Rep:Mod:c01190004

BH₃

3_1G, B3LYP Optimisation

Optimised bond length= 1.19467 a.u.

Optimised bond angle = 120.0°

BH₃ optimisation summary of results

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Extract of Item table from the .log file:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000217     0.000450     YES
 RMS     Force            0.000105     0.000300     YES
 Maximum Displacement     0.000692     0.001800     YES
 RMS     Displacement     0.000441     0.001200     YES
 Predicted change in Energy=-1.635268D-07
 Optimization completed.
    -- Stationary point found.

The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

Q: What definition would you choose for the existence of a bond?

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

Smf115 (talk) 16:20, 26 May 2018 (BST)Nice to see the 3-21G calculation and the symmetrisation presented and awareness shown towards the optimisation procedure and the associated convergence criteria. The next (additional) step would be to consider why the basis set was improved and why the molecule was symmetrised? This isn't necessary for the report but a good consideration.

6_31G (d,p), B3LYP Optimisation

The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

BH₃ optimisation (using higher level basis set: 6-31G(d,p))

Link to log fileː File:CN_BH3_631G_OPT.LOG

Extract of Item table from log fileː

         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=-1.452109D-07
 Optimization completed.
    -- Stationary point found.

We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D₃H symmetry imposed on it.

Following the optimisation run, a D₃H symmetry molecule was obtained.

BH₃ optimisation using 6-31G(d,p), constraining to D₃H

Link to log file: File:CN_BH3_SYM_OPT1.LOG

Extract of the Item table ː

         Item               Value     Threshold  Converged?
 Maximum Force            0.000161     0.000450     YES
 RMS     Force            0.000105     0.000300     YES
 Maximum Displacement     0.000639     0.001800     YES
 RMS     Displacement     0.000418     0.001200     YES
 Predicted change in Energy=-1.545207D-07
 Optimization completed.
    -- Stationary point found.

Frequency analysis

A frequency run was done on the output of the BH₃ 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

BH₃ frequency run using optimisation with 6-31G(d,p) basis set

Link to log fileː File:CN_BH3_SYM_FREQ2.LOG

 Low frequencies ---   -0.2433   -0.1118   -0.0055   44.4606   45.6068   45.6075
 Low frequencies --- 1163.6172 1213.6006 1213.6033

The lowest frequency range is within ±50 cm^-1 range, and hence this run is accepted as successful.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000161     0.000450     YES
 RMS     Force            0.000081     0.000300     YES
 Maximum Displacement     0.000635     0.001800     YES
 RMS     Displacement     0.000318     0.001200     YES
 Predicted change in Energy=-1.536878D-07
 Optimization completed.
    -- Stationary point found.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH₃.

Vibrational spectrum for BH₃

Vibrations (cm^-1 )	Intensities(arbitrary)	Symmetry	IR active	Type
1163	6.6	A2"	Yes	Symmetric bend
1213	1	E'	Very slightly	Asymetric bend
1213	1	E'	Very slightly	Asymetric bend
2580	0	A1'	No	Symmetric stretch
2713	9	E'	Yes	Asymmetric stretch
2713	9	E'	Yes	Asymmetric stretch

Snapshot of the IR spectrum:

IR spectrum of BH₃

There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

Molecular orbitals of BH₃

Modified MO diagram of BH₃ with the calculated MOs, adapted from ^[1].

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

jmol of BH₃

BH3 molecule

NH₃

Optimisation using 6_31G (d,p) , B3LYP

A 6_31G optimisation with B3LYP method was also run for the NH₃ molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

NH₃ results summary for optimisation with 6-31G(d,p) basis set

Link to log file: File:CN_NH3_631G_OPT.LOG

Extract of Item table from .log file ː

         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=-7.830786D-11
 Optimization completed.
    -- Stationary point found.

