Atomic Partitioning of the MPn (n= 2, 3, 4) Dynamic Electron Correlation Energy by the Interacting Quantum Atoms Method: A Fast and Accurate Electrostatic Potential Integral Approach

Abstract

Recently, the quantum topological energy partitioning method called interacting quantum atoms (IQA) has been extended to MPn (n = 2, 3, 4) wave functions. This enables the extraction of chemical insight related to dynamic electron correlation. The large computational expense of the IQA‐MPn approach is compensated by the advantages that IQA offers compared to older nontopological energy decomposition schemes. This expense is problematic in the construction of a machine learning training set to create kriging models for topological atoms. However, the algorithm presented here markedly accelerates the calculation of atomically partitioned electron correlation energies. Then again, the algorithm cannot calculate pairwise interatomic energies because it applies analytical integrals over whole space (rather than over atomic volumes). However, these pairwise energies are not needed in the quantum topological force field FFLUX, which only uses the energy of an atom interacting with all remaining atoms of the system that it is part of. Thus, it is now feasible to generate accurate and sizeable training sets at MPn level of theory. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Contributions of IQA electron correlation in understanding the chemical bond and non-covalent interactions

“…The interaction energy, V AB corr , of each atom with itself (A = B) or with one of the other atoms (A ≠ B) is obtained from the 2PDM via a 6D quadrature integration. The 3D ESP [51] approach was more recently developed with the intent of ultimate implementation in our polarizable multipolar [52] topological force field FFLUX [53][54][55][56][57], since 3D ESP is faster and more accurate when compared to the 6D approach. The master equation for the 3D ESP integration is given just below, where any derivation details are not repeated here but can be found in the selfcontained account of ref.…”

“…The master equation for the 3D ESP integration is given just below, where any derivation details are not repeated here but can be found in the selfcontained account of ref. [51],…”

“…26 is solved analytically. The AA' (or 3D ESP) approach is a very recent achievement [51]. Atoms can now be calculated 50 times faster with greater accuracy compared to the AB (or 6D) version.…”

A Comparison of the Interacting Quantum Atoms (IQA) Analysis of the Two‐Particle Density‐Matrices of MP4SDQ and CCSD

“…We have developed an approach, called ESP, whereby one of the numerical integrations given in Equation (1) is replaced by an analytical one . The latter involves integrals, reminiscent of those occurring in the calculation of the electrostatic potential, which we have generated via G09.…”

Efficient implementation of the interacting quantum atoms energy partition of the second‐order Møller–Plesset energy

“…We have recently included dyanmical electron correlation in the IQA method by considering either coupled‐cluster (CC) and Hartree–Fock (HF) transition density matrices or CC Lagrangians . There have been also implementations of IQA coupled with Møller–Plesset density functions . Because dynamical correlation occupies partially most of the orbitals of the Fock space of a system, and the number of IQA two‐electron integrals scales with the fourth power of this set, IQA calculations based on post‐HF wave functions are still unfeasible for basis sets comprised of more than a few hundred orbitals.…”