Roy PO, Henkes T, Ernzerhof M. The electron-centric approach to the exchange-correlation energy.
J Chem Phys 2023;
159:151104. [PMID:
37861115 DOI:
10.1063/5.0166486]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 10/02/2023] [Indexed: 10/21/2023] Open
Abstract
The Kohn-Sham theory addresses the challenge of representing the kinetic energy by re-quantizing density functional theory at a level of non-interacting electrons. It transforms the many-electron problem into a fictitious non-interacting electron problem, with the many-electron effects concealed within the exchange-correlation (XC) energy, which is expressed in terms of the electron density ρ(r). Unlike the wave function, ρ(r) can be viewed as a classical quantity, and expressing the XC energy in terms of it circumvents the need for correlated wave functions. In this work, we once again employ the re-quantization strategy and determine the XC energy using a local one-particle Schrödinger equation. The ground-state eigenfunction of the corresponding Hamiltonian is a reference point (r) dependent orbital φr,σ(u, σ') which is subsequently used to generate the XC hole and the XC energy. The spin coordinate is denoted by σ and u is the electron-electron separation. The one-particle equation for φr,σ(u, σ') includes a local potential vr,σ(u, σ') that we approximate using two simple physical constraints. We assess the approximation by applying it to the helium iso-electronic series, the homogeneous electron gas, and the dissociation of the hydrogen molecule.
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