Unified Implementation\nof Relativistic Wave Function\nMethods: 4C-iCIPT2 as a Showcase

In parallel to the unified construction\nof relativistic Hamiltonians\nbased solely on physical arguments (<i>J. Chem. Phys.</i> <b>2024</b>, <i>160</i>, 084111), a unified implementation\nof relativistic wave function methods is achieved here via programming\ntechniques (e.g., template metaprogramming and polymorphism in C++).\nThat is, once the code for constructing the Hamiltonian matrix is\nmade ready, all the rest can be generated automatically from existing\ntemplates used for the nonrelativistic counterparts. This is facilitated\nby decomposing a second-quantized relativistic Hamiltonian into diagrams\nthat are topologically the same as those required for computing the\nbasic coupling coefficients between spin-free configuration state\nfunctions (CSF). Moreover, both time reversal and binary double point\ngroup symmetries can readily be incorporated into molecular integrals\nand Hamiltonian matrix elements. The latter can first be evaluated\nin the space of (randomly selected) spin-dependent determinants and\nthen transformed to that of spin-dependent CSFs, thanks to simple\nrelations in between. As a showcase, we consider here the no-pair\nfour-component relativistic iterative configuration interaction with\nselection and perturbation correction (4C-iCIPT2), which is a natural\nextension of the spin-free iCIPT2 (<i>J. Chem. Theory Comput.</i> <b>2021</b>, <i>17</i>, 949), and can provide near-exact\nnumerical results within the manifold of positive energy states (PES),\nas demonstrated by numerical examples.