Relativistic reduced density matrix functional theory

Abstract

As a new approach to efficiently describe correlation effects in the relativistic quantum world we propose to consider reduced density matrix functional theory, where the key quantity is the first-order reduced density matrix (1-RDM). In this work, we first introduce the theoretical foundations to extend the applicability of this theory to the relativistic domain. Then, using the so-called no-pair (np) approximation, we arrive at an approximate treatment of the relativistic effects by focusing on electronic wavefunctions and neglecting explicit contributions from positrons. Within the np approximation the theory becomes similar to the nonrelativistic case, with as unknown only the functional that describes the electron-electron interactions in terms of the 1-RDM. This requires the construction of functional approximations, and we therefore also present the relativistic versions of some common RDMFT approximations that are used in the nonrelativistic context and discuss their properties.

Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations

“…Recent developments − show that NOF theory has become an active field of research. Nowadays, an open-source implementation of NOF-based methods is available (github.com/DoNOF) to the scientific community.…”

Refining and relating fundamentals of functional theory

“…The main goal of this work is to elaborate on the vrepresentability problem and its relation to other fundamental features and concepts in 1RDMFT. Accordingly, we complement all the recent theoretical investigations of 1RDMFT and hope that our insights could guide the intense development of novel functionals and their implementations [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] . To achieve this, we first discuss by concise means the so-called scope of a functional theory and explain how it identifies a functional variable in a natural way.…”