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Optimising a molecule of BH3

3-21G

The structure of BH3 was manipulated with each BH unit having a different bond length (1.53, 1.54, 1.55 Angstroms) in order to break the symmetry of the molecule. This structure was optimized using the basis set 3-21G;

summary of Gaussian information

log file: File:JNBH3 OPT.LOG

  • average bond lengths for BH unit= (1.19445+1.91467+1.9480)/3 = 1.19464Å≈1.19Å
  • literature [1]: 1.19001Å
  • average bond angle= (119.989+120.016+119.998)= 120.048°≈ 120.0°

Gaussview reduced the bond length of the structure and made the lengths the same to 2 decimal places(dp). Showing that the inputted structure was not favorable, also the bond angles show that BH3 is a D3h point group. The bond length calculation is longer than the reference but similar by 2dp which is acceptable, the structure can be optimised further by using a higher basis set.

Gaussian Calculation Summary
BH3 Optimisation
file type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 3-21G
Final Energy -26.46226429 a.u.
gradient 0.00008851 a.u
dipole moment 0.0003 Debye
point group CS
length 25.0 seconds 
Item               Value     Threshold  Converged?

Maximum Force            0.000220     0.000450     YES

RMS     Force            0.000106     0.000300     YES

Maximum Displacement     0.000940     0.001800     YES

RMS     Displacement     0.000447     0.001200     YES

Predicted change in Energy=-1.672479D-07

Optimization completed.

-- Stationary point found.

----------------------------

!   Optimized Parameters   !

! (Angstroms and Degrees)  !

using 6-31G(d,p)

The optimised BH3 structure was optimised further by using a higher basis set of 6-31G. Initially this produced a structure of point group CS which converged, however when running the frequency analysis the low frequency range exceeded the acceptable level of ±15. Summary of Gaussion information

link to log file: File:JNBH3 OPT 631G DP.LOG log file with additional keywords:File:JN BH3 OPT 10.LOG

  • average bond length:1.19231≈1.19Å
  • average bond angle: 120°
  • average bond length(additional keywords): 1.19233Å≈1.19Å
  • average bond angle (additional key words): 120°

The optimisation of the higher basis set has reduced the bond length further to have a similar value of the literature.

Gaussian Calculation Summary
BH3 Optimisation
file type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G (d,p)
Final Energy -26.61532360 a.u.
gradient 0.00000706 a.u
dipole moment 0.0001 Debye
point group CS
length 5.0 seconds
Gaussian Calculation Summary
BH3 Optimisation
additional keywords int= ultrafine opt=vtight
file type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G (d,p)
Final Energy -26.61532364 a.u.
gradient 0.0000000 a.u
dipole moment 0.0000 Debye
point group D3h
length 9.0 seconds


Item table: point group cs 

 Item               Value     Threshold  Converged?
 Maximum Force            0.000012     0.000450     YES
 RMS     Force            0.000008     0.000300     YES
 Maximum Displacement     0.000061     0.001800     YES
 RMS     Displacement     0.000038     0.001200     YES
 Predicted change in Energy=-1.068574D-09
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1923         -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.1923         -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.1923         -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              119.9938         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0055         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.0007         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------

Item table for D3h point group. 

 Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000000     0.000006     YES
 RMS     Displacement     0.000000     0.000004     YES
 Predicted change in Energy=-1.215929D-18
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------

For the total energy for the 3-21G optimised structure I obtained -26.46226429 a.u. and for total energy for the 6-31G(d,p) optimised structure I obtained -26.61532360 a.u

GaBr3 optimization

The symmetry of GaBr3 was restricted to D3h and the calculation was carried out on the HPC with a basis set LANL2DZ

Summary of Gaussian information

  • log file from HPC: DOI:10042/26875
  • bond length= 2.35108Å≈2.35Å
  • literature bond length= 2.3525Å [2]
  • bond angle= 120.00°

The literature bond length is similar to the calculated by 3sf indicating that the optimisation has worked

Gaussian Calculation Summary: Using HPC
GaBr3 Optimisation
file type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set LANL2DZ
Final Energy -41.70082783 a.u.
gradient 0.00000016 a.u
dipole moment 0.0000 Debye
point group D3H
length 14.5 seconds

Item Table 

 Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000003     0.001800     YES
 RMS     Displacement     0.000002     0.001200     YES
 Predicted change in Energy=-1.282693D-12
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !

BBr3 Optimisation

Using the optimised BH3 structure with 6-31G(d,p) basis set, the hydrogen atoms were replaced with bromine and an omptimisation was carried out on the HPC. The log file before submission was edited to ensure the correct basis set was applied to Br (LanL2DZ ) and B (6-31G(d,p))

Gaussian Summary

  • log file from HPC: DOI:10042/26895
  • Average bond length: 1.93397Å=1.93Å
  • bond length in literature: 1.893Å [3]
  • Average bond Angle: 120°
Gaussian Calculation Summary
BBr3 Optimisation
file type .log
Additional keywords gfinput pseudo=read
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set Gen
Final Energy -64.43644904 a.u.
gradient 0.00000962 a.u
dipole moment 0.0003 Debye
point group CS
length 22.4 seconds

Item Table 

Item               Value     Threshold  Converged?
 Maximum Force            0.000017     0.000450     YES
 RMS     Force            0.000010     0.000300     YES
 Maximum Displacement     0.000107     0.001800     YES
 RMS     Displacement     0.000062     0.001200     YES
 Predicted change in Energy=-2.170128D-09
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !

Structure Comparison

Bond Distance (Å)
molecule bond length (Å)
BH3 1.19Å
BBr3 1.93Å
GaBr3 2.35Å


  • Now compare and contrast the bond distances for BH3, BBr3, and GaBr3: The idea of bond overlap,polarity, electronegativity and size.

Changing the ligand can affect the strength of the bond, length and bond order. Larger ligands have more diffused orbitals therefore there will be poorer orbital overlap with atomic centers, resulting in weaker/ longer bonds. Furthermore the number of valence electrons can also affect bond orders. H and Br are both similar as they form D3h complexes with Boron and require one electron to complete their “octet”. However from the calculation B-Br has a longer bond length than B-H as Br is heavier therefore there is a poor overlap with the Boron center, due to miss match of 2p and 4p orbitals.

Changing the central atom affects the length of bonds as large atoms have poor overlap. Also changing the central atom/ ligand can alter the polarity of the bonds. The more polar the bonds the short the distance as it is becoming more ionic. More polar bonds have shorter distances but the size of the molecule dominates. B and Ga are both similar as they are in the same group therefore the structure of BX3 and GaX3 should have similar structures. However as Ga is further down the group the bonds are longer for Ga-Br compared to B-Br.

  • In some structures gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why?
  • What is a bond?

As gaussview is optimising the structure the programme varies the bond lengths to obtain an optimised structure. During the first optimisation for BH3 there is “no bond”, as gaussview has computes the interactions too low to be interpreted as bonds. There possibly is a bond there but as the bond order is < 1 it is negligible.

Generally a bond is an interaction between two molecules with their electrons and nucleus. This can be categorized as a covalent bond which is the sharing of electrons, though the location of electron density will vary dependent on the polarity of the bond. Ionic bonds are electrostatic interactions of ions which the strength again is determined by electronegativity. When there are more interactions with different orbitals the bond order can increase to form multiple bonds.

Frequency analysis

BH3

Optimized bond length:1.19231Å≈ 1.19Å Optimized Bond angle:120.001°≈120.0°

Gaussian Calculation Summary
BH3 Frequency Optimisation
file type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
keyword N/A
Final Energy -26.61532360 a.u.
gradient 0.00000704 a.u
dipole moment 0.0001 Debye
point group CS
length 12.0 seconds
Gaussian Calculation Summary
BH3 Frequency Optimisation
file type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
keyword int=ultrafine opt=vtight
Final Energy -26.61532364 a.u.
gradient 0.00000001 a.u
dipole moment 0.0000 Debye
point group D3h
length 6.0 seconds

File:JN BH3 OPT FREQ.LOG link to frequency analysis with no key words

As seen from the data the calculated point group of BH3 is CS this assumption effected the low frequency of the molecule, therefore the structure had to be re-optimized using the additional key words: int=ultrafine opt=vtight. However this resulted in the same point group of CS being produced, and the frequency calculation again did not produce the desired low frequency range. As a result the BH3 molecule was redrawn in gaussview and the optimization of 6-31G(d,p) was run with the additional key words to obtain the values below: File:JN BH3 OPT FREQ 11.LOG (frequency log file)

low freq cs point group: 

Low frequencies ---  -25.0262  -12.9599   -0.0004    0.0009    0.0010   15.1275
Low frequencies --- 1162.9971 1213.0313 1213.1466

low freq D3h 

Low frequencies ---   -9.3741   -9.3588   -0.0753   -0.0006    0.5350    2.4499
Low frequencies --- 1162.9902 1213.1495 1213.1497

Vibrational modes

The table's caption
No form of vibration frequency intensity symmetry D3h Point group
1
All the hydrogen have concerted motion up and down,whilst the B atom moves in the opposite direction 		1162.99 92.5666 A2
2
two pairs of hydrogen have scissor motions i.e h(1)/h(2) and h(2)/h(3). Whilst a pair of hydrogens have a rocking motion i.e h(1)/h(1) and the B atom is stationary 		1213.15 14.0552 E'
3
Two of the hydrogen's are moving in a scissor motion. whilst the hydrogen and Boron is stationary 		1213.15 14.0557 E'
4
the B atom is stationary whilst the hydrogen's move in and out in a concerted (symmetric) motion. 		2582.53 0.0000 A1
5
Two hydrogen atoms stretch in an asymmetric motion whilst the other hydrogen and Boron is stationary. 		2715.66 126.3339 E'
6
Two hydogens have concerted (symmetric) motion whilst the other hydrogen moves asymmetrically with the boron atom stationary. 		2715.66 126.3279 E'

Explain why there are less than six peaks in the spectrum, when there are obviously six vibrations.

