Explicitly Correlated Coupled-Cluster Theory

Abstract

The theoretical prediction of molecular energies and properties to chemical accuracy is often achieved using coupled-cluster methods and large orbital basis sets. Through recent advances in F12 explicitly correlated methods it is now possible to obtain the same high accuracy far more efficiently, using much smaller orbital basis sets. In CCSD(T)-F12 methods, the basis set truncation error is almost entirely eliminated by introducing a small set of two-particle basis functions that depend explicitly on the inter-electronic distances and closely resemble the correlation hole. The computational expense of including the F12 geminals can be reduced to a fraction of that of the underlying CCSD(T) calculation through judicious insertions of resolution of the identity approximations and further simplifications. In this chapter we present CCSD(T)-F12 theory and review the simplified models CCSD(T)(F12), CCSD(T)-F12x and CCSD(T) $$_{\overline{F12}}$$ , demonstrating their utility for practical applications. In contrast to standard CCSD(T), the Hartree–Fock basis set error may limit the accuracy of a CCSD(T)-F12 calculation and we therefore also describe methods for improving the Hartree–Fock energy within an F12 calculation. A brief discussion on the extension of F12 theory to reduce basis set errors in connected triples and response properties is also presented.