Ruth

Lab2 Marking

You did a great job especially with the formatting. However, you missed to include the Me3NH+…Cl second-to-last item table and N-Cl distance. Unfortunately your one value of IE for project molecule and H-Cl answers are incorrect. It would be good if you uploaded all the files. If you have any queries, please contact Prof. Hunt.

Lab 2

HMim-Cl Ion Pair

Comment

Note that an initial calculation was performed and converged on a structure with one imaginary frequency. This structure was perturbed and the PES reused for a second attempt at optimisation. The results of this (converged) second attempt are given below.

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Calculation Data

name of submitted log file	TR HMIM-CL A2 OPTF.LOG
molecule	HMim+-Cl-
method	RB3LYP
basis set	3-21G
final energy	-722.68731 Hartree
RMS gradient	1.2277e-05 Hartree/Bohr
charge	0

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Logfile and Relevant Excerpts

Media:TR HMIM-CL A2 OPTF.LOG

         Item               Value     Threshold  Converged?
 Maximum Force            0.000010     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.000941     0.001800     YES
 RMS     Displacement     0.000223     0.001200     YES

 Full mass-weighted force constant matrix:
 Low frequencies ---   -5.2981   -2.8139    0.0022    0.0030    0.0035    2.7813
 Low frequencies ---   36.1361   64.4962   80.8265

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Optimised angles and distances to H-bonding proton

r(N-H)	1.178 Â
r(H-Cl)	1.719 Â
θ(N-H-Cl)	172.9°

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Comment

Note that the forces and low frequencies are converged, but the displacement is above Gaussian's convergence threshold. Overall, we can still interpret this as having converged - the displacement is well within an order of magnitude (0.0026 vs 0.0018) of the threshold, and all other metrics of interest are converged.

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Calculation Data

name of submitted log file	TR HMIM-CL B OPTF.LOG
molecule	HMim+-Cl-
method	RB3LYP
basis set	3-21G
final energy	-722.6662 Hartree
RMS gradient	2.8835e-05 Hartree/Bohr
charge	0

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Logfile and Relevant Excerpts

Media:TR HMIM-CL B OPTF.LOG

         Item               Value     Threshold  Converged?
 Maximum Force            0.000098     0.000450     YES
 RMS     Force            0.000016     0.000300     YES
 Maximum Displacement     0.002600     0.001800     NO 
 RMS     Displacement     0.000838     0.001200     YES

 Full mass-weighted force constant matrix:
 Low frequencies ---   -4.8731   -2.6379    0.0003    0.0023    0.0025    0.6478
 Low frequencies ---   45.5502  161.9279  198.7219

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Geometric Data

Optimised angles and distances to H-bonding proton

r(HIm-Cl)	2.134 Â
r(CIm-HIm)	1.104 Â
r(HMe-Cl)	2.277 Â
r(CMe-HMe)	1.106 Â
θ(HIm-Cl-HMe)	63.8°

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Comment

Note that the final optimised structure converged upon had the chloride ion between the imidazole methine CH and the methyl CH (although clearly closer to the imidazole CH, by 0.372 Â). This was repeatedly the case even after performing calculations with the chloride ion perturbed to be even further from the methyl group. So, an optimised structure with the chloride solely hydrogen-bonding to the imidazole methine proton was not obtained, and therefore two sets of H-Cl and C-H lengths are listed below.

Calculation Data

name of submitted log file	TR HMIM-CL C OPTF.LOG
molecule	HMim+-Cl-
method	RB3LYP
basis set	3-21G
final energy	-722.67881 Hartree
RMS gradient	3.223e-05 Hartree/Bohr
charge	0

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Logfile and Relevant Excerpts

Media:TR HMIM-CL C OPTF.LOG

         Item               Value     Threshold  Converged?
 Maximum Force            0.000109     0.000450     YES
 RMS     Force            0.000021     0.000300     YES
 Maximum Displacement     0.001165     0.001800     YES
 RMS     Displacement     0.000298     0.001200     YES

 Full mass-weighted force constant matrix:
 Low frequencies ---   -1.4609   -0.0026    0.0020    0.0035    2.1056    3.9537
 Low frequencies ---   54.7201  142.4209  216.3517

