Rep:Mod:wsk811

Week 1 Inorganic computational

BH₃

BH3 optimisation

BH3 optimisation [BH3 321G optimisation]
File Name	SW_BH3_OPT
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	3-21G
Change	0
Spin	Singlet
E(RB3LYP)	-26.46226429	a.u.
RMS Gradient Norm	0.00008851	a.u.
Imaginary Freq
Dipole Moment	0.0003	Debye
Point Group	CS
Job cpu time: 0 days 0 hours 0 minutes 20.0 seconds.

 BH3 Optimisation 
         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)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1948         -DE/DX =   -0.0002              !
 ! R2    R(1,3)                  1.1947         -DE/DX =   -0.0002              !
 ! R3    R(1,4)                  1.1944         -DE/DX =   -0.0001              !
 ! A1    A(2,1,3)              120.0157         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              119.986          -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              119.9983         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

BH3 optimisation 631G [BH3 631G optimisation]
File Name	SW_bh3_opt_631G
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Change	0
Spin	Singlet
E(RB3LYP)	-26.61532358	a.u.
RMS Gradient Norm	0.00008206	a.u.
Imaginary Freq
Dipole Moment	0.0003	Debye
Point Group	CS
Job cpu time: 0 days 0 hours 0 minutes 14.0 seconds.
Optimised Bond Length	1.19, 1.19, 1.19	Å
Optimised Bond Angle	120.0, 120.0, 120.0

 BH3 Optimisation 631G
 Item               Value     Threshold  Converged?
 Maximum Force            0.000204     0.000450     YES
 RMS     Force            0.000099     0.000300     YES
 Maximum Displacement     0.000875     0.001800     YES
 RMS     Displacement     0.000418     0.001200     YES
 Predicted change in Energy=-1.452086D-07
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1928         -DE/DX =   -0.0002              !
 ! R2    R(1,3)                  1.1926         -DE/DX =   -0.0002              !
 ! R3    R(1,4)                  1.1924         -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              120.0146         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              119.9866         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              119.9988         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

BH3 optimisation 631G 2nd time

BH3 optimisation 2nd time [BH3 321G optimisation 2nd]
File Name	BH3_OPT_3
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Change	0
Spin	Singlet
E(RB3LYP)	-26.61532364	a.u.
RMS Gradient Norm	0.00000000	a.u.
Imaginary Freq
Dipole Moment	0.0000	Debye
Point Group	D3H
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.
Optimised Bond Length	1.19, 1.19, 1.19	Å
Literature Bond Length^{lit 2}	1.2325	Å
Optimised Bond Angle	120.0, 120.0, 120.0

 BH3 Optimisation 2nd time
         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=-1.214719D-18
 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)              120.0            -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0            -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.0            -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

BH3 Frequency

BH3 Frequency [BH3 Frequency]
File Name	SW_BH3_FREQ
File Type	.log
Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Change	0
Spin	Singlet
E(RB3LYP)	-26.61532358	a.u.
RMS Gradient Norm	0.00008199	a.u.
Imaginary Freq	0
Dipole Moment	0.0003	Debye
Point Group	CS
Job cpu time: 0 days 0 hours 0 minutes 11.0 seconds.

 BH3 Frequency
 Low frequencies --- 0.0006    0.0007    0.0007   33.8245   41.5797   43.6874
 Low frequencies --- 1163.5016 1213.4680 1213.5880

comment since the frequency is too high. Therefore point group constraint is added to run a 2nd time.

BH3 Frequency 2nd

BH3 Frequency 2nd [BH3 Frequency 2nd]
File Name	BH3_FREQ_3
File Type	.log
Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Change	0
Spin	Singlet
E(RB3LYP)	-26.61532364	a.u.
RMS Gradient Norm	0.00000001	a.u.
Imaginary Freq	0
Dipole Moment	0.0000	Debye
Point Group	D3H
Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

 BH3 Frequency
 Low frequencies ---   -9.3741   -9.3588   -0.0753    0.0007    0.5350    2.4499
 Low frequencies --- 1162.9902 1213.1495 1213.1497

BH3 Vibration

BH3 Vibration
No.	Form of the Vibration	Frequency	Vibration	Symmetry of D_3H Point group
1	Symmetric stretching. all H atoms in and out of the plane, B atom is going the opposite direction slowly	1163	93	A₂"
2	Assymmetric stretching. H atoms are rocking and scissoring at the same time. B atom moves slightly	1213	14	E'
3	two H atoms are Scissoring, B atom and the other H atom are moving slightly	1213	14	E'
4	Symmetrical stretching. all H atoms moves towards and opposite to the centre, B atom remains stationary	2583	0	A₁'
5	Assymmetric stretching of two H atoms. The other two atoms vibrate a bit at their points	2716	126	E'
6	It is symmetrical stretching of two of the H atoms while the other H is doing assymmetrical to them. The B atom changes a bit at its position.	2716	126	E'

In your wiki also explain why are there less than six peaks in the spectrum, when there are obviously six vibrations.