There are less than 6 vibrations, as vibration number 4 is totally symmetric therefore there is no change in dipole (intensity = 0). Furthermore there are two pairs of vibrations 2/3 and 5/6 which have the same the same frequency as they are degenerate. This results in 3 distinct vibration peaks.
A Calculated IR spectrum of BH3.

GaBr3

data from hpc: DOI:10042/26940

Gaussian Calculation Summary
GaBr3 Frequency Optimisation
file type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set LANL2DZ
Final Energy -41.70082783 a.u.
gradient 0.00000011 a.u
dipole moment 0.0000 Debye
point group D3h
length 9.2 seconds 
Low frequencies ---   -0.5252   -0.5247   -0.0024   -0.0010    0.0235    1.2010
 Low frequencies ---   76.3744   76.3753   99.6982

stretching frequencies

The table's caption
No form of vibration frequency intensity symmetry D3h Point group
1
Pair of Bromine are in a rocking motion, two pairs of Bromine scissoring and Ga atom is moving side to side 		76.37 3.3447 E'
2
Pair of Bromine atoms are moving in a scissoring motion, one Bromine atom is moving assymetrically to the scissoring (up and down) Ga atom stationary 		76.38 3.3447 E'
3
Bromine atoms have concerted (symmetrical) motion and Ga atom is moving in the opposite direction. 		99.70 9.2161 A2"
4
Br atoms have concerted (symmetric) motion and Ga atom is stationary 		316.18 0.0000 A1'
5
symmetric stretch of two Ga-Br units and one Br stationary 		316.18 57.0704 E'
6
Ga-Br bond is stretching asymmetrically and Br stretching 		316.19 57.0746 E'
A Calculated IR spectrum of GaBr3.
Stretching Frequencies
symmetry BBr3 GaBr3
A2 (vibration out of plane) 1162.99 99.70
E' (bending vibrations in plane) 1213.15 76.37
E' (bending vibrations in plane) 1213.15 76.38
A1 (stretching) 2582.53 316.18
E' (stretching) 2715.66 316.18
E' (stretching) 2715.66 316.19

What is the lowest "real" normal mode? 76.37

  • now compare and contrast the frequencies for BH3, and GaBr3

The large difference in value of frequency for BH3 compared to GaBr3 indicates the change in dipole is weaker for GaBr3. As BH unit is smaller (1.19231A), there is a stronger chemical bond; therefore more force is required to change the bond. Explaining why BH3 is shifted to the right compared to GaBr3. The vibration modes have re-ordered, for the bending vibrations, this is due to the A2 vibration being higher in energy for Ga than B. Because Ga is moving in this vibration and B is stationary, the movement of Ga requires more energy.

The spectrums are similar due to both compounds having point group, therefore there is the same number of active IR vibrations. Though the positions of the peaks have shifted due to bond strength, the relative intensities are the same.

A2 and E’ are fairly close together as they are both bending vibrations and A1 and E’ are both stretching frequencies. A2 and E’ are lower frequencies as it is easier to bend a bond than stretch, as stretching reduces the electron density between the molecules which is unfavourable. Resulting in higher energies for A2 and E’.


  • Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?

To be able to effectively compare data computed.

  • What is the purpose of carrying out a frequency analysis?

To confirm if the proposed structure has been optimised by gaussview. Also if the structure is a minima (positive value), or maxima, (negative value) or transition state.

  • What do the "Low frequencies" represent?

Normal vibration modes which should be as close to 0.

molecular orbitals of BH3

Gaussian Calculation Summary
BH3 Molecular Orbitals
file type .fch
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Final Energy -26.61532363 a.u.
gradient 0.00000000 a.u
dipole moment 0.0000 Debye
point group no point group
length no time
dspace DOI:10042/26942
Mo diagram of BH3 with calculated MO in Gaussian

Are there any significant differences between the real and LCAO MOs?


The real MO’s and LCAO are identical for non-bonding orbitals. For bonding orbitals as this compound highest configuration is 2p, there is no significant difference. The computed MO calculate "constructive and destructive" interference dependent on phases and alters the size of the orbital dependent on electron contribution. Though it is clear from observing the real MO's which orbitals contribute to a certain energy level.

