Rep:Mod:annyinorganic

Week One

Optimization Analysis of BH₃

3-21G optimized BH₃

A BH₃ molecule has been created by Gaussview program; before optimization, the bond length of three B-H bonds have been changed to be 1.55Å, 1.54Å, 1.53Å in order to break the symmetry of the molecule. Then the molecule was optimized using B3LYP method and 3-21G basis set.

The out-put log file:BH₃ 3-21G

Table 1. Optimization Results of 3-21G optimised BH₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
BH₃	.log	FOPT	RB3LYP	3-21G	0	Singlet	-26.46226433	0.00004507	0.0000	D3H	0 days 0 hours 0 minutes 5.0 seconds

To check if the job has been successfully converged, an 'Item' table is shown below. It tells what forces have been converged. Also, according to the table, all gradient values were quite close to zero, ie less than 0.001; hence, the optimization job was complete.

        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)                  1.1944         -DE/DX =   -0.0001              !
 ! R3    R(1,4)                  1.1947         -DE/DX =   -0.0002              !
 ! A1    A(2,1,3)              119.986          -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0157         -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

Optimized B-H bond length and H-B-H bond angle have summarized in the following table. Bond length was accurate to 0.01Å, and bond angle was accurate to 0.1^o. By comparing to literature, both bond distance and angle were the quite close to the theoretical values; the molecule also had a point group of D3H.

Basis Set	B-H Bond Length(Å)	H-B-H Bond Angle(°)
	1.19	120.0
	1.19	120.0
	1.19	120.0
Average	1.19	120.0
Literature^[1]	1.19	120

6-31G(d,p) optimized BH₃

A new optimization of BH₃ was done using a higher level basis: 6-31G(d,p).

The out-put log file:BH₃ 6-31G(d,p)

Table 2. Optimization Results of 6-31G(d,p) optimised optimised BH₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
BH₃	.log	FOPT	RB3LYP	6-31G(d,p)	0	Singlet	-26.61532363	0.00000296	0.00	D3H	0 days 0 hours 0 minutes 6.0 seconds

Again, the optimization job was checked by the item table. Since all gradient terms were close to zero and forces were all converged, it can be concluded that the optimization job was successful.

        Item               Value     Threshold  Converged?
 Maximum Force            0.000006     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000023     0.001800     YES
 RMS     Displacement     0.000015     0.001200     YES
 Predicted change in Energy=-2.008834D-10
 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

Basis Set	B-H Bond Length(Å)	H-B-H Bond Angle(°)
	1.19	120.0
	1.19	120.0
	1.19	120.0
Average	1.19	120.0
Literature^[1]	1.19	120

The total energies of the molecule BH₃ using different basis set were compared in the following table. It could be seen that the higher basis set had a lower energy (about 400 kJ/mol).

Table 3. Total Energies of Optimized BH₃
3-21G	6-31G(d,p)
-26.46226433 au	-26.61532363 au

Optimization Analysis of GaBr₃

In order to investigate pseudo-potentials and larger basis sets, GaBr₃ has been created by Gaussview followed by optimization using B3LYP method and LANL2DZ basis set. Its point group was restricted to D3h.

The out-put file: DOI:10042/26238

Table 4. Optimization Results of LANL2DZ optimised optimised GaBr₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
GaBr₃	.log	FOPT	RB3LYP	LANL2DZ	0	Singlet	-41.70082783	0.00000016	0.00	D3H	0 days 0 hours 0 minutes 8.0 seconds

Item table was used to check the optimization job was successfully converged.

         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)  !
 --------------------------                            --------------------------
 ! 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

By comparing the bond length and angles with literature, it could be seen that the optimized bond length was longer than the theoretical value and the Br-Ga-Br bond angles were smaller than the literature. This could be caused by the ignorance of crystal packing in the computational calculation. The literature gives a bond length of the solid form of the molecule whereas the computational calculation treated the molecule in the gas form; therefore, the bond length of our optimization could be much longer.

Basis Set	Bond length(Å)	Angle(°)
LANL2DZ	2.35	120.0
	2.35	120.0
	2.35	120.0
Average	2.35	120.0
Literature^[2]	2.24	123.1

Optimization Analysis of BBr₃

In order to investigate a mixture of basis-sets and pseudo-potentials, BBr₃ was created by Gaussview on the basis of 6-31(d,p) optimized BH₃, followed by optimization using B3LYP method and Gen basis set (LANL2DZ on Br and6-31G(d,p) on B).