There are indeed six vibrational modes shown in the table. However, the No.2 and No.3 both have frequency at 1213 cm^-1 and No. 5 and No. 6 both have the same frequency at 2716 cm^-1. So they overlap to each other and only appear two peaks. On the other hand, the vibration of No. 4 is zero, as it is symmetrical stretching and no change in dipole. So it is IR inactive. Therefore there are only 3 peaks appear in the spectrum.

Molecular Orbital of BH₃

[Molecular Orbital of BH₃ D space]

Answer the following questions:

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

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

As can be seen from the diagram, the calculated MO diagram matches quite well with the MO theory diagram, apart from MO theory shows the atomic orbitals and its interactions while Gaussview merges all the orbitals together. Overall, it is a pretty good assumption. However, the limitation takes place when the molecule becomes very complicated. So it will be very hard to draw the MO diagrams out by LCAO.

GaBr₃

GaBr₃ optimisation

GaBr₃ optimisation [GaBr₃ LANL2DZ optimisation] [GaBr₃ optimisation D space]
File Name	SW_GABR3_OPT
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	LANL2DZ
Change	0
Spin	Singlet
E(RB3LYP)	-41.70082783	a.u.
RMS Gradient Norm	0.00000016	a.u.
Imaginary Freq
Dipole Moment	0.0000	Debye
Point Group	D3H
Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.
Optimised Bond Length	2.35, 2.35, 2.35	Å
Literature Bond Length^{lit 2}	2.3525	Å
Optimised Bond Angle	120.0, 120.0, 120.0

 GaBr3 optimisation
 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=-1.282691D-12
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  2.3502         -DE/DX =    0.0                 !
 ! R2    R(1,3)                  2.3502         -DE/DX =    0.0                 !
 ! R3    R(1,4)                  2.3502         -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              120.0            -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0            -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.0            -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

GaBr₃ Frequency

GaBr₃ Frequency 2nd [GaBr₃ Frequency] [GaBr₃ Frequency D space]
File Name	SW_GABR3_FREQ
File Type	.log
Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	LANL2DZ
Change	0
Spin	Singlet
E(RB3LYP)	-41.70082783	a.u.
RMS Gradient Norm	0.00000011	a.u.
Imaginary Freq	0
Dipole Moment	0.0000	Debye
Point Group	D3H
Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

 GaBr<sub>3</sub> Frequency
 Low frequencies ---   -0.5252   -0.5247   -0.0024   -0.0010    0.0235    1.2010
 Low frequencies ---   76.3744   76.3753   99.6982

GaBr₃ Vibration

BH3 Vibration
No.	Form of the Vibration	Frequency	Vibration	Symmetry of D_3H Point group
1	It is stretching on the same plane with one H scissoring with another H and rocking with the other. Central Ga is moving slightly as well.	76	3	E'
2	Two H atoms are scissoring and the remaining H and Ga are going up and down.	76	3	E'
3	Only the central Ga atom is swinging in and out of plane vigorously.	100	9	A₂
4	Symmetrical stretching. all H atoms moves towards and opposite to the centre, Ga atom remains stationary	197	0	A₁'
5	One of the H keeps stationary while the central Ga is associating with the other two antisymmetrical stretching H atoms	316	57	E'
6	Ga is stretching along the bond while three H atoms only vibrate a bit.	316	57	E'

GaBr₃_IRspectrum

BBr₃

BBr₃ optimisation

BBr3 optimisation [BBr₃ optimisation] [BBr₃ optimisation D space]
File Name	SW_BBr3_OPT_GEN
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	Gen
Change	0
Spin	Singlet
E(RB3LYP)	-64.43644666	a.u.
RMS Gradient Norm	0.00001415	a.u.
Imaginary Freq
Dipole Moment	0.0003	Debye
Point Group	CS
Job cpu time: 0 days 0 hours 0 minutes 15.0 seconds.
Optimised Bond Length	1.93, 1.93, 1.93	Å
Literature Bond Length^{lit 2}	1.893	Å
Optimised Bond Angle	120.0, 120.0, 120.0

 BBr3 optimisation
         Item               Value     Threshold  Converged?
 Maximum Force            0.000026     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000131     0.001800     YES
 RMS     Displacement     0.000065     0.001200     YES
 Predicted change in Energy=-3.258105D-09
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.934          -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.934          -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.9339         -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              119.9975         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0005         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.002          -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Comparisons

Bond lengths Comparisons
Compounds	Optimised Bond Length	Mean Bond Length
BH₃	1.19, 1.19, 1.19	1.19	Å
GaBr₃	2.35, 2.35, 2.35	2.35	Å
BBr₃	1.93, 1.93, 1.93	1.93	Å

Comments

What difference does changing the ligand have?

How are H and Br similar, how are they different?

What difference does changing the central element make?

How are B and Ga similar, how are they different?''

There are mainly four aspects: Change of overlap, change of atom size, change of polarity, change of the electronegativity.

