Advances in Approximate Natural Orbital Functionals: From Historical Perspectives to Contemporary Developments

TL;DR

This chapter reviews the development and application of approximate natural orbital functionals in quantum chemistry, highlighting their theoretical foundations, recent advancements, and practical implementations for static and dynamic electron correlation.

Contribution

It provides a comprehensive overview of approximate NOFs, including new approaches like the Global NOF and extensions to excited and charged states, with open-source tools for implementation.

Findings

Introduction of the Global NOF approach

Extension of NOFs to excited and charged states

Availability of open-source implementations like DoNOF

Abstract

This chapter provides a comprehensive review of fundamental concepts related to approximate natural orbital functionals (NOFs), emphasizing their significance in quantum chemistry and physics. Focusing on fermions, the discussion excludes considerations of finite temperature and systems with a variable number of particles. The theoretical foundation for approximate NOFs is laid out, with a particular emphasis on functional N-representability. Various two-index reconstructions for the two-particle reduced density matrix (2RDM) are introduced, accompanied by discussions on challenges. The analysis delves deeply into NOFs grounded in electron pairing, specifically focusing on PNOF5, PNOF7, and the Global NOF, a more versatile approach addressing both static and dynamic electron correlation components. The extension of NOFs to multiplets while conserving total spin is presented, and the availability of open-source implementations like DoNOF (http://github.com/DoNOF) and its associated programs is highlighted. A detailed overview of optimization procedures for single-point calculations is provided. Sections on geometry optimization and ab initio molecular dynamics, closely connected to the availability of analytical gradients in NOF theory, are presented. The chapter concludes with the extension of NOFs to both charged and excited states.