File:DmongMO42chemdraw.png

2019-05-24T14:44:19Z

Dm1417:

File:DmongMO40chemdraw3.png

2019-05-24T14:44:04Z

Dm1417:

Rep:Mod:dariomong01351899MO

2019-05-24T11:39:28Z

Dm1417: /* [Cr(CO)6] analysis */

== '''BH3 molecule''' ==

'''3-21G optimisation'''

[[File:DmongBH3321goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.

[[File:DmongBH3321ggraphs.jpg]]

The optimisation file is linked [[Media:DMONGBH3OPT.LOG| here]].

'''6-21G optimisation'''

[[File:DmongBH3621goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128957D-09
Optimization completed.
-- Stationary point found.

The molecule was then constrained to a D3h symmetry and then optimised again by 6-21G.

[[File: DmongBH3621gd3hoptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-1.240669D-09
Optimization completed.
-- Stationary point found.

'''Frequency analysis of BH3'''

[[File:DmongBH3621gbfreqoptdata.jpg]]

'''Low frequencies --- -15.9849 -15.9818 -12.7207 0.0007 0.0143 0.3137'''
'''Low frequencies --- 1162.9365 1213.1134 1213.1136'''
Diagonal vibrational polarizability:
0.7178921 0.7178603 1.8420487
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9365 1213.1134 1213.1136
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9985 0.9600 0.9600
IR Inten -- 92.5721 14.0532 14.0527
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.7141 2715.8636 2715.8645
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9608 4.8992 4.8992
IR Inten -- 0.0000 126.3274 126.3214
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
4 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00

The optimised molecule can be found [[Media:DMONGBH3OPT631GB.LOG| here]]

'''Jmol of optimised BH3 molecule'''
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGBH3OPT631GB.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Infrared Spectrum of BH3'''
[[File:DmongBH3621gbfreqvibr.jpg|700x700px]]

{| class="wikitable" border="1"
|+ Infrared Spectrum Vibrations
! Vibrational frequency (cm-1) !! Intensity (dimensionless) !! Symmetry !! IR Active !! Type !
|-
| 1163 || 93 || A2" || Yes || symmetric bend (wagging)
|-
| 1213 || 14 || E' || Yes || antisymmetric bend (rocking)
|-
| 1213 || 14 || E' || Yes || symmetric bend (scissoring)
|-
| 2583 || 0 || A1' || No || symmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|}

Despite showing 6 vibrational modes, only 3 appear in the actual spectrum. There are two sets of degenerate vibrational modes at 1213cm-1 and 2716cm-1 respectively, which only appear in the spectrum as one peak respectively.In addition to this, the vibration at 2583cm-1 is not IR active as its vibrational mode does not incur a change in dipole moment as each H atom stretches out from the central B atom in a symmetrical fashion, as seen below.

[[File:Dariomongnoniractivemodeofbh3.jpg|300x300px]]

'''Molecular Orbital diagram of BH3'''

[[File:DmongBH3MOdiagram.jpg]]
''T.Hunt, 2018,Figure 5,Problem class 1: the MO diagram of BH3,''
''Molecular Orbitals in Inorganic Chemistry, Imperial College London, delivered November'' ''2018.''

There are no significant differences between the computed MOs and the LCAO derived MOs. For the most part LCAO is a reliable model for showing the MOs of a molecule, however there are certain aspects it fails to capture, such as the overlap of orbitals from the same fragment (see a1'). Electronic distribution is key to understanding reactivity of molecules, which is why LCAO is good for MO diagrams but less effective for more complex cases.

=='''NH3 molecule'''==

[[File:DmongNH3631goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843977D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !

Low frequencies --- -0.0137 -0.0027 0.0007 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

=='''NH3BH3'''==

[[File:DmongNH3BH3631goptdataNEW.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.656419D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,8) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,8) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,7) 1.21 -DE/DX = -0.0001 !
! R5 R(5,7) 1.21 -DE/DX = -0.0001 !
! R6 R(6,7) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 113.8746 -DE/DX = 0.0 !
! A2 A(4,7,6) 113.8746 -DE/DX = 0.0 !
! A3 A(4,7,8) 104.5965 -DE/DX = 0.0 !
! A4 A(5,7,6) 113.8746 -DE/DX = 0.0 !
! A5 A(5,7,8) 104.5965 -DE/DX = 0.0 !
! A6 A(6,7,8) 104.5965 -DE/DX = 0.0 !
! A7 A(1,8,2) 107.8683 -DE/DX = 0.0 !
! A8 A(1,8,3) 107.8683 -DE/DX = 0.0 !
! A9 A(1,8,7) 111.0301 -DE/DX = 0.0 !
! A10 A(2,8,3) 107.8683 -DE/DX = 0.0 !
! A11 A(2,8,7) 111.0301 -DE/DX = 0.0 !
! A12 A(3,8,7) 111.0301 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 180.0 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 60.0 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 60.0 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 180.0 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0 -DE/DX = 0.0 !
! D8 D(6,7,8,2) 180.0 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0 -DE/DX = 0.0 !

Low frequencies --- -0.0251 -0.0029 0.0014 17.1170 17.1195 37.1145
Low frequencies --- 265.7734 632.2034 639.3448

'''NH3BH3 bond energy'''

{| class="wikitable" border="1"
|+ Energies
! Molecule !! Energy (atomic units)
|-
| NH3 || -56.56
|-
| BH3 || -26.62
|-
| NH3BH3 || -83.22
|}

(error associated with energy is 5 kjmol-1, which corresponds to 0.002 au, so calculations are given to 2dp)

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-83.22-(-56.56-26.62)
=-83.22 + 83.18
=-0.04 au
=-105.02 kjmol-1

A value of -105.02 kjmol-1 indicates an exothermic process as the overall energy change is negative, meaning that the process gives products which are more thermodynamically stable than the reactants. Comparing to a C-C bond in ethane which has an energy of formation of 346 kjmol-1, and the C-N bond in methylamine which has an energy of formation of 360 kjmol-1, we can ascertain that the dative covalent bond formed is quite weak relative to commonplace bonds in chemistry.

=='''NI3 molecule'''==

The optimised molecule can be found [[Media:DMONGNI3OPTFREQATT3.LOG| here]]

'''Jmol'''
<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGNI3OPTFREQATT3.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -12.3845 -12.3781 -5.6129 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2332

Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000630 0.001200 YES
Predicted change in Energy=-1.193062D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1842 -DE/DX = -0.0001 !
! R2 R(1,3) 2.1842 -DE/DX = -0.0001 !
! R3 R(1,4) 2.1842 -DE/DX = -0.0001 !
! A1 A(2,1,3) 110.8579 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8579 -DE/DX = -0.0001 !
! A3 A(3,1,4) 110.8579 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) -123.5674 -DE/DX = 0.0001 !

N-I bond lengthː 2.184 angstroms

=='''Mini-project: Metal Carbonyls'''==

for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

I am looking for comments and annotations:

indicating directly bonded vs through space interactions
the distance dependence ie weak vs medium vs strong interactions
discussion of polarized or directed interactions
mention of s,p or d relative intensity of overlap
the nodal character, on atoms is less antibonding than between atoms
AND a clean tidy diagram that is well annotated

In this mini-project I will be comparing the vibrational frequencies and bond lengths in three metal carbonyl complexesː [Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]. I will run optimisations on each of the structures and determine the bond lengths, and then will run frequency analysis on each of these optimised structures to give the vibrational frequencies.

The strength of the C=O is related to the extent of backbonding from the metal to the pi* star orbital of C=O - "increased electron density in the 2pi* orbital of the C=O molecule leads to a lower C-O bond order (and hence longer & weaker bond)" - see diagram below.

[[File:Dmongbackbondingdiag.jpg]]

Theory allows for prediction of the extent of backbonding, which will then be compared to the vibrational frequencies given from frequency analysis - the stretching frequencies of the C=O bond can be correlated to the bond strength, as given by the equation w = h/2pi x (kf/meff)^0.5, which shows that the fundamental frequency w is directly proportional to the spring constant kf which is effectively the bond strength. My prediction of which complex has the highest vibrational frequencies for C=O will be compared to the actual values from the frequency analysis and analysed for any discrepancies.

As shown above, theory predicts that the increased backbonding will incur a decrease in bond order of the C=O bond, and hence a longer bond. My prediction of which complex has the longest C=O bond will be compared to the actual bond lengths from the optimised molecule.

'''Predictions'''

The complexes I will be analysing are very similiar - they are all isoelectronic with d6 occupancy of the metal, have identical ligands (carbonyl - strong field) and are all low spin complexes with 18 electrons total. This means the only parameter which is different across the three is the charge on the metal, which since we're using neutral ligands is simply its oxidation state.

Theory provides a relationship between charge on a metal and the extent of backbonding; "Increasing negative charge leads to the expansion of d-orbitals, therefore greater overlap of M(dpi) with CO pi* / increased backbonding" - see diagram below.

[[File:Dmongcarbonylmetalcharge.jpg]]

In the three complexes I will be analysing ([Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]), the charges are as follows: Ti(2-), V(-1) and Cr(0). Given the order of magnitude of charge being Ti > V > Cr, and the theory stated previously, the predictions for vibrational frequencies and bond lengths are as follows:

Vibrational frequencies: Cr > V > Ti
Bond length of C=O: Ti > V > Cr

==='''[Ti(CO)6]2- analysis'''===

The molecule was first optimised and then frequency analysis was performed.

The link to the frequency file can be found [[Media:DMONGTIGEN.LOG| here]].

[[File:DmongTigenoptdata.jpg]]

Low frequencies --- -0.0010 -0.0004 0.0002 13.1492 13.1492 13.1492
Low frequencies --- 29.8870 29.8870 29.8870

Item Value Threshold Converged?
Maximum Force 0.000247 0.000450 YES
RMS Force 0.000086 0.000300 YES
Maximum Displacement 0.000128 0.001800 YES
RMS Displacement 0.000061 0.001200 YES
Predicted change in Energy=-1.882613D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1833 -DE/DX = 0.0002 !
! R2 R(1,13) 2.0467 -DE/DX = 0.0 !
! R3 R(3,4) 1.1833 -DE/DX = 0.0002 !
! R4 R(3,13) 2.0467 -DE/DX = 0.0 !
! R5 R(5,6) 1.1833 -DE/DX = 0.0002 !
! R6 R(5,13) 2.0467 -DE/DX = 0.0 !
! R7 R(7,8) 1.1833 -DE/DX = 0.0002 !
! R8 R(7,13) 2.0467 -DE/DX = 0.0 !
! R9 R(9,10) 1.1833 -DE/DX = 0.0002 !
! R10 R(9,13) 2.0467 -DE/DX = 0.0 !
! R11 R(11,12) 1.1833 -DE/DX = 0.0002 !
! R12 R(11,13) 2.0467 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for the C=O bond in this complex was found to be 1.18330 angstroms.

'''Vibrational Analysis'''

[[File:DmongTigenfreqdata.jpg]]

Here we can see two distinct peaks in the IR spectrum despite there being 33 unique vibrational modes. The vast majority of these peaks do not have a large enough intensity to be visible in IR. The two peaks lie at 639.19cm-1 and 1856.22cm-1. The peak at 639.19cm-1 represents the bending modes of the IR spectrum - there are 3 degenerate modes which have equal intensity and incur a change in dipole moment.
At 1856.22cm-1 there is a peak for stretching mode of the molecule, which has three degenerate modes of equal intensity. This indicates the extent of pi backbonding as discussed previously and will be compared against the other molecules.

==='''[V(CO)6]- analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGVGEN.LOG| here]].

[[File:DmongVgenoptdata.jpg]]

Low frequencies --- 0.0006 0.0006 0.0011 14.1311 14.1311 14.1311
Low frequencies --- 52.8916 52.8916 52.8916

Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000070 0.000300 YES
Maximum Displacement 0.001210 0.001800 YES
RMS Displacement 0.000591 0.001200 YES
Predicted change in Energy=-7.154807D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9542 -DE/DX = -0.0002 !
! R2 R(1,4) 1.9542 -DE/DX = -0.0002 !
! R3 R(1,6) 1.9542 -DE/DX = -0.0002 !
! R4 R(1,8) 1.9542 -DE/DX = -0.0002 !
! R5 R(1,10) 1.9542 -DE/DX = -0.0002 !
! R6 R(1,12) 1.9542 -DE/DX = -0.0002 !
! R7 R(2,3) 1.166 -DE/DX = 0.0 !
! R8 R(4,5) 1.166 -DE/DX = 0.0 !
! R9 R(6,7) 1.166 -DE/DX = 0.0 !
! R10 R(8,9) 1.166 -DE/DX = 0.0 !
! R11 R(10,11) 1.166 -DE/DX = 0.0 !
! R12 R(12,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,10) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,12) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,10,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,12,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) -90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,10,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,12,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The C=O bond length in this complex was found to be 1.16599 angstroms.

'''Vibrational Analysis'''

[[File:DmongVgenfreqdata.jpg]]

There are 2 distinct peaks in the IR spcetrum, similarly to the Ti complex. The larger peak is at 1968.91cm-1, and represents the C=O stretching mode. The lesser peak is at 689.44cm-1, and represents the bending mode of the complex. The other modes present are not intense enough to be visible on an IR spectrum.

==='''[Cr(CO)6] analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGCRGEN.LOG| here]].

[[File:DmongCrgenoptdata.jpg]]

Low frequencies --- -0.0012 -0.0011 -0.0011 10.3820 10.3820 10.3820
Low frequencies --- 66.4094 66.4094 66.4094

Item Value Threshold Converged?
Maximum Force 0.000154 0.000450 YES
RMS Force 0.000055 0.000300 YES
Maximum Displacement 0.000386 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.123831D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1494 -DE/DX = 0.0002 !
! R2 R(1,13) 1.9149 -DE/DX = 0.0 !
! R3 R(3,4) 1.1494 -DE/DX = 0.0002 !
! R4 R(3,13) 1.9149 -DE/DX = 0.0 !
! R5 R(5,6) 1.1494 -DE/DX = 0.0002 !
! R6 R(5,13) 1.9149 -DE/DX = 0.0 !
! R7 R(7,8) 1.1494 -DE/DX = 0.0002 !
! R8 R(7,13) 1.9149 -DE/DX = 0.0 !
! R9 R(9,10) 1.1494 -DE/DX = 0.0002 !
! R10 R(9,13) 1.9149 -DE/DX = 0.0 !
! R11 R(11,12) 1.1494 -DE/DX = 0.0002 !
! R12 R(11,13) 1.9149 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for C=O in this complex was found to be 1.14938 angstroms.

'''Vibrational Analysis'''

[[File:DmongCrgenfreqdata.jpg]]

'''MO analysis'''

[[File:DmongMO40.jpg]]
MO 40

[[File:DmongMO42.jpg]]
MO 42

[[File:DmongMO47.jpg]]
MO 47

Rep:Mod:dariomong01351899MO

2019-05-24T11:38:47Z

Dm1417:

== '''BH3 molecule''' ==

'''3-21G optimisation'''

[[File:DmongBH3321goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.

[[File:DmongBH3321ggraphs.jpg]]

The optimisation file is linked [[Media:DMONGBH3OPT.LOG| here]].

'''6-21G optimisation'''

[[File:DmongBH3621goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128957D-09
Optimization completed.
-- Stationary point found.

The molecule was then constrained to a D3h symmetry and then optimised again by 6-21G.

[[File: DmongBH3621gd3hoptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-1.240669D-09
Optimization completed.
-- Stationary point found.

'''Frequency analysis of BH3'''

[[File:DmongBH3621gbfreqoptdata.jpg]]

'''Low frequencies --- -15.9849 -15.9818 -12.7207 0.0007 0.0143 0.3137'''
'''Low frequencies --- 1162.9365 1213.1134 1213.1136'''
Diagonal vibrational polarizability:
0.7178921 0.7178603 1.8420487
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9365 1213.1134 1213.1136
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9985 0.9600 0.9600
IR Inten -- 92.5721 14.0532 14.0527
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.7141 2715.8636 2715.8645
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9608 4.8992 4.8992
IR Inten -- 0.0000 126.3274 126.3214
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
4 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00

The optimised molecule can be found [[Media:DMONGBH3OPT631GB.LOG| here]]

'''Jmol of optimised BH3 molecule'''
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGBH3OPT631GB.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Infrared Spectrum of BH3'''
[[File:DmongBH3621gbfreqvibr.jpg|700x700px]]

{| class="wikitable" border="1"
|+ Infrared Spectrum Vibrations
! Vibrational frequency (cm-1) !! Intensity (dimensionless) !! Symmetry !! IR Active !! Type !
|-
| 1163 || 93 || A2" || Yes || symmetric bend (wagging)
|-
| 1213 || 14 || E' || Yes || antisymmetric bend (rocking)
|-
| 1213 || 14 || E' || Yes || symmetric bend (scissoring)
|-
| 2583 || 0 || A1' || No || symmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|}

Despite showing 6 vibrational modes, only 3 appear in the actual spectrum. There are two sets of degenerate vibrational modes at 1213cm-1 and 2716cm-1 respectively, which only appear in the spectrum as one peak respectively.In addition to this, the vibration at 2583cm-1 is not IR active as its vibrational mode does not incur a change in dipole moment as each H atom stretches out from the central B atom in a symmetrical fashion, as seen below.