What does this say about the accuracy and usefulness of qualitative MO theory?

This shows that MO theory is very useful at estimating contribution of electron density of bonds. It can be used as a guide to indicate if a calculation has worked and also as reference to find the lowest possible basis set to use whilst running a calculation. Therefore the use of long and detailed for heavier molecules can be reduced.

NH3

optimisation

To optimise the molecule of NH3 the same process BH3 using 6-31G(d,p)as a basis straight away with the keywords "nosymm", this is to ensure that Gaussian does not automatically produce the structure as a D3h point group.

Summary of Gaussian Information

log file of NH3 optimisation File:JN NH3 OPT 6-31G.LOG

  • average NH length= 1.01798Å≈ 1.02Å
  • average bond angle= 105.746°≈ 105.7°
Gaussian Calculation Summary
NH3 Optimisation
key words nosymm
file type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Final Energy -56.55776856 a.u.
gradient 0.00000885 a.u
dipole moment 1.8464 Debye
point group C1
length 16.0 seconds

Item table 

  Item               Value     Threshold  Converged?
 Maximum Force            0.000024     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000079     0.001800     YES
 RMS     Displacement     0.000053     0.001200     YES
 Predicted change in Energy=-1.629715D-09
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !

Frequency

Initially the frequency calculation was undertaken with no keywords, however the low frequency again exceeded the the optimal range of +/-15

Summary of Gaussian Information

log file with no additional keywords: File:JN NH3 FREQ 6-31G.LOG

log file with keywords: File:JN NH3 FREQ2 6-31G.LOG


Gaussian Calculation Summary
NH3 Frequency
keywords int=ultrafine opt=vtight
file type .log .log
Calculation Type FREQ FREQ
Calculation Method RB3LYP RB3LYP
Basis Set 6-31G(d,p) 6-31G(d,p)
Final Energy -56.55776856 -56.55776872 a.u.
gradient 0.00000888 a.u 0.00000014 a.u
dipole moment 1.8464 1.8465 Debye
point group C1 C1
length 8.0 seconds 6.0 seconds 
Low frequencies ---  -30.7764   -0.0006    0.0006    0.0013   20.3142   28.2484
Low frequencies --- 1089.5557 1694.1237 1694.1868

Low frequencies ---   -8.2826   -6.5111   -4.3703   -0.0019   -0.0017    0.0009
Low frequencies --- 1089.3408 1693.9230 1693.9271
Vibrations
No1 form of vibration frequency intensity symmetry Point group
1 symmetric bending of hydrogen
1089.34 145.4309 A1
2 2 pairs of scissoring H's
1693.92 13.5575 E
3 2 pairs of scissoring H's
1693.93 13.5573 E
4 symmetric stretches of all hydrogens
3461.37 1.0592 A1
5 symmetric stretch of 2H's and assymetric stretch of 1 H
3589.91 0.2698 E
6 asymmetric stretch of 2 H's
3589.93 0.2698 E
calculated IR spectrum of NH3

mo

file: File:JN NH3 MO 6-31G.chk

Gaussian Calculation Summary
NH3 MO
file type .chk
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Final Energy -56.55776856 a.u.
gradient 0.00000000 a.u
dipole moment 1.8464 Debye
point group N/A
length N/A
The LUMO energy for NH3 is very unfavorable as the the energy is +0.07985 a.u., indicating to the possibility of NH3 donating the lone pair of electrons whilst bonding as the HOMO shows a non bonding lobe for the p orbital.

nbo

file: File:JN NH3 MO 6-31G.LOG

NBO of NH3 with a colour range of -1.125 to 1.125

charge on hydrogen: 0.375 and on nitrogen is -1.125. This show that Nitrogen is electronegative.

Association energies: Ammonia-Borane

optimisation

FILE: File:JN NH3BH3 OPT 6-31G.LOG

  • average bond length NH unit= 1.01861Å ≈ 1.02Å
  • average HNH angle= 107.869°≈ 107.9
  • average bond length BH unit= 1.21007Å ≈ 1.21Å
  • average HBH angle=113.872°≈ 113.9°

From the optimisation the molecule prefers to be in gauche configuration to avoid steric interactions. Also the bond length of the BH units has increased compared to BH3 as there is electron density in the previously empty Pz orbital, therefore electrons from the hydrogen are no longer needed to stabilize the molecule

