Energy density analysis for second‐order Møller‐Plesset perturbation theory and coupled‐cluster theory with singles and doubles: Application to C₂H₄CH₄ complexes

Abstract

Grid-based energy density analysis (EDA), in which numerical integration is performed for two-electron integrals by the pseudospectral method (Imamura et al., J. Chem. Phys. 2007, 126, 034103), is extended to correlated methods: second-order Møller-Plesset (MP2) perturbation and coupled-cluster singles and doubles (CCSD). Using EDA for MP2 and CCSD, we estimate atomic correlation energy differences and correlation energy density difference maps for C(2)H(4)--CH(4) complexes. The analyses confirm that polarization and diffuse functions essentially contribute to the descriptions of weak interaction around the nuclei and in the area between C(2)H(4) and CH(4), respectively.

Fast Estimation of Møller–Plesset Correlation Energies Based on Atomic Contributions

“…In the reaction data set, training on 3.6% of the molecules can reach an MAE of 3.5 and 1.2 mH for the calculation level MP4/pVTZ and MP4–2/pVTZ, respectively. The small error from our concise models (up to first neighbor information) also strongly suggests the local property of dynamic correlation and confirms the effectiveness of local descriptors used in related ML works. ,,,,,− A possible limitation can be, however, that the approach is especially designed for equilibrium structures, so it cannot predict correlation energy of any frames of a molecular dynamic trajectory, as was achieved in our previous study using neural networks . Our novel approach has been tested for a variety of organic molecules containing H, C, N, and O atoms.…”

“…Dynamic correlation, though it cannot be unambiguously separated from static correlation, is essential for an accurate description of compounds and plays a key role, for example, in the calculation of (near-)­equilibrium structures of many (organic) compounds (given that the multiconfigurational effect is negligible). One feature of the dynamic correlation is its little effect on the electronic density, which means that one can define a “local correlation energy” − on real-space density grids as correlation energy density (ε C ). This kind of local property also allows the summation of ε C over the atomic region to give the estimation of atomic contribution (AC) of the correlation energy .…”

A Machine Learning Approach for MP2 Correlation Energies and Its Application to Organic Compounds

“…MP2 as a widely used electron correlation method usually recovers most of the dynamic electron correlation and we have chosen this as the target and the reference of our ML models in this work. The MP2 local energy used was first proposed by Imamura and Nakai and the idea behind is a grid-based one-body energy decomposition scheme introduced earlier. , Previous studies , have also applied this scheme for fitting of density functionals.…”

Kinetic energy decomposition scheme based on information theory

“…Our group has developed analyzing methodologies based on the information of atomic orbitals (AOs) for total energy, which is the key quantity for quantum chemistry . This type of energy decomposition for ab initio methods such as Hartree–Fock in analogy to Mulliken‐type population analysis has a long history, and been proposed even now by several groups .…”