Frequency analysis

As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

NH₃ results summary for the frequency run

Link to the log file: File:CN_NH3_FREQ.LOG

Extract of the "low frequencies" from the .log file

 Low frequencies ---  -11.6527  -11.6490   -0.0048    0.0332    0.1312   25.5724
 Low frequencies --- 1089.6616 1694.1736 1694.1736

The lowest frequency range is within the ±50 cm^-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH₃.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000012     0.001800     YES
 RMS     Displacement     0.000006     0.001200     YES
 Predicted change in Energy=-8.435065D-11
 Optimization completed.
    -- Stationary point found.

Vibrational spectrum for NH₃

Wavenumber(cm^-1)	Intensity (Arbitrary units)	Symmetry	IR active?	type
1089	538	A	Yes	Symmetric bend
1694	50	E	Yes	Asymmetric bend
1694	50	E	Yes	Asymmetric bend
3461	4	A	No	Symmetric stretch
3589	1	E	No	Asymmetric stretch
3589	1	E	No	Asymmetric stretch

Snapshot of the spectrum:

NH₃ IR spectrum

There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

jmol of NH₃

NH3 molecule

NH₃-BH₃

Optimisation using 6_31G, B3LYP

A 6_31G optimisation with B3LYP method was also run for the NH₃ molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

NH₃-BH₃ results summary

Link to the log file: File:CN_NH3BH3_OPT.LOG

         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.

Frequency analysis

As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

NH₃-BH₃ results summary for the frequency run

Link to the log file: File:CN_NH3BH3_FREQ.LOG

Extract of the "low frequencies" from the .log file

Low frequencies ---   -0.0613   -0.0448   -0.0067   22.1060   22.1116   40.5984
Low frequencies ---  265.9056  632.3740  640.1221

The lowest frequency range is within the ±50 cm^-1 range, there are now negative frequencies and hence this frequency analysis is accepted.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000121     0.000450     YES
 RMS     Force            0.000067     0.000300     YES
 Maximum Displacement     0.000779     0.001800     YES
 RMS     Displacement     0.000426     0.001200     YES
 Predicted change in Energy=-2.165787D-07
 Optimization completed.
    -- Stationary point found.

Vibrational spectrum for NH₃-BH₃

Wavenumber(cm^-1)	Intensity (Arbitrary units)	Symmetry	IR active?
265	0	A2	No
632	5.6	A1	Slightly
640	1.4	E	Very slightly
640	1.4	E	Very slightly
1069	16.2	E	Yes
1069	16.2	E	Yes
1196	43.6	A1	Yes
1203	1.4	E	Very slightly
1203	1.4	E	Very slightly
1330	45.4	A1	Yes
1676	11	E	Slightly
1676	11	E	Slightly
2470	26.9	A1	Yes
2530	92.5	E	Yes
2530	92.5	E	Yes
3462	1	A1	very very slightly
3579	11.2	E	Slightly
3579	11.2	E	Slightly

Q: Look at your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol^[2]

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy^[3] at 377.9 kJmol^-1, which is taken from a molecule in which there is a B-N single covalent bond.

Smf115 (talk) 16:21, 26 May 2018 (BST)Good comparison made but there doesn't seem to be any calculation of the association energy itself.

jmol of NH₃-BH₃

NH3-BH3 molecule

BBr₃

Optimisation using pseudo potentials

Summary of results for optimisation of BBr_{3</suɓ> using pseudo-potentials.}

Link to log fileː File:CN_Bbr3_OPT_PP.LOG

Item table shows convergence and a successful run.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000030     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000154     0.001800     YES
 RMS     Displacement     0.000080     0.001200     YES
 Predicted change in Energy=-3.282217D-09
 Optimization completed.
    -- Stationary point found.

