Posts Tagged ‘Potential theory’

A record polarity for a neutral compound?

Friday, April 13th, 2018

In several posts a year or so ago I considered various suggestions for the most polar neutral molecules, as measured by the dipole moment. A record had been claimed[1] for a synthesized molecule of ~14.1±0.7D. I pushed this to a calculated 21.7D for an admittedly hypothetical and unsynthesized molecule. Here I propose a new family of compounds which have the potential to extend the dipole moment for a formally neutral molecule up still further.

These molecules derive from a well-known class of molecule known as ortho-quinomethides. If the methide part is substituted with an electron donating substituent such as an amino group in 3, a push-pull opportunity now arises, which is strongly driven by aromatisation of the quinomethide ring. This allows one to design “neutral” molecules such as 1 and 2, which now contain respectively two and three rings that will be aromatised by the process. The aromatisation stabilization energy is balanced of course by an opposing increase in energy resulting from charge separation. You can observe that partially aromatising three independent rings as in 2 can drive a great deal of charge separation. One may indeed wonder how much charge separation can be sustained before a triplet instability occurs, driving the molecule back to being neutral. In the case of 2, the wavefunction is in fact stable to such an open shell state, but higher homologues may not be. An aspect worth investing!

1 2
DM 12.3 DM 31.5
DOI: 10.14469/hpc/4004 DOI: 10.14469/hpc/4059

Molecule 1 does have some precedent in 3[2] but this system exists as a phenol, having abstracted a proton from an acid and leaving behind the acid anion, as per below for 1. Any attempts to deprotonate this phenol with a superstrong base were unreported.

Unsurprisingly therefore, molecules such as 1 and 2 could be regarded as even more highly potent bases than 3, driven again by further aromatisation. The properties of such a potential superbase will be investigated in the next post.

References

  1. J. Wudarczyk, G. Papamokos, V. Margaritis, D. Schollmeyer, F. Hinkel, M. Baumgarten, G. Floudas, and K. Müllen, "Hexasubstituted Benzenes with Ultrastrong Dipole Moments", Angewandte Chemie International Edition, vol. 55, pp. 3220-3223, 2016. https://doi.org/10.1002/anie.201508249
  2. N.R. Candeias, L.F. Veiros, C.A.M. Afonso, and P.M.P. Gois, "Water: A Suitable Medium for the Petasis Borono‐Mannich Reaction", European Journal of Organic Chemistry, vol. 2009, pp. 1859-1863, 2009. https://doi.org/10.1002/ejoc.200900056

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The dipole moments of highly polar molecules: glycine zwitterion.

Saturday, December 24th, 2016

The previous posts produced discussion about the dipole moments of highly polar molecules. Here to produce some reference points for further discussion I look at the dipole moment of glycine, the classic zwitterion (an internal ion-pair).

Dielectric relaxation studies of glycine–water mixtures yield values that range from 15.7D[1] to 11.9D[2] although these have to be derived using various approximations and assumptions for up to 4 independent Debye processes. Before proceeding to calculations, I looked at the properties of ionized amino acids in the solid state, using the following search query for the Cambridge structure database (CSD). 

The distance measures hydrogen bonds to the carboxylate oxygens and the torsion their orientation. The O…H hydrogen bond distances vary between 1.7-1.85Å, which are short. The orientation of the hydrogen bond can be to the in-plane oxygen “σ-lone pair” (torsion 0 or 180°) and also an out-of-plane ~π form (torsion ~60-90°).

In aqueous solution, it is normally assumed that glycine sustains five such strong H-bonds (three to the H3N+ group and two[3] to the carboxylate anion), forming a polarised “salt bridge” across the ion-pair. Two model types were subjected to calculation using ωB97XD/Def2-TZVPP/SCRF=water. Aqueous glycine without any added explicit water molecules yields a dipole moment of 12.9D (DOI: 10.14469/hpc/2000), which is within the range noted above.‡

The solvated form is shown below, in one specific conformation of the three studied (ωB97XD/Def2-TZVPP/SCRF=water). The calculated O…H hydrogen bond lengths fall into the range revealed from crystal structures. The calculated dipole moments range from 12.6 (DOI: 10.14469/hpc/2007), 15.3 (DOI: 10.14469/hpc/2006) and 14.9D (DOI: 10.14469/hpc/2005), which is a modest increase over the model with no explicit water molecules. The actual dipole is of course a Boltzmann average over these and other as yet unexplored conformations, as well as other values for the number of water molecules.

Given the difficulties in interpreting the dipole moment of a complex Debye system such as hydrated glycine, the agreement between the limited range of solvated models and the measured values seems reasonable, and provides at least some measure of “calibration” for the polar molecules commented on previously.

‡Optimized with the solvent field on. If a vacuum model is used, the proton transfers from the N to the O.

References

  1. M.W. Aaron, and E.H. Grant, "Dielectric relaxation of glycine in water", Transactions of the Faraday Society, vol. 59, pp. 85, 1963. https://doi.org/10.1039/tf9635900085
  2. T. Sato, R. Buchner, . Fernandez, A. Chiba, and W. Kunz, "Dielectric relaxation spectroscopy of aqueous amino acid solutions: dynamics and interactions in aqueous glycine", Journal of Molecular Liquids, vol. 117, pp. 93-98, 2005. https://doi.org/10.1016/j.molliq.2004.08.001
  3. T. Shikata, "Dielectric Relaxation Behavior of Glycine Betaine in Aqueous Solution", The Journal of Physical Chemistry A, vol. 106, pp. 7664-7670, 2002. https://doi.org/10.1021/jp020957j

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A molecular balance for dispersion energy?