BBr₃ out-put file: DOI:10042/26243

Table 5. Optimization Results of GEN Optimized BBr₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
BBr₃	.log	FOPT	RB3LYP	GEN	0	Singlet	-64.43645296	0.00000382	0.00	D3H	0 days 0 hours 0 minutes 16.4 seconds

The optimization job was checked by the item table. Since all gradient terms were close to zero and forces were all converged, it can be concluded that the optimization job was successful.

     Item                  Value     Threshold  Converged?
 Maximum Force            0.000008     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.000036     0.001800     YES
 RMS     Displacement     0.000023     0.001200     YES
 Predicted change in Energy=-4.027688D-10
 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)                  1.934          -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

Optimized Ga-Br bond length and Br-Ga-Br bond angle have summarized in the following table. By comparing to literature, both bond distance and angle were the quite close to the theoretical values; the difference could be explained by the same way as before.

Basis Set	Bond length(Å)	Angle(°)
GEN	1.93	120.0
	1.93	120.0
	1.93	120.0
Average	1.93	120.0
Literature^[3]	1.89	120.0

Structure Comparison

Molecule	BH₃	GaBr₃	BBr₃
Average Bond length(Å)	1.19	2.35	1.93
Avergar Angle(°)	120.0	120.0	120.0

By comparing the bond length between BH₃ and BBr₃, it could be concluded that changing the ligand from hydride to bromide would result in a longer bond. H and Br are both one electron donor ligands and form the 2c-2e bond with boron. However, bromine is more electronegative than hydrogen; so the difference in electronegativity between Br and B is larger than the difference between H and B resulting in a more polar and longer B-Br bond. Moreover, B-Br bond is longer than B-H because bromine has larger atomic radius and more diffuse orbital than hydrogen leading to a poor orbital overlap between Br and B. Hydrogen, on the other hand has a better orbital overlap with boron due to closer electronic configuration. (H: 1s; B: 1s²2s²2p¹; Br:[Ar]3d¹⁰4s²4p⁵))

By comparing the bond length between BBr₃ and GaBr₃, it could be concluded that changing the central atom from boron to gallium would result in a longer bond length. Both Br and Ga are group 13 elements and form the 2c-2e bonds. However, Ga has larger atomic radius than Br and poorer orbital overlap with boron due to mismatch of orbital size. (B: 1s²2s²2p¹; Ga:[Ar]3d¹⁰4s²4p¹; B: 1s²2s²2p¹)2p-4p orbital overlap between B and Br is better than 4p-4p overlap between Ga and Br resulting in a longer Ga-Br bond. In addition, gallium is highly polarizing element, and it is less electronegative than boron and has a more polarized and longer Ga-Br bond.

In Gaussview, there was a bond distance limit which meant that the bond would be invisible if its length exceeded the limit. In the optimization analysis of BH₃ using basis set of 3-21G, the bond length was changed to be longer than the limit before optimization; thus all B-H bonds were invisible. However, they still existed, and the molecule remained the same symmetry. After the optimization, the bonds became visible again when the bond length had decreased to be lower than the limit.

Bond is the electrostatic attraction between two atoms due to electron-sharing or electron-transfer.

Frequency Analysis for BH₃

Frequency Analysis

In order to study the frequency of BH₃, the point group of the optimized molecule was firstly restricted to be D3H followed by frequency analysis using the same procedure as optimization. The frequency result was listed below.

The out-put log file:BH₃ 6-21G(d,p)

Table 6. Frequency Results of BH₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
BH₃	.log	FREQ	RB3LYP	6-31G(d,p)	0	Singlet	-26.61532363	0.00000291	0.00	D3H	0 days 0 hours 0 minutes 7.0 seconds

Again, item table was used to check if the frequency job was complete. All forces were converged and gradient terms were close to zero, so the frequency was successful.

      Item                  Value     Threshold  Converged?
 Maximum Force            0.000006     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000023     0.001800     YES
 RMS     Displacement     0.000011     0.001200     YES
 Predicted change in Energy=-1.996524D-10
 Optimization completed.
    -- Stationary point found.
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

The low frequencies were also listed below and the values had a range of ± 15 cm^-1 .

