Canonical transcorrelated theory with projected Slater-type geminals

An effective Hamiltonian perturbed with explicit interelectronic correlation is derived from similarity transformation of Hamiltonian using a unitary operator with Slater-type geminals. The Slater-type geminal is projected onto the excitation (and deexcitation) component as in the F12 theory. Simplification is made by truncating higher-body operators, resulting in a correlated Hamiltonian which is Hermitian and has exactly the same complexity as the original Hamiltonian in the second quantized form. It can thus be easily combined with arbitrary correlation models proposed to date. The present approach constructs a singularity-free Hamiltonian a priori, similarly to the so-called transcorrelated theory, while the use of the canonical transformation assures that the effective Hamiltonian is two-body and Hermite. Our theory is naturally extensible to multireference calculations on the basis of the generalized normal ordering. The construction of the effective Hamiltonian is non-iterative. The numerical assessments demonstrate that the present scheme improves the basis set convergence of the post-mean-field calculations at a similar rate to the explicitly correlated methods proposed by others that couple geminals and conventional excitations.