PNNL

Abstract

Various approximations of combined coupled-cluster (CC) and many-body perturbation theories (MBPT) have been derived and implemented into parallel execution programs that take account of spin, spatial (real Abelian), and permutation symmetries within the spin-orbital formalisms for closed- and open-shell molecules. The models range from CCSD(T), CCSD[T], CCSD(2)T, CCSD(2)TQ, CCSDT(2)Q to the completely renormalized CCSD(T) and CCSD[T], where CCSD (CCSDT) is the CC with connected single and double (and triple) excitation operators and subscripted or parenthesized 2, T, and Q indicate the order of perturbation or the rank of connected excitation operators in the correction. The derivation and implementation have been semi-automated by the algebraic and symbolic manipulation program. The computer-synthesized subroutines generate the tensors with the highest rank in a block-wise manner so that they never need to be stored in their entirety, reusing the other pre-calculated intermediate tensors defined also prioritizing the memory optimization (subroutines for these are also computer synthesized). Consequently, the overall memory cost for the perturbation corrections of connected triple and quadruple excitation operators scales as O(n4) and O(n6), respectively (n is the number of orbitals). For systems with different multi-reference character in their wave functions, we found the order of accuracy is roughly CCSD