CO)4(pip)2] (pip = NC5H10) were optimised initially to a loose convergence using the B3LYP/LANL2MB method and basis set and then to a increased convergence using the more accurate B3LYP/LANL2DZ method and basis set.

Cis-[Mo(CO)4(pip)2] {{DOI|10042/to-1972}}

<jmol><jmolApplet><title>Cis complex</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Reb_cisMo.mol‎</uploadedFileContents>
</jmolApplet></jmol>

Trans-[Mo(CO)4(pip)2] {{DOI|10042/to-1974}}

<jmol><jmolApplet><title>Trans complex</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Reb_transMocplx.mol</uploadedFileContents>
</jmolApplet></jmol>

The first obvious difference in the geometry of the two complexes is that the Trans complex is very close to perfect octohedral geometry at the Mo centre with a varience from the expected bond angles of 90 degrees of only 4 degrees in C-Mo-C and less than 1 degree in C-Mo-N. The trans complex also has equal Mo-L bond lengths of 2.06 angstroms for all ligands, both CO and pip. In the Cis complex however the steric bulk of the ligands has forced a large distortion in the expected octohedral geometry with an N-Mo-N bond angle of 110 degrees. Bond lengths are also no longer equal with the majority of the bonds shortened to ~2.05 angstroms and the Mo-C bonds Trans to the piperidine ligands lengthened to 2.08 and 2.09 angstroms. Mo-N bond lengths typically range between 2.45 and 2.06 angstroms <ref>Bart, J.C.J; Ragaini, V.; Acta Crystallogr. B, Struct. Crystallogr. Cryst. Chem., 1980, B36, 1351-4</ref> placing both complexs at the extreme lower end of the range and suggesting double bond character.
The Trans complex is the more thermodynamically favoured due to the strain described with an energy difference between conformations of 0.00194 a.u. (5.11 kJ/mol). This could be altered by substituting less bulky ligands or by linking the piperidine ligands to create a single bidentate ligand.

==Vibrational analysis of [Mo(CO)4(pip)2]==

[[Image:Reb_cisMocplx_IR.JPG|thumb|left|200|Predicted IR spectrum for Cis-[Mo(CO)4(pip)2]]] [[Image:Reb_transMocplx_IR.JPG|thumb|right|200|Predicted IR spectrum for Trans-[Mo(CO)4(pip)2]]]

Vibrations of [Mo(CO)4(pip)2] were then calculated from the previous models for both Cis {{DOI|10042/to-1976}} and Trans {{DOI|10042/to-1977}} forms of the complex producing the predicted spectra shown here.

=Mini Project=

==Dimerisation of the ruthenocenium ion==
[[Image:Ru-dimer.gif|thumb|left|200|Ruthenocene dimer equilibrium (Image taken from journal<ref name=prim><a href=http://pubs.acs.org/doi/full/10.1021/ic802105b>J.C. Swarts et. al., Inorg. Chem., Article ASAP, DOI: 10.1021/ic802105b, Publication Date (Web): January 26, 2009</a></ref>)]] J.C. Swarts et. al. <ref name=prim><a href=http://pubs.acs.org/doi/full/10.1021/ic802105b>J.C. Swarts et. al., Inorg. Chem., Article ASAP, DOI: 10.1021/ic802105b, Publication Date (Web): January 26, 2009</a></ref> observed that upon electrochemical oxidation of ruthenocene, [RuCp2], to Ruthenocenium, [RuCp2]+, the resultant complex tended to dimerize to a Ru-Ru linked dication '''2''' which converted reversibly with loss of dihydrogen to a Ru-Cp linked dication '''3''' upon heating.

In this mini project this thermal equilibrium will be investigated. Firstly to see if dication '''3''' is intrinsically thermodynamically favoured when the effects of solvent and coordinating anion are removed and secondly to see what effect changing the sustituents on the Cp rings has upon the position of the equilibrium.

All calculations use the B3LYP/LANL2MB method and basis set as the LANL2MB basis set, although more accurate, was thought too computationally demanding for a molecule of this size.

The unsubstituted dimers were calculated first with the following results:
{| border="1" cellpadding="5" cellspacing="0"
|-
|'''2'''
|'''3'''
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Ru_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Cp_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|{{DOI|10042/to-1996}}
|{{DOI|10042/to-1999}}
|-
|}

The energy difference between the two complexes was a extremely high 2034 kJ/mol. Although it is to be expected that the figure in solution would be altered this demonstrates that dication '''3''' is intrinsically much more stable than cation '''2''' which is supported experimentally by the rapid conversion of '''2''' to '''3''' once heated above the temperature of 243K at which it is synthesised.

This energy difference can be either increaced or reversed, so that the Ru-Ru linked dimer is thermodynamically prefered, by tuning the ring substituents. When analogus structures where the hydrogens of the Cp rings are replaced by highly electron withdrawing fluorines were calculated the results were as follows:
{| border="1" cellpadding="5" cellspacing="0"
|-
|[Ru2(η5C5F5)4]2+ (analogous to '''2''')
|[Ru2(η5C5F5)2(σ:η5C5F4)2]2+ (analogous to '''3''')
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Ru_F_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Cp_F_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|{{DOI|10042/to-1998}}
|{{DOI|10042/to-1994}}
|-
|}

These complexes proved so high in energy compared to the initial complexes (the energy difference between the H-substituted and F-substituted complexes is of the order of 106 kJ/mol) that it is highly unlikely they could be synthesised in reality. However they demonstrate the theoretical influence of electron withdrawing substituents which is indicative of the influence that fewer or less electron withdrawing substituents would have. As for the origional complex the Ru-Ru linked dimer is thermodynamically more stable with the energy difference between conformations being huge at 516000 kJ/mol. Electron withdrawing substituents on the rings will therefore tend to push the equilibrium further towards the Ru-Cp linked dimers.