SUMMARY

Gaussian Calculation Summary
NH3BH3 optimisation
file type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Final Energy -83.22469007 a.u.
gradient 0.00006839 a.u
dipole moment 5.5653 Debye
point group C1
length 33.0 seconds 
 Item               Value     Threshold  Converged?
 Maximum Force            0.000139     0.000450     YES
 RMS     Force            0.000063     0.000300     YES
 Maximum Displacement     0.000771     0.001800     YES
 RMS     Displacement     0.000338     0.001200     YES
 Predicted change in Energy=-2.028054D-07
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------

frequency

file: File:JN NH3BH3 FREQ 6-31G.LOG summary

Gaussian Calculation Summary
NH3BH3 Frequency
file type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Final Energy -83.22468908 a.u.
gradient 0.00000065 a.u
dipole moment 5.5646 Debye
point group C1
length 27.0 seconds 
 Low frequencies ---   -2.7651   -0.6319   -0.0006   -0.0003    0.0002    5.0677
 Low frequencies ---  263.4977  632.9696  638.4423

From the log file Gaussian has manged to optimise the the structure

IR SPECTRUM

calculated IR spectrum of NH3BH3

ANALYSIS OF RESULT:

  • E(NH3)= -56.55776856 a.u.
  • E(BH3)= -26.61532364 a.u.
  • E(NH3BH3)= -83.22469007 a.u.

energy difference: ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05159787 a.u = -135.470218005 kJ/mol

therefore the dissociation energy= 135.470218005 kJ/mol

project

Part 1

Three cations are under investigation [N(CH3)4]+, [P(CH3)4]+, [S(CH3)3]+. theese cations were optimised using Gaussview with a basis set of 6-31G and frequency analysis to confirm the optimized structure. However as the low frequency values had a high range the all calculations were carried out using keywords: nosymm int=ultrafine opt=vtight originally ran optimisation however low freq range to wide therfore re ran optimisations with no symm

Summary Table

Gaussian Calculation Summary
Optimisation (no keywords)
molecule [N(CH3)4]+ [P(CH3)4]+ [S(CH3)3]+
file type .log .log .log
Calculation Type FOPT FOPT FOPT
Calculation Method RB3LYP RB3LYP RB3LYP
Basis Set 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Final Energy -214.18127301 a.u. 6-31G(d,p) -517.68326752 a.u.
gradient 0.00002263 a.u 0.00003603 a.u 0.00002305 a.u
dipole moment 0.0003 Debye 0.0006 Debye 0.9652 Debye
point group C1 C1 C1
length 7 minutes 35.3 seconds 6 minutes 55.0 seconds
dspace DOI:10042/27074 DOI:10042/27075 DOI:10042/27085
Gaussian Calculation Summary
Frequency (no keywords)
Molecule [N(CH3)4]+ [P(CH3)4]+ [S(CH3)3]+
file type .log .log .log
Calculation Type FREQ FREQ FREQ
Calculation Method RB3LYP RB3LYP RB3LYP
Basis Set 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Final Energy -214.18127292 a.u. -500.82700799 a.u. -517.68326759 a.u
gradient 0.00002246 a.u 0.00003604 a.u 0.00002301 a.u
dipole moment 0.0003 Debye 0.0006 Debye 0.9652 debye
point group C1 C1 C1
length 8 minutes 54.9 seconds 8 minutes 44.9 seconds 3minutes 49.9 seconds
d space DOI:10042/27076 DOI:10042/27087 DOI:10042/27099

Item table [N(CH3)4]+ 

 Item               Value     Threshold  Converged?
 Maximum Force            0.000058     0.000450     YES
 RMS     Force            0.000019     0.000300     YES
 Maximum Displacement     0.000507     0.001800     YES
 RMS     Displacement     0.000150     0.001200     YES
 Predicted change in Energy=-5.458753D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------

low freq [N(CH3)4]+: 

Low frequencies ---  -19.2112    0.0003    0.0005    0.0009    9.4138   15.5427
Low frequencies ---  178.9881  279.3470  287.8508


[P(CH3)4]+ item table 

 Item               Value     Threshold  Converged?
 Maximum Force            0.000119     0.000450     YES
 RMS     Force            0.000030     0.000300     YES
 Maximum Displacement     0.000695     0.001800     YES
 RMS     Displacement     0.000193     0.001200     YES
 Predicted change in Energy=-1.514909D-07
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------

Low Freq [P(CH3)4]+ 

Low frequencies ---  -21.6073    0.0004    0.0006    0.0022    8.1480   16.6852
 Low frequencies ---  152.3369  186.9810  188.9031

Item table [S(CH3)3]+ 

Item               Value     Threshold  Converged?
 Maximum Force            0.000072     0.000450     YES
 RMS     Force            0.000023     0.000300     YES
 Maximum Displacement     0.000772     0.001800     YES
 RMS     Displacement     0.000202     0.001200     YES
 Predicted change in Energy=-4.042913D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------