Low frequencies ---   -0.9432   -0.8611   -0.0056    5.7455   11.7246   11.7625
Low frequencies --- 1162.9963 1213.1826 1213.1853

Animating The Vibrations

NO.	Form of Vibration	Description	Frequency(cm^-1)	Internsity	Symmetry(D3h) Point Group
1		Three hydrogen atoms are moving towards the same direction whereas the boron moves towards the opposite direction.	1163	93	A2"
2		Two hydrogen atoms are moving towards each other by the plane of symmetry while the other atoms are moving along the plane.	1213	14	E' (degenerate)
3		Hydrogen atoms are moving towards opposite directions respective to each other along the xz plane.	1213	14	E' (degenerate)
4		Three hydrogen atoms are moving towards the boron.	2582	0	A1' (totally symmetric)
5		One of the hydrogens moves towards boron while another one is moving away from boron; the other atoms stay.	2715	126	E' (degenerate)
6		One hydrogen moves toward Boron while the other two are moving away from boron.	2715	126	E' (degenerate)

There are only three peaks shown in the IR spectrum although six different vibrations exist because vibration No.2 and 3 as well as No. 5 and 6 are degenerate and they have the same the frequencies which would only show a single peak on the spectrum. Also, No. 4 vibration has zero intensity and would not have a peak neither because the H-B-H angles are all 120° and all dipole moments are cancelled out resulting in a zero intensity on IR spectrum.

Frequency Analysis of GaBr₃

To compare GaBr₃ and BH₃, frequency analysis of GaBr₃ using the same method and basis set has been done and the results were listed below.

GaBr₃ out-put file: DOI:10042/26269

Table 7. Frequency Results of GaBr₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
GaBr₃	.log	FREQ	RB3LYP	LANL2DZ	0	Singlet	-41.70082783	0.00000011	0.00	D3H	0 days 0 hours 0 minutes 11.1 seconds

Item table was used to check the completion of frequency job.

       Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000002     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES
 Predicted change in Energy=-6.142796D-13
 Optimization completed.
    -- Stationary point found.
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Low frequencies result:

Low frequencies ---   -0.5252   -0.5247   -0.0024   -0.0010    0.0235    1.2011
Low frequencies ---   76.3744   76.3753   99.6982

The lowest real normal mode was 76 cm^-1 .

Compare and Contrast the Frequencies for BH₃, and GaBr₃

**Table 8. Comparison of Vibrational Frequencies between BH₃ and GaBr₃**
No.	BH₃ Frequency (cm^-1)	BH₃ Intensity	BH₃ Symmetry D₃h point group	No.	GaBr₃ Frequency (cm^-1)	GaBr₃ Intensity	GaBr₃ Symmetry D₃h point group
1	1163	93	A2"	1	76	3	E' (degenerate)
2	1213	14	E' (degenerate)	2	76	3	E' (degenerate)
3	1213	14	E' (degenerate)	3	100	9	A2"
4	2582	0	A1' (totally symmetric)	4	197	0	A1' (totally symmetric)
5	2715	126	E' (degenerate)	5	316	57	E' (degenerate)
6	2715	126	E' (degenerate)	6	316	57	E' (degenerate)

Both BH₃ and GaBr₃ have the point group of D3h, so they have similar vibraional environments; and it was expected to have 6 different vibrations for each molecule. However, there were only three peaks in each IR spectrum.

By comparing the frequencies of the two molecules, GaBr₃ clearly had much lower frequencies than BH₃. This could be explained first by the stronger B-H bond as frequency is proportional to the force constant. Moreover, gallium has larger atomic radius than boron; therefore, GaBr₃ has a poorer orbital overlap and vibrates slower as well.

In addition, although the two molecules have the same symmetry labels, the vibration mode a"₂in molecule BH₃ has the lowest frequencies and e' is numbered third; however, the order of these two vibrations is switched in the mole GaBr₃. This is because a"₂ vibration involves one gallium atom whereas e' involves all atoms, a"₂would then vibrates quicker than e' and has a higher frequency in the molecule GaBr₃.

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

The key to the optimization and frequency analysis is to make sure that the minimum energy has been reached. The total energy for both analysis is highly dependent on the level of the basis set. As before when we did the optimization for BH₃ molecule using two different basis set, the total energy had about 400 kJ/mol difference. What this means is that we should never compare the energy with different basis set, it would have no significance. Therefore, we must use the same method and basis set for any calculations, then we will be able to analyze the result and compare the difference.

