TY - JOUR
T1 - Higher-order explicitly correlated coupled-cluster methods
AU - Shiozaki, Toru
AU - Kamiya, Muneaki
AU - Hirata, So
AU - Valeev, Edward F.
N1 - Funding Information:
S.H. thanks the U.S. Department of Energy (Grant No. DE-FG02-04ER15621) and the Donors of the American Chemical Society Petroleum Research Fund (Grant No. 48440-AC6). E.F.V. thanks the donors of the American Chemical Society Petroleum Research Fund (Grant No. 46811-G6). T.S. thanks the Japan Society for the Promotion of Science Research Fellowship for Young Scientist and Professor Kimihiko Hirao for his continuous encouragement. Dr. Andreas Köhn is thanked for providing the preprint of Ref. .
PY - 2009
Y1 - 2009
N2 - Efficient computer codes for the explicitly correlated coupled-cluster (CC-R12 or F12) methods with up to triple (CCSDT-R12) and quadruple excitations (CCSDTQ-R12), which take account of the spin, Abelian point-group, and index-permutation symmetries and are based on complete diagrammatic equations, have been implemented with the aid of the computerized symbolic algebra SMITH. Together with the explicitly correlated coupled-cluster singles and doubles (CCSD-R12) method reported earlier [T. Shiozaki, J. Chem. Phys. 129, 071101 (2008)], they form a hierarchy of systematic approximations (CCSD-R12<CCSDT- R12<CCSDTQ-R12) that converge very rapidly toward the exact solutions of the polyatomic Schrödinger equations with respect to both the highest excitation rank and basis-set size. Using the Slater-type function exp (-γ r12) as a correlation function, a CC-R12 method can provide the aug-cc-pV5Z-quality results of the conventional CC method of the same excitation rank using only the aug-cc-pVTZ basis set. Combining these CC-R12 methods with the grid-based, numerical Hartree-Fock equation solver [T. Shiozaki and S. Hirata, Phys. Rev. A 76, 040503(R) (2007)], the solutions (eigenvalues) of the Schrödinger equations of neon, boron hydride, hydrogen fluoride, and water at their equilibrium geometries have been obtained as -128.9377±0.0004, -25.2892±0.0002, -100.459±0.001, and -76.437±0.003 Eh, respectively, without resorting to complete-basis-set extrapolations. These absolute total energies or the corresponding correlation energies agree within the quoted uncertainty with the accurate, nonrelativistic, Born-Oppenheimer values derived experimentally and/or computationally.
AB - Efficient computer codes for the explicitly correlated coupled-cluster (CC-R12 or F12) methods with up to triple (CCSDT-R12) and quadruple excitations (CCSDTQ-R12), which take account of the spin, Abelian point-group, and index-permutation symmetries and are based on complete diagrammatic equations, have been implemented with the aid of the computerized symbolic algebra SMITH. Together with the explicitly correlated coupled-cluster singles and doubles (CCSD-R12) method reported earlier [T. Shiozaki, J. Chem. Phys. 129, 071101 (2008)], they form a hierarchy of systematic approximations (CCSD-R12<CCSDT- R12<CCSDTQ-R12) that converge very rapidly toward the exact solutions of the polyatomic Schrödinger equations with respect to both the highest excitation rank and basis-set size. Using the Slater-type function exp (-γ r12) as a correlation function, a CC-R12 method can provide the aug-cc-pV5Z-quality results of the conventional CC method of the same excitation rank using only the aug-cc-pVTZ basis set. Combining these CC-R12 methods with the grid-based, numerical Hartree-Fock equation solver [T. Shiozaki and S. Hirata, Phys. Rev. A 76, 040503(R) (2007)], the solutions (eigenvalues) of the Schrödinger equations of neon, boron hydride, hydrogen fluoride, and water at their equilibrium geometries have been obtained as -128.9377±0.0004, -25.2892±0.0002, -100.459±0.001, and -76.437±0.003 Eh, respectively, without resorting to complete-basis-set extrapolations. These absolute total energies or the corresponding correlation energies agree within the quoted uncertainty with the accurate, nonrelativistic, Born-Oppenheimer values derived experimentally and/or computationally.
UR - http://www.scopus.com/inward/record.url?scp=59949105902&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=59949105902&partnerID=8YFLogxK
U2 - 10.1063/1.3068302
DO - 10.1063/1.3068302
M3 - Article
C2 - 19206952
AN - SCOPUS:59949105902
SN - 0021-9606
VL - 130
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 5
M1 - 054101
ER -