To obtain the F12 correction to the MP2 energy, the data group $rir12 must be added to the control file. A typical run will include the input:
$ricc2 mp2 energy only $rir12
The MP2-F12 ground-state energy is
|E||= EMP2 + EF12,||(8.3)|
The F12 correction is obtained by minimizing the functional
|FF12||= cijTBijcij +2cijTvij||(8.5)|
|vij(kl )||= 〈kl|f12r12-1|ij〉,||(8.6)|
|Bij(kl, mn)||= 〈kl|f12( + - - )f12|mn〉,||(8.7)|
A MP2-F12 calculation is defined through a number of choices concerning the nature of the geminals (f12 and ), the geminal excitation space (ijkl or ijij) and approximations in computing the B matrix (GBC, EBC, [, f12] ). These choices correspond to keywords in the $rir12 data group, explained below.
To run a MP2-F12 calculation, one has to select the auxiliary basis sets
cabs and optionally
The ricc2 program uses the robust fitting techniques of Ref. 
for the F12 integrals and the
cbas basis is used for both the F12
and the usual MP2 Coulomb integrals. For the density fitting of the Coulomb and
exchange matrices of the Fock matrix, the
jkbas will be used
instead of the
cbas basis if it is included in the control file (this is
recommended and is achieved using the
rijk menu in define).
For the RI approximation of the 3- and 4-electron integrals as sums of products
of 2-electron integrals, intrinsic to the F12 method, the complementary auxiliary
basis (CABS) approach is used . If define is
used to set up the
cabs basis, the library
cabasen is searched. This library contains the
cabs basis sets  for the
cc-pVXZ-F12 basis sets of Peterson et al. .
For other basis sets, the auxilliary basis in the library
is identical with the auxilliary basis in the library
The $rir12 data group may be set by choosing the
option in the
cc menu when running define.
This command activates the
f12 menu, where the default
options may be changed if desired:
Orbital basis : cc-pVTZ-F12 Cardinal number : T Recommended exponent: 1.0000 Actual exponent: 1.0000 INPUT MENU FOR MP2-F12 CALCULATIONS ansatz : CHOOSE ANSATZ 2 [1,2*,2] r12model : CHOOSE MODEL B [A,B] comaprox : COMMUTATOR APPROXIMATION F+K [F+K,T+V] cabs : CABS ORTHOGONALIZATION svd 1.0D-08 [cho,svd] examp : CHOOSE FORMULATION fixed noflip [inv,fixed,noinv, flip,noflip] r12orb : CHOOSE GEMINAL ORBITALS hf [hf,rohf,boys,pipek] corrfac : CHOOSE CORRELATION FACTOR LCG [R12,LCG] cabsingles: CABS SINGLE EXCITATIONS on [on,off] pairenergy: PRINT OUT PAIRENERGIES off [on,off] slater : SLATER EXPONENT 1.0000 * / end : write $rir12 to file and leave the menu & : go back - leaving $rir12 unchanged...
2(default), which gives much improved energies over ansatz
1(see Ref.  for details). The principal additional cost of using ansatz
1is concerned with the coupling between the F12 and conventional amplitudes. This is avoided by choosing
2*, which corresponds to neglecting EBC (Extended Brillouin Condition) terms in the Fock matrix elements.
B. It is recommended to use
B(default). The energies computed using
Aare then also printed out in the output.
F+K(the core Hamiltonian plus Coulomb term) is recommended and is the default.
svd) or Cholesky decomposition (
cho) are available.
svdis recommended and is the default, with a threshold of
1.0d-08. The basis set used for CABS is set from the
invis the orbital-invariant merhod of Ref. , with amplitudes cij(kl ) .
noinvis the original orbital-dependent diagonal "ijij" method of Ref. , with amplitudes cij(ij) (not recommended, unless in combination with localised orbitals).
fixedis the (diagonal and orbital-invariant) rational generator approach of Ref. , where the F12 amplitudes are not optimised but predetermined using the coalescence conditions (default). An additional keyword
noflipsuppresses the use of spin-flipped geminals in open-shell calculations; by default spin-flipped geminals are used as described in Ref. .
hfmeans that (semi-)canonical Hartree-Fock orbitals are used (default).
rohfmeans that ROHF orbitals are used (any frozen orbitals will then also implicitly be ROHF). For calculations on closed-shell systems, localised orbitals may be used. Both the Boys  and Pipek-Mezey  methods are available for localisation of the orbitals.
R12results in a calculation using linear-r12 and
LCGresults in a calculation using the Slater-type correlation factor with exponent 1.4 a0-1 , represented as a linear combination of six Gaussians (see Ref. ). Note that the exponents 0.9, 1.0 and 1.1 a0-1 are recommended for use with the cc-pVXZ-F12 basis sets .
F+K). The computation of CABS singles cannot be switched off if it is free of costs.
LCG refers to a further data group for the definition
of the correlation factor. When define is used, the default is
$lcg nlcg 6 slater 1.4000The nature of the LCG correlation factor may be changed by editing this data group in the control file. For example, to use a Slater-type correlation factor with exponent 1.0 a0-1 , represented as a linear combination of three Gaussians, use
$lcg nlcg 3 slater 1.0000Alternatively, the exponents and coefficients of the fit may be given explicitly:
$lcg nlcg 3 expo1 coef1 expo2 coef2 expo3 coef3
MP2-F12 calculations may be combined with Grimme's SCS approach (S. Grimme, J. Chem. Phys. 118 (2003) 9095.)by inserting scs in $ricc2,
$ricc2 mp2 energy only scsIn this case, the SCS parameters cos=6/5 and css=1/3 are used. Also individual scaling factors for the same-spin and opposite-spin contributions may be defined, see Section 9.7.
For open-shell calculations, two choices of the examp
are available. These are controled by a keyword in the $rir12 data group
ump2fixed full [diag,full]These differ in the treatment of the αβ block, where either only the diagonal excitations enter (with amplitude 0.5)
diag, or the equivalent of the spin-adapted singlet and triplet pair excitations enter (as far as possible)
full. Note that the
diagmethod with UMP2-F12 yields a result different to that of
fixedMP2-F12, even for identical RHF and UHF determinants. However, the
diagmethod is somewhat less expensive than the
Recommendations for orbital and auxiliary basis sets:
The best orbital basis sets to use for MP2-F12 calculations are probably
the cc-pVXZ-F12 basis sets, specially
optimised for MP2-F12 calculations 
for the atoms H, He, B-Ne and Al-Ar.
In conjunction with these cc-pVXZ-F12 basis sets,
we recommend to use the optimised cc-pVXZ-F12 sets of Yousaf and
Peterson  as
jkbas basis sets can be selected from the
jkbasen libraries, respectively, using the
alias cc-pVXZ-F12 (a
jkbas is currently not available for
He, Ne and Ar). This alias points to the
jkbas. These recommendations are on the side
of caution and are likely to be refined as more experience is
For atoms other than H, He, B-Ne and Al-Ar, optimised F12
basis sets are not yet available. In this case, basis sets must
be selected and/or optimised carefully. It is advised to
contact the Theoretical Chemistry Group in Karlsruhe for support