Comparing the bond length of BH₃ and BBr₃, BBr bond is 0.74 Å longer than BH bond. The replacement of the H to Br group leads a poorer overlap between the ligand and boron, because the H has the s orbital overlap while the Br has the p orbital overlap. More electron density in Br increases the size of the atom due to stronger electrostatic repulsion as well as its electronegativity. The electronegativity of H, B and Br are 2.300, 2.051 and 2.685 ^{lit 1} respectively. Therefore the polarity of the molecules is bigger in BBr₃. Overall it gives a better interaction in BH₃ than BBr₃, hence a shorter bond appears in BH₃.

The bond length of GaBr₃ is 0.42 longer than BBr₃. Both of Ga and B are in group 13, so their frontier orbitals are both p orbital. However Ga is a transition metal and B is electron deficient. So the 4p orbital in Ga is more deffused. As the group is going down, the size of the central element goes up as a consequence of the poorer overlap between the central atom and ligands. Ga is also more electropositive (1.756 ^{lit 1}) than B. So the bigger polarity leads to a weaker overlap and gives a longer bond.

A chemical bond is the electrostatic interaction between two opposite charged atoms.

Some strong interactions (common bonds) are identified as the covalent bonds (the pair of electrons are shared between two atoms), dative covalent bond (the electron pair is donated from one atom), the ionic bond (the Coulomb Force between a positive charged atom and a negative charged atom and the metallic bond (the delocalised electrons in the metal lattices).

Some weak interactions also can be found between molecules, such as London dispersion force, dipole-dipole interaction and hydrogen bond.

The bonds can be presented by the frontier orbital electrons. It valence bond theory and the molecular bond theory. So there are also single bond, double bond, triple bond, aromatic bond, etc. ^{lit 3}

In some structures, it doesn't mean there is no bond although Gaussview doesn't draw it out, although there is no bond drawn in the first few structures. It is because the bonds are presented based on a distance criteria in Gaussview. So no bond shown doesn't mean no bonds, but the bonds exceed the pre-defined distance value. There interaction is still there.

Vibrational frequencies of BH₃ and GaBr₃

Vibrational frequencies of BH₃ and GaBr₃
No.	Frequency of BH₃	Frequency of GaBr₃
1	1163	76
2	1213	76
3	1213	100
4	2583	197
5	2716	316
6	2716	316

The higher frequency means the higher in energy. Therefore, it implies that the BH₃ vibration is much higher in energy than GaBr₃. It is compliance with the bonds lengths as a shorter bond distance is observed in B-H than in Ga-Br. It shows a higher interaction between B-H than Ga-Br. Ga-Br is weakly bonded.

There are six vibration modes in both of the molecules, because they have got the same symmetry and the same number of atoms in the molecule. However in BH3, it is mode 2&3 and 5&6 (degenerate) overlapping (single peak) to each other and mode 4 is zero in intensity. But in GaBr₃, it is mode 1&2 and 5&6 (degenerate) overlapping (single peak) and mode 4 is zero in intensity.

The consequence of the observation of A2&E' modes/ A1'&E'modes lying close to each other but the latter is higher in energy is due to an orbital mixing occurs in GaBr₃ but not in BH₃.

Method and basis set have to be strickly the same to allow the comparison (even the keyword has to be the same). There is no worth comparing when the basic setting is different.

The purpose of carrying out a frequency calculation is to compare it with the real value obtained from lab to see the difference and the compliance. If two values match to each other, that's great. Otherwise it may either be something wrong with the experiment or something interesting on going.

Low frequency represents the translational an rotational degrees of freedom.

NH₃

NH₃ optimisation

NH₃ optimisation [NH₃ optimisation] [NH₃ optimisation D space]
File Name	SW_BBr3_OPT_GEN
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Change	0
Spin	Singlet
E(RB3LYP)	-56.55776863	a.u.
RMS Gradient Norm	0.00000289	a.u.
Imaginary Freq
Dipole Moment	1.8464	Debye
Point Group	C3V
Job cpu time: 0 days 0 hours 0 minutes 10.0 seconds.
Optimised Bond Length	1.02, 1.02, 1.02	Å
Literature Bond Length***	2.35018	Å
Optimised Bond Angle	106, 106, 106
Literature Bond Angle***	2.35018
Reference***	2.35018

 NH3 optimisation
         Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000010     0.001800     YES
 RMS     Displacement     0.000007     0.001200     YES
 Predicted change in Energy=-7.830455D-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)              105.7463         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7463         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7463         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.867          -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

NH₃ Frequency

NH₃ Frequency [NH₃ Frequency] [NH₃ Frequency D space]
File Name	SW_NH3_freq2
File Type	.log
Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Change	0
Spin	Singlet
E(RB3LYP)	-56.55776873	a.u.
RMS Gradient Norm	0.00000028	a.u.
Imaginary Freq	0
Dipole Moment	1.8465	Debye
Point Group	C3V
Job cpu time: 0 days 0 hours 0 minutes 4.0 seconds.

 NH3 Frequency
 Low frequencies ---   -6.1415   -4.4910   -4.4904    0.0014    0.0035    0.0150
 Low frequencies --- 1089.3562 1693.9270 1693.9271

NH₃ MO

NH₃ MO [NH₃ MO] NH₃ MO D space]
File Name	SW_NH3_MO
File Type	.chk
Calculation Type	SP
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Change	0
Spin	Singlet
E(RB3LYP)	-56.55776863	a.u.
RMS Gradient Norm	0.00000000	a.u.
Imaginary Freq	0
Dipole Moment	1.8464	Debye
Point Group	C3V
Job cpu time: 0 days 0 hours 0 minutes 6.0 seconds.