[[File:Dariomongnoniractivemodeofbh3.jpg|300x300px]]

'''Molecular Orbital diagram of BH3'''

[[File:DmongBH3MOdiagram.jpg]]
''T.Hunt, 2018,Figure 5,Problem class 1: the MO diagram of BH3,''
''Molecular Orbitals in Inorganic Chemistry, Imperial College London, delivered November'' ''2018.''

There are no significant differences between the computed MOs and the LCAO derived MOs. For the most part LCAO is a reliable model for showing the MOs of a molecule, however there are certain aspects it fails to capture, such as the overlap of orbitals from the same fragment (see a1'). Electronic distribution is key to understanding reactivity of molecules, which is why LCAO is good for MO diagrams but less effective for more complex cases.

=='''NH3 molecule'''==

[[File:DmongNH3631goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843977D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !

Low frequencies --- -0.0137 -0.0027 0.0007 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

=='''NH3BH3'''==

[[File:DmongNH3BH3631goptdataNEW.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.656419D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,8) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,8) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,7) 1.21 -DE/DX = -0.0001 !
! R5 R(5,7) 1.21 -DE/DX = -0.0001 !
! R6 R(6,7) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 113.8746 -DE/DX = 0.0 !
! A2 A(4,7,6) 113.8746 -DE/DX = 0.0 !
! A3 A(4,7,8) 104.5965 -DE/DX = 0.0 !
! A4 A(5,7,6) 113.8746 -DE/DX = 0.0 !
! A5 A(5,7,8) 104.5965 -DE/DX = 0.0 !
! A6 A(6,7,8) 104.5965 -DE/DX = 0.0 !
! A7 A(1,8,2) 107.8683 -DE/DX = 0.0 !
! A8 A(1,8,3) 107.8683 -DE/DX = 0.0 !
! A9 A(1,8,7) 111.0301 -DE/DX = 0.0 !
! A10 A(2,8,3) 107.8683 -DE/DX = 0.0 !
! A11 A(2,8,7) 111.0301 -DE/DX = 0.0 !
! A12 A(3,8,7) 111.0301 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 180.0 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 60.0 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 60.0 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 180.0 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0 -DE/DX = 0.0 !
! D8 D(6,7,8,2) 180.0 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0 -DE/DX = 0.0 !

Low frequencies --- -0.0251 -0.0029 0.0014 17.1170 17.1195 37.1145
Low frequencies --- 265.7734 632.2034 639.3448

'''NH3BH3 bond energy'''

{| class="wikitable" border="1"
|+ Energies
! Molecule !! Energy (atomic units)
|-
| NH3 || -56.56
|-
| BH3 || -26.62
|-
| NH3BH3 || -83.22
|}

(error associated with energy is 5 kjmol-1, which corresponds to 0.002 au, so calculations are given to 2dp)

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-83.22-(-56.56-26.62)
=-83.22 + 83.18
=-0.04 au
=-105.02 kjmol-1

A value of -105.02 kjmol-1 indicates an exothermic process as the overall energy change is negative, meaning that the process gives products which are more thermodynamically stable than the reactants. Comparing to a C-C bond in ethane which has an energy of formation of 346 kjmol-1, and the C-N bond in methylamine which has an energy of formation of 360 kjmol-1, we can ascertain that the dative covalent bond formed is quite weak relative to commonplace bonds in chemistry.

=='''NI3 molecule'''==

The optimised molecule can be found [[Media:DMONGNI3OPTFREQATT3.LOG| here]]

'''Jmol'''
<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGNI3OPTFREQATT3.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -12.3845 -12.3781 -5.6129 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2332

Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000630 0.001200 YES
Predicted change in Energy=-1.193062D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1842 -DE/DX = -0.0001 !
! R2 R(1,3) 2.1842 -DE/DX = -0.0001 !
! R3 R(1,4) 2.1842 -DE/DX = -0.0001 !
! A1 A(2,1,3) 110.8579 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8579 -DE/DX = -0.0001 !
! A3 A(3,1,4) 110.8579 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) -123.5674 -DE/DX = 0.0001 !

N-I bond lengthː 2.184 angstroms

=='''Mini-project: Metal Carbonyls'''==

for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

I am looking for comments and annotations:

indicating directly bonded vs through space interactions
the distance dependence ie weak vs medium vs strong interactions
discussion of polarized or directed interactions
mention of s,p or d relative intensity of overlap
the nodal character, on atoms is less antibonding than between atoms
AND a clean tidy diagram that is well annotated

In this mini-project I will be comparing the vibrational frequencies and bond lengths in three metal carbonyl complexesː [Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]. I will run optimisations on each of the structures and determine the bond lengths, and then will run frequency analysis on each of these optimised structures to give the vibrational frequencies.

The strength of the C=O is related to the extent of backbonding from the metal to the pi* star orbital of C=O - "increased electron density in the 2pi* orbital of the C=O molecule leads to a lower C-O bond order (and hence longer & weaker bond)" - see diagram below.

[[File:Dmongbackbondingdiag.jpg]]

Theory allows for prediction of the extent of backbonding, which will then be compared to the vibrational frequencies given from frequency analysis - the stretching frequencies of the C=O bond can be correlated to the bond strength, as given by the equation w = h/2pi x (kf/meff)^0.5, which shows that the fundamental frequency w is directly proportional to the spring constant kf which is effectively the bond strength. My prediction of which complex has the highest vibrational frequencies for C=O will be compared to the actual values from the frequency analysis and analysed for any discrepancies.

As shown above, theory predicts that the increased backbonding will incur a decrease in bond order of the C=O bond, and hence a longer bond. My prediction of which complex has the longest C=O bond will be compared to the actual bond lengths from the optimised molecule.

'''Predictions'''

The complexes I will be analysing are very similiar - they are all isoelectronic with d6 occupancy of the metal, have identical ligands (carbonyl - strong field) and are all low spin complexes with 18 electrons total. This means the only parameter which is different across the three is the charge on the metal, which since we're using neutral ligands is simply its oxidation state.

Theory provides a relationship between charge on a metal and the extent of backbonding; "Increasing negative charge leads to the expansion of d-orbitals, therefore greater overlap of M(dpi) with CO pi* / increased backbonding" - see diagram below.

[[File:Dmongcarbonylmetalcharge.jpg]]

In the three complexes I will be analysing ([Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]), the charges are as follows: Ti(2-), V(-1) and Cr(0). Given the order of magnitude of charge being Ti > V > Cr, and the theory stated previously, the predictions for vibrational frequencies and bond lengths are as follows:

Vibrational frequencies: Cr > V > Ti
Bond length of C=O: Ti > V > Cr

==='''[Ti(CO)6]2- analysis'''===

The molecule was first optimised and then frequency analysis was performed.

The link to the frequency file can be found [[Media:DMONGTIGEN.LOG| here]].

[[File:DmongTigenoptdata.jpg]]

Low frequencies --- -0.0010 -0.0004 0.0002 13.1492 13.1492 13.1492
Low frequencies --- 29.8870 29.8870 29.8870

Item Value Threshold Converged?
Maximum Force 0.000247 0.000450 YES
RMS Force 0.000086 0.000300 YES
Maximum Displacement 0.000128 0.001800 YES
RMS Displacement 0.000061 0.001200 YES
Predicted change in Energy=-1.882613D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1833 -DE/DX = 0.0002 !
! R2 R(1,13) 2.0467 -DE/DX = 0.0 !
! R3 R(3,4) 1.1833 -DE/DX = 0.0002 !
! R4 R(3,13) 2.0467 -DE/DX = 0.0 !
! R5 R(5,6) 1.1833 -DE/DX = 0.0002 !
! R6 R(5,13) 2.0467 -DE/DX = 0.0 !
! R7 R(7,8) 1.1833 -DE/DX = 0.0002 !
! R8 R(7,13) 2.0467 -DE/DX = 0.0 !
! R9 R(9,10) 1.1833 -DE/DX = 0.0002 !
! R10 R(9,13) 2.0467 -DE/DX = 0.0 !
! R11 R(11,12) 1.1833 -DE/DX = 0.0002 !
! R12 R(11,13) 2.0467 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for the C=O bond in this complex was found to be 1.18330 angstroms.

'''Vibrational Analysis'''

[[File:DmongTigenfreqdata.jpg]]

Here we can see two distinct peaks in the IR spectrum despite there being 33 unique vibrational modes. The vast majority of these peaks do not have a large enough intensity to be visible in IR. The two peaks lie at 639.19cm-1 and 1856.22cm-1. The peak at 639.19cm-1 represents the bending modes of the IR spectrum - there are 3 degenerate modes which have equal intensity and incur a change in dipole moment.
At 1856.22cm-1 there is a peak for stretching mode of the molecule, which has three degenerate modes of equal intensity. This indicates the extent of pi backbonding as discussed previously and will be compared against the other molecules.

==='''[V(CO)6]- analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGVGEN.LOG| here]].

[[File:DmongVgenoptdata.jpg]]

Low frequencies --- 0.0006 0.0006 0.0011 14.1311 14.1311 14.1311
Low frequencies --- 52.8916 52.8916 52.8916

Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000070 0.000300 YES
Maximum Displacement 0.001210 0.001800 YES
RMS Displacement 0.000591 0.001200 YES
Predicted change in Energy=-7.154807D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9542 -DE/DX = -0.0002 !
! R2 R(1,4) 1.9542 -DE/DX = -0.0002 !
! R3 R(1,6) 1.9542 -DE/DX = -0.0002 !
! R4 R(1,8) 1.9542 -DE/DX = -0.0002 !
! R5 R(1,10) 1.9542 -DE/DX = -0.0002 !
! R6 R(1,12) 1.9542 -DE/DX = -0.0002 !
! R7 R(2,3) 1.166 -DE/DX = 0.0 !
! R8 R(4,5) 1.166 -DE/DX = 0.0 !
! R9 R(6,7) 1.166 -DE/DX = 0.0 !
! R10 R(8,9) 1.166 -DE/DX = 0.0 !
! R11 R(10,11) 1.166 -DE/DX = 0.0 !
! R12 R(12,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,10) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,12) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,10,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,12,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) -90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,10,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,12,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The C=O bond length in this complex was found to be 1.16599 angstroms.

'''Vibrational Analysis'''

[[File:DmongVgenfreqdata.jpg]]

There are 2 distinct peaks in the IR spcetrum, similarly to the Ti complex. The larger peak is at 1968.91cm-1, and represents the C=O stretching mode. The lesser peak is at 689.44cm-1, and represents the bending mode of the complex. The other modes present are not intense enough to be visible on an IR spectrum.

==='''[Cr(CO)6] analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGCRGEN.LOG| here]].

[[File:DmongCrgenoptdata.jpg]]

Low frequencies --- -0.0012 -0.0011 -0.0011 10.3820 10.3820 10.3820
Low frequencies --- 66.4094 66.4094 66.4094

Item Value Threshold Converged?
Maximum Force 0.000154 0.000450 YES
RMS Force 0.000055 0.000300 YES
Maximum Displacement 0.000386 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.123831D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1494 -DE/DX = 0.0002 !
! R2 R(1,13) 1.9149 -DE/DX = 0.0 !
! R3 R(3,4) 1.1494 -DE/DX = 0.0002 !
! R4 R(3,13) 1.9149 -DE/DX = 0.0 !
! R5 R(5,6) 1.1494 -DE/DX = 0.0002 !
! R6 R(5,13) 1.9149 -DE/DX = 0.0 !
! R7 R(7,8) 1.1494 -DE/DX = 0.0002 !
! R8 R(7,13) 1.9149 -DE/DX = 0.0 !
! R9 R(9,10) 1.1494 -DE/DX = 0.0002 !
! R10 R(9,13) 1.9149 -DE/DX = 0.0 !
! R11 R(11,12) 1.1494 -DE/DX = 0.0002 !
! R12 R(11,13) 1.9149 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for C=O in this complex was found to be 1.14938 angstroms.

'''Vibrational Analysis'''

[[File:DmongCrgenfreqdata.jpg]]

'''MO analysis'''

[[File:DmongMO40.jpg]]
[[File:DmongMO42.jpg]]
[[File:DmongMO47.jpg]]

File:DmongMO47.jpg

2019-05-24T11:37:59Z

Dm1417:

File:DmongMO42.jpg

2019-05-24T11:37:48Z

Dm1417:

File:DmongMO40.jpg

2019-05-24T11:37:29Z

Dm1417:

Rep:Mod:dariomong01351899MO

2019-05-23T18:14:42Z

Dm1417:

== '''BH3 molecule''' ==

'''3-21G optimisation'''

[[File:DmongBH3321goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.

[[File:DmongBH3321ggraphs.jpg]]

The optimisation file is linked [[Media:DMONGBH3OPT.LOG| here]].

'''6-21G optimisation'''

[[File:DmongBH3621goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128957D-09
Optimization completed.
-- Stationary point found.

The molecule was then constrained to a D3h symmetry and then optimised again by 6-21G.

[[File: DmongBH3621gd3hoptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-1.240669D-09
Optimization completed.
-- Stationary point found.

'''Frequency analysis of BH3'''

[[File:DmongBH3621gbfreqoptdata.jpg]]

'''Low frequencies --- -15.9849 -15.9818 -12.7207 0.0007 0.0143 0.3137'''
'''Low frequencies --- 1162.9365 1213.1134 1213.1136'''
Diagonal vibrational polarizability:
0.7178921 0.7178603 1.8420487
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9365 1213.1134 1213.1136
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9985 0.9600 0.9600
IR Inten -- 92.5721 14.0532 14.0527
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.7141 2715.8636 2715.8645
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9608 4.8992 4.8992
IR Inten -- 0.0000 126.3274 126.3214
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
4 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00

The optimised molecule can be found [[Media:DMONGBH3OPT631GB.LOG| here]]

'''Jmol of optimised BH3 molecule'''
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGBH3OPT631GB.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Infrared Spectrum of BH3'''
[[File:DmongBH3621gbfreqvibr.jpg|700x700px]]

{| class="wikitable" border="1"
|+ Infrared Spectrum Vibrations
! Vibrational frequency (cm-1) !! Intensity (dimensionless) !! Symmetry !! IR Active !! Type !
|-
| 1163 || 93 || A2" || Yes || symmetric bend (wagging)
|-
| 1213 || 14 || E' || Yes || antisymmetric bend (rocking)
|-
| 1213 || 14 || E' || Yes || symmetric bend (scissoring)
|-
| 2583 || 0 || A1' || No || symmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|}

Despite showing 6 vibrational modes, only 3 appear in the actual spectrum. There are two sets of degenerate vibrational modes at 1213cm-1 and 2716cm-1 respectively, which only appear in the spectrum as one peak respectively.In addition to this, the vibration at 2583cm-1 is not IR active as its vibrational mode does not incur a change in dipole moment as each H atom stretches out from the central B atom in a symmetrical fashion, as seen below.

[[File:Dariomongnoniractivemodeofbh3.jpg|300x300px]]

'''Molecular Orbital diagram of BH3'''

[[File:DmongBH3MOdiagram.jpg]]
''T.Hunt, 2018,Figure 5,Problem class 1: the MO diagram of BH3,''
''Molecular Orbitals in Inorganic Chemistry, Imperial College London, delivered November'' ''2018.''

There are no significant differences between the computed MOs and the LCAO derived MOs. For the most part LCAO is a reliable model for showing the MOs of a molecule, however there are certain aspects it fails to capture, such as the overlap of orbitals from the same fragment (see a1'). Electronic distribution is key to understanding reactivity of molecules, which is why LCAO is good for MO diagrams but less effective for more complex cases.

=='''NH3 molecule'''==

[[File:DmongNH3631goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843977D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !

Low frequencies --- -0.0137 -0.0027 0.0007 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

=='''NH3BH3'''==

[[File:DmongNH3BH3631goptdataNEW.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.656419D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,8) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,8) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,7) 1.21 -DE/DX = -0.0001 !
! R5 R(5,7) 1.21 -DE/DX = -0.0001 !
! R6 R(6,7) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 113.8746 -DE/DX = 0.0 !
! A2 A(4,7,6) 113.8746 -DE/DX = 0.0 !
! A3 A(4,7,8) 104.5965 -DE/DX = 0.0 !
! A4 A(5,7,6) 113.8746 -DE/DX = 0.0 !
! A5 A(5,7,8) 104.5965 -DE/DX = 0.0 !
! A6 A(6,7,8) 104.5965 -DE/DX = 0.0 !
! A7 A(1,8,2) 107.8683 -DE/DX = 0.0 !
! A8 A(1,8,3) 107.8683 -DE/DX = 0.0 !
! A9 A(1,8,7) 111.0301 -DE/DX = 0.0 !
! A10 A(2,8,3) 107.8683 -DE/DX = 0.0 !
! A11 A(2,8,7) 111.0301 -DE/DX = 0.0 !
! A12 A(3,8,7) 111.0301 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 180.0 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 60.0 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 60.0 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 180.0 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0 -DE/DX = 0.0 !
! D8 D(6,7,8,2) 180.0 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0 -DE/DX = 0.0 !