When analogus structures where the hydrogens of the Cp rings are replaced by highly electron withdrawing fluorines were calculated the results were as follows:
{| border="1" cellpadding="5" cellspacing="0"
|-
|[Ru2(η5C5F5)4]2+ (analogous to '''2''')
|[Ru2(η5C5F5)2(σ:η5C5F4)2]2+ (analogous to '''3''')
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Ru_F_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Cp_F_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|{{DOI|10042/to-1998}}
|{{DOI|10042/to-1994}}
|-
|}

Rep:Mod:noyjitat

2009-02-18T15:23:13Z

Reb06: /* Dimerisation of the ruthenocenium ion */

=Computational inorganic chemistry=

==BCl3==

A molecule of BCl3 was optimised using the B3LYP/3-21G method with the following results:
{| border="0" cellpadding="0" cellspacing="0"
|-
|Bond distance - 1.87 A
|-
|Bond angle - 120.0
|-
|File type - .log
|-
|Calculation type - FOPT
|-
|Calculation method - RB3LYP
|-
|Basis set - LANL2MB
|-
|Final energy - -69.439 a.u.
|-
|Dipole moment - 0.00 Deby
|-
|Point group - D3H
|-
|Calculation time - 11.0 seconds
|-
|}

==BF3==

This was repeated for BF3 with the following results:

Atomic positions (Angstroms)
{| border="1" cellpadding="3" cellspacing="3"
|-
|Centre Number
|Atomic Type
|X Coordinate
|Y Coordinate
|Z Coordinate
|-
|1
|C
|"0.000"
|"0.000"
|"0.000"
|-
|2
|F
|"0.000"
|"1.334"
|"0.000"
|-
|3
|F
|"1.155"
|"-0.667"
|"0.000"
|-
|4
|F
|"-1.155"
|"-0.667"
|"0.000"
|-
|}

{| border="0" cellpadding="0" cellspacing="0"
|-
|Bond distance - 1.33 A
|-
|Bond angle - 120.0
|-
|File type - .log
|-
|Calculation type - FOPT
|-
|Calculation method - RB3LYP
|-
|Basis set - LANL2MB
|-
|Final energy - -319.872 a.u.
|-
|Dipole moment - 0.00 Deby
|-
|Point group - D3H
|-
|Calculation time - 18.0 seconds
|-
|}

'''Upload log file'''

==BH3 vibrational analysis==

BH3 was optimised in the same manner as above and the vibrations were then calculated:
{| border="1" cellpadding="3" cellspacing="3"
|-
|No
|Form of the vibration
|Frequency
|Intensity
|Symmetry
(Dh3 point group)
|-
|1
|[[Image:Reb_BH3_vib_image1.JPG|thumb|left|200|Hydrogens all move in a concerted motion in the z direction. B atom is stationary.]]
|1145.71
|92.6991
|A'2
|-
|2
|[[Image:Reb BH3 vib image2.JPG|thumb|left|200|Two hydrogens move in a scissoring motion. Third hydrogen and B atom are stationary]]
|1204.66
|12.3789
|A'1
|-
|3
|[[Image:Reb BH3 vib image3.JPG|thumb|left|200|Hydrogen wagging motion. B atom is stationary]]
|1204.66
|12.3814
|E'
|-
|4
|[[Image:Reb_BH3_vib_image4.JPG|thumb|left|200|Hydrogens all move in and out in a concerted motion. B atom is stationary.]]
|2592.79
|0
|A'1
|-
|5
|[[Image:Reb_BH3_vib_image5.JPG|thumb|left|200|Two hydrogens move in and out alternately. Third hydrogen and B atom are stationary.]]
|2731.31
|103.837
|A'2
|-
|6
|[[Image:Reb_BH3_vib_image6.JPG|thumb|left|200|Two hydrogens move in and out in a concerted motion with the third hydrogen moving in and out in alternate motion. B atom is stationary.]]
|2731.31
|103.83
|A'2
|-
|}

[[Image:Reb BH3 vib spec.JPG|thumb|right|800|Computed IR spectrum for BH3]]

Giving the followng IR spectrum

==BH3 molecular orbitals==

[[Image:REB_BH3_MO.GIF|thumb|left|800|Qualitative MO diagram for BH3]] The molecular orbitals for BH3 can now be calculated by the same method as above and compared to the qualitative MO diagram.

{| border="1" cellpadding="3" cellspacing="3"
|-
|[[Image:Reb_BH3_mo_lumo+2.JPG|thumb|left|800|LUMO +2
(energy 0.188)]]
|[[Image:Reb_BH3_mo_lumo+1.JPG|thumb|left|800|LUMO +1
(energy 0.188)]]
|-
|[[Image:Reb_BH3_mo_lumo.JPG|thumb|left|800|LUMO
(energy -0.074)]]
|[[Image:Reb_BH3_mo_homo.JPG|thumb|left|800|HOMO
(energy -0.356)]]
|-
|[[Image:Reb_BH3_mo_homo-1.JPG|thumb|left|800|HOMO -1
(energy -0.356)]]
|[[Image:Reb_BH3_mo_homo-2.JPG|thumb|left|800|HOMO -2
(energy -0.517)]]
|-
|[[Image:Reb_BH3_mo_homo-3.JPG|thumb|left|800|HOMO -3
(energy -6.730)]]
|
|-
|}

There is good agreement between the occupied qualitative MOs and the occupied quantatative calculated MOs. The shapes are reasonable when compared to the linear combination of orbitals and the predicted degeneracies hold. The unoccupied orbitals however, show little agreement. The predicted LUMO for BH3 is a simple Pz orbital on the boron whereas the calculated LUMO is far more complex and presents a different symmetry making the predicted LUMO a very bad model. The quantative LUMO+1 and LUMO+2 levels are also given as degenerate, differing again from prediction.

