MOLPRO

31 EXPLICITLY CORRELATED METHODS 231
31.2.3 The fixed amplitude ansatz (FIX)
The diagonal ansatz is used and the amplitudes of the explicitly correlated configurations are
determined by the wavefunction cusp conditions, i.e.
T i j,1
i j = 1 2
T i j,−1
i j = 1 4
This ansatz is orbital invariant, size consistent and free of GBSSE.
31.3 RI Approximations
Various approximations such as A, B, C, HY1, HY2 exist for the matrix elements of the firstorder
Hamiltonian (see I). They differ in the way the RI approximations are made. In the limit
of a complete RI basis, approximations B and C are identical and yield the exact result for a
given wave function ansatz. We generally recommend approximation C, which is simpler and
more efficient than approximation B. Normally, the union of the AO and RI basis sets is used
to approximate the resolution of the identity (CABS approach). In the hybrid approximations
(HY1, HY2, HX) only the AO basis is used in some less important terms. Together with the
recommended approximation C, HY1 or HY2 can be used; HY2 is more accurate, HY1 more
efficient. In most cases, approximation 3C(HY1) provides an excellent compromise between
accuracy and efficiency. In approximation A, all terms involving exchange operators are neglected.
This approximation is used along with local approximations in our low-order scaling
LMP2-F12/3*A(loc) method that can be applied to large molecules (cf. section 31.11)
If the extended Brillouin condition (EBC, see I) is assumed, the explicitly correlated and conventional
amplitude equations decouple and can be solved independently. These approximations
are denoted by a star, e.g. 3*C.
31.4 Basis sets
In MOLPRO the F12 integrals can only be computed using density fitting (DF) approximations.
The many electron integrals are approximated by resolutions of the identity (RI) expansions.
Thus, F12 calculations require three different basis sets: the orbital (AO) basis, the DF basis,
and the RI basis.
We recommend as AO basis sets the augmented correlation consistent basis sets (denoted AVnZ)
or the specially optimized correlation consistent F12 basis sets (denoted VnZ-F12, cf. K.A.
Peterson and H.-J. Werner, J. Chem. Phys. 128, 084102 (2008)). Normally, triples zeta basis
sets (AVTZ or VTZ-F12) yield excellent results that are close to the basis set limit. Diffuse
basis functions are rather essential both for the HF and MP2-F12 energies, and therefore the
standard VTZ sets are not recommended. If the AVnZ or VnZ-F12 orbital basis sets are used,
suitable density fitting (DF) basis and resolution of the identity (RI) basis sets are automatically
chosen. For the AVnZ orbital basis sets, AVnZ/MP2FIT amd VnZ/JKFIT basis sets are used by
default for the DF and RI, respectively. The associated optimized CABS basis set of Peterson
et al. can be chosen by specifying RI BASIS=OPTRI. For the VnZ-F12 orbital basis, the
associated CABS (OPTRI) basis sets are used by default. Other basis sets can be chosen using
the DF BASIS, DF BASIS EXCH and RI BASIS options (cf. section 31.6). See section 15 for
more details about density fitting.
This is an example for using multiple basis sets for density fitting and resolution of the identity