Low frequencies --- -0.0251 -0.0029 0.0014 17.1170 17.1195 37.1145
Low frequencies --- 265.7734 632.2034 639.3448

'''NH3BH3 bond energy'''

{| class="wikitable" border="1"
|+ Energies
! Molecule !! Energy (atomic units)
|-
| NH3 || -56.56
|-
| BH3 || -26.62
|-
| NH3BH3 || -83.22
|}

(error associated with energy is 5 kjmol-1, which corresponds to 0.002 au, so calculations are given to 2dp)

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-83.22-(-56.56-26.62)
=-83.22 + 83.18
=-0.04 au
=-105.02 kjmol-1

A value of -105.02 kjmol-1 indicates an exothermic process as the overall energy change is negative, meaning that the process gives products which are more thermodynamically stable than the reactants. Comparing to a C-C bond in ethane which has an energy of formation of 346 kjmol-1, and the C-N bond in methylamine which has an energy of formation of 360 kjmol-1, we can ascertain that the dative covalent bond formed is quite weak relative to commonplace bonds in chemistry.

=='''NI3 molecule'''==

The optimised molecule can be found [[Media:DMONGNI3OPTFREQATT3.LOG| here]]

'''Jmol'''
<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGNI3OPTFREQATT3.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -12.3845 -12.3781 -5.6129 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2332

Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000630 0.001200 YES
Predicted change in Energy=-1.193062D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1842 -DE/DX = -0.0001 !
! R2 R(1,3) 2.1842 -DE/DX = -0.0001 !
! R3 R(1,4) 2.1842 -DE/DX = -0.0001 !
! A1 A(2,1,3) 110.8579 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8579 -DE/DX = -0.0001 !
! A3 A(3,1,4) 110.8579 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) -123.5674 -DE/DX = 0.0001 !

N-I bond lengthː 2.184 angstroms

=='''Mini-project: Metal Carbonyls'''==

for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

I am looking for comments and annotations:

indicating directly bonded vs through space interactions
the distance dependence ie weak vs medium vs strong interactions
discussion of polarized or directed interactions
mention of s,p or d relative intensity of overlap
the nodal character, on atoms is less antibonding than between atoms
AND a clean tidy diagram that is well annotated

In this mini-project I will be comparing the vibrational frequencies and bond lengths in three metal carbonyl complexesː [Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]. I will run optimisations on each of the structures and determine the bond lengths, and then will run frequency analysis on each of these optimised structures to give the vibrational frequencies.

The strength of the C=O is related to the extent of backbonding from the metal to the pi* star orbital of C=O - "increased electron density in the 2pi* orbital of the C=O molecule leads to a lower C-O bond order (and hence longer & weaker bond)" - see diagram below.

[[File:Dmongbackbondingdiag.jpg]]

Theory allows for prediction of the extent of backbonding, which will then be compared to the vibrational frequencies given from frequency analysis - the stretching frequencies of the C=O bond can be correlated to the bond strength, as given by the equation w = h/2pi x (kf/meff)^0.5, which shows that the fundamental frequency w is directly proportional to the spring constant kf which is effectively the bond strength. My prediction of which complex has the highest vibrational frequencies for C=O will be compared to the actual values from the frequency analysis and analysed for any discrepancies.

As shown above, theory predicts that the increased backbonding will incur a decrease in bond order of the C=O bond, and hence a longer bond. My prediction of which complex has the longest C=O bond will be compared to the actual bond lengths from the optimised molecule.

'''Predictions'''

The complexes I will be analysing are very similiar - they are all isoelectronic with d6 occupancy of the metal, have identical ligands (carbonyl - strong field) and are all low spin complexes with 18 electrons total. This means the only parameter which is different across the three is the charge on the metal, which since we're using neutral ligands is simply its oxidation state.

Theory provides a relationship between charge on a metal and the extent of backbonding; "Increasing negative charge leads to the expansion of d-orbitals, therefore greater overlap of M(dpi) with CO pi* / increased backbonding" - see diagram below.

[[File:Dmongcarbonylmetalcharge.jpg]]

In the three complexes I will be analysing ([Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]), the charges are as follows: Ti(2-), V(-1) and Cr(0). Given the order of magnitude of charge being Ti > V > Cr, and the theory stated previously, the predictions for vibrational frequencies and bond lengths are as follows:

Vibrational frequencies: Cr > V > Ti
Bond length of C=O: Ti > V > Cr

==='''[Ti(CO)6]2- analysis'''===

The molecule was first optimised and then frequency analysis was performed.

The link to the frequency file can be found [[Media:DMONGTIGEN.LOG| here]].

[[File:DmongTigenoptdata.jpg]]

Low frequencies --- -0.0010 -0.0004 0.0002 13.1492 13.1492 13.1492
Low frequencies --- 29.8870 29.8870 29.8870

Item Value Threshold Converged?
Maximum Force 0.000247 0.000450 YES
RMS Force 0.000086 0.000300 YES
Maximum Displacement 0.000128 0.001800 YES
RMS Displacement 0.000061 0.001200 YES
Predicted change in Energy=-1.882613D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1833 -DE/DX = 0.0002 !
! R2 R(1,13) 2.0467 -DE/DX = 0.0 !
! R3 R(3,4) 1.1833 -DE/DX = 0.0002 !
! R4 R(3,13) 2.0467 -DE/DX = 0.0 !
! R5 R(5,6) 1.1833 -DE/DX = 0.0002 !
! R6 R(5,13) 2.0467 -DE/DX = 0.0 !
! R7 R(7,8) 1.1833 -DE/DX = 0.0002 !
! R8 R(7,13) 2.0467 -DE/DX = 0.0 !
! R9 R(9,10) 1.1833 -DE/DX = 0.0002 !
! R10 R(9,13) 2.0467 -DE/DX = 0.0 !
! R11 R(11,12) 1.1833 -DE/DX = 0.0002 !
! R12 R(11,13) 2.0467 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for the C=O bond in this complex was found to be 1.18330 angstroms.

'''Vibrational Analysis'''

[[File:DmongTigenfreqdata.jpg]]

Here we can see two distinct peaks in the IR spectrum despite there being 33 unique vibrational modes. The vast majority of these peaks do not have a large enough intensity to be visible in IR. The two peaks lie at 639.19cm-1 and 1856.22cm-1. The peak at 639.19cm-1 represents the bending modes of the IR spectrum - there are 3 degenerate modes which have equal intensity and incur a change in dipole moment.
At 1856.22cm-1 there is a peak for stretching mode of the molecule, which has three degenerate modes of equal intensity. This indicates the extent of pi backbonding as discussed previously and will be compared against the other molecules.

==='''[V(CO)6]- analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGVGEN.LOG| here]].

[[File:DmongVgenoptdata.jpg]]

Low frequencies --- 0.0006 0.0006 0.0011 14.1311 14.1311 14.1311
Low frequencies --- 52.8916 52.8916 52.8916

Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000070 0.000300 YES
Maximum Displacement 0.001210 0.001800 YES
RMS Displacement 0.000591 0.001200 YES
Predicted change in Energy=-7.154807D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9542 -DE/DX = -0.0002 !
! R2 R(1,4) 1.9542 -DE/DX = -0.0002 !
! R3 R(1,6) 1.9542 -DE/DX = -0.0002 !
! R4 R(1,8) 1.9542 -DE/DX = -0.0002 !
! R5 R(1,10) 1.9542 -DE/DX = -0.0002 !
! R6 R(1,12) 1.9542 -DE/DX = -0.0002 !
! R7 R(2,3) 1.166 -DE/DX = 0.0 !
! R8 R(4,5) 1.166 -DE/DX = 0.0 !
! R9 R(6,7) 1.166 -DE/DX = 0.0 !
! R10 R(8,9) 1.166 -DE/DX = 0.0 !
! R11 R(10,11) 1.166 -DE/DX = 0.0 !
! R12 R(12,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,10) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,12) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,10,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,12,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) -90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,10,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,12,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The C=O bond length in this complex was found to be 1.16599 angstroms.

'''Vibrational Analysis'''

[[File:DmongVgenfreqdata.jpg]]

There are 2 distinct peaks in the IR spcetrum, similarly to the Ti complex. The larger peak is at 1968.91cm-1, and represents the C=O stretching mode. The lesser peak is at 689.44cm-1, and represents the bending mode of the complex. The other modes present are not intense enough to be visible on an IR spectrum.

==='''[Cr(CO)6] analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGCRGEN.LOG| here]].

[[File:DmongCrgenoptdata.jpg]]

Low frequencies --- -0.0012 -0.0011 -0.0011 10.3820 10.3820 10.3820
Low frequencies --- 66.4094 66.4094 66.4094

Item Value Threshold Converged?
Maximum Force 0.000154 0.000450 YES
RMS Force 0.000055 0.000300 YES
Maximum Displacement 0.000386 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.123831D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1494 -DE/DX = 0.0002 !
! R2 R(1,13) 1.9149 -DE/DX = 0.0 !
! R3 R(3,4) 1.1494 -DE/DX = 0.0002 !
! R4 R(3,13) 1.9149 -DE/DX = 0.0 !
! R5 R(5,6) 1.1494 -DE/DX = 0.0002 !
! R6 R(5,13) 1.9149 -DE/DX = 0.0 !
! R7 R(7,8) 1.1494 -DE/DX = 0.0002 !
! R8 R(7,13) 1.9149 -DE/DX = 0.0 !
! R9 R(9,10) 1.1494 -DE/DX = 0.0002 !
! R10 R(9,13) 1.9149 -DE/DX = 0.0 !
! R11 R(11,12) 1.1494 -DE/DX = 0.0002 !
! R12 R(11,13) 1.9149 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for C=O in this complex was found to be 1.14938 angstroms.

'''Vibrational Analysis'''

[[File:DmongCrgenfreqdata.jpg]]

'''MO analysis'''

Rep:Mod:dariomong01351899MO

2019-05-23T16:40:12Z

Dm1417: /* [Ti(CO)6]2- analysis */

== '''BH3 molecule''' ==

'''3-21G optimisation'''

[[File:DmongBH3321goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.

[[File:DmongBH3321ggraphs.jpg]]

The optimisation file is linked [[Media:DMONGBH3OPT.LOG| here]].

'''6-21G optimisation'''

[[File:DmongBH3621goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128957D-09
Optimization completed.
-- Stationary point found.

The molecule was then constrained to a D3h symmetry and then optimised again by 6-21G.

[[File: DmongBH3621gd3hoptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-1.240669D-09
Optimization completed.
-- Stationary point found.

'''Frequency analysis of BH3'''

[[File:DmongBH3621gbfreqoptdata.jpg]]

'''Low frequencies --- -15.9849 -15.9818 -12.7207 0.0007 0.0143 0.3137'''
'''Low frequencies --- 1162.9365 1213.1134 1213.1136'''
Diagonal vibrational polarizability:
0.7178921 0.7178603 1.8420487
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9365 1213.1134 1213.1136
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9985 0.9600 0.9600
IR Inten -- 92.5721 14.0532 14.0527
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.7141 2715.8636 2715.8645
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9608 4.8992 4.8992
IR Inten -- 0.0000 126.3274 126.3214
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
4 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00

The optimised molecule can be found [[Media:DMONGBH3OPT631GB.LOG| here]]

'''Jmol of optimised BH3 molecule'''
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGBH3OPT631GB.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Infrared Spectrum of BH3'''
[[File:DmongBH3621gbfreqvibr.jpg|700x700px]]

{| class="wikitable" border="1"
|+ Infrared Spectrum Vibrations
! Vibrational frequency (cm-1) !! Intensity (dimensionless) !! Symmetry !! IR Active !! Type !
|-
| 1163 || 93 || A2" || Yes || symmetric bend (wagging)
|-
| 1213 || 14 || E' || Yes || antisymmetric bend (rocking)
|-
| 1213 || 14 || E' || Yes || symmetric bend (scissoring)
|-
| 2583 || 0 || A1' || No || symmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|}

Despite showing 6 vibrational modes, only 3 appear in the actual spectrum. There are two sets of degenerate vibrational modes at 1213cm-1 and 2716cm-1 respectively, which only appear in the spectrum as one peak respectively.In addition to this, the vibration at 2583cm-1 is not IR active as its vibrational mode does not incur a change in dipole moment as each H atom stretches out from the central B atom in a symmetrical fashion, as seen below.

[[File:Dariomongnoniractivemodeofbh3.jpg|300x300px]]

'''Molecular Orbital diagram of BH3'''

[[File:DmongBH3MOdiagram.jpg]]
''T.Hunt, 2018,Figure 5,Problem class 1: the MO diagram of BH3,''
''Molecular Orbitals in Inorganic Chemistry, Imperial College London, delivered November'' ''2018.''

There are no significant differences between the computed MOs and the LCAO derived MOs. For the most part LCAO is a reliable model for showing the MOs of a molecule, however there are certain aspects it fails to capture, such as the overlap of orbitals from the same fragment (see a1'). Electronic distribution is key to understanding reactivity of molecules, which is why LCAO is good for MO diagrams but less effective for more complex cases.

=='''NH3 molecule'''==

[[File:DmongNH3631goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843977D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !

Low frequencies --- -0.0137 -0.0027 0.0007 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

=='''NH3BH3'''==

[[File:DmongNH3BH3631goptdataNEW.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.656419D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,8) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,8) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,7) 1.21 -DE/DX = -0.0001 !
! R5 R(5,7) 1.21 -DE/DX = -0.0001 !
! R6 R(6,7) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 113.8746 -DE/DX = 0.0 !
! A2 A(4,7,6) 113.8746 -DE/DX = 0.0 !
! A3 A(4,7,8) 104.5965 -DE/DX = 0.0 !
! A4 A(5,7,6) 113.8746 -DE/DX = 0.0 !
! A5 A(5,7,8) 104.5965 -DE/DX = 0.0 !
! A6 A(6,7,8) 104.5965 -DE/DX = 0.0 !
! A7 A(1,8,2) 107.8683 -DE/DX = 0.0 !
! A8 A(1,8,3) 107.8683 -DE/DX = 0.0 !
! A9 A(1,8,7) 111.0301 -DE/DX = 0.0 !
! A10 A(2,8,3) 107.8683 -DE/DX = 0.0 !
! A11 A(2,8,7) 111.0301 -DE/DX = 0.0 !
! A12 A(3,8,7) 111.0301 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 180.0 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 60.0 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 60.0 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 180.0 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0 -DE/DX = 0.0 !
! D8 D(6,7,8,2) 180.0 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0 -DE/DX = 0.0 !

Low frequencies --- -0.0251 -0.0029 0.0014 17.1170 17.1195 37.1145
Low frequencies --- 265.7734 632.2034 639.3448

'''NH3BH3 bond energy'''

{| class="wikitable" border="1"
|+ Energies
! Molecule !! Energy (atomic units)
|-
| NH3 || -56.56
|-
| BH3 || -26.62
|-
| NH3BH3 || -83.22
|}

(error associated with energy is 5 kjmol-1, which corresponds to 0.002 au, so calculations are given to 2dp)

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-83.22-(-56.56-26.62)
=-83.22 + 83.18
=-0.04 au
=-105.02 kjmol-1

A value of -105.02 kjmol-1 indicates an exothermic process as the overall energy change is negative, meaning that the process gives products which are more thermodynamically stable than the reactants. Comparing to a C-C bond in ethane which has an energy of formation of 346 kjmol-1, and the C-N bond in methylamine which has an energy of formation of 360 kjmol-1, we can ascertain that the dative covalent bond formed is quite weak relative to commonplace bonds in chemistry.

=='''NI3 molecule'''==

The optimised molecule can be found [[Media:DMONGNI3OPTFREQATT3.LOG| here]]

'''Jmol'''
<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGNI3OPTFREQATT3.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -12.3845 -12.3781 -5.6129 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2332

Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000630 0.001200 YES
Predicted change in Energy=-1.193062D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1842 -DE/DX = -0.0001 !
! R2 R(1,3) 2.1842 -DE/DX = -0.0001 !
! R3 R(1,4) 2.1842 -DE/DX = -0.0001 !
! A1 A(2,1,3) 110.8579 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8579 -DE/DX = -0.0001 !
! A3 A(3,1,4) 110.8579 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) -123.5674 -DE/DX = 0.0001 !