What is the purpose of carrying out a frequency analysis?

The purpose of carrying out a frequency analysis is to find the structure of the molecule with a minimum total energy and then to find out the vibration modes which could generate the IR spectrum.

What do the "Low frequencies" represent?

Low frequency is the vibrational motion which is the center of the molecule mass; therefore, it is lower than the real frequency. The formula of number of the vibration modes is 3N-6. N is the total number of atoms and -6 is the low frequency.

Molecular Orbitals Analysis of BH₃

BH₃ out-put file: DOI:10042/26258

Table 9. Results of BH₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
BH₃	.log	SP	RB3LYP	6-31G(d,p)	0	Singlet	-26.61532363		0.0000	D3H	0 days 0 hours 0 minutes 6.5 seconds

Figure 3.Molecular Orbital Diagram of BH₃

Clearly, LCAO molecular orbitals are not the same as the real MOs because in LCAO MOs, the electron density is localized on individual atoms; however, the real MOs are more diffuse and have the electron density that are delocalized on the entire molecular orbitals. Despite this, LCAO still gives accurate information about nodal planes and nodes. Therefore, we could use LCAO to predict how the orbitals are combined as well as the positions of nodal planes and use the real MOs to tell the electron density.

NBO Analysis

NH₃ Optimisation out-put file:NH₃ Optimisation

Table 10. Optimisation Results of NH₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
NH₃	.log	FOPT	RB3LYP	6-31G(d,p)	0	Singlet	-56.55776856	0.00000367	1.85	CS	0 days 0 hours 0 minutes 6.0 seconds

      Item                 Value     Threshold  Converged?
 Maximum Force            0.000008     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000023     0.001800     YES
 RMS     Displacement     0.000018     0.001200     YES
 Predicted change in Energy=-2.074950D-10
 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)              105.7462         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.867          -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

NH₃ Frequency out-put file:NH₃ Frequency

Table 11. Frequency Results of NH₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
NH₃	.log	FREQ	RB3LYP	6-31G(d,p)	0	Singlet	-56.55776863	0.00000281	1.85	C3V	0 days 0 hours 0 minutes 7.0 seconds

     Item                  Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000011     0.001800     YES
 RMS     Displacement     0.000006     0.001200     YES
 Predicted change in Energy=-8.415874D-11
 Optimization completed.
    -- Stationary point found.
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

 Low frequencies ---  -11.6206  -11.5851   -0.0030    0.0244    0.1403   25.5610
 Low frequencies --- 1089.6630 1694.1734 1694.1737

NH₃ MO Analysis out-put file:NH₃ MO

Table 12. MO Results of NH₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
NH₃	.chk	SP	RB3LYP	6-31G(d,p)	0	Singlet	-56.55776856		1.85	C3	0 days 0 hours 0 minutes 5.0 seconds

The charge range is -1.000 to +1.000 and the green color indicates the highly positive charge whereas the red color indicates the highly negative charge. Nitrogen is bright red and the specific NBO charge of nitrogen is -1.125 while hydrogen is 0.375.

Association energies: Ammonia-Borane

NH₃BH₃ Optimisation out-put file:NH₃BH₃ Optimisation

Table 13. Optimisation Results of NH₃BH₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
NH₃BH₃	.log	FOPT	RB3LYP	6-31G(d,p)	0	Singlet	-83.22468999	0.00006054	5.57	C1	0 days 0 hours 0 minutes 4.0 seconds

        Item               Value     Threshold  Converged?
 Maximum Force            0.000128     0.000450     YES
 RMS     Force            0.000057     0.000300     YES
 Maximum Displacement     0.000630     0.001800     YES
 RMS     Displacement     0.000363     0.001200     YES
 Predicted change in Energy=-1.665405D-07
 Optimization completed.
    -- Stationary point found.