==NH3==
Three versions of the NH3 molecule restrained to different symmetries were optimised using a 6-31G basis set and the B3LYP method. Summeries of these optisations are given below

{| border="1" cellpadding="3" cellspacing="3"
|-
|[[Image:Reb_nh3_summary2.JPG|thumb|left|200|]]
|[[Image:Reb_nh3_summary1.JPG|thumb|left|200|]]
|[[Image:Reb_nh3_summary3.JPG|thumb|left|200|]]
|-
|This model was optimised after setting one bond to 1.01 angstroms to restrain the molecule to C1 symmetry
|This model was optimised as a standard C3v symmetry NH3
|This model was optimised using a dummy atom to restrain the molecule to Dh3 symmetry
|-
|Bond lengths all 1.006 angstroms
Bond angles all 116 degrees
|Bond lengths 1.000, 1.000, 1.010 angstroms
Bond angles all 109 degrees
|Bond lengths all 0.998 angstroms
Bond angles all 120 degrees
|-
|Relative energy 4.95 kJ/mol
|Relative energy 0 kJ/mol
|Relative energy 4.05 kJ/mol
|-
|}

By changing the symmetry we change the structure of the optimised molecule in terms of both bond lengths and angles.
Time needed to optimise the geometry increaced with increacing degree of symmetry. This is due to the fact that the molecule cannot break symmetry at any stage of the optimization and so each step must be calculated to conform to the correct symmetry. This takes more time for a higher symmetry since it contains more symmetry elements which must be calculated. This indicates that calculations on molecules with very high symmetry (for example Oh) would be very time consuming indeed.
The lowest energy geometry was the C1 geometry, with the energy differences between the diffrent geometries given above. These differences represent the energy barrier to movement between differering geometries. This barrier is clearly small.

The C3V and D3H calculations were then repeated from scratch using the higher level MP2/6-311+G(d,p) method and basis set. These calculations took 33.0 sec and 1 min 35.0 sec respectively, an increace of around 20% on the calulation time for the B3LYP/6-31G calculation. The energy has also been reduced in the order of 0.1 a.u. giving an energy difference between D3H and C3V symmetries of 20.5 kJ/mol. Since the D3H symmetry represents the trasition state for inversion of ammonia this figure represents the barrier height to inversion and is in reasonable agreement with the experimental value of 24.3 kJ/mol.

==NH3 vibrational analysis==
[[Image:Reb_NH3_c3v_vib_spec.JPG|thumb|right|800|Computed IR spectrum for C3v NH3]] [[Image:Reb_NH3_d3h_vib_spec.JPG|thumb|left|800|Computed IR spectrum for Dh3 BH3]]The vibrations for NH3 were then calculated from the B3LYP/6-31G optimised structures of C3v and D3h symmetry. The IR spectra are seen here.

{| border="1" cellpadding="3" cellspacing="3"
|-
|Calculated frequency (D3h)/cm-1
|Calculated frequency (C3v)/cm-1
|Experimental frequency/cm-1
|-
|452
|"-318"
|950
|-
|1680
|1641
|1627
|-
|1680
|1641
|1627
|-
|3575
|3636
|3336
|-
|3776
|3854
|3414
|-
|3776
|3854
|3414
|-
|}

These results show the C3v structure to be the ground state since it has all positive frequencies. The D3h structure has a sigle negative frequency at -318 which shows it to be a transition state. The vibration at this frequency is the a'2 "umberella" like stretch and this is the vibration which follows the inversion reaction path.

==Cis-Trans isomerism of [Mo(CO)4(pip)2]==

Models of both the cis and trans forms of [Mo(CO)4(pip)2] (pip = NC5H10) were optimised initially to a loose convergence using the B3LYP/LANL2MB method and basis set and then to a increased convergence using the more accurate B3LYP/LANL2DZ method and basis set.

Cis-[Mo(CO)4(pip)2] {{DOI|10042/to-1972}}

<jmol><jmolApplet><title>Cis complex</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Reb_cisMo.mol‎</uploadedFileContents>
</jmolApplet></jmol>

Trans-[Mo(CO)4(pip)2] {{DOI|10042/to-1974}}

<jmol><jmolApplet><title>Trans complex</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Reb_transMocplx.mol</uploadedFileContents>
</jmolApplet></jmol>

The first obvious difference in the geometry of the two complexes is that the Trans complex is very close to perfect octohedral geometry at the Mo centre with a varience from the expected bond angles of 90 degrees of only 4 degrees in C-Mo-C and less than 1 degree in C-Mo-N. The trans complex also has equal Mo-L bond lengths of 2.06 angstroms for all ligands, both CO and pip. In the Cis complex however the steric bulk of the ligands has forced a large distortion in the expected octohedral geometry with an N-Mo-N bond angle of 110 degrees. Bond lengths are also no longer equal with the majority of the bonds shortened to ~2.05 angstroms and the Mo-C bonds Trans to the piperidine ligands lengthened to 2.08 and 2.09 angstroms. Mo-N bond lengths typically range between 2.45 and 2.06 angstroms <ref>Bart, J.C.J; Ragaini, V.; Acta Crystallogr. B, Struct. Crystallogr. Cryst. Chem., 1980, B36, 1351-4</ref> placing both complexs at the extreme lower end of the range and suggesting double bond character.
The Trans complex is the more thermodynamically favoured due to the strain described with an energy difference between conformations of 0.00194 a.u. (5.11 kJ/mol). This could be altered by substituting less bulky ligands or by linking the piperidine ligands to create a single bidentate ligand.

==Vibrational analysis of [Mo(CO)4(pip)2]==

[[Image:Reb_cisMocplx_IR.JPG|thumb|left|200|Predicted IR spectrum for Cis-[Mo(CO)4(pip)2]]] [[Image:Reb_transMocplx_IR.JPG|thumb|right|200|Predicted IR spectrum for Trans-[Mo(CO)4(pip)2]]]

Vibrations of [Mo(CO)4(pip)2] were then calculated from the previous models for both Cis {{DOI|10042/to-1976}} and Trans {{DOI|10042/to-1977}} forms of the complex producing the predicted spectra shown here.

