A new Green's function formalism for kinetic energy density functional for atomic and molecular system: Emergence of $N-$dependence using model potentials

TL;DR

This paper introduces a new Green's function-based formalism for calculating the kinetic energy density in atomic and molecular systems, capturing N-dependence and enabling systematic improvements over existing functionals.

Contribution

The authors develop an exact Green's function formalism for kinetic energy density that is applicable to arbitrary spin systems and demonstrates N-dependence using model potentials.

Findings

Qualitative N-dependence of kinetic energy in model systems

Systematic improvement of kinetic energy via perturbation series

Establishment of correspondence with traditional Green's function formalism

Abstract

An accurate expression of the kinetic energy density of an electronic distribution in terms of the single particle reduced density matrix for atomic and molecular systems is a long-standing problem in electron structure theory. Existing kinetic energy density functionals are generally expressed as modifications over kinetic energy of homogeneous electron gas and/or von Weizs\"acker kinetic energy. A large class of these functionals also require empirical parametrizations to make accurate predictions of the kinetic energy for atomic and molecular systems restricting their transferability. Moreover, the correct kinetic energy density which produces accurate local properties such as atomic shell structure is still an unsolved problem. In this work, we have developed an exact methodology that can be used to derive the kinetic energy of an electronic system of arbitrary spin multiplicity. One of the attractive features of this present analytical formalism is the possibility of systematic improvement of the kinetic energy by virtue of a novel perturbation series. Applying this methodology to simple model systems such as one-dimensional quantum harmonic oscillator and homogeneous electron gas produces a qualitatively correct $N$-dependence of kinetic energy as a result. A one-to-one correspondence between our formalism to the traditional Green's function formalism is also demonstrated.