To obtain the R12 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 $rir12
The MP2-R12 ground-state energy is
The R12 correction is obtained by minimizing the functional
A MP2-R12 calculation is defined through a number of choices concerning the nature of the geminals ( and ), the geminal excitation space (ijkl or ijij) and approximations in computing the matrix (GBC, EBC, ). These choices correspond to keywords in the $rir12 data group, explained below.
To run a MP2-R12 calculation, one has to select the auxiliary basis sets
cabs and optionally
The ricc2 program uses the robust fitting techniques of Ref. 
for the R12 integrals and the
cbas basis is used for both the R12
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 R12 method, the complementary auxiliary
basis (CABS) approach is used . If define is
used to set up the
cabs basis, the basis sets in the
The $rir12 data group may be set by choosing the
option in the
ricc2 menu when running define.
This command activates the
mp2-f12 menu, where the default
options may be changed if desired:
INPUT MENU FOR MP2-F12 CALCULATIONS ansatz : CHOOSE ANSATZ 2 [1,2*,2] r12model : CHOOSE MODEL B [A,A',B] comaprox : COMMUTATOR APPROXIMATION T [F+K,T] cabs : CABS ORTHOGONALIZATION svd [cho,svd] examp : CHOOSE FORMULATION fixed [inv,fixed,noinv] pairenergy: PRINT OUT PAIRENERGIES yes [yes,no] local : CHOOSE LOCALIZATION METHOD off [off,boys,pipek] corrfac : CHOOSE CORRELATION FACTOR LCG [R12,LCG] * / 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 R12 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.
T+V(the core Hamiltonian) is recommended and is the default.
svd) or Choleski decomposition are available.
svdis recommended and is the default. The basis set used for CABS is set from the
invis the orbital-invariant merhod of Ref. , with amplitudes .
noinvis the original orbital-dependent diagonal "ijij" method of Ref. , with amplitudes (not recommended, unless in combination with localised orbitals).
fixedis the (diagonal and orbital-invariant) rational generator approach of Ref. , where the R12 amplitudes are not optimised, but predetermined using the coalescence conditions (default).
offmeans that (semi-)canonical Hartree-Fock orbitals are used (default). For calculations using linear- as correlation factor, and r12model
A', localized orbitals may be used. Both the Boys  and Pipek-Mezey  methods are available for localisation of the orbitals.
R12results in a calculation using linear- and
LCGresults in a calculation using the Slater-type correlation factor with exponent 1.4 , represented as a linear combination of six Gaussians (see Ref. ).
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 , 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
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 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 different result to that of
fixedMP2-F12, even for identical RHF and UHF determinants. However, the
diagmethod is somewhat less expensive than the
The single excitations into the CABS basis are always computed if the CABS Fock
matrix elements are anyway required for the R12 calculation (i.e., for ansatz
B or comaprox
F+K). The computation of CABS singles
may be suppressed or enforced by using the cabsingles
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.
cabs, we currently recommend to use the
basis, where X is the cardinal number of the selected orbital basis.
jkbas basis sets are used for integrals involving
both the orbital and
cabs basis sets, and we therefore recommend to use
the aug-cc-pV(X+1)Z fitting sets. These recommendations err on the side of
caution and are likely to be refined as more experience is gained.