Low freq [S(CH3)3]+ 

Low frequencies ---  -22.8241  -12.3987    0.0028    0.0045    0.0053   11.1467
 Low frequencies ---  161.5062  195.6610  206.7175

with nosymm

Gaussian Calculation Summary
Optimisation (keyword= nosymm)
molecule [N(CH3)4]+ [P(CH3)4]+ [S(CH3)3]+
file type .log .log .log
Calculation Type FOPT FOPT FOPT
Calculation Method RB3LYP RB3LYP RB3LYP
Basis Set 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Final Energy -214.18127259 a.u. -500.82700326 -517.68327919 a.u.
gradient 0.00004413 a.u 0.00001658 a.u 0.0000866 a.u
dipole moment 7.0634 Debye 22.2795 Debye 10.5114Debye
point group C1 C1 C1
length 4 minutes 1.3 seconds 3 minutes 30.7 seconds 3minutes 41.1 seconds
dspace DOI:10042/27325 DOI:10042/27101 DOI:10042/27106
Gaussian Calculation Summary
Frequency summary
Molecule [N(CH3)4]+ [P(CH3)4]+ [S(CH3)3]+
file type .log .log .log
Calculation Type FREQ FREQ FREQ
Calculation Method RB3LYP RB3LYP RB3LYP
Basis Set 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Final Energy -214.18127259 a.u. -500.82700325 a.u. -517.68327919 a.u
gradient 0.00004415 a.u 0.00001658 a.u 0.00000867 a.u
dipole moment 7.0634 Debye 22.2795 Debye 10.5114 Debeye
point group C1 C1 C1
length 8 minutes 57.8 seconds 7 minutes 39.2 seconds 3minutes 51.0 seconds
d space DOI:10042/27100 DOI:10042/27109 DOI:10042/27111
IR spectrum

Item table [N(CH3)4]+ 

 Item               Value     Threshold  Converged?
 Maximum Force            0.000068     0.000450     YES
 RMS     Force            0.000027     0.000300     YES
 Maximum Displacement     0.000463     0.001800     YES
 RMS     Displacement     0.000126     0.001200     YES
 Predicted change in Energy=-8.909420D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------

Low Freq [N(CH3)4]+ 

 Low frequencies ---  -12.9962    0.0009    0.0010    0.0012    6.2302   12.1424
 Low frequencies ---  181.5431  279.9767  286.8030

Item table [P(CH3)4]+ 

Item               Value     Threshold  Converged?
 Maximum Force            0.000032     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.001163     0.001800     YES
 RMS     Displacement     0.000298     0.001200     YES
 Predicted change in Energy=-4.054453D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------

Low freq [P(CH3)4]+ 

 Low frequencies ---  -18.0695   -4.7611   -0.0011    0.0010    0.0019   14.5096
 Low frequencies ---  153.6960  183.3817  191.3161

Item table [S(CH3)3]+ 

Item               Value     Threshold  Converged?
 Maximum Force            0.000015     0.000450     YES
 RMS     Force            0.000008     0.000300     YES
 Maximum Displacement     0.000552     0.001800     YES
 RMS     Displacement     0.000171     0.001200     YES
 Predicted change in Energy=-9.000389D-09
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------

Low freq [S(CH3)3]+ 

Low frequencies ---  -13.4833   -9.6160   -0.0029    0.0022    0.0025   22.4526
 Low frequencies ---  158.3128  194.2683  198.3584

analysis

N-C P-C S-C
Average bond length/Å 1.50930≈ 1.51 1.81643≈ 1.82 1.82263

≈1.82|-

Literature bond length [4] /Å 1.510 1.800
Average angle/° 109.571≈ 109.6 109.497≈109.5 102.738 ≈ 102.7

The calculated values are reasonable when comparing to literature results. As previously discussed, S-C has the longest bond length due poor orbital overlap between the heteroatom and carbon as S is the heaviest. The average bond angles show [N(CH3)4]+ and [P(CH3)4]+ have the same structure of tetrahedral (Td) and [S(CH3)3]+ is trigonal pyramidal. The bond angle for S(CH3)3]+ is smaller due to the lone pair repelling the methyl groups

The frequency analysis shows that all the molecules have been optimised. The IR spectrum of [N(CH3)4]+ and [P(CH3)4]+ are similar as they both have the same point group. The most intense peak for all three structures is the methyl stretches, as it is the biggest change in dipole and there are more methyl groups. Furthermore the C-X bending frequency and intensity decreases as the heteroatom size increases , as polarity of the bonds decreases .this data indicates that in “real life” situation the best way to identify these compounds is by x ray diffraction.