NH₃ NBO Analysis

NH₃ NBO [NH₃ MO] [NH₃ Frequency D space]
NH₃ NBO Analysis	Comment
	charge distributionColour range -1.000 to 1.000
	NBO charges for the nitrogen: -1.125 and hydrogen atom: 0.375

NH₃BH₃

NH₃BH₃ Optimisation

NH₃BH₃ Optimisation [NH₃BH₃ Optimisation ] [NH₃BH₃ Optimisation D space]
File Name	SW_NH3BH3_OPT
File Type	.log
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Change	0
Spin	Singlet
E(RB3LYP)	-83.22468910	a.u.
RMS Gradient Norm	0.00000031	a.u.
Imaginary Freq	0
Dipole Moment	5.5646	Debye
Point Group	C1
Job cpu time: 0 days 0 hours 0 minutes 25.0 seconds.

 NH<sub>3</sub>BH<sub>3</sub> Optimisation
         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000005     0.000006     YES
 RMS     Displacement     0.000002     0.000004     YES
 Predicted change in Energy=-3.646599D-12
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,7)                  1.0185         -DE/DX =    0.0                 !
 ! R2    R(2,7)                  1.0185         -DE/DX =    0.0                 !
 ! R3    R(3,7)                  1.0185         -DE/DX =    0.0                 !
 ! R4    R(4,8)                  1.2098         -DE/DX =    0.0                 !
 ! R5    R(5,8)                  1.2098         -DE/DX =    0.0                 !
 ! R6    R(6,8)                  1.2098         -DE/DX =    0.0                 !
 ! R7    R(7,8)                  1.6677         -DE/DX =    0.0                 !
 ! A1    A(1,7,2)              107.876          -DE/DX =    0.0                 !
 ! A2    A(1,7,3)              107.876          -DE/DX =    0.0                 !
 ! A3    A(1,7,8)              111.023          -DE/DX =    0.0                 !
 ! A4    A(2,7,3)              107.876          -DE/DX =    0.0                 !
 ! A5    A(2,7,8)              111.0227         -DE/DX =    0.0                 !
 ! A6    A(3,7,8)              111.0228         -DE/DX =    0.0                 !
 ! A7    A(4,8,5)              113.8738         -DE/DX =    0.0                 !
 ! A8    A(4,8,6)              113.8739         -DE/DX =    0.0                 !
 ! A9    A(4,8,7)              104.5973         -DE/DX =    0.0                 !
 ! A10   A(5,8,6)              113.8739         -DE/DX =    0.0                 !
 ! A11   A(5,8,7)              104.5975         -DE/DX =    0.0                 !
 ! A12   A(6,8,7)              104.5974         -DE/DX =    0.0                 !
 ! D1    D(1,7,8,4)           -179.9991         -DE/DX =    0.0                 !
 ! D2    D(1,7,8,5)            -59.9992         -DE/DX =    0.0                 !
 ! D3    D(1,7,8,6)             60.0009         -DE/DX =    0.0                 !
 ! D4    D(2,7,8,4)            -59.9991         -DE/DX =    0.0                 !
 ! D5    D(2,7,8,5)             60.0008         -DE/DX =    0.0                 !
 ! D6    D(2,7,8,6)           -179.9991         -DE/DX =    0.0                 !
 ! D7    D(3,7,8,4)             60.0008         -DE/DX =    0.0                 !
 ! D8    D(3,7,8,5)           -179.9992         -DE/DX =    0.0                 !
 ! D9    D(3,7,8,6)            -59.9991         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

NH₃BH₃ Frequency

NH₃BH₃ Frequency [NH₃BH₃ Frequency] [NH₃BH₃ Frequency D space]
File Name	SW_NH3BH3_freq
File Type	.log
Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Change	0
Spin	Singlet
E(RB3LYP)	-83.22468906	a.u.
RMS Gradient Norm	0.00000024	a.u.
Imaginary Freq	0
Dipole Moment	5.5646	Debye
Point Group	C1
Job cpu time: 0 days 0 hours 0 minutes 28.0 seconds.

 NH3BH3 Frequency 
 Low frequencies ---   -3.1658   -2.5379    0.0014    0.0015    0.0015    1.8917
 Low frequencies ---  263.4226  632.9765  638.4394

NH₃BH₃

Association Energy

Association Energy of NH₃+BH₃->NH₃BH₃

Basis Set: 6-31G(d,p)

E(NH3)= -56.55776863 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468906 a.u.

then still in AU compute the energy difference and report this on your wiki ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468906-[(-26.61532364)+(-56.55776863)]= -0.05159679 a.u.

the final step is to convert the energy difference from AU to kJ/mol

1 a.u. = 1 hartree = 2625.50 KJ/mol

ΔE=-0.0516 a.u. *2625.50 kJ/mol = -135.47 = KJ/mol

So the dissociation energy is +135.47 KJ/mol, endothermic dissociation. this number tells us the association energy for combinging a molecule of NH3 with one of BH3, conversely it is also the dissociation energy!

