Quantum Chemical Topology: Towards a novel protein force field with polarisable multipolar electrostatics

Paul L.A. Popelier (University of Manchester, Manchester, UK), T. Fletcher, S. J. Davie, and M. Mills

Quantum Chemical Topology (QCT) [1,2] is the collective modern name for all approaches that use the central idea of partitioning a quantum function by means of its gradient vector field. QCT creates the topological atoms of the “Quantum Theory of Atoms in Molecules” [3-5], which serves as the basis of this novel force field. Topological atoms are finite-volume, malleable boxes that do not overlap nor leave gaps between them; they exhaust space and form a mosaic of complementary shapes. The figure shows peptide-capped tryptophan with topological atoms (C: gold, N: blue, O: red, H: white) superimposed over the molecular graph, showing the intramolecular hydrogen bonds via dotted lines. This picture was generated using in-house methodology developed earlier [6,7].

We first discuss how QCT defines bonds [8]: how to draw a molecule from a molecular wave function. The quantity that is at the basis of this important realization is Vxc, a measure of interatomic exchange-correlation energy, also interpretable as a measure of covalency. This quantity, alongside with atomic self-energies (and their deformation) [9] is also crucial in a modern interpretation of stereo-electronic effects (thereby replacing concepts such as steric hindrance and (hype)conjugation) Conveniently, such energies are transferable (for 1, n interactions in saturated linear hydrocarbons) and can provide an accurate estimation of the covalent-like contribution between pairs of given interacting topological atoms A and B.

Then we focus on the electrostatic interaction, with most detail, and then on the non-electrostatic part. If atomic coordinates change then the shapes of the atoms change too, as well as their multipole moments. This complex relationship is captured by a machine learning technique called kriging. Here we show how these ideas [10] can be used to enhance the realism of the electrostatic energy [11-13], and put polarisation and charge transfer on the same footing, without having a polarisation catastrophe.

[1] Popelier, P. L. A.; Brémond, É. A. G., Int.J.Quant.Chem. 2009, 109, 2542.
[2] Popelier, P. L. A., In Structure and Bonding. Intermolecular Forces and Clusters, Ed, D.J.Wales; Springer: Heidelberg, Germany, 2005; Vol. 115, p 1.
[3] Bader, R. F. W. Atoms in Molecules. A Quantum Theory.; Oxford Univ. Press: Oxford, Great Britain, 1990.
[4] Popelier, P. L. A. Atoms in Molecules. An Introduction.; Pearson Education: London, Great Britain, 2000.
[5] Popelier, P. L. A. In The Nature of the Chemical Bond Revisited; Frenking, G., Shaik, S., Eds.; Wiley-VCH, Ch.8: 2014, p 271.
[6] Rafat, M.; Devereux, M.; Popelier, P. L. A. J. Mol. Graphics Modell. 2005, 24, 11.
[7] Rafat, M.; Popelier, P. L. A. J.Comput.Chem. 2007, 28, 2602.
[8] Garcia-Revilla, M.; Francisco, E.; Popelier , P. L. A.; Martin-Pendas, A. M. ChemPhysChem 2013, 14, 1211.
[9] Pendas, A. M.; Blanco, M. A.; Francisco, E. J.Comput.Chem. 2009, 30, 98.
[10] Popelier, P. L. A. AIP Conf.Proc. 2012, 1456, 261.
[11] Mills, M. J. L.; Popelier, P. L. A. Theor.Chem.Acc. 2012, 131, 1137.
[12] Kandathil, S. M.; Fletcher, T. L.; Yuan, Y.; Knowles, J.; Popelier, P. L. A. , J.Comput.Chem. 2013, 34, 1850.
[13] Fletcher, T.; Davie, S. J.; Popelier, P. L. A. J. Chem. Theory Comput. 2014, dx.doi.org/10.1021/ct500416k.