N-I bond lengthː 2.184 angstroms

=='''Mini-project: Metal Carbonyls'''==

for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

I am looking for comments and annotations:

indicating directly bonded vs through space interactions
the distance dependence ie weak vs medium vs strong interactions
discussion of polarized or directed interactions
mention of s,p or d relative intensity of overlap
the nodal character, on atoms is less antibonding than between atoms
AND a clean tidy diagram that is well annotated

In this mini-project I will be comparing the vibrational frequencies and bond lengths in three metal carbonyl complexesː [Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]. I will run optimisations on each of the structures and determine the bond lengths, and then will run frequency analysis on each of these optimised structures to give the vibrational frequencies.

The strength of the C=O is related to the extent of backbonding from the metal to the pi* star orbital of C=O - "increased electron density in the 2pi* orbital of the C=O molecule leads to a lower C-O bond order (and hence longer & weaker bond)" - see diagram below.

[[File:Dmongbackbondingdiag.jpg]]

Theory allows for prediction of the extent of backbonding, which will then be compared to the vibrational frequencies given from frequency analysis - the stretching frequencies of the C=O bond can be correlated to the bond strength, as given by the equation w = h/2pi x (kf/meff)^0.5, which shows that the fundamental frequency w is directly proportional to the spring constant kf which is effectively the bond strength. My prediction of which complex has the highest vibrational frequencies for C=O will be compared to the actual values from the frequency analysis and analysed for any discrepancies.

As shown above, theory predicts that the increased backbonding will incur a decrease in bond order of the C=O bond, and hence a longer bond. My prediction of which complex has the longest C=O bond will be compared to the actual bond lengths from the optimised molecule.

'''Predictions'''

The complexes I will be analysing are very similiar - they are all isoelectronic with d6 occupancy of the metal, have identical ligands (carbonyl - strong field) and are all low spin complexes with 18 electrons total. This means the only parameter which is different across the three is the charge on the metal, which since we're using neutral ligands is simply its oxidation state.

Theory provides a relationship between charge on a metal and the extent of backbonding; "Increasing negative charge leads to the expansion of d-orbitals, therefore greater overlap of M(dpi) with CO pi* / increased backbonding" - see diagram below.

[[File:Dmongcarbonylmetalcharge.jpg]]

In the three complexes I will be analysing ([Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]), the charges are as follows: Ti(2-), V(-1) and Cr(0). Given the order of magnitude of charge being Ti > V > Cr, and the theory stated previously, the predictions for vibrational frequencies and bond lengths are as follows:

Vibrational frequencies: Cr > V > Ti
Bond length of C=O: Ti > V > Cr

==='''[Ti(CO)6]2- analysis'''===

The molecule was first optimised and then frequency analysis was performed.

The link to the frequency file can be found [[Media:DMONGTIGEN.LOG| here]].

[[File:DmongTigenoptdata.jpg]]

Low frequencies --- -0.0010 -0.0004 0.0002 13.1492 13.1492 13.1492
Low frequencies --- 29.8870 29.8870 29.8870

Item Value Threshold Converged?
Maximum Force 0.000247 0.000450 YES
RMS Force 0.000086 0.000300 YES
Maximum Displacement 0.000128 0.001800 YES
RMS Displacement 0.000061 0.001200 YES
Predicted change in Energy=-1.882613D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1833 -DE/DX = 0.0002 !
! R2 R(1,13) 2.0467 -DE/DX = 0.0 !
! R3 R(3,4) 1.1833 -DE/DX = 0.0002 !
! R4 R(3,13) 2.0467 -DE/DX = 0.0 !
! R5 R(5,6) 1.1833 -DE/DX = 0.0002 !
! R6 R(5,13) 2.0467 -DE/DX = 0.0 !
! R7 R(7,8) 1.1833 -DE/DX = 0.0002 !
! R8 R(7,13) 2.0467 -DE/DX = 0.0 !
! R9 R(9,10) 1.1833 -DE/DX = 0.0002 !
! R10 R(9,13) 2.0467 -DE/DX = 0.0 !
! R11 R(11,12) 1.1833 -DE/DX = 0.0002 !
! R12 R(11,13) 2.0467 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for the C=O bond in this complex was found to be 1.18330 angstroms.

'''Vibrational Analysis'''

[[File:DmongTigenfreqdata.jpg]]

Here we can see two distinct peaks in the IR spectrum despite there being 33 unique vibrational modes. The vast majority of these peaks do not have a large enough intensity to be visible in IR. The two peaks lie at 639.19cm-1 and 1856.22cm-1. The peak at 639.19cm-1 represents the bending modes of the IR spectrum - there are 3 degenerate modes which have equal intensity and incur a change in dipole moment.
At 1856.22cm-1 there is a peak for stretching mode of the molecule, which has three degenerate modes of equal intensity. This indicates the extent of pi backbonding as discussed previously and will be compared against the other molecules.

==='''[V(CO)6]- analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGVGEN.LOG| here]].

[[File:DmongVgenoptdata.jpg]]

Low frequencies --- 0.0006 0.0006 0.0011 14.1311 14.1311 14.1311
Low frequencies --- 52.8916 52.8916 52.8916

Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000070 0.000300 YES
Maximum Displacement 0.001210 0.001800 YES
RMS Displacement 0.000591 0.001200 YES
Predicted change in Energy=-7.154807D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9542 -DE/DX = -0.0002 !
! R2 R(1,4) 1.9542 -DE/DX = -0.0002 !
! R3 R(1,6) 1.9542 -DE/DX = -0.0002 !
! R4 R(1,8) 1.9542 -DE/DX = -0.0002 !
! R5 R(1,10) 1.9542 -DE/DX = -0.0002 !
! R6 R(1,12) 1.9542 -DE/DX = -0.0002 !
! R7 R(2,3) 1.166 -DE/DX = 0.0 !
! R8 R(4,5) 1.166 -DE/DX = 0.0 !
! R9 R(6,7) 1.166 -DE/DX = 0.0 !
! R10 R(8,9) 1.166 -DE/DX = 0.0 !
! R11 R(10,11) 1.166 -DE/DX = 0.0 !
! R12 R(12,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,10) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,12) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,10,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,12,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) -90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,10,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,12,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The C=O bond length in this complex was found to be 1.16599 angstroms.

'''Vibrational Analysis'''

[[File:DmongVgenfreqdata.jpg]]

There are 2 distinct peaks in the IR spcetrum, similarly to the Ti complex. The larger peak is at 1968.91cm-1, and represents the C=O stretching mode. The lesser peak is at 689.44cm-1, and represents the bending mode of the complex. The other modes present are not intense enough to be visible on an IR spectrum.

==='''[Cr(CO)6] analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGCRGEN.LOG| here]].

[[File:DmongCrgenoptdata.jpg]]

Low frequencies --- -0.0012 -0.0011 -0.0011 10.3820 10.3820 10.3820
Low frequencies --- 66.4094 66.4094 66.4094

Item Value Threshold Converged?
Maximum Force 0.000154 0.000450 YES
RMS Force 0.000055 0.000300 YES
Maximum Displacement 0.000386 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.123831D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1494 -DE/DX = 0.0002 !
! R2 R(1,13) 1.9149 -DE/DX = 0.0 !
! R3 R(3,4) 1.1494 -DE/DX = 0.0002 !
! R4 R(3,13) 1.9149 -DE/DX = 0.0 !
! R5 R(5,6) 1.1494 -DE/DX = 0.0002 !
! R6 R(5,13) 1.9149 -DE/DX = 0.0 !
! R7 R(7,8) 1.1494 -DE/DX = 0.0002 !
! R8 R(7,13) 1.9149 -DE/DX = 0.0 !
! R9 R(9,10) 1.1494 -DE/DX = 0.0002 !
! R10 R(9,13) 1.9149 -DE/DX = 0.0 !
! R11 R(11,12) 1.1494 -DE/DX = 0.0002 !
! R12 R(11,13) 1.9149 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for C=O in this complex was found to be 1.14938 angstroms.

'''Vibrational Analysis'''

[[File:DmongCrgenfreqdata.jpg]]

Rep:Mod:dariomong01351899MO

2019-05-23T16:38:38Z

Dm1417: /* [Ti(CO)6]2- analysis */

== '''BH3 molecule''' ==

'''3-21G optimisation'''

[[File:DmongBH3321goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.

[[File:DmongBH3321ggraphs.jpg]]

The optimisation file is linked [[Media:DMONGBH3OPT.LOG| here]].

'''6-21G optimisation'''

[[File:DmongBH3621goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128957D-09
Optimization completed.
-- Stationary point found.

The molecule was then constrained to a D3h symmetry and then optimised again by 6-21G.

[[File: DmongBH3621gd3hoptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-1.240669D-09
Optimization completed.
-- Stationary point found.

'''Frequency analysis of BH3'''

[[File:DmongBH3621gbfreqoptdata.jpg]]

'''Low frequencies --- -15.9849 -15.9818 -12.7207 0.0007 0.0143 0.3137'''
'''Low frequencies --- 1162.9365 1213.1134 1213.1136'''
Diagonal vibrational polarizability:
0.7178921 0.7178603 1.8420487
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9365 1213.1134 1213.1136
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9985 0.9600 0.9600
IR Inten -- 92.5721 14.0532 14.0527
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.7141 2715.8636 2715.8645
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9608 4.8992 4.8992
IR Inten -- 0.0000 126.3274 126.3214
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
4 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00

The optimised molecule can be found [[Media:DMONGBH3OPT631GB.LOG| here]]

'''Jmol of optimised BH3 molecule'''
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGBH3OPT631GB.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Infrared Spectrum of BH3'''
[[File:DmongBH3621gbfreqvibr.jpg|700x700px]]

{| class="wikitable" border="1"
|+ Infrared Spectrum Vibrations
! Vibrational frequency (cm-1) !! Intensity (dimensionless) !! Symmetry !! IR Active !! Type !
|-
| 1163 || 93 || A2" || Yes || symmetric bend (wagging)
|-
| 1213 || 14 || E' || Yes || antisymmetric bend (rocking)
|-
| 1213 || 14 || E' || Yes || symmetric bend (scissoring)
|-
| 2583 || 0 || A1' || No || symmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|}

Despite showing 6 vibrational modes, only 3 appear in the actual spectrum. There are two sets of degenerate vibrational modes at 1213cm-1 and 2716cm-1 respectively, which only appear in the spectrum as one peak respectively.In addition to this, the vibration at 2583cm-1 is not IR active as its vibrational mode does not incur a change in dipole moment as each H atom stretches out from the central B atom in a symmetrical fashion, as seen below.

[[File:Dariomongnoniractivemodeofbh3.jpg|300x300px]]

'''Molecular Orbital diagram of BH3'''

[[File:DmongBH3MOdiagram.jpg]]
''T.Hunt, 2018,Figure 5,Problem class 1: the MO diagram of BH3,''
''Molecular Orbitals in Inorganic Chemistry, Imperial College London, delivered November'' ''2018.''

There are no significant differences between the computed MOs and the LCAO derived MOs. For the most part LCAO is a reliable model for showing the MOs of a molecule, however there are certain aspects it fails to capture, such as the overlap of orbitals from the same fragment (see a1'). Electronic distribution is key to understanding reactivity of molecules, which is why LCAO is good for MO diagrams but less effective for more complex cases.

=='''NH3 molecule'''==

[[File:DmongNH3631goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843977D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !

Low frequencies --- -0.0137 -0.0027 0.0007 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

=='''NH3BH3'''==

[[File:DmongNH3BH3631goptdataNEW.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.656419D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,8) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,8) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,7) 1.21 -DE/DX = -0.0001 !
! R5 R(5,7) 1.21 -DE/DX = -0.0001 !
! R6 R(6,7) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 113.8746 -DE/DX = 0.0 !
! A2 A(4,7,6) 113.8746 -DE/DX = 0.0 !
! A3 A(4,7,8) 104.5965 -DE/DX = 0.0 !
! A4 A(5,7,6) 113.8746 -DE/DX = 0.0 !
! A5 A(5,7,8) 104.5965 -DE/DX = 0.0 !
! A6 A(6,7,8) 104.5965 -DE/DX = 0.0 !
! A7 A(1,8,2) 107.8683 -DE/DX = 0.0 !
! A8 A(1,8,3) 107.8683 -DE/DX = 0.0 !
! A9 A(1,8,7) 111.0301 -DE/DX = 0.0 !
! A10 A(2,8,3) 107.8683 -DE/DX = 0.0 !
! A11 A(2,8,7) 111.0301 -DE/DX = 0.0 !
! A12 A(3,8,7) 111.0301 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 180.0 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 60.0 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 60.0 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 180.0 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0 -DE/DX = 0.0 !
! D8 D(6,7,8,2) 180.0 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0 -DE/DX = 0.0 !

Low frequencies --- -0.0251 -0.0029 0.0014 17.1170 17.1195 37.1145
Low frequencies --- 265.7734 632.2034 639.3448

'''NH3BH3 bond energy'''

{| class="wikitable" border="1"
|+ Energies
! Molecule !! Energy (atomic units)
|-
| NH3 || -56.56
|-
| BH3 || -26.62
|-
| NH3BH3 || -83.22
|}

(error associated with energy is 5 kjmol-1, which corresponds to 0.002 au, so calculations are given to 2dp)

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-83.22-(-56.56-26.62)
=-83.22 + 83.18
=-0.04 au
=-105.02 kjmol-1

A value of -105.02 kjmol-1 indicates an exothermic process as the overall energy change is negative, meaning that the process gives products which are more thermodynamically stable than the reactants. Comparing to a C-C bond in ethane which has an energy of formation of 346 kjmol-1, and the C-N bond in methylamine which has an energy of formation of 360 kjmol-1, we can ascertain that the dative covalent bond formed is quite weak relative to commonplace bonds in chemistry.

=='''NI3 molecule'''==

The optimised molecule can be found [[Media:DMONGNI3OPTFREQATT3.LOG| here]]

'''Jmol'''
<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGNI3OPTFREQATT3.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -12.3845 -12.3781 -5.6129 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2332

Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000630 0.001200 YES
Predicted change in Energy=-1.193062D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1842 -DE/DX = -0.0001 !
! R2 R(1,3) 2.1842 -DE/DX = -0.0001 !
! R3 R(1,4) 2.1842 -DE/DX = -0.0001 !
! A1 A(2,1,3) 110.8579 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8579 -DE/DX = -0.0001 !
! A3 A(3,1,4) 110.8579 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) -123.5674 -DE/DX = 0.0001 !

N-I bond lengthː 2.184 angstroms

=='''Mini-project: Metal Carbonyls'''==

for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

I am looking for comments and annotations:

indicating directly bonded vs through space interactions
the distance dependence ie weak vs medium vs strong interactions
discussion of polarized or directed interactions
mention of s,p or d relative intensity of overlap
the nodal character, on atoms is less antibonding than between atoms
AND a clean tidy diagram that is well annotated

In this mini-project I will be comparing the vibrational frequencies and bond lengths in three metal carbonyl complexesː [Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]. I will run optimisations on each of the structures and determine the bond lengths, and then will run frequency analysis on each of these optimised structures to give the vibrational frequencies.

The strength of the C=O is related to the extent of backbonding from the metal to the pi* star orbital of C=O - "increased electron density in the 2pi* orbital of the C=O molecule leads to a lower C-O bond order (and hence longer & weaker bond)" - see diagram below.

[[File:Dmongbackbondingdiag.jpg]]

Theory allows for prediction of the extent of backbonding, which will then be compared to the vibrational frequencies given from frequency analysis - the stretching frequencies of the C=O bond can be correlated to the bond strength, as given by the equation w = h/2pi x (kf/meff)^0.5, which shows that the fundamental frequency w is directly proportional to the spring constant kf which is effectively the bond strength. My prediction of which complex has the highest vibrational frequencies for C=O will be compared to the actual values from the frequency analysis and analysed for any discrepancies.

As shown above, theory predicts that the increased backbonding will incur a decrease in bond order of the C=O bond, and hence a longer bond. My prediction of which complex has the longest C=O bond will be compared to the actual bond lengths from the optimised molecule.

'''Predictions'''

The complexes I will be analysing are very similiar - they are all isoelectronic with d6 occupancy of the metal, have identical ligands (carbonyl - strong field) and are all low spin complexes with 18 electrons total. This means the only parameter which is different across the three is the charge on the metal, which since we're using neutral ligands is simply its oxidation state.

Theory provides a relationship between charge on a metal and the extent of backbonding; "Increasing negative charge leads to the expansion of d-orbitals, therefore greater overlap of M(dpi) with CO pi* / increased backbonding" - see diagram below.

[[File:Dmongcarbonylmetalcharge.jpg]]

In the three complexes I will be analysing ([Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]), the charges are as follows: Ti(2-), V(-1) and Cr(0). Given the order of magnitude of charge being Ti > V > Cr, and the theory stated previously, the predictions for vibrational frequencies and bond lengths are as follows:

Vibrational frequencies: Cr > V > Ti
Bond length of C=O: Ti > V > Cr

==='''[Ti(CO)6]2- analysis'''===

The molecule was first optimised and then frequency analysis was performed.