Week 2: Project: Ionic Liquids: Designer Solvents

Part 1: Comparison of selected 'onium' cations'

Optimisation and frequency of [N(CH₃)₄]⁺, [P(CH₃)₄]⁺ and [S(CH₃)₄]⁺

Optimisation and frequency of [N(CH₃)₄]⁺, [P(CH₃)₄]⁺ and [S(CH₃)₃]⁺
onium cations	[N(CH₃)₄]⁺	[P(CH₃)₄]⁺	[S(CH₃)₄]⁺
File Name	SW_[N(CH3)4]+_OPT_freq	SW_[P(CH3)4]+_OPT_freq3	SW_[S(CH3)3]+_OPT_freq
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)
Change	1	1	1
Spin	Singlet	Singlet	Singlet
E(RB3LYP) (a.u.)	-214.18127521	-500.82700333	-517.68325777
RMS Gradient Norm (a.u.)	0.00004006	0.00001637	0.00004777
Imaginary Freq	0	0	0
Dipole Moment (Debye)	0.0004	2.8852	0.9653
Point Group	C1	C1	C1
Job cpu time	7 minutes 31.2 seconds.	7 minutes 12.1 seconds.	3 minutes 39.2 seconds.
IR Spectrum
Log file	[[N(CH₃)₄⁺ ]]	[[P(CH₃)₄⁺ ]]	[[S(CH₃)₃⁺ ]]
D Space file	[N(CH₃)₄⁺]]	[[P(CH₃)₄⁺]]	[[S(CH₃)₃⁺]]

Optimisation of [N(CH₃)₄]⁺

 
         Item               Value     Threshold  Converged?
 Maximum Force            0.000111     0.000450     YES
 RMS     Force            0.000028     0.000300     YES
 Maximum Displacement     0.001413     0.001800     YES
 RMS     Displacement     0.000314     0.001200     YES
 Predicted change in Energy=-1.051115D-07
 Optimization completed.
    -- Stationary point found.

Frequency of [N(CH₃)₄]⁺

 
 Low frequencies ---  -19.1188   -9.8202   -0.0009   -0.0006   -0.0001   21.7729
 Low frequencies ---  180.8192  277.3212  288.7343

Optimisation of [P(CH₃)₄]⁺

 
         Item               Value     Threshold  Converged?
 Maximum Force            0.000031     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000856     0.001800     YES
 RMS     Displacement     0.000253     0.001200     YES
 Predicted change in Energy=-3.411912D-08
 Optimization completed.
    -- Stationary point found.

Frequency of [P(CH₃)₄]⁺

 Low frequencies ---  -18.0294   -4.5198   -0.0036   -0.0032    0.0009   14.5481
 Low frequencies ---  153.7212  183.3695  191.3300

Optimisation of [S(CH₃)₃]⁺

         Item               Value     Threshold  Converged?
 Maximum Force            0.000158     0.000450     YES
 RMS     Force            0.000050     0.000300     YES
 Maximum Displacement     0.000943     0.001800     YES
 RMS     Displacement     0.000280     0.001200     YES
 Predicted change in Energy=-2.620616D-07
 Optimization completed.
    -- Stationary point found.

Frequency of [S(CH₃)₃]⁺

 Low frequencies ---  -29.1030  -19.8918   -0.0034   -0.0031   -0.0024   11.1429
 Low frequencies ---  159.6295  192.4985  205.8541

Molecular Orbital of [N(CH₃)₄]⁺, [P(CH₃)₄]⁺ and [S(CH₃)₄]⁺

Molecular Orbitals [N(CH₃)₄]⁺, [P(CH₃)₄]⁺ and [S(CH₃)₃]⁺
onium cations	[N(CH₃)₄]⁺	[P(CH₃)₄]⁺	[S(CH₃)₄]⁺
File Name	SW_[N(CH3)4]+_MO	SW_[P(CH3)4]+_MO	SW_[S(CH3)3]+_MO
File Type	.log	.log	.log
Calculation Type	SP	SP	SP
Calculation Method	RB3LYP	RB3LYP	RB3LYP
Basis Set	6-31G(d,p)	6-31G(d,p)	6-31G(d,p)
Change	1	1	1
Spin	Singlet	Singlet	Singlet
E(RB3LYP) (a.u.)	-214.18127521	-500.82698242	-517.68325777
RMS Gradient Norm (a.u.)	n/a	n/a	n/a
Imaginary Freq	n/a	n/a	n/a
Dipole Moment (Debye)	0.0004	0.0021	0.9653
Point Group	C1	C1	C1
Job cpu time	0 minutes 52.5 seconds	1 minutes 15.4 seconds	0 minutes 36.5 seconds
Image
General Structure	tetrahedral	tetrahedral	pyramidal
Bond length (C-X) Å	1.51	1.82	1.82
Litt Bond length (C-X)	for N(CH₃)₄⁺N₃^-:1.47 to 1.53
Bond angle (C-X-C)	109.5	109.5	102.8
Litt Bond angle
D Space file	[N(CH₃)₄⁺]]	[[P(CH₃)₄⁺]]	[[S(CH₃)₃⁺]]

Comment on geometries

The bond length increases as the central nitrogen atom is replaced by phosphorus and sulfur. It indicates less bonding interaction and more diffused orbitals. In tetramethylammonium the bond length is within the range of the literature value. The literature value is influence in the presence of N₃^- group. ^{lit 4}

The bond angles remain the same at 109.5 degrees for N and P atoms. But it decreases to 102.8 degrees due to the lone pair repulsion on the sulfur atom.

