Coupling term derivation and general implementation of state-specific multireference coupled cluster theories

Simple closed-form expressions are derived for the "same vacuum" renormalization terms that arise in state-specific multireference coupled cluster (MRCC) theories. Explicit equations are provided for these coupling terms through the triple excitation level of MRCC theory, and a general expression is included for arbitrary-order excitations. The first production-level code (PSIMRCC) for state-specific and rigorously size-extensive Mukherjee multireference coupled cluster singles and doubles (MkCCSD) computations has been written. This code is also capable of evaluating analogous Brillouin-Wigner multireference energies (BWCCSD), including a posteriori size-extensivity corrections. Using correlation-consistent basis sets (cc-pVXZ, X=D,T,Q), MkCCSD and BWCCSD were tested and compared on two classic multireference problems: (1) the dissociation potential curve of molecular fluorine (F(2)) and (2) the structure and vibrational frequencies of ozone. Comparison with experimental data shows that the Mukherjee method is generally superior to the Brillouin-Wigner theory in predicting energies, structures, and vibrational frequencies. Particularly accurate results for F(2) are obtained by applying the MkCCSD method with localized molecular orbitals. Although the MkCCSD theory greatly improves upon single-reference CCSD for the geometric parameters and a(1) vibrational frequencies of ozone, the antisymmetric stretching frequency omega(3)(b(2)) remains pathological and cannot be properly treated without the inclusion of connected triple excitations. Finally, preliminary multireference MkCCSD results are reported for the singlet-triplet splittings in ortho-, meta-, and para-benzyne, coming within 1.5 kcal mol(-1) of experiment in all cases.