Combined Coupled-Cluster and Many-body Perturbation Theories: Automated Derivation and Parallel Implementation

Journal Article · Wed Dec 22 04:00:00 EST 2004 · Journal of Chemical Physics, 121(24):12197-12207

DOI:https://doi.org/10.1063/1.1814932· OSTI ID:892240

Hirata, So; Fan, Peng-Dong; Auer, Alexander A; Nooijen, Marcel; Piecuch, Piotr

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 < CR-CCSD(T) ? CCSD(2)T ? CCSD(T) < CCSD(2)TQ ? CCSDT < CCSDT(2)Q, whereas CR-CCSD(T) is effective for extreme cases of quasi-degeneracy (particularly for stretched single bonds) and the operation costs of CCSD(2)TQ and CCSDT(2)Q in the present implementations scale as rather steep O(n9). The perturbation correction part of the CCSD(T)/cc-pVDZ calculations for azulene exhibited a 45-fold speedup upon a 64-fold increase in the number of processors to 512 processors.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (US), Environmental Molecular Sciences Laboratory (EMSL)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 892240
• Report Number(s): PNNL-SA-42308; 3410
• Journal Information: Journal of Chemical Physics, 121(24):12197-12207, Journal Name: Journal of Chemical Physics, 121(24):12197-12207
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
99 GENERAL AND MISCELLANEOUS
AZULENE
CHEMICAL BONDS
COMPUTER CALCULATIONS
EXCITATION
Environmental Molecular Sciences Laboratory
PERTURBATION THEORY
SPIN
WAVE FUNCTIONS