MO of [N(CH₃)₄]⁺
Energy Level	[N(CH₃)₄]⁺	ChemDraw Hypothesis	Description
MO6: E=-1.19645			It is a₁ symmetry. s-orbital on all atoms and with all same phase. So the visulisded orbital is more like a sphere. It is a highly bonding orbital.
MO7: E=-0.92557			Energy level 7, 8, 9 are degenerate. Therefore it is t₂ symmetry. p orbital is on N. Hence it is opposite phases. While two methyl group are the same phase and the other two are opposite. There is only one node between two phases. So it is a fairly strong bonding orbital as well.
MO10: E=-0.80747			It is a₁ symmetry. Central N is positively charged, whereas methyl group are mainly negatively charged with opposite phases. however, as the central phase contributes more on N-C bond, it indicates an opposite phase occurs on C. It could be a p-orbital on carbon after overlap. There are four nodes on this MO diagram. The nodes are more like 'points' at the inter-phase. So it is becoming less bonding.
MO11: E=-0.69898			E energy level 11, 12, 13 are degenerate. The symmetry label is t₂ It is a p-orbital on central atom with two methyl group (mainly carbon atom) bonding and the other two methyl groups anti-bonding via pi-interaction. There are five nodes on four carbons and nitrogen respectively. The through space weakly repulsion also can be seen between each two methyl groups. Overall it is a weakly bonding orbital.
MO21: E=-0.57933			It is the HOMO orbital of the cation. There are five nodes on the carbon and nitrogen with pi-interaction between three methyl group at the bottom. The p orbital on nitrogen is a bit distorted and bond with the p orbital on the top carbon. There are slightly through space bonding between the hydrogen atoms of the top methyl group and two hydrogen atoms of each methyl group at the bottom. As it is a cation, it is assumed that it is likely to be a MO with weak interaction.
MO 22: E=-0.13301 (unoccupied)			It is the LUMO orbital of the cation. The central N is in phase while it is out-of-phase all around it. There are also other four in phase at each methyl group. It gives orbitals strongly repelling to each other. Therefore it is a strong antibonding orbital. The high energy gap between HOMO and LUMO orbitals (ΔE = 0.44692a.u.) gives the stability of the cation.

Charge Distribution Analysis

Charge Distribution of [N(CH₃)₄]⁺, [P(CH₃)₄]⁺ and [S(CH₃)₃]⁺
onium cations	[N(CH₃)₄]⁺	[P(CH₃)₄]⁺	[S(CH₃)₄]⁺
Ditribution with number
	N=-0.295	P=1.667	S=0.917
	C=-0.483	C=-1.060	C=-0.845
	H=0.269	H=0.298	H=0.297,0.279
Ditribution with colour
Colour range	-1.000 to 1.000	-1.000 to 1.000	-1.000 to 1.000
Description	Nitrogen is most electronegative one so it gives a dark centre. But it gives a most electropositive carbon among these three.	The phosphorus is very electropositive and gives a bright green atom at centre. But the carbon is more electronegative. So it is dark in colour. And the charge difference is the highest	Sulfur is relatively very electropositive as well. So it is also quite bright. And the carbon is quite electronegative. So the overall charge difference is relatively big as well.

In sulfur cation, there is a slight difference in charge distribution between axial and equatorial hydrogen atoms. It is due to the H atoms are in the difference phase at its HOMO orbital.

Orbital contribution of the C-heteroatom bond
Bond C-X	C-N	C-P	C-S
contribution of X	66.4%, s(25.0%), p(75.0%)	40.4%, s(25.0%), p(74.1%)	51.3%, s(17.0%), p(83.4%)
Contribution of C	33.7%, s(20.8%), p(79.1%)	59.6%, s(25.2%), p(74.7%)	48.7%, s(19.7%), p(80.1%)

Comment

Nitrogen contributes the most in comparison to the other two heteratoms in their C-X bonds with 66.4% and the phosphorus contributes the least. It matches the charge distribution of where nitrogen is the most electronegative and phosphorus is the most electropositive. In C-N, the nitrogen is sp³ hybridised, but there is more interaction with carbon p orbital than its s orbital. In C-P, both are sp³ hybrids bonded to each other as it is 25% contribution from s orbital and 75% contribution from p orbital. In C-S, approximately same contribution from two atoms, the about 20% contribution from s orbital and 80% from p orbital.

