Many‐body perturbation theory, coupled‐pair many‐electron theory, and the importance of quadruple excitations for the correlation problem

TLDR

Many‑body perturbation theory, coupled‑pair many‑electron theory, and configuration interaction are examined, highlighting that quadruple excitations are crucial for accurate correlation, especially in systems like Be₂ where a single‑reference assumption fails. The authors compute single, double, and quadruple excitation contributions to the correlation energy for molecules such as CO₂, HCN, N₂, CO, BH₃, and NH₃, and demonstrate CPMET’s superior reliability across internuclear separations by analyzing the ¹Σ potential curve of Be₂. They show that the sum of double and quadruple diagrams up to fourth order closely matches CPMET results at equilibrium geometries, and that including all quadruple terms resolves the improper behavior of Be₂’s potential curve.

Abstract

Abstract Many‐body (diagrammatic) perturbation theory ( MBPT ), coupled‐pair many‐electron theory ( CPMET ), and configuration interaction ( CI ) are investigated with particular emphasis on the importance of quadruple excitations in correlation theories. These different methods are used to obtain single, double, and quadruple excitation contributions to the correlation energy for a series of molecules including CO 2 , HCN, N 2 , CO, BH 3 , and NH 3 . It is demonstrated that the sum of double and quadruple excitation diagrams through fourth‐order perturbation theory is usually quite close to the CPMET result for these molecules at equilibrium geometries. The superior reliability of the CPMET model as a function of internuclear separation is illustrated by studying the 1 ∑ potential curve of Be 2 . This molecule violates the assumption common to nondegenerate perturbation theory that only a single reference function is important and this causes improper behavior of the potential curve as a function of R . This is resolved once the quadruple excitation terms are fully included by CPMET .