=Mini Project=

==Dimerisation of the ruthenocenium ion==
[[Image:Ru-dimer.gif|thumb|left|200|Ruthenocene dimer equilibrium (Image taken from journal<ref name=prim><a href=http://pubs.acs.org/doi/full/10.1021/ic802105b>J.C. Swarts et. al., Inorg. Chem., Article ASAP, DOI: 10.1021/ic802105b, Publication Date (Web): January 26, 2009</a></ref>)]] J.C. Swarts et. al. <ref name=prim><a href=http://pubs.acs.org/doi/full/10.1021/ic802105b>J.C. Swarts et. al., Inorg. Chem., Article ASAP, DOI: 10.1021/ic802105b, Publication Date (Web): January 26, 2009</a></ref> observed that upon electrochemical oxidation of ruthenocene, [RuCp2], to Ruthenocenium, [RuCp2]+, the resultant complex tended to dimerize to a Ru-Ru linked dication '''2''' which converted reversibly with loss of dihydrogen to a Ru-Cp linked dication '''3''' upon heating.

In this mini project this thermal equilibrium will be investigated. Firstly to see if dication '''3''' is intrinsically thermodynamically favoured when the effects of solvent and coordinating anion are removed and secondly to see what effect changing the sustituents on the Cp rings has upon the position of the equilibrium.

All calculations use the B3LYP/LANL2MB method and basis set as the LANL2MB basis set, although more accurate, was thought too computationally demanding for a molecule of this size.

The unsubstituted dimers were calculated first with the following results:
{| border="1" cellpadding="5" cellspacing="0"
|-
|'''2'''
|'''3'''
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Ru_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Cp_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|{{DOI|10042/to-1996}}
|{{DOI|10042/to-1999}}
|-
|}

The energy difference between the two complexes was a extremely high 2034 kJ/mol. Although it is to be expected that the figure in solution would be altered this demonstrates that dication '''3''' is intrinsically much more stable than cation '''2''' which is supported experimentally by the rapid conversion of '''2''' to '''3''' once heated above the temperature of 243K at which it is synthesised.

This energy difference can be either increaced or reversed, so that the Ru-Ru linked dimer is thermodynamically prefered, by tuning the ring substituents. When analogus structures where the hydrogens of the Cp rings are replaced by highly electron withdrawing fluorines were calculated the results were as follows:
{| border="1" cellpadding="5" cellspacing="0"
|-
|[Ru2(η5C5F5)4]2+ (analogous to '''2''')
|[Ru2(η5C5F5)2(σ:η5C5F4)2]2+ (analogous to '''3''')
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Ru_F_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Cp_F_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|{{DOI|10042/to-1998}}
|{{DOI|10042/to-1994}}
|-
|}

File:Reb Ru-Ru F opt1.mol

2009-02-18T15:22:15Z

Reb06:

File:Reb Ru-Cp F opt1.mol

2009-02-18T15:21:45Z

Reb06:

Rep:Mod:noyjitat

2009-02-18T15:20:24Z

Reb06: /* Dimerisation of the ruthenocenium ion */

=Computational inorganic chemistry=

==BCl3==

A molecule of BCl3 was optimised using the B3LYP/3-21G method with the following results:
{| border="0" cellpadding="0" cellspacing="0"
|-
|Bond distance - 1.87 A
|-
|Bond angle - 120.0
|-
|File type - .log
|-
|Calculation type - FOPT
|-
|Calculation method - RB3LYP
|-
|Basis set - LANL2MB
|-
|Final energy - -69.439 a.u.
|-
|Dipole moment - 0.00 Deby
|-
|Point group - D3H
|-
|Calculation time - 11.0 seconds
|-
|}

==BF3==

This was repeated for BF3 with the following results:

Atomic positions (Angstroms)
{| border="1" cellpadding="3" cellspacing="3"
|-
|Centre Number
|Atomic Type
|X Coordinate
|Y Coordinate
|Z Coordinate
|-
|1
|C
|"0.000"
|"0.000"
|"0.000"
|-
|2
|F
|"0.000"
|"1.334"
|"0.000"
|-
|3
|F
|"1.155"
|"-0.667"
|"0.000"
|-
|4
|F
|"-1.155"
|"-0.667"
|"0.000"
|-
|}

{| border="0" cellpadding="0" cellspacing="0"
|-
|Bond distance - 1.33 A
|-
|Bond angle - 120.0
|-
|File type - .log
|-
|Calculation type - FOPT
|-
|Calculation method - RB3LYP
|-
|Basis set - LANL2MB
|-
|Final energy - -319.872 a.u.
|-
|Dipole moment - 0.00 Deby
|-
|Point group - D3H
|-
|Calculation time - 18.0 seconds
|-
|}

'''Upload log file'''

==BH3 vibrational analysis==

BH3 was optimised in the same manner as above and the vibrations were then calculated:
{| border="1" cellpadding="3" cellspacing="3"
|-
|No
|Form of the vibration
|Frequency
|Intensity
|Symmetry
(Dh3 point group)
|-
|1
|[[Image:Reb_BH3_vib_image1.JPG|thumb|left|200|Hydrogens all move in a concerted motion in the z direction. B atom is stationary.]]
|1145.71
|92.6991
|A'2
|-
|2
|[[Image:Reb BH3 vib image2.JPG|thumb|left|200|Two hydrogens move in a scissoring motion. Third hydrogen and B atom are stationary]]
|1204.66
|12.3789
|A'1
|-
|3
|[[Image:Reb BH3 vib image3.JPG|thumb|left|200|Hydrogen wagging motion. B atom is stationary]]
|1204.66
|12.3814
|E'
|-
|4
|[[Image:Reb_BH3_vib_image4.JPG|thumb|left|200|Hydrogens all move in and out in a concerted motion. B atom is stationary.]]
|2592.79
|0
|A'1
|-
|5
|[[Image:Reb_BH3_vib_image5.JPG|thumb|left|200|Two hydrogens move in and out alternately. Third hydrogen and B atom are stationary.]]
|2731.31
|103.837
|A'2
|-
|6
|[[Image:Reb_BH3_vib_image6.JPG|thumb|left|200|Two hydrogens move in and out in a concerted motion with the third hydrogen moving in and out in alternate motion. B atom is stationary.]]
|2731.31
|103.83
|A'2
|-
|}

[[Image:Reb BH3 vib spec.JPG|thumb|right|800|Computed IR spectrum for BH3]]

Giving the followng IR spectrum

==BH3 molecular orbitals==

[[Image:REB_BH3_MO.GIF|thumb|left|800|Qualitative MO diagram for BH3]] The molecular orbitals for BH3 can now be calculated by the same method as above and compared to the qualitative MO diagram.

