Failure of the random phase approximation correlation energy

TL;DR

This paper evaluates the performance of the random phase approximation (RPA) for fractional charges and spins, revealing its strengths in bond dissociation but significant delocalization errors, and highlights the need for more advanced methods.

Contribution

The study extends RPA to fractional occupations and systematically examines its adherence to exact conditions, identifying limitations and the necessity for beyond-smooth functional approaches.

Findings

RPA satisfies the constancy condition for fractional spins, ensuring correct bond dissociation.

RPA exhibits large delocalization errors for fractional charges, even in simple systems.

Range-separated RPA reduces delocalization errors but increases static correlation errors.

Abstract

The random phase approximation (RPA) to the correlation energy is extended to fractional occupations and its performance examined for exact conditions on fractional charges and fractional spins. RPA satisfies the constancy condition for fractional spins that leads to correct bond dissociation and no static correlation error for H$_2$ but massively fails for fractional charges, with an enormous delocalization error even for a one-electron system such as H$_2^+$. Other methods such as range-separated RPA can reduce this delocalization error but only at the cost of increasing the static correlation error. None of the RPA methods seem to have the discontinuous nature required to satisfy both exact conditions and the full unified condition, emphasizing the need to go further than just smooth functionals of the orbitals.