Sunday, February 7th, 2016

The geometry of cyclo-octatetraenes differs fundamentally from the lower homologue benzene in exhibiting slow (nuclear) valence bond isomerism rather than rapid (electronic) bond-equalising resonance. In 1992 Anderson and Kirsch[1] exploited this property to describe a simple molecular balance for estimating how two alkyl substituents on the ring might interact via the (currently very topical) mechanism of dispersion (induced-dipole-induced-dipole) attractions. These electron correlation effects are exceptionally difficult to model using formal quantum mechanics and are nowadays normally replaced by more empirical functions such as Grimme's D3BJ correction.[2] Here I explore aspects of how the small molecule below might be used to investigate the accuracy of such estimates of dispersion energies.

bu

The concentration of the two forms shown above can be readily estimated by NMR spectroscopy (the barrier is slow enough to allow peaks for both isomers to be integrated). This shows that the 1,6 form is present in greater concentrations than the 1,4 form, equivalent to a difference in free energy ΔΔG298 of 0.39 kcal/mol in favour of the former. Why is this? Because, it is claimed,  in the 1,6 isomer the two t-butyl groups are close enough to experience mutual dispersion attractions not experienced by the 1,4 form. This can be illustrated using the NCI display below for the two forms.

Click for 3D. Addition NCI interactions ringed in red.

Click for 3D. 1,6-isomer: Additional NCI interactions ringed in red.

Click for 3D

Click for 3D, 1,4 isomer.

Method Equilibrium constant, 298K ΔΔE ΔΔH298 ΔΔS298 ΔΔG298 Source
Experiment 1.93 – 1.14 -2.5 0.387 [1]
B3LYP/Def2-TZVPP/CDCl3 (no dispersion) 1.906‡ 0.05 0.00 +1.3‡ 0.382‡ [3],[4]
B3LYP/Def2-TZVPP/CDCl3 (gd3bj dispersion) 8.36 0.75 0.66 +2.0 1.25 [5],[6]

‡This contains a contribution of RTLn 2 (= 0.410 kcal/mol = 1.04 in ΔS), where 2 is the symmetry number for a species with C2 rotational symmetry, to the 1,4-isomer only.

The interpretation of these results, as is often found, is non-trivial.

  1. The relative concentrations of species in equilibrium equates with their relative free energies, ΔG298 and not ΔE (the difference in total energy computed using either quantum or molecular mechanics).
  2. ΔG298  has a component derived from the entropy of the system, and this in turn has contributions from symmetry (numbers).  Only the 1,6-isomer has two-fold rotational symmetry for the lowest energy pose of the two t-butyl groups, and this contributes 0.41 kcal/mol to ΔG298. This aspect is not discussed in the original article.[1]
  3. The B3LYP/Def2-TZVPP DFT method predicts ΔΔE to be +0.05 kcal/mol without the inclusion of the D3BJ dispersion correction but +0.75 kcal/mol with. One might approximately equate the latter to the contributions ringed in red in the NCI distributions shown above. The enthalpies (where ΔΔE is corrected for zero point energies) are very similar.
  4. Conversion to ΔG298 involves use of the vibrational frequencies to obtain the entropy; here one encounters a difference between the two double bond isomers. The lowest energy vibration for C2-symmetric 1,4 is 23 cm-1, whereas that for the 1,6 is only 7 cm-1 (a value which also depends on round-off errors and accuracies in the calculation). These errors in the RRHO (rigid-rotor-harmonic-oscillator) approximations makes meaningful calculation of ΔS298 and hence ΔG298 problematic at this small energy difference level. In both cases, this approach suggests that the entropy of the 1,6 form is slightly larger than the 1,4 isomer, whereas the reverse is apparently true by experimental measurement. It might all boil down to those low-frequency vibrations!

So we may conclude that whereas the dispersion uncorrected method gets the right answer for the equilibrium constant for probably the wrong reasons, inclusion of a dispersion correction would get the right answer were it not for the error in the entropy. Agreement with experiment would be obtained if the calculated entropy difference were to be -0.9 kcal/mol K-1 instead of +2.0. Thus the 1,6 isomer has the two t-butyl groups weakly interacting (red circle above), which intuition tends to suggest would reduce the entropy (reduce the disorder) of the system and not increase it. 

At least in this relatively small molecule, we now have a handle for estimating these sorts of effects in terms of variables such as the basis set used, the energy Hamiltonian (e.g. type of functional etc) and of course the dispersion correction.

References

  1. J.E. Anderson, and P.A. Kirsch, "Structural equilibria determined by attractive steric interactions. 1,6-Dialkylcyclooctatetraenes and their bond-shift and ring inversion investigated by dynamic NMR spectroscopy and molecular mechanics calculations", Journal of the Chemical Society, Perkin Transactions 2, pp. 1951, 1992. https://doi.org/10.1039/p29920001951
  2. S. Grimme, S. Ehrlich, and L. Goerigk, "Effect of the damping function in dispersion corrected density functional theory", Journal of Computational Chemistry, vol. 32, pp. 1456-1465, 2011. https://doi.org/10.1002/jcc.21759
  3. H.S. Rzepa, "C 16 H 24", 2016. https://doi.org/10.14469/ch/191875
  4. H.S. Rzepa, "C 16 H 24", 2016. https://doi.org/10.14469/ch/191876
  5. H.S. Rzepa, "C 16 H 24", 2016. https://doi.org/10.14469/ch/191874
  6. H.S. Rzepa, and H.S. Rzepa, "C 16 H 24", 2016. https://doi.org/10.14469/ch/191880

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