One- and two-center physical space partitioning of the energy in the density functional theory

Abstract

A conceptually new approach is introduced for the decomposition of the molecular energy calculated at the density functional theory level of theory into sum of one-and two-atomic energy components, and is realized in the "fuzzy atoms" framework. ͑Fuzzy atoms mean that the three-dimensional physical space is divided into atomic regions having no sharp boundaries but exhibiting a continuous transition from one to another.͒ The new scheme uses the new concept of "bond order density" to calculate the diatomic exchange energy components and gives them unexpectedly close to the values calculated by the exact ͑Hartree-Fock͒ exchange for the same Kohn-Sham orbitals.

Application of the Interacting Quantum Atoms Approach to the S66 and Ionic‐Hydrogen‐Bond Datasets for Noncovalent Interactions

“…The Kohn–Sham formalism of density functional theory (DFT) does not yield well‐defined second‐order density matrices, what prevents a direct IQA application within DFT. One‐ and two‐atom partitions of the DFT energies have already been proposed in the framework defined by the Hilbert space of atom‐centered basis functions and the concept of fuzzy atoms . Within the IQA approach, it has also been realized that the lack of second‐order DFT density matrices can be circumvented by defining ad hoc additive exchange–correlation (xc) energies and use them to scale the one‐ and two‐atom terms of the Kohn–Sham xc energy such that the total DFT energy is exactly recovered .…”

“…The Kohn-Sham formalism of density functional theory (DFT) does not yield well-defined second-order density matrices, what prevents ad irect IQA applicationw ithin DFT.O ne-and two-atom partitions of the DFT energies have already been proposed in the framework defined by the Hilbert space of atom-centered basis functions [20,21] andt he concept of fuzzy atoms. [22] Within the IQA approach, it has also been realized that the lack of The interacting quantum atoms (IQA) methodc an assess, systematically and in great detail, the strengtha nd physics of both covalenta nd noncovalent interactions. The lack of ap air density in density functional theory( DFT), whichp recludes the direct IQA decomposition of the characteristic exchange-correlation energy,h as been recentlyo vercome by means of as caling technique, which can largely expand the applicabilityo f the method.…”

Molecular energy decompositions

“…1 An alternative of the AIM scheme is the use of "fuzzy atoms" i.e., such divisions of the 3D physical space into atomic regions in which the regions assigned to the individual atoms have no sharp boundaries but exhibit a continuous transition from one to another [6,7]. The energy decompositions performed in terms of fuzzy atoms also gave interesting results [8,9] -they are, however, out of our present scope.…”

Nine questions on energy decomposition analysis

“…Methods for fuzzy atom partitioning have been developed by Salvador and Mayer. [52,53] Finally, Experimental Quantum Chemistry (EQC) is an energybased partitioning unique in that it can interchangeably rely on quantum chemical calculations, at any level of theory, as well as on experimental thermochemical data, vibrational and photoelectron spectroscopy, and X-ray diffraction and absorption measurements. [54,55] EQC, which is developed by Rahm and Hoffmann, EQC makes use of observable "reference frames."…”

“…However, other nonoverlapping partition schemes, such as ELF basins, can be considered at the expense of the determination of the fragment kinetic energies. Methods for fuzzy atom partitioning have been developed by Salvador and Mayer …”