35 EXPLICITLY CORRELATED METHODS

Explicitly correlated calculations provide a dramatic improvement of the basis set convergence of MP2, CCSD, CASPT2, and MRCI 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 35.2,35.7). **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 35.2,35.7). **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 35.10. **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 35.10.
**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.
**DCSD-F12**- Closed-shell CCSD-F12 approximations applied to DCSD method, see CCSD-F12 for more details.
**UDCSD-F12**- Open-shell unrestricted CCSD-F12 approximations applied to DCSD method, see UCCSD-F12 for more details.
**RDCSD-F12**- Open-shell partially spin-adapted CCSD-F12 approximations applied to DCSD method.
**RS2-F12**- CASPT2-F12 method as described in J. Chem. Phys.
**133**, 141103 (2010). **MRCI-F12**- MRCI-F12 method as described in J. Chem. Phys.
**134**, 034113 (2011), J. Chem. Phys.**134**, 184104 (2011), and Mol. Phys.**111**, 607 (2013).

**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, 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)

H.-J. Werner, G. Knizia, and F. R. Manby (Mol. Phys. 109, 407 (2011);

Kirk A. Peterson , C. Krause, H. Stoll, J. G. Hill, and H.-J. Werner, Mol. Phys. 109, 2607 (2011)

(for calculations with multiple geminal exponents).

H.-J. Werner, J. Chem. Phys. **129**, 101103 (2008);

T. B. Adler, F. R. Manby, and H.-J. Werner, J. Chem. Phys. 130, 054106 (2009);

T. B. Adler and H.-J. Werner, J. Chem. Phys. 130, 241101 (2009);

T. B. Adler and H.-H. Werner, J. Chem. Phys. 135, 144117 (2011)

(for all local local F12 calculations)

T. Shiozaki and H.-J. Werner, J. Chem. Phys. **133**, 141103 (2010);

T. Shiozaki, G. Knizia, and H.-J. Werner, J. Chem. Phys. **134**, 034113 (2011);

T. Shiozaki and H.-J. Werner, J. Chem. Phys. **134**, 184104 (2011);

T. Shiozaki and H.-J. Werner, Mol. Phys. **111**, 607 (2013)

(for all explicitly correlated multireference calculations).

D. Kats, D. Kreplin, H.-J. Werner, F. R. Manby, J. Chem. Phys. 142, 064111 (2015)

(for DCSD-F12, RDCSD-F12, and UDCSD-F12 calculations).

In the following, we briefly summarize the ansätze and approximations that can be used in single-reference treatments.
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**).
More information about MRCI-F12 calculations are given in section 20.8

- 35.1 Reference functions
- 35.2 Wave function Ansätze
- 35.3 RI Approximations
- 35.4 Basis sets
- 35.5 Symmetry
- 35.6 Options
- 35.7 Choosing the ansatz and the level of approximation
- 35.8 CABS Singles correction
- 35.9 Pair specific geminal exponents
- 35.10 CCSD(T)-F12
- 35.11 DF-LMP2-F12 calculations with local approximations
- 35.12 Variables set by the F12 programs