Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

Nektarios N Lathiotakis,Angel Rubio,Nikitas I Gidopoulos,Nicole Helbig

doi:10.1103/physreva.90.032511

Abstract

We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules.

Highlights

Computational simulations have opened a new avenue for the exploration and prediction of “ala carte” molecular complexes and materials, i.e., with tailored properties and functionality, due to the development of powerful algorithms and an increase in computational power
We propose a scheme to bring reduced-density-matrix-functional theory into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes
The local Reduced-density-matrix-functional theory (RDMFT) framework provides an energy eigenvalue spectrum connected to the natural orbitals (NOs) and as we show, single electron properties, like the ionization potentials (IPs)’s of small molecules, are well reproduced by the energies of the highest occupied molecular orbitals (HOMOs)

Summary

INTRODUCTION

Computational simulations have opened a new avenue for the exploration and prediction of “ala carte” molecular complexes and materials, i.e., with tailored properties and functionality, due to the development of powerful algorithms and an increase in computational power. A main difference from DFT is the introduction of fractional occupation numbers which allows the exact treatment of the kinetic energy and potentially leads to improved accuracy whenever the ground-state many-body wave function is far from a single Slater determinant. We propose such a framework that combines the best of both DFT and RDMFT One can regard this approach as either an extension of DFT, where fractional occupations for the orbitals are introduced using an approximation for the xc energy functional borrowed from RDMFT, or, alternatively, as a constrained RDMFT calculation. The local RDMFT framework provides an energy eigenvalue spectrum connected to the NOs and as we show, single electron properties, like the IP’s of small molecules, are well reproduced by the energies of the highest occupied molecular orbitals (HOMOs). In the Appendix we show that pure density xc functionals are not adequate for the present scheme since they cannot lead to fractional occupations in a minimization procedure and we need to employ functionals of the 1RDM as we do in the present work

LOCAL RDMFT

APPLICATIONS

Method

CONCLUSION

Findings

Corollary from Janak’s theorem