Dynamic and Nondynamic Electron Correlation Energy Decomposition Based on the Node of the Hartree-Fock Slater Determinant

Distinguishing between dynamic and nondynamic electron correlation energy is a fundamental concept in quantum chemistry. It can be challenging to make a clear distinction between the two types of correlation energy or to determine their actual contributions in specific cases using wave function theory. This is because both single-reference and multireference methods cover both types of correlation energy to some extent. Fixed-node diffusion quantum Monte Carlo (FNDMC) accurately covers dynamic correlations, but it is limited in overall accuracy by the node of the trial wave function. We introduce a methodology for partitioning an exact electron correlation energy into its dynamic and nondynamic components. This is accomplished by restricting a ground-state solution from sharing its node with a spin-restricted Hartree-Fock Slater determinant. The FNDMC method is used as a tool to conveniently project out a lowest-energy state obeying such a boundary condition. The proposed approach provides an unambiguous and useful procedure for separating electron correlation energy, as demonstrated on multiple systems, including the He atom, bond breaking of H-2, the parametric H-2-H-2 system, the Be-Ne atomic series with low- and high-spin states for C, N, and O atoms, and small molecules such as BH, HF, and CO at both equilibrium and elongated configurations, respectively.

Automated summary

Distinguishing between dynamic and nondynamic electron correlation energy is a fundamental concept in quantum chemistry. Existing methods have limitations in making a clear distinction between the two types of correlation energy. In this study, a new approach is proposed to partition electron correlation energy into dynamic and nondynamic components by restricting the ground-state solution from sharing its node with a spin-restricted Hartree-Fock Slater determinant. This provides an unambiguous and effective procedure for separating electron correlation energy, which has been verified on multiple systems.