[NR₄]⁺ According to the charge distribution just analysed, the nitrogen is actually negatively charged, although it is less negative than carbon atom. The positive charge is actually located on its hydrogen atom.

Part 2: Influence of functional groups

Optimisation and frequency of [N(CH₃)₃(CH₂OH)]⁺ and [N(CH₃)₃(CH₂CN)]⁺

Optimisation and frequency of [N(CH₃)₃(CH₂OH)]⁺ and [N(CH₃)₃(CH₂CN)]⁺
cations	[N(CH₃)₃(CH₂OH)]⁺	[N(CH₃)₃(CH₂CN)]⁺
File Name	SW_[N(CH3)3(CH2OH)]+_OPT_freq_vtight	SW_[N(CH3)3(CH2CN)]+_OPT_freq_vtight
File Type	.log	.log
Calculation Type	FREQ	FREQ
Calculation Method	RB3LYP	RB3LYP
Basis Set	6-31G(d,p)	6-31G(d,p)
Change	1	1
Spin	Singlet	Singlet
E(RB3LYP) (a.u.)	-289.39470636	-306.39376141
RMS Gradient Norm (a.u.)	0.00000035	0.00000041
Imaginary Freq	0	0
Dipole Moment (Debye)	8.2355	8.6721
Point Group	C1	C1
Job cpu time	21 minutes 54.9 seconds.	24 minutes 50.5 seconds.
IR Spectrum
Log file	[[N(CH₃)₃(CH₂OH)⁺ ]]	[[N(CH₃)₃(CH₂CN)⁺ ]]
D Space file	[[N(CH₃)₃(CH₂OH)⁺]]	[[N(CH₃)₃(CH₂CN)⁺]]

Optimisation of [N(CH₃)₃(CH₂OH)]⁺

 
         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000005     0.000006     YES
 RMS     Displacement     0.000001     0.000004     YES
 Predicted change in Energy=-2.728296D-13
 Optimization completed.
    -- Stationary point found.

Frequency of [N(CH₃)₃(CH₂OH)]⁺

 
 Low frequencies ---   -9.6930   -7.6045   -4.7654   -0.0004   -0.0001    0.0005
 Low frequencies ---  130.7079  213.6972  255.6339

Optimisation of [N(CH₃)₃(CH₂CN)]⁺

 
         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000003     0.000006     YES
 RMS     Displacement     0.000001     0.000004     YES
 Predicted change in Energy=-3.560461D-13
 Optimization completed.
    -- Stationary point found.

Frequency of [N(CH₃)₃(CH₂CN)]⁺

 
 Low frequencies ---   -4.7020   -4.2767   -0.0012   -0.0009   -0.0003    4.5253
 Low frequencies ---   91.5853  153.8209  211.2666

Molecular Orbital of [N(CH₃)₃(CH₂OH)]⁺ and [N(CH₃)₃(CH₂CN)]⁺

MO of [N(CH₃)₃(CH₂OH)]⁺ and [N(CH₃)₃(CH₂CN)]⁺
cations	[N(CH₃)₃(CH₂OH)]⁺	[N(CH₃)₃(CH₂CN)]⁺
File Name	SW_[N(CH3)3(CH2OH)]+MO	SW_[N(CH3)3(CH2CN)]+MO_vtight
File Type	.log	.log
Calculation Type	SP	SP
Calculation Method	RB3LYP	RB3LYP
Basis Set	6-31G(d,p)	6-31G(d,p)
Change	1	1
Spin	Singlet	Singlet
E(RB3LYP) (a.u.)	-289.39471123	-306.39377029
RMS Gradient Norm (a.u.)	n/a	n/a
Imaginary Freq	n/a	n/a
Dipole Moment (Debye)	2.1359	5.7642
Point Group	C1	C1
Job cpu time	1 minutes 25.5 seconds.	1 minutes 38.8 seconds.
D Space file	[[N(CH₃)₃(CH₂OH)⁺]]	[[N(CH₃)₃(CH₂CN)⁺]]

HOMO LUMO comparison of [N(CH₃)₃(CH₂OH)]⁺ and [N(CH₃)₃(CH₂CN)]⁺
onium cations	[N(CH₃)₄]⁺	[N(CH₃)₃(CH₂OH)]⁺	[N(CH₃)₃(CH₂CN)]⁺
LUMO
LUMO positive phase
LUMO Level	E22=-0.13301	E26=-0.12459	E28=-0.18183
HOMO
HOMO Level	E21=-0.57933	E25=-0.48764	E27=-0.50047
HOMO-LUMO gap (a.u.)	ΔE=0.44632	ΔE=0.36305	ΔE=0.31864

Comment:

how has the shape of the orbitals changed?

LUMO: In tetramethylammonium LUMO orbital is central symmetrical with one positive phase on the central N atom and other four positive phases on methyl groups. In the cation with OH group, there is an additional positive phase on oxygen. So there is an overlap between the oxygen, the Carbon of CH₂ and the central nitrogen. It stabilises the LUMO energy level. In the cation with CN group, the positive phase density is getting bigger. The negative phase density goes down so the repulsion between two phases gets weaker. Thus the LUMO energy goes down as well.