{| border="1" cellpadding="3" cellspacing="3"
|-
|[[Image:Reb_BH3_mo_lumo+2.JPG|thumb|left|800|LUMO +2
(energy 0.188)]]
|[[Image:Reb_BH3_mo_lumo+1.JPG|thumb|left|800|LUMO +1
(energy 0.188)]]
|-
|[[Image:Reb_BH3_mo_lumo.JPG|thumb|left|800|LUMO
(energy -0.074)]]
|[[Image:Reb_BH3_mo_homo.JPG|thumb|left|800|HOMO
(energy -0.356)]]
|-
|[[Image:Reb_BH3_mo_homo-1.JPG|thumb|left|800|HOMO -1
(energy -0.356)]]
|[[Image:Reb_BH3_mo_homo-2.JPG|thumb|left|800|HOMO -2
(energy -0.517)]]
|-
|[[Image:Reb_BH3_mo_homo-3.JPG|thumb|left|800|HOMO -3
(energy -6.730)]]
|
|-
|}

There is good agreement between the occupied qualitative MOs and the occupied quantatative calculated MOs. The shapes are reasonable when compared to the linear combination of orbitals and the predicted degeneracies hold. The unoccupied orbitals however, show little agreement. The predicted LUMO for BH3 is a simple Pz orbital on the boron whereas the calculated LUMO is far more complex and presents a different symmetry making the predicted LUMO a very bad model. The quantative LUMO+1 and LUMO+2 levels are also given as degenerate, differing again from prediction.

==NH3==
Three versions of the NH3 molecule restrained to different symmetries were optimised using a 6-31G basis set and the B3LYP method. Summeries of these optisations are given below

{| border="1" cellpadding="3" cellspacing="3"
|-
|[[Image:Reb_nh3_summary2.JPG|thumb|left|200|]]
|[[Image:Reb_nh3_summary1.JPG|thumb|left|200|]]
|[[Image:Reb_nh3_summary3.JPG|thumb|left|200|]]
|-
|This model was optimised after setting one bond to 1.01 angstroms to restrain the molecule to C1 symmetry
|This model was optimised as a standard C3v symmetry NH3
|This model was optimised using a dummy atom to restrain the molecule to Dh3 symmetry
|-
|Bond lengths all 1.006 angstroms
Bond angles all 116 degrees
|Bond lengths 1.000, 1.000, 1.010 angstroms
Bond angles all 109 degrees
|Bond lengths all 0.998 angstroms
Bond angles all 120 degrees
|-
|Relative energy 4.95 kJ/mol
|Relative energy 0 kJ/mol
|Relative energy 4.05 kJ/mol
|-
|}

By changing the symmetry we change the structure of the optimised molecule in terms of both bond lengths and angles.
Time needed to optimise the geometry increaced with increacing degree of symmetry. This is due to the fact that the molecule cannot break symmetry at any stage of the optimization and so each step must be calculated to conform to the correct symmetry. This takes more time for a higher symmetry since it contains more symmetry elements which must be calculated. This indicates that calculations on molecules with very high symmetry (for example Oh) would be very time consuming indeed.
The lowest energy geometry was the C1 geometry, with the energy differences between the diffrent geometries given above. These differences represent the energy barrier to movement between differering geometries. This barrier is clearly small.

The C3V and D3H calculations were then repeated from scratch using the higher level MP2/6-311+G(d,p) method and basis set. These calculations took 33.0 sec and 1 min 35.0 sec respectively, an increace of around 20% on the calulation time for the B3LYP/6-31G calculation. The energy has also been reduced in the order of 0.1 a.u. giving an energy difference between D3H and C3V symmetries of 20.5 kJ/mol. Since the D3H symmetry represents the trasition state for inversion of ammonia this figure represents the barrier height to inversion and is in reasonable agreement with the experimental value of 24.3 kJ/mol.

==NH3 vibrational analysis==
[[Image:Reb_NH3_c3v_vib_spec.JPG|thumb|right|800|Computed IR spectrum for C3v NH3]] [[Image:Reb_NH3_d3h_vib_spec.JPG|thumb|left|800|Computed IR spectrum for Dh3 BH3]]The vibrations for NH3 were then calculated from the B3LYP/6-31G optimised structures of C3v and D3h symmetry. The IR spectra are seen here.

{| border="1" cellpadding="3" cellspacing="3"
|-
|Calculated frequency (D3h)/cm-1
|Calculated frequency (C3v)/cm-1
|Experimental frequency/cm-1
|-
|452
|"-318"
|950
|-
|1680
|1641
|1627
|-
|1680
|1641
|1627
|-
|3575
|3636
|3336
|-
|3776
|3854
|3414
|-
|3776
|3854
|3414
|-
|}

These results show the C3v structure to be the ground state since it has all positive frequencies. The D3h structure has a sigle negative frequency at -318 which shows it to be a transition state. The vibration at this frequency is the a'2 "umberella" like stretch and this is the vibration which follows the inversion reaction path.

==Cis-Trans isomerism of [Mo(CO)4(pip)2]==

Models of both the cis and trans forms of [Mo(CO)4(pip)2] (pip = NC5H10) were optimised initially to a loose convergence using the B3LYP/LANL2MB method and basis set and then to a increased convergence using the more accurate B3LYP/LANL2DZ method and basis set.