NBO/MO

MO orbital of [N(CH3)4]+
highly bonding (MO 6) MO 9 MO 12 MO 19 Highly antibonding (MO 21)

comment on colour range

NBO Charges
[N(CH3)4]+ [P(CH3)4]+ [S(CH3)3]+
NBO
NBO
NBO
N= -0.295 P= 1.667 S= 0.917
C= -0.484 C= -1.06 C= -0.845
H= 0.269 H= 0.298 H= 0.279 (3H) and 0.297(6H)
DOI:10042/27181 DOI:10042/27183 DOI:10042/27184
Population analysis
molecule contrinution % s% p% d%
[N(CH3)4]+ N/C= 66.35/ 33.65 25/20.78 74.97/79.05 0.03/0.16
[P(CH3)4]+ P/C= 40.43/59.57 24.98/25.24 74.17/74.68 0.85/0.08
[S(CH3)3]+ S/C=16.95/19.70 16.95/19.70 82.42/ 80.16 0.63/0.14

All the images for the NBO are done from a charge range of ±1.0

Using the NBO charge analysis compare and contrast the charge distribution across this trio of cations. How can your results be rationalised? The trio of cations are similar as all the hydrogen's are in a positive environment and the carbons have electron density. However there is a difference in charge density on the heteroatoms which reflect the electronegativity of the atom. The more electronegative and “core” like the heteroatom the more electron density it holds N>P>S.

The H values for [S(CH3)3]+ are different, this is due to the HOMO orbital, as 3 hydrogens are in the same phase and 6 are in opposing phases. Whereas for [N(CH3)4]+ and [P(CH3)4]+ there is no variance in the H charge.

Using the NBO population analysis compare and contrast the relative contribution of the C and heteroatom to the C-X bond. How do your results relate to the charge distribution just studied? NBO population analysis relates to the charge distribution as Nitrogen is contributing most to the bond as it has a higher electronegativity. Also contribution of S-C is nearly 50:50 as both atoms have very similar electronegativity proving that the bond is non polar. This data also shows that [N(CH3)4]+ and [P(CH3)4]+ have the similar structure of tetrahedral resulting in sp 3 hybridised orbitals.

HOMO of [S(CH3)3]+

[NR4]+ (R=alkyl) is often depicted with the positive charge placed on the nitrogen center. Based on your results for [N(CH3)4]+ , discuss the validity of the traditional description. The formal positive charge on Nitrogen represents that the atom has lost an electron, as the valence electron count on N if it were an [NR4] complex would be 9 which exceeds the octet rule. Therefore an electron needs to be removed if considering the “dot and cross” structure. However this is untrue from the NBO calculation the positive charge is spread evenly across the hydrogens. As nitrogen and carbon are more stable on a MO diagram, the nearest electron to remove is the hydrogens. And as they are all in the same environment they are all equally likely to loose and electron collectively.

part 2

The optimisation of the new cations were based on the optimisation of [N(CH3)4]+ with as basis set of 6-31G

Gaussian Calculation Summary
Optimisation (keyword= nosymm)
molecule [N(CH3)3(CH2OH)]+ [N(CH3)3(CN)]+
file type .log .log
Calculation Type FOPT FOPT
Calculation Method RB3LYP RB3LYP
Basis Set 6-31G(d,p) 6-31G(d,p)
Final Energy -289.39323129 a.u. -306.39376846 a.u
gradient 0.00001952 a.u 0.00006060 a.u
dipole moment 6.9846 Debye 9.6181 Debye
point group C1 C1
length 7 minutes 24.0 seconds 7minutes 35.2 seconds
dspace DOI:10042/27169 DOI:10042/27172

Item table[N(CH3)3(CH2OH)]+ 

 Item               Value     Threshold  Converged?
 Maximum Force            0.000088     0.000450     YES
 RMS     Force            0.000011     0.000300     YES
 Maximum Displacement     0.000475     0.001800     YES
 RMS     Displacement     0.000144     0.001200     YES
 Predicted change in Energy=-1.696345D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------

Item table [N(CH3)3(CN)]+ 

 Item               Value     Threshold  Converged?
 Maximum Force            0.000142     0.000450     YES
 RMS     Force            0.000026     0.000300     YES
 Maximum Displacement     0.001640     0.001800     YES
 RMS     Displacement     0.000503     0.001200     YES
 Predicted change in Energy=-1.956785D-07
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------


whilst carrying out the frequency analysis for [N(CH3)3(CH2OH)]+ the low frequency is extremely out of range therefore I ran the calculations with additional keywords: int=ultrafine opt=vtight 

Low frequencies --- -124.1049   -8.9936   -0.0006   -0.0006    0.0003   15.6082
Low frequencies ---   17.5157  131.0005  219.5622