NH₃BH₃ Frequency out-put file:NH₃BH₃ Frequency

Table 14. Frequency Results of NH₃BH₃
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
NH₃BH₃	.log	FREQ	RB3LYP	6-31G(d,p)	0	Singlet	-83.22468999	0.00006054	5.57	C1	0 days 0 hours 0 minutes 15.0 seconds

        Item               Value     Threshold  Converged?
 Maximum Force            0.000119     0.000450     YES
 RMS     Force            0.000061     0.000300     YES
 Maximum Displacement     0.000777     0.001800     YES
 RMS     Displacement     0.000452     0.001200     YES
 Predicted change in Energy=-1.750924D-07
 Optimization completed.
    -- Stationary point found.
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Low frequencies ---   -0.0009    0.0008    0.0010   18.2527   22.7948   41.2547
 Low frequencies ---  266.2766  632.3264  639.2582

	Energy
NH₃BH₃	-83.22468999
NH₃	-56.55776856
BH₃	-26.61532363
Energy Difference (au) ΔE=E(NH₃BH₃)-[E(NH₃)+E(BH₃)]	-0.0515978
Energy Difference (kJ/mol)	-136

Combining a NH₃ molecule with a BH₃ molecule would have an association energy of -136 kJ/mol; this energy is also the dissociation/bond energy of the newly formed dative covalent bond. The product NH₃BH₃ has a more negative energy than either the reactants; therefore, the product is more stable. The covalent bond is formed by the sigma-donation from lone pair of nitrogen to the empty p orbital of borane.

Reference

↑ ^1.0 ^1.1 "Physical Constants of Organic Compounds", in CRC Handbook of Chemistry and Physics, Internet Version 2005, David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.
↑ "Gallium tribromide: molecular geometry of monomer and dimer from gas-phase electron diffraction", Reffy, Balazs; Kolonits, Maria; Hargittai, Magdolna Journal of Molecular Structure, 1998, 445, 139–148.
↑ W. M. Haynes, D. R. Lide and T. J. Bruno, CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data, 2012.

Week Two

Optimization

Optimization

A

B

C

D

ah_test

Dspace

Real Point Group

D2H

C2V

C2H

C1

Table 15. Optimization Results of Optimised Isomers
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
Isomer A	.log	FOPT	RB3LYP	Gen	Singlet	-2352.40630798	0.00000079	0.0006	C2V	0 days 0 hours 2 minutes 38.1 seconds
Isomer B	.log	FOPT	RB3LYP	Gen	Singlet	-2352.41626667	0.00003572	0.1673	C1	0 days 0 hours 3 minutes 31.2 seconds
Isomer C	.log	FOPT	RB3LYP	Gen	Singlet	-2352.41631610	0.00001372	0.0013	CS	0 days 0 hours 4 minutes 21.4 seconds
Isomer D	.log	FOPT	RB3LYP	Gen	Singlet	-2352.41109947	0.00001120	0.1386	C1	0 days 0 hours 1 minutes 23.0 seconds

Optimisation Item Table

Isomer A

        Item               Value     Threshold  Converged?
 Maximum Force            0.000002     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000578     0.001800     YES
 RMS     Displacement     0.000255     0.001200     YES
 Predicted change in Energy=-6.076901D-10
 Optimization completed.
    -- Stationary point found.

Isomer B

     Item                   Value     Threshold  Converged?
 Maximum Force            0.000078     0.000450     YES
 RMS     Force            0.000022     0.000300     YES
 Maximum Displacement     0.000877     0.001800     YES
 RMS     Displacement     0.000223     0.001200     YES
 Predicted change in Energy=-5.660144D-08
 Optimization completed.
    -- Stationary point found.

Isomer C

         Item               Value     Threshold  Converged?
 Maximum Force            0.000022     0.000450     YES
 RMS     Force            0.000008     0.000300     YES
 Maximum Displacement     0.001107     0.001800     YES
 RMS     Displacement     0.000483     0.001200     YES
 Predicted change in Energy=-1.142041D-08
 Optimization completed.
    -- Stationary point found.

Isomer D

         Item               Value     Threshold  Converged?
 Maximum Force            0.000020     0.000450     YES
 RMS     Force            0.000011     0.000300     YES
 Maximum Displacement     0.000806     0.001800     YES
 RMS     Displacement     0.000250     0.001200     YES
 Predicted change in Energy=-1.518942D-08
 Optimization completed.
    -- Stationary point found.