Cis-[Mo(CO)4(pip)2] {{DOI|10042/to-1972}}

<jmol><jmolApplet><title>Cis complex</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Reb_cisMo.mol‎</uploadedFileContents>
</jmolApplet></jmol>

Trans-[Mo(CO)4(pip)2] {{DOI|10042/to-1974}}

<jmol><jmolApplet><title>Trans complex</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Reb_transMocplx.mol</uploadedFileContents>
</jmolApplet></jmol>

The first obvious difference in the geometry of the two complexes is that the Trans complex is very close to perfect octohedral geometry at the Mo centre with a varience from the expected bond angles of 90 degrees of only 4 degrees in C-Mo-C and less than 1 degree in C-Mo-N. The trans complex also has equal Mo-L bond lengths of 2.06 angstroms for all ligands, both CO and pip. In the Cis complex however the steric bulk of the ligands has forced a large distortion in the expected octohedral geometry with an N-Mo-N bond angle of 110 degrees. Bond lengths are also no longer equal with the majority of the bonds shortened to ~2.05 angstroms and the Mo-C bonds Trans to the piperidine ligands lengthened to 2.08 and 2.09 angstroms. Mo-N bond lengths typically range between 2.45 and 2.06 angstroms <ref>Bart, J.C.J; Ragaini, V.; Acta Crystallogr. B, Struct. Crystallogr. Cryst. Chem., 1980, B36, 1351-4</ref> placing both complexs at the extreme lower end of the range and suggesting double bond character.
The Trans complex is the more thermodynamically favoured due to the strain described with an energy difference between conformations of 0.00194 a.u. (5.11 kJ/mol). This could be altered by substituting less bulky ligands or by linking the piperidine ligands to create a single bidentate ligand.

==Vibrational analysis of [Mo(CO)4(pip)2]==

[[Image:Reb_cisMocplx_IR.JPG|thumb|left|200|Predicted IR spectrum for Cis-[Mo(CO)4(pip)2]]] [[Image:Reb_transMocplx_IR.JPG|thumb|right|200|Predicted IR spectrum for Trans-[Mo(CO)4(pip)2]]]

Vibrations of [Mo(CO)4(pip)2] were then calculated from the previous models for both Cis {{DOI|10042/to-1976}} and Trans {{DOI|10042/to-1977}} forms of the complex producing the predicted spectra shown here.

=Mini Project=

==Dimerisation of the ruthenocenium ion==
[[Image:Ru-dimer.gif|thumb|left|200|Ruthenocene dimer equilibrium (Image taken from journal<ref name=prim><a href=http://pubs.acs.org/doi/full/10.1021/ic802105b>J.C. Swarts et. al., Inorg. Chem., Article ASAP, DOI: 10.1021/ic802105b, Publication Date (Web): January 26, 2009</a></ref>)]] J.C. Swarts et. al. <ref name=prim><a href=http://pubs.acs.org/doi/full/10.1021/ic802105b>J.C. Swarts et. al., Inorg. Chem., Article ASAP, DOI: 10.1021/ic802105b, Publication Date (Web): January 26, 2009</a></ref> observed that upon electrochemical oxidation of ruthenocene, [RuCp2], to Ruthenocenium, [RuCp2]+, the resultant complex tended to dimerize to a Ru-Ru linked dication '''2''' which converted reversibly with loss of dihydrogen to a Ru-Cp linked dication '''3''' upon heating.

In this mini project this thermal equilibrium will be investigated. Firstly to see if dication '''3''' is intrinsically thermodynamically favoured when the effects of solvent and coordinating anion are removed and secondly to see what effect changing the sustituents on the Cp rings has upon the position of the equilibrium.

All calculations use the B3LYP/LANL2MB method and basis set as the LANL2MB basis set, although more accurate, was thought too computationally demanding for a molecule of this size.

The unsubstituted dimers were calculated first with the following results:
{| border="1" cellpadding="5" cellspacing="0"
|-
|'''2'''
|'''3'''
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Ru_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Cp_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|{{DOI|10042/to-1996}}
|{{DOI|10042/to-1999}}
|-
|}

The energy difference between the two complexes was a extremely high 2034 kJ/mol. Although it is to be expected that the figure in solution would be altered this demonstrates that dication '''3''' is intrinsically much more stable than cation '''2''' which is supported experimentally by the rapid conversion of '''2''' to '''3''' once heated above the temperature of 243K at which it is synthesised.

This energy difference can be either increaced or reversed, so that the Ru-Ru linked dimer is thermodynamically prefered, by tuning the ring substituents. When analogus structures where the hydrogens of the Cp rings are replaced by highly electron withdrawing fluorines were calculated the results were as follows:
{| border="1" cellpadding="5" cellspacing="0"
|-
|[Ru2(η5C5F5)4]2+ (analogous to '''2''')
|[Ru2(η5C5F5)2(σ:η5C5F4)2]2+ (analogous to '''3''')
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Ru_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Cp_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|{{DOI|10042/to-1996}}
|{{DOI|10042/to-1999}}
|-
|}

Rep:Mod:noyjitat

2009-02-18T14:58:25Z

Reb06: /* Dimerisation of the ruthenocenium ion */

=Computational inorganic chemistry=

==BCl3==

A molecule of BCl3 was optimised using the B3LYP/3-21G method with the following results:
{| border="0" cellpadding="0" cellspacing="0"
|-
|Bond distance - 1.87 A
|-
|Bond angle - 120.0
|-
|File type - .log
|-
|Calculation type - FOPT
|-
|Calculation method - RB3LYP
|-
|Basis set - LANL2MB
|-
|Final energy - -69.439 a.u.
|-
|Dipole moment - 0.00 Deby
|-
|Point group - D3H
|-
|Calculation time - 11.0 seconds
|-
|}

==BF3==

This was repeated for BF3 with the following results:

Atomic positions (Angstroms)
{| border="1" cellpadding="3" cellspacing="3"
|-
|Centre Number
|Atomic Type
|X Coordinate
|Y Coordinate
|Z Coordinate
|-
|1
|C
|"0.000"
|"0.000"
|"0.000"
|-
|2
|F
|"0.000"
|"1.334"
|"0.000"
|-
|3
|F
|"1.155"
|"-0.667"
|"0.000"
|-
|4
|F
|"-1.155"
|"-0.667"
|"0.000"
|-
|}