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Geometric Data

Optimised angles and distances to H-bonding proton

r(HIm-Cl)	2.020 Â
r(CIm-HIm)	1.121 Â
r(HMe-Cl)	2.392 Â
r(CMe-HMe)	1.102 Â
θ(HIm-Cl-HMe)	63.2°

Calculation Data

name of submitted log file	TR HMIM OPTF.LOG
molecule	HMim+
method	RB3LYP
basis set	3-21G
final energy	-264.45512 Hartree
RMS gradient	4.4921e-05 Hartree/Bohr
charge	1

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Logfile and Relevant Excerpts

Media:TR HMIM OPTF.LOG

         Item               Value     Threshold  Converged?
 Maximum Force            0.000064     0.000450     YES
 RMS     Force            0.000021     0.000300     YES
 Maximum Displacement     0.000999     0.001800     YES
 RMS     Displacement     0.000241     0.001200     YES

 Full mass-weighted force constant matrix:
 Low frequencies ---    0.0008    0.0009    0.0010    3.2626    4.0683    5.3119
 Low frequencies ---   81.1878  248.2574  352.9903

Calculation Data

name of submitted log file	TR CHLORIDE OPTF.LOG
molecule	Cl-
method	RB3LYP
basis set	3-21G
final energy	-458.05709 Hartree
RMS gradient	0 Hartree/Bohr
charge	-1

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Logfile and Relevant Excerpts

Media:TR CHLORIDE OPTF.LOG

         Item               Value     Threshold  Converged?
 Maximum Force            0.000064     0.000450     YES
 RMS     Force            0.000021     0.000300     YES
 Maximum Displacement     0.000999     0.001800     YES
 RMS     Displacement     0.000241     0.001200     YES

 Full mass-weighted force constant matrix:
 Low frequencies ---    0.0008    0.0009    0.0010    3.2626    4.0683    5.3119
 Low frequencies ---   81.1878  248.2574  352.9903

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Distances

H-Cl Bond Distances

Conformation A	1.719 Â
Conformation B, HIm	2.134 Â
Conformation B, HMe	2.277 Â
Conformation C, HIm	2.020 Â
Conformation C, HMe	2.392 Â
Me3NH-Cl	1.738 Â

Notice that the N-H⁺---Cl^- hydrogen bonds between both the HMim and Me₃NH ion pairs are similar in length, about 1.7 Â, which is not unexpected given the similar environments. However, the HMim C-H H---Cl lengths are considerably longer, all being > 2 Â. Summing the H (1.2 Â) and Cl (1.75 Â) van der Waals radii for comparison to give 2.95 Â, we find that even the C-H H---Cl lengths are shorter than the expected distance between the completely unbonded H and Cl atoms. This is in favour of a C-H---Cl hydrogen bond made possible by the opposing ionic charges, although the greater length indicates it is weaker than a usual hydrogen bond. This is probably due to the weaker polarisation of the C-H bond compared to N-H.

Note that the van der Waals distance-based assessment above is flawed considering that the non-interacting H and Cl atoms in this case would actually be ionic, so the H radius would be smaller and the Cl radius larger. We could investigate how much of a difference this actually makes by using quantum chemical methods to find the electron density contour within an appropriate cutoff, e.g. 0.0015 au, for both the H atom (within the HMim cation) and Cl anion. This would allow us to find the van der Waals radii of the ions involved - note this technique has precedence in literature (https://pubs.acs.org/doi/10.1021/acs.jctc.2c01255) and gives distinct results from ionic radii (which are measured experimentally within a lattice environment).