HOMO: There are less bonding interactions between the phases from left to right as the lobe on the atoms are smaller. Therefore the HOMO energy goes up.

has the energy of these orbitals moved?

The HOMO energy level rises up and LUMO energy level goes down when the functional groups are introduced. The effect is more obvious on CN group cation than OH group cation.

has the HOMO-LUMO gap changed in size?

The HOMO-LUMO gap decreases from left to right (no functional group to electron donating group to electron withdrawing group).

what chemical impact could these changes have?

The chemical impact of these is that it is more reactive with functional groups on the onium cation. And electron withdrawing group has a bigger influence than the electron donating group.

Charge Distribution Analysis

Charge Distribution of [N(CH₃)₃(CH₂OH)]⁺ and [N(CH₃)₃(CH₂CN)]⁺
onium cations	[N(CH₃)₃(CH₂OH)]⁺	[N(CH₃)₃(CH₂CN)]⁺
Ditribution with number
	N(Central)=-0.322	N(Central)=-0.289
	O= -0.725	N(CN)=-0.186
	H(OH)=0.521	C(CN)=0.209
	C(CH3)=-0.491 to -0.494	C(CH3)=-0.489 to -0.485
	C(CH2)=0.088	C(CH2)=-0.358
	H(CH3)=0.262 to 0.282	H(CH3)=0.269 to 0.282
	H(CH2)=0.249, 0.237	H(CH2)=0.309
Ditribution with colour
Colour range	-1.000 to 1.000	-1.000 to 1.000
Description	OH is an electron donating group. As can be seen, the central N atom is more electronegative than the central N atom on the right. It is because OH donates more electron density to it. But the Carbon atom at CH₂ is more electron-positive as OH group is donating via a resonance form. Therefore it is not directly inductive effect, but the atoms at the alternating position are affected. The bond length also show the CH2-N is slightly longer than the others. Hence it is easier to break.	CN is electron withdrawing group. It takes away the electron density from the central N atom and makes it more electropositive. This inductive effect also results in the less electronegative charge on the CH₂ atom than other carbon of CH₃ atoms. The electron density of methyl groups is less influenced by the EWG and EDG as they are relatively further away.

Bond length:

in alcohol: CH₂-OH 1.37, CH₂-N 1.55 CH₃-N 1.50

in cyanide: CH₂-CN 1.46, CH₂-N 1.53 CH₃-N 1.51

Reference

1. L. C. Allen, J. Am. Chem. Soc., 1989, 111:9003

2. Kagaku Benran, CRC Handbook of Chemistry and Physics, 87th Edition, 1984, 2, 649–661

3. G. N. Lewis, J. Am. Chem. Soc., 1916, 38(4), 762-785 [1]

4. K. O. Christe, W. W. Wilson, R. Bau and S. W. Bunte, J. Am. Chem. Soc., 1992, 114, 3411-3414 [2]

Week 1 Inorganic computational

BH3

BH3 optimisation

BH3 optimisation 631G 2nd time

BH3 Frequency

BH3 Frequency 2nd

BH3 Vibration

Molecular Orbital of BH3

GaBr3

GaBr3 optimisation

GaBr3 Frequency

GaBr3 Vibration

BBr3

BBr3 optimisation

Comparisons

Vibrational frequencies of BH3 and GaBr3

NH3

NH3 optimisation

NH3 Frequency

NH3 MO

NH3 NBO Analysis

NH3BH3

NH3BH3 Optimisation

NH3BH3 Frequency

Association Energy

Association Energy of NH3+BH3->NH3BH3

Week 2: Project: Ionic Liquids: Designer Solvents

Part 1: Comparison of selected 'onium' cations'

Optimisation and frequency of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)4]+

Molecular Orbital of [N(CH3)4]+, [P(CH3)4]+ and [S(CH3)4]+

Charge Distribution Analysis

Part 2: Influence of functional groups

Optimisation and frequency of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+

Molecular Orbital of [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+

Charge Distribution Analysis

Reference

BH₃

Molecular Orbital of BH₃

GaBr₃

GaBr₃ optimisation

GaBr₃ Frequency

GaBr₃ Vibration

BBr₃

BBr₃ optimisation

Vibrational frequencies of BH₃ and GaBr₃

NH₃

NH₃ optimisation

NH₃ Frequency

NH₃ MO

NH₃ NBO Analysis

NH₃BH₃

NH₃BH₃ Optimisation

NH₃BH₃ Frequency

Association Energy of NH₃+BH₃->NH₃BH₃

Optimisation and frequency of [N(CH₃)₄]⁺, [P(CH₃)₄]⁺ and [S(CH₃)₄]⁺

Molecular Orbital of [N(CH₃)₄]⁺, [P(CH₃)₄]⁺ and [S(CH₃)₄]⁺

Optimisation and frequency of [N(CH₃)₃(CH₂OH)]⁺ and [N(CH₃)₃(CH₂CN)]⁺

Molecular Orbital of [N(CH₃)₃(CH₂OH)]⁺ and [N(CH₃)₃(CH₂CN)]⁺