{| border="0" cellpadding="0" cellspacing="0"
|-
|Bond distance - 1.33 A
|-
|Bond angle - 120.0
|-
|File type - .log
|-
|Calculation type - FOPT
|-
|Calculation method - RB3LYP
|-
|Basis set - LANL2MB
|-
|Final energy - -319.872 a.u.
|-
|Dipole moment - 0.00 Deby
|-
|Point group - D3H
|-
|Calculation time - 18.0 seconds
|-
|}

'''Upload log file'''

==BH3 vibrational analysis==

BH3 was optimised in the same manner as above and the vibrations were then calculated:
{| border="1" cellpadding="3" cellspacing="3"
|-
|No
|Form of the vibration
|Frequency
|Intensity
|Symmetry
(Dh3 point group)
|-
|1
|[[Image:Reb_BH3_vib_image1.JPG|thumb|left|200|Hydrogens all move in a concerted motion in the z direction. B atom is stationary.]]
|1145.71
|92.6991
|A'2
|-
|2
|[[Image:Reb BH3 vib image2.JPG|thumb|left|200|Two hydrogens move in a scissoring motion. Third hydrogen and B atom are stationary]]
|1204.66
|12.3789
|A'1
|-
|3
|[[Image:Reb BH3 vib image3.JPG|thumb|left|200|Hydrogen wagging motion. B atom is stationary]]
|1204.66
|12.3814
|E'
|-
|4
|[[Image:Reb_BH3_vib_image4.JPG|thumb|left|200|Hydrogens all move in and out in a concerted motion. B atom is stationary.]]
|2592.79
|0
|A'1
|-
|5
|[[Image:Reb_BH3_vib_image5.JPG|thumb|left|200|Two hydrogens move in and out alternately. Third hydrogen and B atom are stationary.]]
|2731.31
|103.837
|A'2
|-
|6
|[[Image:Reb_BH3_vib_image6.JPG|thumb|left|200|Two hydrogens move in and out in a concerted motion with the third hydrogen moving in and out in alternate motion. B atom is stationary.]]
|2731.31
|103.83
|A'2
|-
|}

[[Image:Reb BH3 vib spec.JPG|thumb|right|800|Computed IR spectrum for BH3]]

Giving the followng IR spectrum

==BH3 molecular orbitals==

[[Image:REB_BH3_MO.GIF|thumb|left|800|Qualitative MO diagram for BH3]] The molecular orbitals for BH3 can now be calculated by the same method as above and compared to the qualitative MO diagram.

{| border="1" cellpadding="3" cellspacing="3"
|-
|[[Image:Reb_BH3_mo_lumo+2.JPG|thumb|left|800|LUMO +2
(energy 0.188)]]
|[[Image:Reb_BH3_mo_lumo+1.JPG|thumb|left|800|LUMO +1
(energy 0.188)]]
|-
|[[Image:Reb_BH3_mo_lumo.JPG|thumb|left|800|LUMO
(energy -0.074)]]
|[[Image:Reb_BH3_mo_homo.JPG|thumb|left|800|HOMO
(energy -0.356)]]
|-
|[[Image:Reb_BH3_mo_homo-1.JPG|thumb|left|800|HOMO -1
(energy -0.356)]]
|[[Image:Reb_BH3_mo_homo-2.JPG|thumb|left|800|HOMO -2
(energy -0.517)]]
|-
|[[Image:Reb_BH3_mo_homo-3.JPG|thumb|left|800|HOMO -3
(energy -6.730)]]
|
|-
|}

There is good agreement between the occupied qualitative MOs and the occupied quantatative calculated MOs. The shapes are reasonable when compared to the linear combination of orbitals and the predicted degeneracies hold. The unoccupied orbitals however, show little agreement. The predicted LUMO for BH3 is a simple Pz orbital on the boron whereas the calculated LUMO is far more complex and presents a different symmetry making the predicted LUMO a very bad model. The quantative LUMO+1 and LUMO+2 levels are also given as degenerate, differing again from prediction.

==NH3==
Three versions of the NH3 molecule restrained to different symmetries were optimised using a 6-31G basis set and the B3LYP method. Summeries of these optisations are given below

{| border="1" cellpadding="3" cellspacing="3"
|-
|[[Image:Reb_nh3_summary2.JPG|thumb|left|200|]]
|[[Image:Reb_nh3_summary1.JPG|thumb|left|200|]]
|[[Image:Reb_nh3_summary3.JPG|thumb|left|200|]]
|-
|This model was optimised after setting one bond to 1.01 angstroms to restrain the molecule to C1 symmetry
|This model was optimised as a standard C3v symmetry NH3
|This model was optimised using a dummy atom to restrain the molecule to Dh3 symmetry
|-
|Bond lengths all 1.006 angstroms
Bond angles all 116 degrees
|Bond lengths 1.000, 1.000, 1.010 angstroms
Bond angles all 109 degrees
|Bond lengths all 0.998 angstroms
Bond angles all 120 degrees
|-
|Relative energy 4.95 kJ/mol
|Relative energy 0 kJ/mol
|Relative energy 4.05 kJ/mol
|-
|}

By changing the symmetry we change the structure of the optimised molecule in terms of both bond lengths and angles.
Time needed to optimise the geometry increaced with increacing degree of symmetry. This is due to the fact that the molecule cannot break symmetry at any stage of the optimization and so each step must be calculated to conform to the correct symmetry. This takes more time for a higher symmetry since it contains more symmetry elements which must be calculated. This indicates that calculations on molecules with very high symmetry (for example Oh) would be very time consuming indeed.
The lowest energy geometry was the C1 geometry, with the energy differences between the diffrent geometries given above. These differences represent the energy barrier to movement between differering geometries. This barrier is clearly small.

The C3V and D3H calculations were then repeated from scratch using the higher level MP2/6-311+G(d,p) method and basis set. These calculations took 33.0 sec and 1 min 35.0 sec respectively, an increace of around 20% on the calulation time for the B3LYP/6-31G calculation. The energy has also been reduced in the order of 0.1 a.u. giving an energy difference between D3H and C3V symmetries of 20.5 kJ/mol. Since the D3H symmetry represents the trasition state for inversion of ammonia this figure represents the barrier height to inversion and is in reasonable agreement with the experimental value of 24.3 kJ/mol.

