The effects of higher orders of perturbation theory on the correlation energy of atoms and bonds in molecules

Abstract

We examine, for the first time, the effects of higher orders of Møller-Plesset perturbation theory on the individual atoms within a molecule and the bonds between them, via the topological energy partitioning method of interacting quantum atoms. In real terms (i.e., not by absolute value) MP3 decreases the correlation energy of a bond, and MP4SDQ also decreases the energy of the atoms at either end of the bond. In addition, we investigated long-range through-space dispersive effects on a H 2 oligomer. Overall, MP3 is the largest correction to the correlation energy, and most of that energy is allocated to chemical bonds, reducing their values in actual terms. The MP4SDQ bond correlation correction, despite being relatively small, tends to have two effects: (i) for small or negative correlation energies MP4SDQ tends to decrease the bond correlation values even more, and (ii) for large (positive) bond correlation energies MP4SDQ tends to restore the bond correlation energies from the MP3 back toward the MP2 values. Furthermore, each individual part of a molecule or complex (atom or bond) has a specific convergence pattern for the MPn series: throughspace interactions converge at MP2 but bonds converge at MP3 level. The atomic correlation energy appears to head toward convergence at the MP4 level.glycine, interacting quantum atoms, MPn, QTAIM, quantum chemical topology | I N TR ODU C TI ONThe electron correlation problem is a well-studied field of research with many solutions as to how this residual post-Hartree-Fock energy can be obtained. While accurate and computationally efficient solutions serve the cause of making reliable chemical predictions of energy and geometry, they do not offer chemical insight. If one is interested in chemical insight originating from electron correlation energies then their atomic partitioning is a manifest starting point. An option amongst several possible partitioning methods is that of quantum chemical topology (QCT). [1][2][3][4][5] QCT introduces topological atoms, which are space-filling objects defined without parameters, a hallmark of minimality. Central to QCT are so-called separatrices, which are natural sharp boundaries occurring in a vector field. The vectors in this field are typically gradient vectors but not always. [6] These separatrices partition real space into subspaces; if they partition the electron density then the subspaces are the topological atoms.Very recently QCT has been used to partition the correlation energy of a system (i.e., molecule or molecular complex) such that the correlation energy of an atom or a bond was successfully obtained. [7][8][9][10] The approach that makes this partitioning possible, under the umbrella of QCT, is called interacting quantum atoms (IQA). [11] This topological "energy decomposition analysis" (EDA) does not suffer from the conceptual and numerical problems associated with older EDA schemes, [12,13] as recently reviewed. [14] IQA rigorously defines the primary energy contributions from which all chemical phenomena f...

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

“…) over the grid that does not include the DO‐loops. This large number of DO‐loops has confined the application of to small systems only, with some of our larger systems studied being the water pentamer, glycine and glycine…water …”

“…Although we employ the MP4SDQ 2PDM in this study, any correlation method's 2PDM can actually be employed. We have used the MP2 and MP3 methods to generate the respective 2PDM in our previous studies . In these cases, the density matrices are the same size as the MP4SDQ 2PDM.…”

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

“…The details of our approach have been exhaustively explained in previous publications [32,[41][42][43][44][45]. The IQA method has been developed for over two decades, and was initially applied mainly at Hartree-Fock level [31], but was more recently made compatible with density functional theory [38,46,47].…”

The accuracy of ab initio calculations without ab initio calculations for charged systems: Kriging predictions of atomistic properties for ions in aqueous solutions

“…More importantly, we calculated kriging models for IQA components of the energy, which completes the energy analysis except for dynamical electron correlation. The latter, from which one can derive dispersion energies, will be included in future ionwater models following the recently developed route [39][40][41][42] of MP2-IQA.…”