The link to the frequency file can be found [[Media:DMONGTIGEN.LOG| here]].

[[File:DmongTigenoptdata.jpg]]

Low frequencies --- -0.0010 -0.0004 0.0002 13.1492 13.1492 13.1492
Low frequencies --- 29.8870 29.8870 29.8870

Item Value Threshold Converged?
Maximum Force 0.000247 0.000450 YES
RMS Force 0.000086 0.000300 YES
Maximum Displacement 0.000128 0.001800 YES
RMS Displacement 0.000061 0.001200 YES
Predicted change in Energy=-1.882613D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1833 -DE/DX = 0.0002 !
! R2 R(1,13) 2.0467 -DE/DX = 0.0 !
! R3 R(3,4) 1.1833 -DE/DX = 0.0002 !
! R4 R(3,13) 2.0467 -DE/DX = 0.0 !
! R5 R(5,6) 1.1833 -DE/DX = 0.0002 !
! R6 R(5,13) 2.0467 -DE/DX = 0.0 !
! R7 R(7,8) 1.1833 -DE/DX = 0.0002 !
! R8 R(7,13) 2.0467 -DE/DX = 0.0 !
! R9 R(9,10) 1.1833 -DE/DX = 0.0002 !
! R10 R(9,13) 2.0467 -DE/DX = 0.0 !
! R11 R(11,12) 1.1833 -DE/DX = 0.0002 !
! R12 R(11,13) 2.0467 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for the C=O bond in this complex was found to be 1.18406 angstroms.

'''Vibrational Analysis'''

[[File:DmongTigenfreqdata.jpg]]

Here we can see two distinct peaks in the IR spectrum despite there being 33 unique vibrational modes. The vast majority of these peaks do not have a large enough intensity to be visible in IR. The two peaks lie at 619.05cm-1 and 1850.26cm-1. The peak at 619.05cm-1 represents the bending modes of the IR spectrum - there are 3 degenerate modes which have equal intensity and incur a change in dipole moment.
At 1850.26cm-1 there is a peak for stretching mode of the molecule, which has three degenerate modes of equal intensity. This indicates the extent of pi backbonding as discussed previously and will be compared against the other molecules.

==='''[V(CO)6]- analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGVGEN.LOG| here]].

[[File:DmongVgenoptdata.jpg]]

Low frequencies --- 0.0006 0.0006 0.0011 14.1311 14.1311 14.1311
Low frequencies --- 52.8916 52.8916 52.8916

Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000070 0.000300 YES
Maximum Displacement 0.001210 0.001800 YES
RMS Displacement 0.000591 0.001200 YES
Predicted change in Energy=-7.154807D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9542 -DE/DX = -0.0002 !
! R2 R(1,4) 1.9542 -DE/DX = -0.0002 !
! R3 R(1,6) 1.9542 -DE/DX = -0.0002 !
! R4 R(1,8) 1.9542 -DE/DX = -0.0002 !
! R5 R(1,10) 1.9542 -DE/DX = -0.0002 !
! R6 R(1,12) 1.9542 -DE/DX = -0.0002 !
! R7 R(2,3) 1.166 -DE/DX = 0.0 !
! R8 R(4,5) 1.166 -DE/DX = 0.0 !
! R9 R(6,7) 1.166 -DE/DX = 0.0 !
! R10 R(8,9) 1.166 -DE/DX = 0.0 !
! R11 R(10,11) 1.166 -DE/DX = 0.0 !
! R12 R(12,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,10) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,12) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,10,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,12,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) -90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,10,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,12,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The C=O bond length in this complex was found to be 1.16599 angstroms.

'''Vibrational Analysis'''

[[File:DmongVgenfreqdata.jpg]]

There are 2 distinct peaks in the IR spcetrum, similarly to the Ti complex. The larger peak is at 1968.91cm-1, and represents the C=O stretching mode. The lesser peak is at 689.44cm-1, and represents the bending mode of the complex. The other modes present are not intense enough to be visible on an IR spectrum.

==='''[Cr(CO)6] analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGCRGEN.LOG| here]].

[[File:DmongCrgenoptdata.jpg]]

Low frequencies --- -0.0012 -0.0011 -0.0011 10.3820 10.3820 10.3820
Low frequencies --- 66.4094 66.4094 66.4094

Item Value Threshold Converged?
Maximum Force 0.000154 0.000450 YES
RMS Force 0.000055 0.000300 YES
Maximum Displacement 0.000386 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.123831D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1494 -DE/DX = 0.0002 !
! R2 R(1,13) 1.9149 -DE/DX = 0.0 !
! R3 R(3,4) 1.1494 -DE/DX = 0.0002 !
! R4 R(3,13) 1.9149 -DE/DX = 0.0 !
! R5 R(5,6) 1.1494 -DE/DX = 0.0002 !
! R6 R(5,13) 1.9149 -DE/DX = 0.0 !
! R7 R(7,8) 1.1494 -DE/DX = 0.0002 !
! R8 R(7,13) 1.9149 -DE/DX = 0.0 !
! R9 R(9,10) 1.1494 -DE/DX = 0.0002 !
! R10 R(9,13) 1.9149 -DE/DX = 0.0 !
! R11 R(11,12) 1.1494 -DE/DX = 0.0002 !
! R12 R(11,13) 1.9149 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for C=O in this complex was found to be 1.14938 angstroms.

'''Vibrational Analysis'''

[[File:DmongCrgenfreqdata.jpg]]

Rep:Mod:dariomong01351899MO

2019-05-23T16:27:26Z

Dm1417: /* BH3 molecule */

== '''BH3 molecule''' ==

'''3-21G optimisation'''

[[File:DmongBH3321goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.

[[File:DmongBH3321ggraphs.jpg]]

The optimisation file is linked [[Media:DMONGBH3OPT.LOG| here]].

'''6-21G optimisation'''

[[File:DmongBH3621goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128957D-09
Optimization completed.
-- Stationary point found.

The molecule was then constrained to a D3h symmetry and then optimised again by 6-21G.

[[File: DmongBH3621gd3hoptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-1.240669D-09
Optimization completed.
-- Stationary point found.

'''Frequency analysis of BH3'''

[[File:DmongBH3621gbfreqoptdata.jpg]]

'''Low frequencies --- -15.9849 -15.9818 -12.7207 0.0007 0.0143 0.3137'''
'''Low frequencies --- 1162.9365 1213.1134 1213.1136'''
Diagonal vibrational polarizability:
0.7178921 0.7178603 1.8420487
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9365 1213.1134 1213.1136
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9985 0.9600 0.9600
IR Inten -- 92.5721 14.0532 14.0527
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.7141 2715.8636 2715.8645
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9608 4.8992 4.8992
IR Inten -- 0.0000 126.3274 126.3214
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
4 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00

The optimised molecule can be found [[Media:DMONGBH3OPT631GB.LOG| here]]

'''Jmol of optimised BH3 molecule'''
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGBH3OPT631GB.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Infrared Spectrum of BH3'''
[[File:DmongBH3621gbfreqvibr.jpg|700x700px]]

{| class="wikitable" border="1"
|+ Infrared Spectrum Vibrations
! Vibrational frequency (cm-1) !! Intensity (dimensionless) !! Symmetry !! IR Active !! Type !
|-
| 1163 || 93 || A2" || Yes || symmetric bend (wagging)
|-
| 1213 || 14 || E' || Yes || antisymmetric bend (rocking)
|-
| 1213 || 14 || E' || Yes || symmetric bend (scissoring)
|-
| 2583 || 0 || A1' || No || symmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|}

Despite showing 6 vibrational modes, only 3 appear in the actual spectrum. There are two sets of degenerate vibrational modes at 1213cm-1 and 2716cm-1 respectively, which only appear in the spectrum as one peak respectively.In addition to this, the vibration at 2583cm-1 is not IR active as its vibrational mode does not incur a change in dipole moment as each H atom stretches out from the central B atom in a symmetrical fashion, as seen below.

[[File:Dariomongnoniractivemodeofbh3.jpg|300x300px]]

'''Molecular Orbital diagram of BH3'''

[[File:DmongBH3MOdiagram.jpg]]
''T.Hunt, 2018,Figure 5,Problem class 1: the MO diagram of BH3,''
''Molecular Orbitals in Inorganic Chemistry, Imperial College London, delivered November'' ''2018.''

There are no significant differences between the computed MOs and the LCAO derived MOs. For the most part LCAO is a reliable model for showing the MOs of a molecule, however there are certain aspects it fails to capture, such as the overlap of orbitals from the same fragment (see a1'). Electronic distribution is key to understanding reactivity of molecules, which is why LCAO is good for MO diagrams but less effective for more complex cases.

=='''NH3 molecule'''==

[[File:DmongNH3631goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843977D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !

Low frequencies --- -0.0137 -0.0027 0.0007 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

=='''NH3BH3'''==

[[File:DmongNH3BH3631goptdataNEW.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.656419D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,8) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,8) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,7) 1.21 -DE/DX = -0.0001 !
! R5 R(5,7) 1.21 -DE/DX = -0.0001 !
! R6 R(6,7) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 113.8746 -DE/DX = 0.0 !
! A2 A(4,7,6) 113.8746 -DE/DX = 0.0 !
! A3 A(4,7,8) 104.5965 -DE/DX = 0.0 !
! A4 A(5,7,6) 113.8746 -DE/DX = 0.0 !
! A5 A(5,7,8) 104.5965 -DE/DX = 0.0 !
! A6 A(6,7,8) 104.5965 -DE/DX = 0.0 !
! A7 A(1,8,2) 107.8683 -DE/DX = 0.0 !
! A8 A(1,8,3) 107.8683 -DE/DX = 0.0 !
! A9 A(1,8,7) 111.0301 -DE/DX = 0.0 !
! A10 A(2,8,3) 107.8683 -DE/DX = 0.0 !
! A11 A(2,8,7) 111.0301 -DE/DX = 0.0 !
! A12 A(3,8,7) 111.0301 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 180.0 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 60.0 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 60.0 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 180.0 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0 -DE/DX = 0.0 !
! D8 D(6,7,8,2) 180.0 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0 -DE/DX = 0.0 !

Low frequencies --- -0.0251 -0.0029 0.0014 17.1170 17.1195 37.1145
Low frequencies --- 265.7734 632.2034 639.3448

'''NH3BH3 bond energy'''

{| class="wikitable" border="1"
|+ Energies
! Molecule !! Energy (atomic units)
|-
| NH3 || -56.56
|-
| BH3 || -26.62
|-
| NH3BH3 || -83.22
|}

(error associated with energy is 5 kjmol-1, which corresponds to 0.002 au, so calculations are given to 2dp)

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-83.22-(-56.56-26.62)
=-83.22 + 83.18
=-0.04 au
=-105.02 kjmol-1

A value of -105.02 kjmol-1 indicates an exothermic process as the overall energy change is negative, meaning that the process gives products which are more thermodynamically stable than the reactants. Comparing to a C-C bond in ethane which has an energy of formation of 346 kjmol-1, and the C-N bond in methylamine which has an energy of formation of 360 kjmol-1, we can ascertain that the dative covalent bond formed is quite weak relative to commonplace bonds in chemistry.

=='''NI3 molecule'''==

The optimised molecule can be found [[Media:DMONGNI3OPTFREQATT3.LOG| here]]

'''Jmol'''
<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGNI3OPTFREQATT3.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -12.3845 -12.3781 -5.6129 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2332

Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000630 0.001200 YES
Predicted change in Energy=-1.193062D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1842 -DE/DX = -0.0001 !
! R2 R(1,3) 2.1842 -DE/DX = -0.0001 !
! R3 R(1,4) 2.1842 -DE/DX = -0.0001 !
! A1 A(2,1,3) 110.8579 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8579 -DE/DX = -0.0001 !
! A3 A(3,1,4) 110.8579 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) -123.5674 -DE/DX = 0.0001 !

N-I bond lengthː 2.184 angstroms

=='''Mini-project: Metal Carbonyls'''==

for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

I am looking for comments and annotations:

indicating directly bonded vs through space interactions
the distance dependence ie weak vs medium vs strong interactions
discussion of polarized or directed interactions
mention of s,p or d relative intensity of overlap
the nodal character, on atoms is less antibonding than between atoms
AND a clean tidy diagram that is well annotated

In this mini-project I will be comparing the vibrational frequencies and bond lengths in three metal carbonyl complexesː [Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]. I will run optimisations on each of the structures and determine the bond lengths, and then will run frequency analysis on each of these optimised structures to give the vibrational frequencies.

The strength of the C=O is related to the extent of backbonding from the metal to the pi* star orbital of C=O - "increased electron density in the 2pi* orbital of the C=O molecule leads to a lower C-O bond order (and hence longer & weaker bond)" - see diagram below.

[[File:Dmongbackbondingdiag.jpg]]

Theory allows for prediction of the extent of backbonding, which will then be compared to the vibrational frequencies given from frequency analysis - the stretching frequencies of the C=O bond can be correlated to the bond strength, as given by the equation w = h/2pi x (kf/meff)^0.5, which shows that the fundamental frequency w is directly proportional to the spring constant kf which is effectively the bond strength. My prediction of which complex has the highest vibrational frequencies for C=O will be compared to the actual values from the frequency analysis and analysed for any discrepancies.

As shown above, theory predicts that the increased backbonding will incur a decrease in bond order of the C=O bond, and hence a longer bond. My prediction of which complex has the longest C=O bond will be compared to the actual bond lengths from the optimised molecule.

'''Predictions'''

The complexes I will be analysing are very similiar - they are all isoelectronic with d6 occupancy of the metal, have identical ligands (carbonyl - strong field) and are all low spin complexes with 18 electrons total. This means the only parameter which is different across the three is the charge on the metal, which since we're using neutral ligands is simply its oxidation state.

Theory provides a relationship between charge on a metal and the extent of backbonding; "Increasing negative charge leads to the expansion of d-orbitals, therefore greater overlap of M(dpi) with CO pi* / increased backbonding" - see diagram below.

[[File:Dmongcarbonylmetalcharge.jpg]]

In the three complexes I will be analysing ([Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]), the charges are as follows: Ti(2-), V(-1) and Cr(0). Given the order of magnitude of charge being Ti > V > Cr, and the theory stated previously, the predictions for vibrational frequencies and bond lengths are as follows:

Vibrational frequencies: Cr > V > Ti
Bond length of C=O: Ti > V > Cr

==='''[Ti(CO)6]2- analysis'''===

The molecule was first optimised and then frequency analysis was performed.

The link to the frequency file can be found [[Media:DMONGTI631FREQ.LOG| here]].

[[File:Dmongticomplexdata2.jpg]]

Low frequencies --- -0.0040 0.0052 0.0057 11.0002 11.0002 11.0002
Low frequencies --- 24.7494 24.7494 24.7494

Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000354 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-1.080563D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.0513 -DE/DX = 0.0 !
! R2 R(1,4) 2.0513 -DE/DX = 0.0 !
! R3 R(1,6) 2.0513 -DE/DX = 0.0 !
! R4 R(1,8) 2.0513 -DE/DX = 0.0 !
! R5 R(1,10) 2.0513 -DE/DX = 0.0 !
! R6 R(1,12) 2.0513 -DE/DX = 0.0 !
! R7 R(2,3) 1.1841 -DE/DX = -0.0002 !
! R8 R(4,5) 1.1841 -DE/DX = -0.0002 !
! R9 R(6,7) 1.1841 -DE/DX = -0.0002 !
! R10 R(8,9) 1.1841 -DE/DX = -0.0002 !
! R11 R(10,11) 1.1841 -DE/DX = -0.0002 !
! R12 R(12,13) 1.1841 -DE/DX = -0.0002 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,12) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,10) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,12,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,10,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) 90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,12,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,10,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) -90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for the C=O bond in this complex was found to be 1.18406 angstroms.

'''Vibrational Analysis'''

[[File:DmongticomplexIRdata.jpg]]

Here we can see two distinct peaks in the IR spectrum despite there being 33 unique vibrational modes. The vast majority of these peaks do not have a large enough intensity to be visible in IR. The two peaks lie at 619.05cm-1 and 1850.26cm-1. The peak at 619.05cm-1 represents the bending modes of the IR spectrum - there are 3 degenerate modes which have equal intensity and incur a change in dipole moment.
At 1850.26cm-1 there is a peak for stretching mode of the molecule, which has three degenerate modes of equal intensity. This indicates the extent of pi backbonding as discussed previously and will be compared against the other molecules.

==='''[V(CO)6]- analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGVGEN.LOG| here]].

