Non-covalent interactions from a Quantum Chemical Topology perspective

Abstract

About half a century after its little-known beginnings, the quantum topological approach called QTAIM has grown into a widespread, but still not mainstream, methodology of interpretational quantum chemistry. Although often confused in textbooks with yet another population analysis, be it perhaps an elegant but somewhat esoteric one, QTAIM has been enriched with about a dozen other research areas sharing its main mathematical language, such as Interacting Quantum Atoms (IQA) or Electron Localisation Function (ELF), to form an overarching approach called Quantum Chemical Topology (QCT). Instead of reviewing the latter's role in understanding non-covalent interactions, we propose a number of ideas emerging from the full consequences of the space-filling nature of topological atoms, and discuss how they (will) impact on interatomic interactions, including non-covalent ones. The architecture of a force field called FFLUX, which is based on these ideas, is outlined. A new method called Relative Energy Gradient (REG) is put forward, which is able, by computation, to detect which fragments of a given molecular assembly govern the energetic behaviour of this whole assembly. This method can offer insight into the typical balance of competing atomic energies both in covalent and non-covalent case studies. A brief discussion on so-called bond critical points is given, highlighting concerns about their meaning, mainly in the arena of non-covalent interactions.

Keywords: Atomic electron correlation; Covalency; Exchange energy; FFLUX; Gaussian process regression; Interacting Quantum Atoms (IQA); Machine learning; Multipole moments; Polarisation; QTAIM; Quantum Chemical Topology (QCT); Relative Energy Gradient (REG).

Fig. 1

Examples of topological atoms: an ether oxygen, a pyridine nitrogen, and an amine nitrogen

Fig. 2

The fine-structure of the second-order reduced matrix alongside the specific chemical insight that each of the three contributions offer

Fig. 3

Logarithmic plot linking |V_X(A,B)| with interatomic distance for the global energy minimum of the water dimer calculated at CAS [5, 6]//6-311G(d,p) level of theory. The green line outlines the broad effect that |V_X(A,B)| increases with decreasing distance

Fig. 4

Logarithmic plot of interatomic distance versus |V_X(A,B)| for Gly-Gly-Gly interactions up to 1,6, calculated at both HF/6–31 + G(d,p) and B3LYP/6–31 + G(d,p) level of theory. Key outliers of V_X have been labelled in both the plot and the insert molecular image. The black line shows the overall correlation of the B3LYP energies, with a correlation coefficient r. [2] of 0.91

Fig. 5

An example of the non-overlapping nature of topological atoms as they occur in a methanal…chloroform van der Waals complex. The atoms in methanal are coloured for clarity

Fig. 6

The exact electrostatic interaction energy $V_{\mathit{elec}}^{\mathit{AB}}$ between two (topological) atoms (dashed horizontal line) compared with the energy obtained by multipolar expansion according to interaction rank L for the hydrogen-bonded atoms (O₅ and H₂) in the global minimum of the water dimer [114].

Fig. 7

(Left) The arrow represents the control coordinate governing the REG for the water dimer; (right) the correlation between the total energy of the dimer (y-axis) and the electrostatic interaction energy V_elec(H₃,O₄) (x-axis). The dashed line shows the poor linear fit if the whole curve is considered while much better correlations are obtained after segmentation into a purple and a red curve. Note that all energies were “translated”; i.e., their respective mean energies, averaged over the various lettered geometries, were subtracted

Fig. 8

A variety of inter-atomic CCSD-HF correlation energies (kJ mol⁻.¹) in a linear configuration of the water trimer (H₂O)₃, including both intramolecular and intermolecular (values in black for both), as well as intra-atomic correlation energies (values in red for oxygen and grey for hydrogen). Nuclei are labelled in green. For comparison, a single free water is represented on the left

Fig. 9

Interatomic correlation energy $V_{ee,c}^{\mathit{AB}}$ as a function of internuclear distance for the argon dimer