Frequency Analysis

As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

BBr₃ results summary for the frequency run

Link to the log file: File:CN_BBR3_OPT_PP_FREQ.LOG

Extract of the "low frequencies" from the .log file

 Low frequencies ---   -5.6583   -3.3109   -2.2850   -0.0002    0.0001    0.0002
 Low frequencies ---  155.8429  155.9360  267.6978

The lowest frequency range is within the ±50 cm^-1 range, and hence this frequency analysis is accepted.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000028     0.000450     YES
 RMS     Force            0.000013     0.000300     YES
 Maximum Displacement     0.000106     0.001800     YES
 RMS     Displacement     0.000044     0.001200     YES
 Predicted change in Energy=-2.950687D-09
 Optimization completed.
    -- Stationary point found.

jmol for BBr₃

BBr3 molecule

Project section: Lewis acids and basesː Al₂Cl₄Br₂

Different isomers and their symmetries

Cl bridging, cis, C_s point group
Cl bridging, trans, C₂H point group
CL bridging, both Br on same Al atom, C₂V point group
CL,Br bridge, C₁ point group
Br bridging, D₂H point group

Energies

Isomer with trans terminal Br and bridging Cl

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure. As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

Smf115 (talk) 12:56, 27 May 2018 (BST)Nice detail however, be aware that GEN is not the pseudopotential or the method. It is just an input option to gaussian to tell it that you're using a user-specified basis. The basis set you used was 6-31G(d,p) for Al and Cl and the LanL2DZ basis set and pseudopotential for Br.

Summary of results for optimisation of trans isomer using pseudo-potentials.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000053     0.001800     YES
 RMS     Displacement     0.000023     0.001200     YES
 Predicted change in Energy=-6.046439D-10
 Optimization completed.
    -- Stationary point found.

Link to log fileː File:CN_TRANSBR_OPT.LOG

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

Results summary for the frequency run

Link to the log file: File:CN_TRANSBR_OPT_FREQ.LOG

Extract of the "low frequencies" from the .log file

Low frequencies ---   -5.1504   -0.0036   -0.0021   -0.0011    1.4134    2.0504
 Low frequencies ---   18.1470   49.1065   73.0086

The lowest frequency range is within the ±50 cm^-1 range, and hence this frequency analysis is accepted.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000011     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000439     0.001800     YES
 RMS     Displacement     0.000151     0.001200     YES
 Predicted change in Energy=-3.294505D-09
 Optimization completed.
    -- Stationary point found.

Isomer with two bridging Br

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure. As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.

         Item               Value     Threshold  Converged?
 Maximum Force            0.000003     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000038     0.001800     YES
 RMS     Displacement     0.000014     0.001200     YES
 Predicted change in Energy=-2.660957D-10
 Optimization completed.
    -- Stationary point found.

Link to log fileː File:CN_BRIDGEBR_OPT.LOG

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.

Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.

 Low frequencies ---   -5.1749   -5.0366   -3.1484   -0.0034   -0.0016   -0.0015
 Low frequencies ---   14.8259   63.2702   86.0770

         Item               Value     Threshold  Converged?
 Maximum Force            0.000006     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.000279     0.001800     YES
 RMS     Displacement     0.000136     0.001200     YES
 Predicted change in Energy=-4.311968D-10
 Optimization completed.
    -- Stationary point found.

Link to log fileː File:CN_BRIDGEBR_OPT_FREQ.LOG

Relative energies of the isomers

Energy (isomer with trans Br, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol^-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol^-1

|Energy difference|ː 26.22871 kJmol^-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

Smf115 (talk) 12:54, 27 May 2018 (BST)Correct calculation with a nice justification of the result given.

Dissociation energy of lowest energy conformer

To determine the lowest energy conformer, an optimisation was carried out on the AlCl₂Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure. As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

Summary of results for optimisation of monomer using pseudo-potentials.

              Item               Value     Threshold  Converged?
 Maximum Force            0.000205     0.000450     YES
 RMS     Force            0.000096     0.000300     YES
 Maximum Displacement     0.001133     0.001800     YES
 RMS     Displacement     0.000778     0.001200     YES
 Predicted change in Energy=-1.597568D-07
 Optimization completed.
    -- Stationary point found.