Comparison of Energy

Table 15. Energy Comparison of Isomers
	Energy (au)	Energy (kJ/mol)	Relative Energy(kJ/mol)to the Lowest Energy Conformer
A	-2352.4063	-6176243	26	Highest Energy
B	-2352.4163	-6176269	0.13
C	-2352.4163	-6176269		Lowest Energy
D	-2352.4111	-6176256	13

Discussion

Conformer B and C have quite close total energies and they are relatively lower energies than the other two. The common feature between B and C is that bromine atoms are at the terminal positions, where bromine atoms are at bridging position in conformer A and D. In addition, conformer A has the highest energy, and has two bridging bromine atoms and conformer D has the second highest energy and has only one bridging bromine; hence, the conclusion is that terminal bromine would result in a more stable conformer than bridging bromine.

Optimization of Monomer AlCl₂Br

ah_test

The out-put file is DOI:10042/26369

Table 16. Optimization Result of Optimized Monomer
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
AlCl₂Br	.log	FOPT	RB3LYP	Gen	0	Singlet	-1176.19013679	0.00004196	0.1075	C2V	0 days 0 hours 0 minutes 37.9 seconds

         Item               Value     Threshold  Converged?
 Maximum Force            0.000136     0.000450     YES
 RMS     Force            0.000073     0.000300     YES
 Maximum Displacement     0.000681     0.001800     YES
 RMS     Displacement     0.000497     0.001200     YES
 Predicted change in Energy=-7.984418D-08
 Optimization completed.
    -- Stationary point found.

Term	Energy
Al₂Cl₄Br₂	-2352.4163
AlCl₂Br	-1176.1901
Energy Difference (au) ΔE=E(Al₂Cl₄Br₂)-[E(AlCl₂Br)*2]	-0.03603
Energy Difference (kJ/mol)	-94.5874

Combining two isolated monomers together would have an association energy of -95 kJ/mol which is also the dissociation energy of the product. The product (isomer C) is more stable than the isolated monomers because it has a much lower energy.

Frequency Analysis

Frequency	A	B	C	D
Dspace	DOI:10042/26337	DOI:10042/26364	DOI:10042/26366	DOI:10042/26365

Table 17. Frequency Results of Optimized Isomers
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
Isomer A	.log	FREQ	RB3LYP	Gen	Singlet	-2352.40630798	0.00000076	0.0005	C2V	0 days 0 hours 1 minutes 28 seconds
Isomer B	.log	FREQ	RB3LYP	Gen	Singlet	-2352.41626679	0.00001074	0.1672	C2V	0 days 0 hours 1 minutes 19.5 seconds
Isomer C	.log	FREQ	RB3LYP	Gen	Singlet	-2352.41631610	0.00001368	0.0013	CS	0 days 0 hours 2 minutes 0.2 seconds
Isomer D	.log	FREQ	RB3LYP	Gen	Singlet	-2352.41109946	0.00001128	0.1386	C1	0 days 0 hours 2 minutes 50.8 seconds

Isomer A

Low frequencies ---   -5.1634   -5.0501   -3.1849    0.0037    0.0039    0.0039
Low frequencies ---   14.8310   63.2729   86.0759

         Item               Value     Threshold  Converged?
 Maximum Force            0.000002     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000686     0.001800     YES
 RMS     Displacement     0.000361     0.001200     YES
 Predicted change in Energy=-6.383446D-10
 Optimization completed.
    -- Stationary point found.
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Isomer B

Low frequencies ---   -4.3668   -2.6848   -0.0044   -0.0037   -0.0032    0.8441
Low frequencies ---   17.1260   50.9136   78.5359

         Item               Value     Threshold  Converged?
 Maximum Force            0.000020     0.000450     YES
 RMS     Force            0.000011     0.000300     YES
 Maximum Displacement     0.001003     0.001800     YES
 RMS     Displacement     0.000378     0.001200     YES
 Predicted change in Energy=-2.220935D-08
 Optimization completed.
    -- Stationary point found.
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Isomer C

Low frequencies ---    0.0011    0.0023    0.0034    1.8920    1.9704    3.9624
Low frequencies ---   18.0988   49.0858   72.9223

         Item               Value     Threshold  Converged?
 Maximum Force            0.000040     0.000450     YES
 RMS     Force            0.000014     0.000300     YES
 Maximum Displacement     0.001356     0.001800     YES
 RMS     Displacement     0.000593     0.001200     YES
 Predicted change in Energy=-1.805358D-08
 Optimization completed.
    -- Stationary point found.
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Isomer D

