Gaussian basis functions for an orbital‐free‐related density functional theory of atoms

Abstract

A representation of polymer self-consistent field theory equivalent to quantum density functional theory is given in terms of non-orthogonal basis sets. Molecular integrals and self-consistent equations for spherically symmetric systems using Gaussian basis functions are given, and the binding energies and radial electron densities of neutral atoms hydrogen through krypton are calculated. An exact electron selfinteraction correction is adopted and the Pauli-exclusion principle is enforced through ideas of polymer excluded-volume. The atoms hydrogen through neon are examined without some approximations which permit cancellation of errors and spontaneous shell structure is observed. Correlations are neglected in the interest of simplicity and comparisons are made with Hartree-Fock theory. The implications of the Pauli-exclusion potential and its approximate form are discussed, and the Pauli model is analyzed using scaling theory for the uniform electron density case where the correct form of the Thomas-Fermi quantum kinetic energy and the Dirac exchange correction are recovered.density functional theory, orbital-free, polymer physics, self-consistent field theory | INTRODUCTIONDensity functional theory (DFT) is one of the most widely used and successful methods for calculating structure and properties of many-body quantum systems. In DFT, a one-particle density is the central quantity instead of a many-particle wave function, making DFT computations orders-of-magnitude more tractable than wave function approaches. In particular, Kohn-Sham DFT (KS-DFT), which uses orbital functions as a route to find the density, can achieve chemical accuracy in many cases.It has been recently shown that polymer self-consistent field theory (SCFT) can also be used to study quantum many-body systems [1][2][3][4].Instead of orbitals, SCFT uses propagators which are solutions to modified diffusion equations. It has been shown that these SCFT equations are formally equivalent to KS-DFT [1], and so, through the theorems of , SCFT is guaranteed to make all the same predictions as quantum mechanics [1,2,4]. The SCFT route has several advantages compared to DFT: the propagators are real-valued functions in contrast to the complex-valued orbitals used in KS-DFT, the diffusion equations are initial-value parabolic equations in contrast to the elliptical boundary-value KS equation, the SCFT algorithm can be made parallel in a straightforward way since the propagators do not span entire systems as do KS orbitals, and the classical partition function derivation of the SCFT equations has implications for the foundations of quantum mechanics [4].