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31 EXPLICITLY CORRELATED METHODS

Explicitly correlated calculations provide a dramatic improvement of the basis set convergence of MP2 and CCSD correlation energies. Such calculations can be performed using the commands of the form

command, options

where command can be one of the following:

MP2-F12

Closed-shell canonical MP2-F12. By default, the fixed amplitude ansatz (FIX, see below) is used, but other ansätze are also possible. The F12-corrections is computed using density fitting, and then added to the MP2 correlation energy obtained without density fitting.

DF-MP2-F12

As MP2-F12, but the DF-MP2 correlation energy is used. This is less expensive than MP2-F12.

DF-LMP2-F12

Closed-shell DF-MP2-F12 with localized orbitals. Any method and ansatz as described in J. Chem. Phys. 126, 164102 (2007) can be used (cf. secions 31.2,31.7).

DF-RMP2-F12

Spin-restricted open-shell DF-RMP2-F12 using ansatz 3C. Any method as described in J. Chem. Phys. 128, 154103 (2008) can be used (cf. sections 31.2,31.7).

CCSD-F12

Closed-shell CCSD-F12 approximations as described in J. Chem. Phys. 127, 221106 (2007). By default, the fixed amplitude ansatz is used and the CCSD-F12A and CCSD-F12B energies are computed. Optionally, the command can be appended by A or B, and then only the corresponding energy is computed. For more details see section 31.10.

CCSD-F12c

Closed-shell CCSD(F12*) approximation as proposed by Hättig, Tew and Köhn. In Molpro this is denoted f12c. As compared to CCSD-F12a/b it requires additional computational effort. Since in some parts the implementation is brute-force without paging algorithms, large memory may be required. In most cases there is no gain in accuracy as compared to f12b and therefore the use of this method is normally not recommended. Currently CCSD-F12c is not available for open-shell cases.

CCSD(T)-F12

Same as CCSD-F12, but perturbative triples are added.

CCSD(T)-F12c

Same as CCSD-F12c, but perturbative triples are added.

UCCSD-F12

Open-shell unrestricted UCCSD-F12 approximations as described by G. Knizia, T. B. Adler, and H.-J. Werner, J. Chem. Phys. 130, 054104 (2009). Restricted open-shell Hartree-Fock (RHF) orbitals are used. Optionally, the command can be appended by A or B, and then only the corresponding energy is computed. For more details see section 31.10.

UCCSD(T)-F12

Same as UCCSD-F12, but perturbative triples are added.

RCCSD(T)-F12

Similar to UCCSD(T)-F12, but the partially spin-adapted scheme is used.

Published work arising from these methods should cite the following:

F. R. Manby, J. Chem. Phys. 119, 4607 (2003)
(for the density fitting approximations in linear R12 methods)
A. J. May and F. R. Manby, J. Chem. Phys. 121, 4479 (2004)
(for the frozen geminal expansions)
H.-J. Werner and F. R. Manby, J. Chem. Phys. 124, 054114 (2006);
F. R. Manby, H.-J. Werner, T. B. Adler and A. J. May, J. Chem. Phys. 124, 094103 (2006);
H.-J. Werner, J. Chem. Phys. 129, 101103 (2008);
T. B. Adler, H.-J. Werner, and F. R. Manby, J. Chem. Phys. 130, 054106 (2009);
(for DF-LMP2-F12).
H.-J. Werner, T. B. Adler, and F. R. Manby, J. Chem. Phys. 126, 164102 (2007)
(for all other closed-shell MP2-F12 methods).
G. Knizia and H.-J. Werner, J. Chem. Phys. 128, 154103 (2008)
(for all open-shell F12 calculations).
T. B. Adler, G. Knizia and H.-J. Werner, J. Chem. Phys. 127, 221106 (2007)
(for CCSD(T)-F12).
G. Knizia,T. B. Adler, and H.-J. Werner, J. Chem. Phys. 130, 054104 (2009)
(for CCSD(T)-F12 and UCCSD(T)-F12 calculations).
T. B. Adler and H.-J. Werner, J. Chem. Phys. 130, 241101 (2009)
(for LCCSD-F12).
K.A. Peterson, T. B. Adler, and H.-J. Werner, J. Chem. Phys. 128, 084102 (2008)
(for the VnZ-F12 basis sets)
K. E. Yousaf and K. A. Peterson, J. Chem. Phys. 129, 184108 (2009)
(for the VnZ-F12/OPTRI basis sets)
K. E. Yousaf and K. A. Peterson, Chem. Phys. Lett., 476, 303 (2009)
(for the AVnZ/OPTRI basis sets)

In the following, we briefly summarize the ansätze and approximations that can be used. For more details and further references to related work of other authors see H.-J. Werner, T. B. Adler, and F. R. Manby, General orbital invarient MP2-F12 theory, J. Chem. Phys. 126, 164102 (2007) (in the following denoted I).

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