[[File:DmongVgenoptdata.jpg]]

Low frequencies --- 0.0006 0.0006 0.0011 14.1311 14.1311 14.1311
Low frequencies --- 52.8916 52.8916 52.8916

Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000070 0.000300 YES
Maximum Displacement 0.001210 0.001800 YES
RMS Displacement 0.000591 0.001200 YES
Predicted change in Energy=-7.154807D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9542 -DE/DX = -0.0002 !
! R2 R(1,4) 1.9542 -DE/DX = -0.0002 !
! R3 R(1,6) 1.9542 -DE/DX = -0.0002 !
! R4 R(1,8) 1.9542 -DE/DX = -0.0002 !
! R5 R(1,10) 1.9542 -DE/DX = -0.0002 !
! R6 R(1,12) 1.9542 -DE/DX = -0.0002 !
! R7 R(2,3) 1.166 -DE/DX = 0.0 !
! R8 R(4,5) 1.166 -DE/DX = 0.0 !
! R9 R(6,7) 1.166 -DE/DX = 0.0 !
! R10 R(8,9) 1.166 -DE/DX = 0.0 !
! R11 R(10,11) 1.166 -DE/DX = 0.0 !
! R12 R(12,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,10) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,12) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,10,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,12,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) -90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,10,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,12,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The C=O bond length in this complex was found to be 1.16599 angstroms.

'''Vibrational Analysis'''

[[File:DmongVgenfreqdata.jpg]]

There are 2 distinct peaks in the IR spcetrum, similarly to the Ti complex. The larger peak is at 1968.91cm-1, and represents the C=O stretching mode. The lesser peak is at 689.44cm-1, and represents the bending mode of the complex. The other modes present are not intense enough to be visible on an IR spectrum.

==='''[Cr(CO)6] analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:| here]].

[[File:DmongCrgenoptdata.jpg]]

Low frequencies --- -0.0012 -0.0011 -0.0011 10.3820 10.3820 10.3820
Low frequencies --- 66.4094 66.4094 66.4094

Item Value Threshold Converged?
Maximum Force 0.000154 0.000450 YES
RMS Force 0.000055 0.000300 YES
Maximum Displacement 0.000386 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.123831D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1494 -DE/DX = 0.0002 !
! R2 R(1,13) 1.9149 -DE/DX = 0.0 !
! R3 R(3,4) 1.1494 -DE/DX = 0.0002 !
! R4 R(3,13) 1.9149 -DE/DX = 0.0 !
! R5 R(5,6) 1.1494 -DE/DX = 0.0002 !
! R6 R(5,13) 1.9149 -DE/DX = 0.0 !
! R7 R(7,8) 1.1494 -DE/DX = 0.0002 !
! R8 R(7,13) 1.9149 -DE/DX = 0.0 !
! R9 R(9,10) 1.1494 -DE/DX = 0.0002 !
! R10 R(9,13) 1.9149 -DE/DX = 0.0 !
! R11 R(11,12) 1.1494 -DE/DX = 0.0002 !
! R12 R(11,13) 1.9149 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for C=O in this complex was found to be 1.14938 angstroms.

'''Vibrational Analysis'''

[[File:DmongCrgenfreqdata.jpg]]

File:DMONGCRGEN.LOG

2019-05-23T16:26:01Z

Dm1417:

Rep:Mod:dariomong01351899MO

2019-05-23T16:25:41Z

Dm1417: /* [V(CO)6]- analysis */

== '''BH3 molecule''' ==

'''3-21G optimisation'''

[[File:DmongBH3321goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.

[[File:DmongBH3321ggraphs.jpg]]

The optimisation file is linked [[Media:DMONGBH3OPT.LOG| here]].

'''6-21G optimisation'''

[[File:DmongBH3621goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128957D-09
Optimization completed.
-- Stationary point found.

The molecule was then constrained to a D3h symmetry and then optimised again by 6-21G.

[[File: DmongBH3621gd3hoptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-1.240669D-09
Optimization completed.
-- Stationary point found.

'''Frequency analysis of BH3'''

[[File:DmongBH3621gbfreqoptdata.jpg]]

'''Low frequencies --- -15.9849 -15.9818 -12.7207 0.0007 0.0143 0.3137'''
'''Low frequencies --- 1162.9365 1213.1134 1213.1136'''
Diagonal vibrational polarizability:
0.7178921 0.7178603 1.8420487
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9365 1213.1134 1213.1136
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9985 0.9600 0.9600
IR Inten -- 92.5721 14.0532 14.0527
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.7141 2715.8636 2715.8645
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9608 4.8992 4.8992
IR Inten -- 0.0000 126.3274 126.3214
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
4 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00

The optimised molecule can be found [[Media:DMONGBH3OPT631GB.LOG| here]]

'''Jmol of optimised BH3 molecule'''
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGBH3OPT631GB.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Infrared Spectrum of BH3'''
[[File:DmongBH3621gbfreqvibr.jpg|700x700px]]

{| class="wikitable" border="1"
|+ Infrared Spectrum Vibrations
! Vibrational frequency (cm-1) !! Intensity (dimensionless) !! Symmetry !! IR Active !! Type !
|-
| 1163 || 93 || A2" || Yes || symmetric bend (wagging)
|-
| 1213 || 14 || E' || Yes || antisymmetric bend (rocking)
|-
| 1213 || 14 || E' || Yes || symmetric bend (scissoring)
|-
| 2583 || 0 || A1' || No || symmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|}

Despite showing 6 vibrational modes, only 3 appear in the actual spectrum. There are two sets of degenerate vibrational modes at 1213cm-1 and 2716cm-1 respectively, which only appear in the spectrum as one peak respectively.In addition to this, the vibration at 2583cm-1 is not IR active as its vibrational mode does not incur a change in dipole moment as each H atom stretches out from the central B atom in a symmetrical fashion, as seen below.

[[File:Dariomongnoniractivemodeofbh3.jpg|300x300px]]

'''Molecular Orbital diagram of BH3'''

[[File:DmongBH3MOdiagram.jpg]]
''T.Hunt, 2018,Figure 5,Problem class 1: the MO diagram of BH3,''
''Molecular Orbitals in Inorganic Chemistry, Imperial College London, delivered November'' ''2018.''

There are no significant differences between the computed MOs and the LCAO derived MOs. For the most part LCAO is a reliable model for showing the MOs of a molecule, however there are certain aspects it fails to capture, such as the overlap of orbitals from the same fragment (see a1'). Electronic distribution is key to understanding reactivity of molecules, which is why LCAO is good for MO diagrams but less effective for more complex cases.

'''Optimisation of NH3'''

[[File:DmongNH3631goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843977D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !

Low frequencies --- -0.0137 -0.0027 0.0007 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''NH3BH3 optimisation'''

[[File:DmongNH3BH3631goptdataNEW.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.656419D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,8) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,8) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,7) 1.21 -DE/DX = -0.0001 !
! R5 R(5,7) 1.21 -DE/DX = -0.0001 !
! R6 R(6,7) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 113.8746 -DE/DX = 0.0 !
! A2 A(4,7,6) 113.8746 -DE/DX = 0.0 !
! A3 A(4,7,8) 104.5965 -DE/DX = 0.0 !
! A4 A(5,7,6) 113.8746 -DE/DX = 0.0 !
! A5 A(5,7,8) 104.5965 -DE/DX = 0.0 !
! A6 A(6,7,8) 104.5965 -DE/DX = 0.0 !
! A7 A(1,8,2) 107.8683 -DE/DX = 0.0 !
! A8 A(1,8,3) 107.8683 -DE/DX = 0.0 !
! A9 A(1,8,7) 111.0301 -DE/DX = 0.0 !
! A10 A(2,8,3) 107.8683 -DE/DX = 0.0 !
! A11 A(2,8,7) 111.0301 -DE/DX = 0.0 !
! A12 A(3,8,7) 111.0301 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 180.0 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 60.0 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 60.0 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 180.0 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0 -DE/DX = 0.0 !
! D8 D(6,7,8,2) 180.0 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0 -DE/DX = 0.0 !

Low frequencies --- -0.0251 -0.0029 0.0014 17.1170 17.1195 37.1145
Low frequencies --- 265.7734 632.2034 639.3448

'''NH3BH3 bond energy'''

{| class="wikitable" border="1"
|+ Energies
! Molecule !! Energy (atomic units)
|-
| NH3 || -56.56
|-
| BH3 || -26.62
|-
| NH3BH3 || -83.22
|}

(error associated with energy is 5 kjmol-1, which corresponds to 0.002 au, so calculations are given to 2dp)

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-83.22-(-56.56-26.62)
=-83.22 + 83.18
=-0.04 au
=-105.02 kjmol-1

A value of -105.02 kjmol-1 indicates an exothermic process as the overall energy change is negative, meaning that the process gives products which are more thermodynamically stable than the reactants. Comparing to a C-C bond in ethane which has an energy of formation of 346 kjmol-1, and the C-N bond in methylamine which has an energy of formation of 360 kjmol-1, we can ascertain that the dative covalent bond formed is quite weak relative to commonplace bonds in chemistry.

'''NI3 molecule'''

The optimised molecule can be found [[Media:DMONGNI3OPTFREQATT3.LOG| here]]

'''Jmol'''
<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGNI3OPTFREQATT3.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -12.3845 -12.3781 -5.6129 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2332

Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000630 0.001200 YES
Predicted change in Energy=-1.193062D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1842 -DE/DX = -0.0001 !
! R2 R(1,3) 2.1842 -DE/DX = -0.0001 !
! R3 R(1,4) 2.1842 -DE/DX = -0.0001 !
! A1 A(2,1,3) 110.8579 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8579 -DE/DX = -0.0001 !
! A3 A(3,1,4) 110.8579 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) -123.5674 -DE/DX = 0.0001 !

N-I bond lengthː 2.184 angstroms

=='''Mini-project: Metal Carbonyls'''==

for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

I am looking for comments and annotations:

indicating directly bonded vs through space interactions
the distance dependence ie weak vs medium vs strong interactions
discussion of polarized or directed interactions
mention of s,p or d relative intensity of overlap
the nodal character, on atoms is less antibonding than between atoms
AND a clean tidy diagram that is well annotated

In this mini-project I will be comparing the vibrational frequencies and bond lengths in three metal carbonyl complexesː [Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]. I will run optimisations on each of the structures and determine the bond lengths, and then will run frequency analysis on each of these optimised structures to give the vibrational frequencies.

The strength of the C=O is related to the extent of backbonding from the metal to the pi* star orbital of C=O - "increased electron density in the 2pi* orbital of the C=O molecule leads to a lower C-O bond order (and hence longer & weaker bond)" - see diagram below.

[[File:Dmongbackbondingdiag.jpg]]

Theory allows for prediction of the extent of backbonding, which will then be compared to the vibrational frequencies given from frequency analysis - the stretching frequencies of the C=O bond can be correlated to the bond strength, as given by the equation w = h/2pi x (kf/meff)^0.5, which shows that the fundamental frequency w is directly proportional to the spring constant kf which is effectively the bond strength. My prediction of which complex has the highest vibrational frequencies for C=O will be compared to the actual values from the frequency analysis and analysed for any discrepancies.

As shown above, theory predicts that the increased backbonding will incur a decrease in bond order of the C=O bond, and hence a longer bond. My prediction of which complex has the longest C=O bond will be compared to the actual bond lengths from the optimised molecule.

'''Predictions'''

The complexes I will be analysing are very similiar - they are all isoelectronic with d6 occupancy of the metal, have identical ligands (carbonyl - strong field) and are all low spin complexes with 18 electrons total. This means the only parameter which is different across the three is the charge on the metal, which since we're using neutral ligands is simply its oxidation state.

Theory provides a relationship between charge on a metal and the extent of backbonding; "Increasing negative charge leads to the expansion of d-orbitals, therefore greater overlap of M(dpi) with CO pi* / increased backbonding" - see diagram below.

[[File:Dmongcarbonylmetalcharge.jpg]]

In the three complexes I will be analysing ([Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]), the charges are as follows: Ti(2-), V(-1) and Cr(0). Given the order of magnitude of charge being Ti > V > Cr, and the theory stated previously, the predictions for vibrational frequencies and bond lengths are as follows:

Vibrational frequencies: Cr > V > Ti
Bond length of C=O: Ti > V > Cr

==='''[Ti(CO)6]2- analysis'''===

The molecule was first optimised and then frequency analysis was performed.

The link to the frequency file can be found [[Media:DMONGTI631FREQ.LOG| here]].

[[File:Dmongticomplexdata2.jpg]]

Low frequencies --- -0.0040 0.0052 0.0057 11.0002 11.0002 11.0002
Low frequencies --- 24.7494 24.7494 24.7494

Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000354 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-1.080563D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.0513 -DE/DX = 0.0 !
! R2 R(1,4) 2.0513 -DE/DX = 0.0 !
! R3 R(1,6) 2.0513 -DE/DX = 0.0 !
! R4 R(1,8) 2.0513 -DE/DX = 0.0 !
! R5 R(1,10) 2.0513 -DE/DX = 0.0 !
! R6 R(1,12) 2.0513 -DE/DX = 0.0 !
! R7 R(2,3) 1.1841 -DE/DX = -0.0002 !
! R8 R(4,5) 1.1841 -DE/DX = -0.0002 !
! R9 R(6,7) 1.1841 -DE/DX = -0.0002 !
! R10 R(8,9) 1.1841 -DE/DX = -0.0002 !
! R11 R(10,11) 1.1841 -DE/DX = -0.0002 !
! R12 R(12,13) 1.1841 -DE/DX = -0.0002 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,12) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,10) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,12,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,10,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) 90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,12,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,10,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) -90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for the C=O bond in this complex was found to be 1.18406 angstroms.

'''Vibrational Analysis'''

[[File:DmongticomplexIRdata.jpg]]

Here we can see two distinct peaks in the IR spectrum despite there being 33 unique vibrational modes. The vast majority of these peaks do not have a large enough intensity to be visible in IR. The two peaks lie at 619.05cm-1 and 1850.26cm-1. The peak at 619.05cm-1 represents the bending modes of the IR spectrum - there are 3 degenerate modes which have equal intensity and incur a change in dipole moment.
At 1850.26cm-1 there is a peak for stretching mode of the molecule, which has three degenerate modes of equal intensity. This indicates the extent of pi backbonding as discussed previously and will be compared against the other molecules.

==='''[V(CO)6]- analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGVGEN.LOG| here]].

[[File:DmongVgenoptdata.jpg]]

Low frequencies --- 0.0006 0.0006 0.0011 14.1311 14.1311 14.1311
Low frequencies --- 52.8916 52.8916 52.8916

Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000070 0.000300 YES
Maximum Displacement 0.001210 0.001800 YES
RMS Displacement 0.000591 0.001200 YES
Predicted change in Energy=-7.154807D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9542 -DE/DX = -0.0002 !
! R2 R(1,4) 1.9542 -DE/DX = -0.0002 !
! R3 R(1,6) 1.9542 -DE/DX = -0.0002 !
! R4 R(1,8) 1.9542 -DE/DX = -0.0002 !
! R5 R(1,10) 1.9542 -DE/DX = -0.0002 !
! R6 R(1,12) 1.9542 -DE/DX = -0.0002 !
! R7 R(2,3) 1.166 -DE/DX = 0.0 !
! R8 R(4,5) 1.166 -DE/DX = 0.0 !
! R9 R(6,7) 1.166 -DE/DX = 0.0 !
! R10 R(8,9) 1.166 -DE/DX = 0.0 !
! R11 R(10,11) 1.166 -DE/DX = 0.0 !
! R12 R(12,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,10) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,12) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,10,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,12,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) -90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,10,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,12,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The C=O bond length in this complex was found to be 1.16599 angstroms.

'''Vibrational Analysis'''

[[File:DmongVgenfreqdata.jpg]]

There are 2 distinct peaks in the IR spcetrum, similarly to the Ti complex. The larger peak is at 1968.91cm-1, and represents the C=O stretching mode. The lesser peak is at 689.44cm-1, and represents the bending mode of the complex. The other modes present are not intense enough to be visible on an IR spectrum.

==='''[Cr(CO)6] analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:| here]].

[[File:DmongCrgenoptdata.jpg]]

Low frequencies --- -0.0012 -0.0011 -0.0011 10.3820 10.3820 10.3820
Low frequencies --- 66.4094 66.4094 66.4094

Item Value Threshold Converged?
Maximum Force 0.000154 0.000450 YES
RMS Force 0.000055 0.000300 YES
Maximum Displacement 0.000386 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.123831D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1494 -DE/DX = 0.0002 !
! R2 R(1,13) 1.9149 -DE/DX = 0.0 !
! R3 R(3,4) 1.1494 -DE/DX = 0.0002 !
! R4 R(3,13) 1.9149 -DE/DX = 0.0 !
! R5 R(5,6) 1.1494 -DE/DX = 0.0002 !
! R6 R(5,13) 1.9149 -DE/DX = 0.0 !
! R7 R(7,8) 1.1494 -DE/DX = 0.0002 !
! R8 R(7,13) 1.9149 -DE/DX = 0.0 !
! R9 R(9,10) 1.1494 -DE/DX = 0.0002 !
! R10 R(9,13) 1.9149 -DE/DX = 0.0 !
! R11 R(11,12) 1.1494 -DE/DX = 0.0002 !
! R12 R(11,13) 1.9149 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for C=O in this complex was found to be 1.14938 angstroms.