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Energies

Cl^- energy: -458.05709 au

HMim⁺ energy: -264.45512 au

Total reactant energy (association) = -722.51221 au

Association Energies

	Conformation A	Conformation B	Conformation C
Product energy (au)	-722.68731	-722.66620	-722.67881
Assocation energy (au)	-0.17510	-0.15399	-0.16660
Association energy (kJ/mol)	-460	-404	-437

For reference, all the association energies of the ion pairs are roughly on the order of the N=N double bond enthalpy. This is not insignificant, and indicative of the relative strength of the doubly ionic H-bonding compared to the neutral H-bonding in Me₃NHCl. Comparing A and B, we find that B is at an energy of +56 kJ/mol relative to A, i.e. B is more energetic and less stable. This is probably because the C-H bond is less polar thus a poorer H-bond donor compared to the N-H bond. Comparing with C, we find that its energy of +23 kJ/mol relative to A places it between A and B in stability. This implies that the imidazole C-H bond in the N-C-N position is more polarised than the other two imidazole C-H bonds, making it a better H-bond donor than B. Thus, C-H H-bonding strength (although weaker than traditional H-bonds) can be tuned by using adjacent electronegative atoms, such as N in this case.

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Scan

GaussView PES diagram	HMimCl vs Me3NHCl	Protonation states involved

For both ion pair scans, the N-H distance was scanned from 0.8 Â to 2.1 Â (in increments of 0.1 Â), while the N-Cl distance was set at 3.2 Â. The HMimCl PES plot notably shows two stationary points (minima), separated by a maximum barrier of about 12 kJ/mol. This indicates that the HMimCl system is relatively stable in both its doubly-ionic and neutral H-bonding modes, and the barrier between these is well within the range of thermal fluctuations at room temperature. Thus, both kinds of H-bonding play a role in the room temperature behaviour of HMimCl.

Comparing both PES plots we find that both systems have PES gradients relatively close to 0 in the 1 < r(N-H) < 1.8 Â range - indicating minimal forces/strain for these N-H lengths, and giving rise to the proton sharing typical of H-bonding. However, the HMimCl PES has a true local minimum at r(N-H) = 1.8 Â, whereas the Me₃NHCl PES merely has an inflection point. Thus, the Me₃NHCl system is not truly stable in its neutral H-bonding mode compared to its doubly ionic H-bonding mode, unlike the HMimCl system.

We can hypothesise about these observations:

1. The doubly ionic H-bonding mode is more stable than the neutral H-bonding mode for both systems due to the attraction of the ions better overcoming electronic repulsion
2. The HMimCl neutral H-bonding mode is more stable than the Me₃NHCl neutral H-bonding mode because the imidazole N atom better stabilises the incipient positive charge from the incoming proton (via π delocalisation within the ring) compared to the Me₃NHCl N atom which has no such stabilisation

One way to test the first hypothesis could be using a zwitterionic system, where H-bonding occurs between two zwitterionic species. This should be less stable than an H-bond between two ionic species, but more stable than an H bond between 2 neutral species.

One way to test the second hypothesis could be using an ion pair with a larger delocalised π system, e.g. an analogous methyl-benzimidazolium chloride ion pair. If our hypothesis holds, this should give a deeper energy well for the neutral H-bonding mode compared to HMimCl.

Methyl-benzimidazolium chloride, neutral H-bonding state

Me₃NH-Cl Ion Pair

Calculation Data

name of submitted log file	TR ME3NH-CL OPTF.LOG
molecule	Me3NH+-Cl-
method	RB3LYP
basis set	3-21G
final energy	-632.16208 Hartree
RMS gradient	1.8962e-05 Hartree/Bohr
point group	Gaussian output: C1 (note: actual is C3v)

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Logfile and Relevant Excerpts

Media:TR ME3NH-CL OPTF.LOG

         Item               Value     Threshold  Converged?
 Maximum Force            0.000029     0.000450     YES
 RMS     Force            0.000010     0.000300     YES
 Maximum Displacement     0.002276     0.001800     NO 
 RMS     Displacement     0.000572     0.001200     YES

 Full mass-weighted force constant matrix:
 Low frequencies ---   -9.8211    0.0025    0.0030    0.0032    2.7858    4.2211
 Low frequencies ---   55.2435   56.5270  190.4173

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Optimised Molecule

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Geometric Data

Optimised angles and distances to ammonium proton

r(N-H)	1.164 Â
r(H-Cl)	1.738 Â
θ(N-H-Cl)	180.0°

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Scan

The N-H distance was scanned from 0.8 Â to 2.1 Â (in increments of 0.1 Â), while the N-Cl distance was set at 3.2 Â. So, as the scan progressed, the ion pair shifted away from a doubly-ionic hydrogen bond and towards a usual 'neutral' hydrogen bond. The scan shows that the energy for the neutral hydrogen bonding case is still relatively low, although the system is most stable in its doubly-ionic hydrogen bonding state. The relatively low energy for r(N-H) 1.1 to 1.8 Â is indicative of a hydrogen bond, with the H relatively stable being 'shared' in some range of distances between the two species.