[N(CH3)3(CH2OH)]+ with no keywords DOI:10042/27171

Gaussian Calculation Summary
Frequency summary
Molecule [N(CH3)3(CH2OH)]+ [N(CH3)3(CN)]+
file type .log .log
Calculation Type FREQ FREQ
Calculation Method RB3LYP RB3LYP
Basis Set 6-31G(d,p) 6-31G(d,p)
Final Energy -289.39470767a.u. -306.39376166
gradient 0.00000024 a.u 0.00000041
dipole moment 6.7589 Debye 9.6174 Debye
point group C1 C1
length 21 minutes 53.7 seconds 24 minutes 19.3 seconds
d space DOI:10042/27173 DOI:10042/27175
IR Spectrum

low frequencies [N(CH3)3(CH2OH)]+ 

Low frequencies ---   -9.6765   -0.0015   -0.0012   -0.0005    1.9977    5.3720
 Low frequencies ---  131.1311  214.5349  256.0443

low frequencies [N(CH3)3(CN)]+ 

Low frequencies ---   -4.2789   -3.7543   -0.0002    0.0006    0.0010    5.2749
 Low frequencies ---   91.6162  153.8477  211.3304
molecule average C-N length/ Å average bond angle/°
[N(CH3)3(CH2OH)]+ 1.50934 ≈ 1.51 109.485≈ 109.5
[N(CH3)3(CN)]+ 1.51332≈ 1.51 (N≡CC-N)= 1.5258≈ 1.53 109.469 ≈ 109.5

The bond angles are similar to [N(CH3)4]+ again indicating to tetrahedral configuration however the bond lengths differ due to the functional groups. [N(CH3)3(CN)]+ C-N bonds have lengthen the most as CN is an electron withdrawing group (EWG) therefore the bonds are weakening. Wereas the bonding in [s N(CH3)3(CH2OH)]+ appears not to have altered as the bond length is very similar to [N(CH3)4]+ .

NBO Charges
[N(CH3)3(CH2OH)]+ [C(CH3)3(CN)]+
NBO
NBO
N= -0.313 N= -0.289
C=-0.488, C(bond to Oxygen)= 0.094 C= -0.486 ,C(from C-C≡N)= 0.209 C( from N-C-C)=-0.358
H=0.234, H(bond to Oxygen)= 0.532 H≈ 0.274 H(in N≡CH2)= 0.309
O= -0.757 N (in C≡N)= -0.186
DOI:10042/27187 DOI:10042/27190

OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution? As CN is an EWG the charge distribution on the compound is diffuse as CN is trying to gain as much electron density as possible. Whereas for [N(CH3)3(CH2OH)]+, the electron density concentrated at the oxygen and the nitrogen/ three methyl groups. Because oxygen is an electronegative atom hence the proton adjacent to it is acidic, but it can undergo resonance as the carbon adjacent is positive.


MO
[N(CH3)4]+ [N(CH3)3(CH2OH)]+ [C(CH3)3(CN)]+
HOMO E= -0.57931 E= -0.46629 E= 0.50045
LUMO E= -0.13303 E= -0.11994 E=0.18176
Energy gap 0.44628 0.34035 0.31869

The HOMO for [N(CH3)4]+ is different from the other two as the electron density is spread all the atoms as the molecule is symmetrical. Whereas for [C(CH3)3(CN)]+ and [N(CH3)3(CH2OH)]+ the electron density of the orbitals is located on the functional groups. This indicates possibly the calculation may have slightly gone wrong in generating the HOMO as the data suggests that there is no bonding between the methyl groups. Though the HOMO for CN atom is more diffuse with core likeCH2 as it’s an EWG. Whereas for OH the orbitals are similar in size.

The three cations have similar LUMOs, again suggesting a recalculation of HOMO. The addition of functional groups has destabilised the HOMO suggesting they are more reactive. Also this is seen in the reduction of the HOMO-LUMO gap. Also as the majority of electron density is at the functional groups the site of reaction has changed.

Theese different properties in the cations can effect the way they are used as green solvents, and the variation of functional groups can be explored to manipulate synthesis and electrochemistry.

Reference

<references> [2] [3] [4] [1] DOI:10.1063/1.461942

  1. ↑ 1.0 1.1 Kawaguchi, Kentarou., Fourier transform infrared spectroscopy of the BH3 ν3 band. The Journal of Chemical Physics 1992 96 3411.
  2. ↑ 2.0 2.1 L. E. Sutton, Ed, Tables of Interatomic Distances and Configuration in Molecules andIons The Chemical Society Special Publication 1965, 11 59
  3. ↑ 3.0 3.1 Kagaku Benran, 3rd Edition, Vol.II, pp. 649–661 (1984)
  4. ↑ 4.0 4.1 Frank H. Allen, Olga Kennard, and David G. Watson,Lee Brammer and A. Guy Orpen,Robin Taylor,Tables of Bond Lengths determined by X-Ray and Neutron Diffraction. Part I .Bond Lengths in Organic Compounds, J. CHEM. SOC. PERKIN TRANS. II, 1987,
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