Density functional energy decomposition into one- and two-atom contributions

Abstract

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory ͑DFT͒ case. It is shown that one-and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential V A on a one-atom density A or B . To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale.

Two complementary molecular energy decomposition schemes: The Mayer and Ziegler–Rauk methods in comparison

“…22 Another Hartree-Fock energy partitioning was proposed by Nakai and Kikuchi. 23 Vyboishchikov et al 24 generalized the Mayer partitioning scheme for the case of density-functional theory ͑DFT͒. In this approach the exchange-correlation energy density per electron xc is expanded into a linear combination of atomcentered basis functions, while other terms of the energy expression are treated in the same way as in Mayer's method.…”

“…24,25 First, the total unrestricted Hartree-Fock energy expression is written in terms of electron density and density matrix as follows ͑real spinorbitals will be considered throughout the paper͒:…”

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

“…Along that line, a Hilbert-space decomposition of the DFT energy has also been proposed 6 based on the approximate expansion of the exchange-correlation energy density per electron in terms of the basis orbitals. Reasonable energy components have been obtained for different DFT functionals, although sensitive to the variations of the method and, in particular, to the geometry variations taking place when one turns from HF to different DFT variants.…”

“…In a recent paper, 6 it has been shown that the results of the Hilbert-space Hartree-Fock energy component analysis 5 can also be formulated by introducing effective atomic first order density matrices A ͑r , rЈ͒ and effective atomic potentials V A ͑having a nonlocal component accounting for exchange͒; then the electron-nuclear and electron-electron interaction energies can be presented as a sum of integrals representing effective atomic potentials acting on the different effective atomic density matrices. Along that line, a Hilbert-space decomposition of the DFT energy has also been proposed 6 based on the approximate expansion of the exchange-correlation energy density per electron in terms of the basis orbitals.…”

“…1 For the Hilbert-space analysis, energy decomposition schemes of the Hartree-Fock ͑HF͒ and density functional theory ͑DFT͒ energy have already been devised and successfully applied. [4][5][6] These schemes are obviously restricted to basis sets having true atomic character and become ill defined in the complete basis set limit. In order to carry out a decomposition in the physical space, one must assign in some sense a part of the 3D space to each atom.…”