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NH₃-BH₃ Molecule

Calculation Data

name of submitted log file	TR_NH3-BH3_OPTF_POP.LOG
molecule	NH3-BH3
method	RB3LYP
basis set	6-31G(d,p)
final energy	-83.224689 Hartree
RMS gradient	1.182e-06 Hartree/Bohr
point group	Gaussian output: C3v (note: the actual point group is D3d)

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Logfile and Relevant Excerpts

Media:TR_NH3-BH3_OPTF_POP.LOG

         Item               Value     Threshold  Converged?
 Maximum Force            0.000002     0.000015     YES
 RMS     Force            0.000001     0.000010     YES
 Maximum Displacement     0.000017     0.000060     YES
 RMS     Displacement     0.000008     0.000040     YES

 Full mass-weighted force constant matrix:
 Low frequencies ---   -5.4404   -0.3252   -0.0481   -0.0011    1.1254    1.2097
 Low frequencies ---  263.2923  632.9711  638.4650

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Optimised Molecule

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Geometric Data

Optimised bond angles, dihedrals, and distances

r(B-H)	1.210 Â
θ(H-B-H)	113.9°
r(N-H)	1.018 Â
θ(H-N-H)	107.9°
r(B-N)	1.668 Â
φ(H-B-N-H)	180.0°

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Association Energy

For the formation reaction shown below, we can calculate the association energy by subtracting the total energy of the reactants by the energy of the adduct: NH₃ + BH₃ → NH₃BH₃

That is, we apply ΔE = E(NH₃BH₃) - [E(NH₃) + E(BH₃)].

E(NH3BH3)	-83.224689 Hartree
E(NH3)	-56.557769 Hartree
E(BH3)	-26.615324 Hartree
ΔE	-0.051596 Hartree, -135 kJ/mol

Thus, the formation of NH₃BH₃ is an energetically downhill process, releasing 135 kJ/mol (association energy -135 kJ/mol).

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BH₃ Molecule

Calculation Data

name of submitted log file	TR_BH3_OPTF_POP.LOG
molecule	BH3
method	RB3LYP
basis set	6-31G(d,p)
final energy	-26.615324 Hartree
RMS gradient	2.114e-06 Hartree/Bohr
point group	D3h

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Logfile and Relevant Excerpts

Media:TR_BH3_OPTF_POP.LOG

         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000015     YES
 RMS     Force            0.000003     0.000010     YES
 Maximum Displacement     0.000017     0.000060     YES
 RMS     Displacement     0.000011     0.000040     YES

 Full mass-weighted force constant matrix:
 Low frequencies ---  -11.6940  -11.6861   -6.5543    0.0007    0.0280    0.4289
 Low frequencies --- 1162.9745 1213.1390 1213.1392

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Optimised Molecule

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Geometric Data

Optimised bond angles and distances

r(B-H)	1.192 Â
θ(H-B-H)	120.0°

Lab 1

Lab1 Marking

You did a great job especially with the formatting. However, you missed to include the charge range, and don't forget to consider the accuracy to which you report your data the next time. If you have any queries, please contact Prof. Hunt.

NH₃ Molecule

Calculation Data

name of submitted log file	TR_NH3_OPTF_POP.LOG
molecule	NH3
method	RB3LYP
basis set	6-31G(d,p)
final energy	-56.557769 Hartree
RMS gradient	1.53e-07 Hartree/Bohr
point group	C3v

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Logfile and Relevant Excerpts

Media:TR_NH3_OPTF_POP.LOG

         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000015     YES
 RMS     Force            0.000000     0.000010     YES
 Maximum Displacement     0.000003     0.000060     YES
 RMS     Displacement     0.000001     0.000040     YES