'''Vibrational Analysis'''

[[File:DmongCrgenfreqdata.jpg]]

Rep:Mod:dariomong01351899MO

2019-05-23T16:25:12Z

Dm1417: /* [Ti(CO)6]2- analysis */

== '''BH3 molecule''' ==

'''3-21G optimisation'''

[[File:DmongBH3321goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.

[[File:DmongBH3321ggraphs.jpg]]

The optimisation file is linked [[Media:DMONGBH3OPT.LOG| here]].

'''6-21G optimisation'''

[[File:DmongBH3621goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128957D-09
Optimization completed.
-- Stationary point found.

The molecule was then constrained to a D3h symmetry and then optimised again by 6-21G.

[[File: DmongBH3621gd3hoptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-1.240669D-09
Optimization completed.
-- Stationary point found.

'''Frequency analysis of BH3'''

[[File:DmongBH3621gbfreqoptdata.jpg]]

'''Low frequencies --- -15.9849 -15.9818 -12.7207 0.0007 0.0143 0.3137'''
'''Low frequencies --- 1162.9365 1213.1134 1213.1136'''
Diagonal vibrational polarizability:
0.7178921 0.7178603 1.8420487
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9365 1213.1134 1213.1136
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9985 0.9600 0.9600
IR Inten -- 92.5721 14.0532 14.0527
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.7141 2715.8636 2715.8645
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9608 4.8992 4.8992
IR Inten -- 0.0000 126.3274 126.3214
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
4 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00

The optimised molecule can be found [[Media:DMONGBH3OPT631GB.LOG| here]]

'''Jmol of optimised BH3 molecule'''
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGBH3OPT631GB.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Infrared Spectrum of BH3'''
[[File:DmongBH3621gbfreqvibr.jpg|700x700px]]

{| class="wikitable" border="1"
|+ Infrared Spectrum Vibrations
! Vibrational frequency (cm-1) !! Intensity (dimensionless) !! Symmetry !! IR Active !! Type !
|-
| 1163 || 93 || A2" || Yes || symmetric bend (wagging)
|-
| 1213 || 14 || E' || Yes || antisymmetric bend (rocking)
|-
| 1213 || 14 || E' || Yes || symmetric bend (scissoring)
|-
| 2583 || 0 || A1' || No || symmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|}

Despite showing 6 vibrational modes, only 3 appear in the actual spectrum. There are two sets of degenerate vibrational modes at 1213cm-1 and 2716cm-1 respectively, which only appear in the spectrum as one peak respectively.In addition to this, the vibration at 2583cm-1 is not IR active as its vibrational mode does not incur a change in dipole moment as each H atom stretches out from the central B atom in a symmetrical fashion, as seen below.

[[File:Dariomongnoniractivemodeofbh3.jpg|300x300px]]

'''Molecular Orbital diagram of BH3'''

[[File:DmongBH3MOdiagram.jpg]]
''T.Hunt, 2018,Figure 5,Problem class 1: the MO diagram of BH3,''
''Molecular Orbitals in Inorganic Chemistry, Imperial College London, delivered November'' ''2018.''

There are no significant differences between the computed MOs and the LCAO derived MOs. For the most part LCAO is a reliable model for showing the MOs of a molecule, however there are certain aspects it fails to capture, such as the overlap of orbitals from the same fragment (see a1'). Electronic distribution is key to understanding reactivity of molecules, which is why LCAO is good for MO diagrams but less effective for more complex cases.

'''Optimisation of NH3'''

[[File:DmongNH3631goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843977D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !

Low frequencies --- -0.0137 -0.0027 0.0007 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''NH3BH3 optimisation'''

[[File:DmongNH3BH3631goptdataNEW.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.656419D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,8) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,8) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,7) 1.21 -DE/DX = -0.0001 !
! R5 R(5,7) 1.21 -DE/DX = -0.0001 !
! R6 R(6,7) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 113.8746 -DE/DX = 0.0 !
! A2 A(4,7,6) 113.8746 -DE/DX = 0.0 !
! A3 A(4,7,8) 104.5965 -DE/DX = 0.0 !
! A4 A(5,7,6) 113.8746 -DE/DX = 0.0 !
! A5 A(5,7,8) 104.5965 -DE/DX = 0.0 !
! A6 A(6,7,8) 104.5965 -DE/DX = 0.0 !
! A7 A(1,8,2) 107.8683 -DE/DX = 0.0 !
! A8 A(1,8,3) 107.8683 -DE/DX = 0.0 !
! A9 A(1,8,7) 111.0301 -DE/DX = 0.0 !
! A10 A(2,8,3) 107.8683 -DE/DX = 0.0 !
! A11 A(2,8,7) 111.0301 -DE/DX = 0.0 !
! A12 A(3,8,7) 111.0301 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 180.0 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 60.0 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 60.0 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 180.0 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0 -DE/DX = 0.0 !
! D8 D(6,7,8,2) 180.0 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0 -DE/DX = 0.0 !

Low frequencies --- -0.0251 -0.0029 0.0014 17.1170 17.1195 37.1145
Low frequencies --- 265.7734 632.2034 639.3448

'''NH3BH3 bond energy'''

{| class="wikitable" border="1"
|+ Energies
! Molecule !! Energy (atomic units)
|-
| NH3 || -56.56
|-
| BH3 || -26.62
|-
| NH3BH3 || -83.22
|}

(error associated with energy is 5 kjmol-1, which corresponds to 0.002 au, so calculations are given to 2dp)

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-83.22-(-56.56-26.62)
=-83.22 + 83.18
=-0.04 au
=-105.02 kjmol-1

A value of -105.02 kjmol-1 indicates an exothermic process as the overall energy change is negative, meaning that the process gives products which are more thermodynamically stable than the reactants. Comparing to a C-C bond in ethane which has an energy of formation of 346 kjmol-1, and the C-N bond in methylamine which has an energy of formation of 360 kjmol-1, we can ascertain that the dative covalent bond formed is quite weak relative to commonplace bonds in chemistry.

'''NI3 molecule'''

The optimised molecule can be found [[Media:DMONGNI3OPTFREQATT3.LOG| here]]

'''Jmol'''
<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGNI3OPTFREQATT3.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -12.3845 -12.3781 -5.6129 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2332

Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000630 0.001200 YES
Predicted change in Energy=-1.193062D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1842 -DE/DX = -0.0001 !
! R2 R(1,3) 2.1842 -DE/DX = -0.0001 !
! R3 R(1,4) 2.1842 -DE/DX = -0.0001 !
! A1 A(2,1,3) 110.8579 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8579 -DE/DX = -0.0001 !
! A3 A(3,1,4) 110.8579 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) -123.5674 -DE/DX = 0.0001 !

N-I bond lengthː 2.184 angstroms

=='''Mini-project: Metal Carbonyls'''==

for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

I am looking for comments and annotations:

indicating directly bonded vs through space interactions
the distance dependence ie weak vs medium vs strong interactions
discussion of polarized or directed interactions
mention of s,p or d relative intensity of overlap
the nodal character, on atoms is less antibonding than between atoms
AND a clean tidy diagram that is well annotated

In this mini-project I will be comparing the vibrational frequencies and bond lengths in three metal carbonyl complexesː [Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]. I will run optimisations on each of the structures and determine the bond lengths, and then will run frequency analysis on each of these optimised structures to give the vibrational frequencies.

The strength of the C=O is related to the extent of backbonding from the metal to the pi* star orbital of C=O - "increased electron density in the 2pi* orbital of the C=O molecule leads to a lower C-O bond order (and hence longer & weaker bond)" - see diagram below.

[[File:Dmongbackbondingdiag.jpg]]

Theory allows for prediction of the extent of backbonding, which will then be compared to the vibrational frequencies given from frequency analysis - the stretching frequencies of the C=O bond can be correlated to the bond strength, as given by the equation w = h/2pi x (kf/meff)^0.5, which shows that the fundamental frequency w is directly proportional to the spring constant kf which is effectively the bond strength. My prediction of which complex has the highest vibrational frequencies for C=O will be compared to the actual values from the frequency analysis and analysed for any discrepancies.

As shown above, theory predicts that the increased backbonding will incur a decrease in bond order of the C=O bond, and hence a longer bond. My prediction of which complex has the longest C=O bond will be compared to the actual bond lengths from the optimised molecule.

'''Predictions'''

The complexes I will be analysing are very similiar - they are all isoelectronic with d6 occupancy of the metal, have identical ligands (carbonyl - strong field) and are all low spin complexes with 18 electrons total. This means the only parameter which is different across the three is the charge on the metal, which since we're using neutral ligands is simply its oxidation state.

Theory provides a relationship between charge on a metal and the extent of backbonding; "Increasing negative charge leads to the expansion of d-orbitals, therefore greater overlap of M(dpi) with CO pi* / increased backbonding" - see diagram below.

[[File:Dmongcarbonylmetalcharge.jpg]]

In the three complexes I will be analysing ([Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]), the charges are as follows: Ti(2-), V(-1) and Cr(0). Given the order of magnitude of charge being Ti > V > Cr, and the theory stated previously, the predictions for vibrational frequencies and bond lengths are as follows:

Vibrational frequencies: Cr > V > Ti
Bond length of C=O: Ti > V > Cr

==='''[Ti(CO)6]2- analysis'''===

The molecule was first optimised and then frequency analysis was performed.

The link to the frequency file can be found [[Media:DMONGTI631FREQ.LOG| here]].

[[File:Dmongticomplexdata2.jpg]]

Low frequencies --- -0.0040 0.0052 0.0057 11.0002 11.0002 11.0002
Low frequencies --- 24.7494 24.7494 24.7494

Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000354 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-1.080563D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.0513 -DE/DX = 0.0 !
! R2 R(1,4) 2.0513 -DE/DX = 0.0 !
! R3 R(1,6) 2.0513 -DE/DX = 0.0 !
! R4 R(1,8) 2.0513 -DE/DX = 0.0 !
! R5 R(1,10) 2.0513 -DE/DX = 0.0 !
! R6 R(1,12) 2.0513 -DE/DX = 0.0 !
! R7 R(2,3) 1.1841 -DE/DX = -0.0002 !
! R8 R(4,5) 1.1841 -DE/DX = -0.0002 !
! R9 R(6,7) 1.1841 -DE/DX = -0.0002 !
! R10 R(8,9) 1.1841 -DE/DX = -0.0002 !
! R11 R(10,11) 1.1841 -DE/DX = -0.0002 !
! R12 R(12,13) 1.1841 -DE/DX = -0.0002 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,12) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,10) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,12,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,10,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) 90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,12,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,10,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) -90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for the C=O bond in this complex was found to be 1.18406 angstroms.

'''Vibrational Analysis'''

[[File:DmongticomplexIRdata.jpg]]

Here we can see two distinct peaks in the IR spectrum despite there being 33 unique vibrational modes. The vast majority of these peaks do not have a large enough intensity to be visible in IR. The two peaks lie at 619.05cm-1 and 1850.26cm-1. The peak at 619.05cm-1 represents the bending modes of the IR spectrum - there are 3 degenerate modes which have equal intensity and incur a change in dipole moment.
At 1850.26cm-1 there is a peak for stretching mode of the molecule, which has three degenerate modes of equal intensity. This indicates the extent of pi backbonding as discussed previously and will be compared against the other molecules.

==='''[V(CO)6]- analysis'''===

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGVGEN.LOG| here]].

[[File:DmongVgenoptdata.jpg]]

Low frequencies --- 0.0006 0.0006 0.0011 14.1311 14.1311 14.1311
Low frequencies --- 52.8916 52.8916 52.8916

Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000070 0.000300 YES
Maximum Displacement 0.001210 0.001800 YES
RMS Displacement 0.000591 0.001200 YES
Predicted change in Energy=-7.154807D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9542 -DE/DX = -0.0002 !
! R2 R(1,4) 1.9542 -DE/DX = -0.0002 !
! R3 R(1,6) 1.9542 -DE/DX = -0.0002 !
! R4 R(1,8) 1.9542 -DE/DX = -0.0002 !
! R5 R(1,10) 1.9542 -DE/DX = -0.0002 !
! R6 R(1,12) 1.9542 -DE/DX = -0.0002 !
! R7 R(2,3) 1.166 -DE/DX = 0.0 !
! R8 R(4,5) 1.166 -DE/DX = 0.0 !
! R9 R(6,7) 1.166 -DE/DX = 0.0 !
! R10 R(8,9) 1.166 -DE/DX = 0.0 !
! R11 R(10,11) 1.166 -DE/DX = 0.0 !
! R12 R(12,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,10) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,12) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,10,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,12,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) -90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,10,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,12,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The C=O bond length in this complex was found to be 1.16599 angstroms.

'''Vibrational Analysis'''

[[File:DmongVgenfreqdata.jpg]]

There are 2 distinct peaks in the IR spcetrum, similarly to the Ti complex. The larger peak is at 1968.91cm-1, and represents the C=O stretching mode. The lesser peak is at 689.44cm-1, and represents the bending mode of the complex. The other modes present are not intense enough to be visible on an IR spectrum.

'''[Cr(CO)6] analysis'''

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:| here]].

[[File:DmongCrgenoptdata.jpg]]

Low frequencies --- -0.0012 -0.0011 -0.0011 10.3820 10.3820 10.3820
Low frequencies --- 66.4094 66.4094 66.4094

Item Value Threshold Converged?
Maximum Force 0.000154 0.000450 YES
RMS Force 0.000055 0.000300 YES
Maximum Displacement 0.000386 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.123831D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1494 -DE/DX = 0.0002 !
! R2 R(1,13) 1.9149 -DE/DX = 0.0 !
! R3 R(3,4) 1.1494 -DE/DX = 0.0002 !
! R4 R(3,13) 1.9149 -DE/DX = 0.0 !
! R5 R(5,6) 1.1494 -DE/DX = 0.0002 !
! R6 R(5,13) 1.9149 -DE/DX = 0.0 !
! R7 R(7,8) 1.1494 -DE/DX = 0.0002 !
! R8 R(7,13) 1.9149 -DE/DX = 0.0 !
! R9 R(9,10) 1.1494 -DE/DX = 0.0002 !
! R10 R(9,13) 1.9149 -DE/DX = 0.0 !
! R11 R(11,12) 1.1494 -DE/DX = 0.0002 !
! R12 R(11,13) 1.9149 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for C=O in this complex was found to be 1.14938 angstroms.

'''Vibrational Analysis'''

[[File:DmongCrgenfreqdata.jpg]]

Rep:Mod:dariomong01351899MO

2019-05-23T16:22:33Z

Dm1417:

== '''BH3 molecule''' ==

'''3-21G optimisation'''

[[File:DmongBH3321goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.

[[File:DmongBH3321ggraphs.jpg]]

The optimisation file is linked [[Media:DMONGBH3OPT.LOG| here]].

'''6-21G optimisation'''

[[File:DmongBH3621goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.128957D-09
Optimization completed.
-- Stationary point found.

The molecule was then constrained to a D3h symmetry and then optimised again by 6-21G.

[[File: DmongBH3621gd3hoptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000037 0.001200 YES
Predicted change in Energy=-1.240669D-09
Optimization completed.
-- Stationary point found.

'''Frequency analysis of BH3'''

[[File:DmongBH3621gbfreqoptdata.jpg]]

'''Low frequencies --- -15.9849 -15.9818 -12.7207 0.0007 0.0143 0.3137'''
'''Low frequencies --- 1162.9365 1213.1134 1213.1136'''
Diagonal vibrational polarizability:
0.7178921 0.7178603 1.8420487
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9365 1213.1134 1213.1136
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9985 0.9600 0.9600
IR Inten -- 92.5721 14.0532 14.0527
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.7141 2715.8636 2715.8645
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9608 4.8992 4.8992
IR Inten -- 0.0000 126.3274 126.3214
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
4 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00

The optimised molecule can be found [[Media:DMONGBH3OPT631GB.LOG| here]]

'''Jmol of optimised BH3 molecule'''
<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGBH3OPT631GB.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''Infrared Spectrum of BH3'''
[[File:DmongBH3621gbfreqvibr.jpg|700x700px]]

{| class="wikitable" border="1"
|+ Infrared Spectrum Vibrations
! Vibrational frequency (cm-1) !! Intensity (dimensionless) !! Symmetry !! IR Active !! Type !
|-
| 1163 || 93 || A2" || Yes || symmetric bend (wagging)
|-
| 1213 || 14 || E' || Yes || antisymmetric bend (rocking)
|-
| 1213 || 14 || E' || Yes || symmetric bend (scissoring)
|-
| 2583 || 0 || A1' || No || symmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|-
| 2716 || 126 || E' || Yes || antisymmetric stretch
|}

Despite showing 6 vibrational modes, only 3 appear in the actual spectrum. There are two sets of degenerate vibrational modes at 1213cm-1 and 2716cm-1 respectively, which only appear in the spectrum as one peak respectively.In addition to this, the vibration at 2583cm-1 is not IR active as its vibrational mode does not incur a change in dipole moment as each H atom stretches out from the central B atom in a symmetrical fashion, as seen below.