==NH3 vibrational analysis==
[[Image:Reb_NH3_c3v_vib_spec.JPG|thumb|right|800|Computed IR spectrum for C3v NH3]] [[Image:Reb_NH3_d3h_vib_spec.JPG|thumb|left|800|Computed IR spectrum for Dh3 BH3]]The vibrations for NH3 were then calculated from the B3LYP/6-31G optimised structures of C3v and D3h symmetry. The IR spectra are seen here.

{| border="1" cellpadding="3" cellspacing="3"
|-
|Calculated frequency (D3h)/cm-1
|Calculated frequency (C3v)/cm-1
|Experimental frequency/cm-1
|-
|452
|"-318"
|950
|-
|1680
|1641
|1627
|-
|1680
|1641
|1627
|-
|3575
|3636
|3336
|-
|3776
|3854
|3414
|-
|3776
|3854
|3414
|-
|}

These results show the C3v structure to be the ground state since it has all positive frequencies. The D3h structure has a sigle negative frequency at -318 which shows it to be a transition state. The vibration at this frequency is the a'2 "umberella" like stretch and this is the vibration which follows the inversion reaction path.

==Cis-Trans isomerism of [Mo(CO)4(pip)2]==

Models of both the cis and trans forms of [Mo(CO)4(pip)2] (pip = NC5H10) were optimised initially to a loose convergence using the B3LYP/LANL2MB method and basis set and then to a increased convergence using the more accurate B3LYP/LANL2DZ method and basis set.

Cis-[Mo(CO)4(pip)2] {{DOI|10042/to-1972}}

<jmol><jmolApplet><title>Cis complex</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Reb_cisMo.mol‎</uploadedFileContents>
</jmolApplet></jmol>

Trans-[Mo(CO)4(pip)2] {{DOI|10042/to-1974}}

<jmol><jmolApplet><title>Trans complex</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Reb_transMocplx.mol</uploadedFileContents>
</jmolApplet></jmol>

The first obvious difference in the geometry of the two complexes is that the Trans complex is very close to perfect octohedral geometry at the Mo centre with a varience from the expected bond angles of 90 degrees of only 4 degrees in C-Mo-C and less than 1 degree in C-Mo-N. The trans complex also has equal Mo-L bond lengths of 2.06 angstroms for all ligands, both CO and pip. In the Cis complex however the steric bulk of the ligands has forced a large distortion in the expected octohedral geometry with an N-Mo-N bond angle of 110 degrees. Bond lengths are also no longer equal with the majority of the bonds shortened to ~2.05 angstroms and the Mo-C bonds Trans to the piperidine ligands lengthened to 2.08 and 2.09 angstroms. Mo-N bond lengths typically range between 2.45 and 2.06 angstroms <ref>Bart, J.C.J; Ragaini, V.; Acta Crystallogr. B, Struct. Crystallogr. Cryst. Chem., 1980, B36, 1351-4</ref> placing both complexs at the extreme lower end of the range and suggesting double bond character.
The Trans complex is the more thermodynamically favoured due to the strain described with an energy difference between conformations of 0.00194 a.u. (5.11 kJ/mol). This could be altered by substituting less bulky ligands or by linking the piperidine ligands to create a single bidentate ligand.

==Vibrational analysis of [Mo(CO)4(pip)2]==

[[Image:Reb_cisMocplx_IR.JPG|thumb|left|200|Predicted IR spectrum for Cis-[Mo(CO)4(pip)2]]] [[Image:Reb_transMocplx_IR.JPG|thumb|right|200|Predicted IR spectrum for Trans-[Mo(CO)4(pip)2]]]

Vibrations of [Mo(CO)4(pip)2] were then calculated from the previous models for both Cis {{DOI|10042/to-1976}} and Trans {{DOI|10042/to-1977}} forms of the complex producing the predicted spectra shown here.

=Mini Project=

==Dimerisation of the ruthenocenium ion==
[[Image:Ru-dimer.gif|thumb|left|200|Ruthenocene dimer equilibrium (Image taken from journal<ref name=prim><a href=http://pubs.acs.org/doi/full/10.1021/ic802105b>J.C. Swarts et. al., Inorg. Chem., Article ASAP, DOI: 10.1021/ic802105b, Publication Date (Web): January 26, 2009</a></ref>)]] J.C. Swarts et. al. <ref name=prim><a href=http://pubs.acs.org/doi/full/10.1021/ic802105b>J.C. Swarts et. al., Inorg. Chem., Article ASAP, DOI: 10.1021/ic802105b, Publication Date (Web): January 26, 2009</a></ref> observed that upon electrochemical oxidation of ruthenocene, [RuCp2], to Ruthenocenium, [RuCp2]+, the resultant complex tended to dimerize to a Ru-Ru linked dication '''2''' which converted reversibly with loss of dihydrogen to a Ru-Cp linked dication '''3''' upon heating.

In this mini project this thermal equilibrium will be investigated. Firstly to see if dication '''3''' is intrinsically thermodynamically favoured when the effects of solvent and coordinating anion are removed and secondly to see what effect changing the sustituents on the Cp rings has upon the position of the equilibrium.

All calculations use the B3LYP/LANL2MB method and basis set as the LANL2MB basis set, although more accurate, was thought too computationally demanding for a molecule of this size.

The unsubstituted dimers were calculated first with the following results
{| border="1" cellpadding="5" cellspacing="0"
|-
|'''2'''
|'''3'''
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Ru_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<script>cpk -25;</script>
<uploadedFileContents>Reb_Ru-Cp_opt1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|{{DOI|10042/to-1996}}
|{{DOI|10042/to-1999}}
|-
|}

Rep:Mod:noyjitat

2009-02-18T14:56:57Z

2009-02-18T13:58:45Z

Reb06: /* Vibrational analysis of [Mo(CO)4(pip)2] */