PNNL

Abstract

The equation-of-motion coupled-cluster (EOM-CC) methods with cluster and linear excitation operators truncated after double, triple, or quadruple excitation level (EOM-CCSD, EOM-CCSDT, and EOM-CCSDTQ) for excitation energies, excited-state dipole moments, and transition moments, and also related ? equation solvers for coupled-cluster (CC) methods through and up to connected quadruple excitation (CCSD, CCSDT, and CCSDTQ) have been implemented into programs that execute in parallel, taking advantage of spin, spatial (real Abelian), and permutation symmetries simultaneously and fully (within the spin-orbital formalisms). This has been achieved by virtue of the new implementation paradigm of using an algebraic and symbolic manipulation program that automated the formula derivation and implementation altogether. The EOM-CC methods and CC ? equations introduce a new class of second quantized ansatz with a de-excitation operator ( ), an arbitrary number of excitation operators ( ), and a physical (e.g., the Hamiltonian) operator ( ), the tensor contraction expressions of which can be performed in the order of or at the minimal peak operation cost. Any intermediate tensor resulting from either contraction order is shown to have at most six groups of permutable indices, which finding is used to guide the computer-synthesized programs to fully exploit the permutation symmetry of any tensor to minimize the arithmetic and memory costs.