[[File:Dariomongnoniractivemodeofbh3.jpg|300x300px]]

'''Molecular Orbital diagram of BH3'''

[[File:DmongBH3MOdiagram.jpg]]
''T.Hunt, 2018,Figure 5,Problem class 1: the MO diagram of BH3,''
''Molecular Orbitals in Inorganic Chemistry, Imperial College London, delivered November'' ''2018.''

There are no significant differences between the computed MOs and the LCAO derived MOs. For the most part LCAO is a reliable model for showing the MOs of a molecule, however there are certain aspects it fails to capture, such as the overlap of orbitals from the same fragment (see a1'). Electronic distribution is key to understanding reactivity of molecules, which is why LCAO is good for MO diagrams but less effective for more complex cases.

'''Optimisation of NH3'''

[[File:DmongNH3631goptdata.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.843977D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !

Low frequencies --- -0.0137 -0.0027 0.0007 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

'''NH3BH3 optimisation'''

[[File:DmongNH3BH3631goptdataNEW.jpg]]

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.656419D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.0186 -DE/DX = -0.0001 !
! R2 R(2,8) 1.0186 -DE/DX = -0.0001 !
! R3 R(3,8) 1.0186 -DE/DX = -0.0001 !
! R4 R(4,7) 1.21 -DE/DX = -0.0001 !
! R5 R(5,7) 1.21 -DE/DX = -0.0001 !
! R6 R(6,7) 1.21 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 113.8746 -DE/DX = 0.0 !
! A2 A(4,7,6) 113.8746 -DE/DX = 0.0 !
! A3 A(4,7,8) 104.5965 -DE/DX = 0.0 !
! A4 A(5,7,6) 113.8746 -DE/DX = 0.0 !
! A5 A(5,7,8) 104.5965 -DE/DX = 0.0 !
! A6 A(6,7,8) 104.5965 -DE/DX = 0.0 !
! A7 A(1,8,2) 107.8683 -DE/DX = 0.0 !
! A8 A(1,8,3) 107.8683 -DE/DX = 0.0 !
! A9 A(1,8,7) 111.0301 -DE/DX = 0.0 !
! A10 A(2,8,3) 107.8683 -DE/DX = 0.0 !
! A11 A(2,8,7) 111.0301 -DE/DX = 0.0 !
! A12 A(3,8,7) 111.0301 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 180.0 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 60.0 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 60.0 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 180.0 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0 -DE/DX = 0.0 !
! D8 D(6,7,8,2) 180.0 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0 -DE/DX = 0.0 !

Low frequencies --- -0.0251 -0.0029 0.0014 17.1170 17.1195 37.1145
Low frequencies --- 265.7734 632.2034 639.3448

'''NH3BH3 bond energy'''

{| class="wikitable" border="1"
|+ Energies
! Molecule !! Energy (atomic units)
|-
| NH3 || -56.56
|-
| BH3 || -26.62
|-
| NH3BH3 || -83.22
|}

(error associated with energy is 5 kjmol-1, which corresponds to 0.002 au, so calculations are given to 2dp)

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-83.22-(-56.56-26.62)
=-83.22 + 83.18
=-0.04 au
=-105.02 kjmol-1

A value of -105.02 kjmol-1 indicates an exothermic process as the overall energy change is negative, meaning that the process gives products which are more thermodynamically stable than the reactants. Comparing to a C-C bond in ethane which has an energy of formation of 346 kjmol-1, and the C-N bond in methylamine which has an energy of formation of 360 kjmol-1, we can ascertain that the dative covalent bond formed is quite weak relative to commonplace bonds in chemistry.

'''NI3 molecule'''

The optimised molecule can be found [[Media:DMONGNI3OPTFREQATT3.LOG| here]]

'''Jmol'''
<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>DMONGNI3OPTFREQATT3.LOG</uploadedFileContents>
</jmolApplet></jmol>

Low frequencies --- -12.3845 -12.3781 -5.6129 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2332

Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000630 0.001200 YES
Predicted change in Energy=-1.193062D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1842 -DE/DX = -0.0001 !
! R2 R(1,3) 2.1842 -DE/DX = -0.0001 !
! R3 R(1,4) 2.1842 -DE/DX = -0.0001 !
! A1 A(2,1,3) 110.8579 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8579 -DE/DX = -0.0001 !
! A3 A(3,1,4) 110.8579 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) -123.5674 -DE/DX = 0.0001 !

N-I bond lengthː 2.184 angstroms

=='''Mini-project: Metal Carbonyls'''==

for every molecule studied provide a link to the frequency file (NOT the optimisation). Provide the "summary", the "Item" table, the "low frequencies" lines and show that there are no negative frequencies.

I am looking for comments and annotations:

indicating directly bonded vs through space interactions
the distance dependence ie weak vs medium vs strong interactions
discussion of polarized or directed interactions
mention of s,p or d relative intensity of overlap
the nodal character, on atoms is less antibonding than between atoms
AND a clean tidy diagram that is well annotated

In this mini-project I will be comparing the vibrational frequencies and bond lengths in three metal carbonyl complexesː [Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]. I will run optimisations on each of the structures and determine the bond lengths, and then will run frequency analysis on each of these optimised structures to give the vibrational frequencies.

The strength of the C=O is related to the extent of backbonding from the metal to the pi* star orbital of C=O - "increased electron density in the 2pi* orbital of the C=O molecule leads to a lower C-O bond order (and hence longer & weaker bond)" - see diagram below.

[[File:Dmongbackbondingdiag.jpg]]

Theory allows for prediction of the extent of backbonding, which will then be compared to the vibrational frequencies given from frequency analysis - the stretching frequencies of the C=O bond can be correlated to the bond strength, as given by the equation w = h/2pi x (kf/meff)^0.5, which shows that the fundamental frequency w is directly proportional to the spring constant kf which is effectively the bond strength. My prediction of which complex has the highest vibrational frequencies for C=O will be compared to the actual values from the frequency analysis and analysed for any discrepancies.

As shown above, theory predicts that the increased backbonding will incur a decrease in bond order of the C=O bond, and hence a longer bond. My prediction of which complex has the longest C=O bond will be compared to the actual bond lengths from the optimised molecule.

'''Predictions'''

The complexes I will be analysing are very similiar - they are all isoelectronic with d6 occupancy of the metal, have identical ligands (carbonyl - strong field) and are all low spin complexes with 18 electrons total. This means the only parameter which is different across the three is the charge on the metal, which since we're using neutral ligands is simply its oxidation state.

Theory provides a relationship between charge on a metal and the extent of backbonding; "Increasing negative charge leads to the expansion of d-orbitals, therefore greater overlap of M(dpi) with CO pi* / increased backbonding" - see diagram below.

[[File:Dmongcarbonylmetalcharge.jpg]]

In the three complexes I will be analysing ([Ti(CO)6]2-, [V(CO)6]- and [Cr(CO)6]), the charges are as follows: Ti(2-), V(-1) and Cr(0). Given the order of magnitude of charge being Ti > V > Cr, and the theory stated previously, the predictions for vibrational frequencies and bond lengths are as follows:

Vibrational frequencies: Cr > V > Ti
Bond length of C=O: Ti > V > Cr

==='''[Ti(CO)6]2- analysis'''===

The molecule was first optimised and then frequency analysis was performed.

The link to the frequency file can be found [[Media:DMONGTI631FREQ.LOG| here]].

[[File:Dmongticomplexdata2.jpg]]

Low frequencies --- -0.0040 0.0052 0.0057 11.0002 11.0002 11.0002
Low frequencies --- 24.7494 24.7494 24.7494

Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000354 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-1.080563D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.0513 -DE/DX = 0.0 !
! R2 R(1,4) 2.0513 -DE/DX = 0.0 !
! R3 R(1,6) 2.0513 -DE/DX = 0.0 !
! R4 R(1,8) 2.0513 -DE/DX = 0.0 !
! R5 R(1,10) 2.0513 -DE/DX = 0.0 !
! R6 R(1,12) 2.0513 -DE/DX = 0.0 !
! R7 R(2,3) 1.1841 -DE/DX = -0.0002 !
! R8 R(4,5) 1.1841 -DE/DX = -0.0002 !
! R9 R(6,7) 1.1841 -DE/DX = -0.0002 !
! R10 R(8,9) 1.1841 -DE/DX = -0.0002 !
! R11 R(10,11) 1.1841 -DE/DX = -0.0002 !
! R12 R(12,13) 1.1841 -DE/DX = -0.0002 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,12) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,10) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,12,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,10,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) 90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,12,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,10,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) -90.0 -DE/DX = 0.0 !

'''Bond length'''

The bond length for the C=O bond in this complex was found to be 1.18406 angstroms.

'''Vibrational Analysis'''

[[File:DmongticomplexIRdata.jpg]]

Here we can see two distinct peaks in the IR spectrum despite there being 33 unique vibrational modes. The vast majority of these peaks do not have a large enough intensity to be visible in IR. The two peaks lie at 619.05cm-1 and 1850.26cm-1. The peak at 619.05cm-1 represents the bending modes of the IR spectrum - there are 3 degenerate modes which have equal intensity and incur a change in dipole moment.
At 1850.26cm-1 there is a peak for stretching mode of the molecule, which has three degenerate modes of equal intensity. This indicates the extent of pi backbonding as discussed previously and will be compared against the other molecules.

'''[V(CO)6]- analysis'''

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:DMONGVGEN.LOG| here]].

[[File:DmongVgenoptdata.jpg]]

Low frequencies --- 0.0006 0.0006 0.0011 14.1311 14.1311 14.1311
Low frequencies --- 52.8916 52.8916 52.8916

Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000070 0.000300 YES
Maximum Displacement 0.001210 0.001800 YES
RMS Displacement 0.000591 0.001200 YES
Predicted change in Energy=-7.154807D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9542 -DE/DX = -0.0002 !
! R2 R(1,4) 1.9542 -DE/DX = -0.0002 !
! R3 R(1,6) 1.9542 -DE/DX = -0.0002 !
! R4 R(1,8) 1.9542 -DE/DX = -0.0002 !
! R5 R(1,10) 1.9542 -DE/DX = -0.0002 !
! R6 R(1,12) 1.9542 -DE/DX = -0.0002 !
! R7 R(2,3) 1.166 -DE/DX = 0.0 !
! R8 R(4,5) 1.166 -DE/DX = 0.0 !
! R9 R(6,7) 1.166 -DE/DX = 0.0 !
! R10 R(8,9) 1.166 -DE/DX = 0.0 !
! R11 R(10,11) 1.166 -DE/DX = 0.0 !
! R12 R(12,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,8) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,10) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,12) 90.0 -DE/DX = 0.0 !
! A5 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A6 A(4,1,8) 90.0 -DE/DX = 0.0 !
! A7 A(4,1,10) 90.0 -DE/DX = 0.0 !
! A8 A(6,1,8) 90.0 -DE/DX = 0.0 !
! A9 A(6,1,10) 90.0 -DE/DX = 0.0 !
! A10 A(6,1,12) 90.0 -DE/DX = 0.0 !
! A11 A(8,1,12) 90.0 -DE/DX = 0.0 !
! A12 A(10,1,12) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,6,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,1,12,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(8,1,10,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,3,5,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,4,5,3,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,6,7,5,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,8,9,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,10,11,3,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,12,13,3,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,6,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,1,12,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(8,1,10,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,3,5,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,4,5,3,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,6,7,5,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,8,9,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,10,11,3,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,12,13,3,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,8,4) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,10,4) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,12,8) 90.0 -DE/DX = 0.0 !
! D4 D(2,1,12,10) -90.0 -DE/DX = 0.0 !
! D5 D(4,1,8,6) 90.0 -DE/DX = 0.0 !
! D6 D(4,1,10,6) -90.0 -DE/DX = 0.0 !
! D7 D(6,1,12,8) -90.0 -DE/DX = 0.0 !
! D8 D(6,1,12,10) 90.0 -DE/DX = 0.0 !

'''Bond length'''

The C=O bond length in this complex was found to be 1.16599 angstroms.

'''Vibrational Analysis'''

[[File:DmongVgenfreqdata.jpg]]

There are 2 distinct peaks in the IR spcetrum, similarly to the Ti complex. The larger peak is at 1968.91cm-1, and represents the C=O stretching mode. The lesser peak is at 689.44cm-1, and represents the bending mode of the complex. The other modes present are not intense enough to be visible on an IR spectrum.

'''[Cr(CO)6] analysis'''

After optimisation, frequency analysis was performed. A link to the molecule can be found [[Media:| here]].

[[File:DmongCrgenoptdata.jpg]]

Low frequencies --- -0.0012 -0.0011 -0.0011 10.3820 10.3820 10.3820
Low frequencies --- 66.4094 66.4094 66.4094

Item Value Threshold Converged?
Maximum Force 0.000154 0.000450 YES
RMS Force 0.000055 0.000300 YES
Maximum Displacement 0.000386 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.123831D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1494 -DE/DX = 0.0002 !
! R2 R(1,13) 1.9149 -DE/DX = 0.0 !
! R3 R(3,4) 1.1494 -DE/DX = 0.0002 !
! R4 R(3,13) 1.9149 -DE/DX = 0.0 !
! R5 R(5,6) 1.1494 -DE/DX = 0.0002 !
! R6 R(5,13) 1.9149 -DE/DX = 0.0 !
! R7 R(7,8) 1.1494 -DE/DX = 0.0002 !
! R8 R(7,13) 1.9149 -DE/DX = 0.0 !
! R9 R(9,10) 1.1494 -DE/DX = 0.0002 !
! R10 R(9,13) 1.9149 -DE/DX = 0.0 !
! R11 R(11,12) 1.1494 -DE/DX = 0.0002 !
! R12 R(11,13) 1.9149 -DE/DX = 0.0 !
! A1 A(1,13,3) 90.0 -DE/DX = 0.0 !
! A2 A(1,13,7) 90.0 -DE/DX = 0.0 !
! A3 A(1,13,9) 90.0 -DE/DX = 0.0 !
! A4 A(1,13,11) 90.0 -DE/DX = 0.0 !
! A5 A(3,13,5) 90.0 -DE/DX = 0.0 !
! A6 A(3,13,7) 90.0 -DE/DX = 0.0 !
! A7 A(3,13,9) 90.0 -DE/DX = 0.0 !
! A8 A(5,13,7) 90.0 -DE/DX = 0.0 !
! A9 A(5,13,9) 90.0 -DE/DX = 0.0 !
! A10 A(5,13,11) 90.0 -DE/DX = 0.0 !
! A11 A(7,13,11) 90.0 -DE/DX = 0.0 !
! A12 A(9,13,11) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,13,4,-1) 180.0 -DE/DX = 0.0 !
! A14 L(4,3,13,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,5,13,4,-1) 180.0 -DE/DX = 0.0 !
! A16 L(8,7,13,2,-1) 180.0 -DE/DX = 0.0 !
! A17 L(10,9,13,2,-1) 180.0 -DE/DX = 0.0 !
! A18 L(12,11,13,2,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,13,5,3,-1) 180.0 -DE/DX = 0.0 !
! A20 L(3,13,11,1,-1) 180.0 -DE/DX = 0.0 !
! A21 L(7,13,9,1,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,13,4,-2) 180.0 -DE/DX = 0.0 !
! A23 L(4,3,13,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,5,13,4,-2) 180.0 -DE/DX = 0.0 !
! A25 L(8,7,13,2,-2) 180.0 -DE/DX = 0.0 !
! A26 L(10,9,13,2,-2) 180.0 -DE/DX = 0.0 !
! A27 L(12,11,13,2,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,13,5,3,-2) 180.0 -DE/DX = 0.0 !
! A29 L(3,13,11,1,-2) 180.0 -DE/DX = 0.0 !
! A30 L(7,13,9,1,-2) 180.0 -DE/DX = 0.0 !
! D1 D(1,13,7,3) 90.0 -DE/DX = 0.0 !
! D2 D(1,13,9,3) -90.0 -DE/DX = 0.0 !
! D3 D(1,13,11,7) 90.0 -DE/DX = 0.0 !
! D4 D(1,13,11,9) -90.0 -DE/DX = 0.0 !
! D5 D(3,13,7,5) 90.0 -DE/DX = 0.0 !
! D6 D(3,13,9,5) -90.0 -DE/DX = 0.0 !
! D7 D(5,13,11,7) -90.0 -DE/DX = 0.0 !
! D8 D(5,13,11,9) 90.0 -DE/DX = 0.0 !

'''Vibrational Analysis'''

[[File:DmongCrgenfreqdata.jpg]]

Rep:Mod:dariomong01351899MO

2019-05-23T16:21:58Z

2019-05-23T16:18:29Z

2019-05-23T15:07:17Z

Dm1417: