Unified Implementation of Relativistic Wave Function Methods: 4C-iCIPT2 as a Showcase

TL;DR

This paper presents a unified, template-based implementation of relativistic wave function methods in quantum chemistry, exemplified by the 4C-iCIPT2 method, enabling automatic generation and incorporation of relativistic effects.

Contribution

It introduces a modular, template-driven approach for implementing relativistic wave function methods, streamlining the development process and enabling easy inclusion of symmetries and relativistic effects.

Findings

Successfully implemented 4C-iCIPT2 with relativistic effects

Achieved near-exact results within positive energy states

Demonstrated flexibility and efficiency of the unified code framework

Abstract

In parallel to the unified construction of relativistic Hamiltonians based solely on physical arguments [J. Chem. Phys. 160, 084111 (2024)], a unified implementation of relativistic wave function methods is achieved here via programming techniques (e.g., template metaprogramming and polymorphism in C++). That is, once the code for constructing the Hamiltonian matrix is made ready, all the rest can be generated automatically from existing templates used for the nonrelativistic counterparts. This is facilitated by breaking a second-quantized relativistic Hamiltonian down to diagrams that are topologically the same as those required for computing the basic coupling coefficients between spin-free configuration state functions (CSF). Moreover, both time reversal and binary double point group symmetries can readily be incorporated into molecular integrals and Hamiltonian matrix elements. The latter can first be evaluated in the space of (randomly selected) spin-dependent determinants and then transformed to that of spin-dependent CSFs, thanks to simple relations in between. As a showcase, we consider here the no-pair four-component relativistic iterative configuration interaction with selection and perturbation correction (4C-iCIPT2), which is a natural extension of the spin-free iCIPT2 [J. Chem. Theory Comput. 17, 949 (2021)], and can provide near-exact numerical results within the manifold of positive energy states (PES), as demonstrated by numerical examples.