Link to log fileː File:CN_MONOMER_OPT.LOG

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol^-1

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -1176.19014 a.u. to the optimisation run, and the gradient is low at 0.00000419 a.u. (<0.001 a.u.)

Results summary for the frequency run

Link to the log file: File:CN_MONOMER_OPT_FREQ.LOG

Extract of the "low frequencies" from the .log file

 Low frequencies ---    0.0023    0.0033    0.0045    1.3569    3.6367    4.2604
 Low frequencies ---  120.5042  133.9178  185.8950

The lowest frequency range is within the ±50 cm^-1 range, and hence this frequency analysis is accepted. There are no negative frequencies

         Item               Value     Threshold  Converged?
 Maximum Force            0.000081     0.000450     YES
 RMS     Force            0.000042     0.000300     YES
 Maximum Displacement     0.001588     0.001800     YES
 RMS     Displacement     0.000974     0.001200     YES
 Predicted change in Energy=-1.810813D-07
 Optimization completed.
    -- Stationary point found.

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol^-1 = 94.57048 kJmol^-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol^-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

jmols of optimised isomers

jmol of isomer with trans Br, bridging Cl

Isomer with trans Br, bridging Cl

jmol of isomer with bridging Br

Isomer with bridging Br

Molecular orbitals of lowest energy conformer (trans Br, bridging Cl)

Three occupied MOs were chosen and analysed as below.

Highly antibonding orbital
Highly bonding orbital
Bonding orbital

Smf115 (talk) 12:53, 27 May 2018 (BST)Good LCAO diagrams and MO analysis with the key interactions labelled and details such as the larger Br contribution is the first MO, and explaination why, included. To improve, the number of the MO visualised should be included and some of the points are incorrect or missed, such as the anti-bonding interaction between the end on p orbtials on the bridging Cl's in the final MO.

Smf115 (talk) 12:53, 27 May 2018 (BST)Overall a good wiki report with nice awareness of the optimisation and frequency procedures and the associated convergence criteria shown.

References

↑ H. research group Hunt, Patricia, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
↑ Y.-R. Luo, Comprehensive handbook of chemical bond energies, CRC Press, 2007.
↑ Y.-R. Luo, Comprehensive handbook of chemical bond energies, CRC Press, 2007.

[1] H. research group Hunt, Patricia, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

[2] Y.-R. Luo, Comprehensive handbook of chemical bond energies, CRC Press, 2007.

[3] Y.-R. Luo, Comprehensive handbook of chemical bond energies, CRC Press, 2007.

[1]

[2]

[3]

BH3

3_1G, B3LYP Optimisation

6_31G (d,p), B3LYP Optimisation

Frequency analysis

Vibrational spectrum for BH3

Molecular orbitals of BH3

jmol of BH3

NH3

Optimisation using 6_31G (d,p) , B3LYP

Frequency analysis

Vibrational spectrum for NH3

jmol of NH3

NH3-BH3

Optimisation using 6_31G, B3LYP

Frequency analysis

Vibrational spectrum for NH3-BH3

jmol of NH3-BH3

BBr3

Optimisation using pseudo potentials

Frequency Analysis

jmol for BBr3

Project section: Lewis acids and basesː Al2Cl4Br2

Different isomers and their symmetries

Energies

Isomer with trans terminal Br and bridging Cl

Isomer with two bridging Br

Relative energies of the isomers

Dissociation energy of lowest energy conformer

jmols of optimised isomers

jmol of isomer with trans Br, bridging Cl

jmol of isomer with bridging Br

Molecular orbitals of lowest energy conformer (trans Br, bridging Cl)

References

BH₃

Vibrational spectrum for BH₃

Molecular orbitals of BH₃

jmol of BH₃

NH₃

Vibrational spectrum for NH₃

jmol of NH₃

NH₃-BH₃

Vibrational spectrum for NH₃-BH₃

jmol of NH₃-BH₃

BBr₃

jmol for BBr₃

Project section: Lewis acids and basesː Al₂Cl₄Br₂