Low frequencies ---   -2.2705   -0.0027    0.0017    0.0028    1.2791    3.3179
Low frequencies ---   17.1478   55.9562   80.0556

         Item               Value     Threshold  Converged?
 Maximum Force            0.000034     0.000450     YES
 RMS     Force            0.000011     0.000300     YES
 Maximum Displacement     0.000897     0.001800     YES
 RMS     Displacement     0.000373     0.001200     YES
 Predicted change in Energy=-2.934869D-08
 Optimization completed.
    -- Stationary point found.
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

IR Spectrum

Molecular Orbital Analysis

The out-put log file:DOI:10042/26462

Table 18. Molecular Orbital Results of optimised Isomer C
Compound	File Type	Calculation Type	Calculation Method	Basis Set	Charge	Spin	Final Energy in au	Gradient	Dipole Moment	Point Group	Job cpu Time
Isomer C	.chk	SP	RB3LYP	Gen	0	Singlet	-2352.41631610		0.0013	CS	0 days 0 hours 0 minutes 18.4 seconds

**Molecular Orbital Analysis of isomer C**
MO	Structure	Analysis
40		This is an overall strongly bonding orbital. There is one nodal plane. There is weakly antibonding through space between terminal halides. There are also strong bonding interaction between bridging chlorides and central aluminum.
41		This is an overall strongly bonding orbital. There are both strong and weak through-space bonding. Also, the electron density is mainly delocalized between the halides as well as between the terminal halide and the central atom.
43		This is an overall slightly bonding interaction. There is weakly through-space antibonding but another two bonding interactions which are through-space and directly bonding. Nodal planes are lying in the bridging region
54		This is an overall antibonding interaction. Bonding region is only between two central atoms; and antibonding interactions are between terminal halides and central atoms.
42		This is an strongly antibonding orbital.

Further Study

The out-put file: DOI:10042/26465

Pentahelicene

Optimisation
Calculation Type	FOPT
Calculation Method	RB3LYP
Basis Set	Gen
Charge	0
Spin	Singlet
Final Energy in Atomic Units / ±0.003808780 a.u.	-2352.41632893
Gradient / a.u.	0.00000939
Imaginary Frequency
Dipole Moment	0.19
Point Group	CS
Job cpu Time	0 days 0 hours 3 minutes 7.6 seconds

        Item               Value     Threshold  Converged?
 Maximum Force            0.000021     0.000450     YES
 RMS     Force            0.000009     0.000300     YES
 Maximum Displacement     0.000285     0.001800     YES
 RMS     Displacement     0.000115     0.001200     YES
 Predicted change in Energy=-7.918666D-09
 Optimization completed.
    -- Stationary point found.

[BHbondlength-1] 1.0 ^1.1 "Physical Constants of Organic Compounds", in CRC Handbook of Chemistry and Physics, Internet Version 2005, David R. Lide, ed., <http://www.hbcpnetbase.com>, CRC Press, Boca Raton, FL, 2005.

[GaBrbondlength-2] "Gallium tribromide: molecular geometry of monomer and dimer from gas-phase electron diffraction", Reffy, Balazs; Kolonits, Maria; Hargittai, Magdolna Journal of Molecular Structure, 1998, 445, 139–148.

[GaBr-3] W. M. Haynes, D. R. Lide and T. J. Bruno, CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data, 2012.

[1]

[2]

[3]

Week One

Optimization Analysis of BH3

3-21G optimized BH3

6-31G(d,p) optimized BH3

Optimization Analysis of GaBr3

Optimization Analysis of BBr3

Structure Comparison

Frequency Analysis for BH3

Frequency Analysis

Animating The Vibrations

Frequency Analysis of GaBr3

Compare and Contrast the Frequencies for BH3, and GaBr3

Molecular Orbitals Analysis of BH3

NBO Analysis

Association energies: Ammonia-Borane

Reference

Week Two

Optimization

Frequency Analysis

Molecular Orbital Analysis

Further Study

Optimization Analysis of BH₃

3-21G optimized BH₃

6-31G(d,p) optimized BH₃

Optimization Analysis of GaBr₃

Optimization Analysis of BBr₃

Frequency Analysis for BH₃

Frequency Analysis of GaBr₃

Compare and Contrast the Frequencies for BH₃, and GaBr₃

Molecular Orbitals Analysis of BH₃