 Full mass-weighted force constant matrix:
 Low frequencies ---   -5.6864   -3.6131   -3.6124    0.0017    0.0048    0.0162
 Low frequencies --- 1089.3674 1693.9284 1693.9284

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Optimised Molecule

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Geometric Data

Optimised bond angles and distances

r(N-H)	1.02 Â
θ(H-N-H)	106°

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Vibrational Data

mode	1	2	3	4	5	6
wavenumber (cm-1)	1089	1694	1694	3461	3590	3590
symmetry	A1	E	E	A1	E	E
intensity (arbitrary units)	145	14	14	1	0	0

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Atomic Charges

	Atomic Charge (e)
N	-1.13
H	0.38

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Molecular Orbitals

Frontier MOs

	Energy (Hartree)	GaussView visualisation
LUMO	0.07985
HOMO	-0.25318

Project Molecule: cis-N₂F₂

Calculation Data

name of submitted log file	TR_N2F2_OPTF_POP.LOG
molecule	cis-N2F2
method	RB3LYP
basis set	6-31G(d,p)
final energy	-309.01241 Hartree
RMS gradient	3.17e-07 Hartree/Bohr
point group	C2v

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Logfile and Relevant Excerpts

Media:TR_N2F2_OPTF_POP.LOG

         Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000015     YES
 RMS     Force            0.000000     0.000010     YES
 Maximum Displacement     0.000001     0.000060     YES
 RMS     Displacement     0.000001     0.000040     YES

 Full mass-weighted force constant matrix:
 Low frequencies ---   -0.0019    0.0002    0.0008    3.2225    4.3532    5.1001
 Low frequencies ---  347.8772  561.2472  771.6105

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Optimised Molecule

Note: N-F bonds are not drawn here by GaussView because r(N-F) in the final optimised structure (1.39 Â) exceeds the software's distance threshold for visualisation.

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Geometric Data

Optimised bond angles and distances

r(N=N)	1.23 Â
r(N-F)	1.39 Â
θ(N=N-F)	114°

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Vibrational Data

mode	1	2	3	4	5	6
wavenumber (cm-1)	348	561	772	949	987	1637
symmetry	A1	A2	B2	A1	B2	A1
intensity (arbitrary units)	1	0	75	75	81	21

Discussion

Given cis-N₂F₂ is non-linear, we expect it to have 3N-6 vibrational modes where N=4, i.e. 6 vibrations. Although 6 vibrational modes are indeed calculated, only 4 are visible in the simulated IR spectrum since the 2 lowest energy modes are symmetric bending vibrations which do not induce a change in dipole moment and thus are IR-inactive. Raman spectroscopy would instead be required to investigate those 2 modes. As a general trend, notice that the lower energy vibrational modes are 'bends', whereas the higher energy modes are 'stretches' (e.g. the asymmetric N-F stretch at 772 cm^-1). Indeed, the highest energy mode is a stretching vibration of the N=N double bond, which is not unexpected given the higher force constant of the double bond compared to the single bonds. Notice the orange dipole derivative unit vector of this mode shown in the animation below, indicating the change in dipole moment that allows the mode to be IR active.

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Atomic Charges

	Atomic Charge (e)
N	0.215
F	-0.215

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Molecular Orbitals

Frontier MOs

	Energy (Hartree)	GaussView visualisation
LUMO	-0.08646
HOMO	-0.37454

9^th MO

GaussView visualisation	LCAO diagram

Discussion

Of the 16 occupied MOs, the 4 lowest energy ones are core orbital MOs derived from the bonding-antibonding pairs of 1s orbitals for the 2 N atoms, and the 2 F atoms. These are largely irrelevant for investigating the reactivity and other properties of the molecule compared to non-core MOs, e.g. the HOMO and LUMO. These frontier orbitals can allow us to make some predictions. Firstly, the HOMO-LUMO gap corresponds to light of about 158 nm (deep UV) so cis-N₂F₂ is likely colourless. Secondly, the negative energy of the LUMO (-0.08646 E_h) means that an electron would be lower in energy when occupying it compared to being free, a surprising result given the usual Lewis base behaviour of N, possibly caused by the positive atomic charge on the N atoms (see above).