MOLPRO

21 MULTIREFERENCE RAYLEIGH SCHRÖDINGER PERTURBATION THEORY 172
Alternatively (or in addition), the IPEA shift of G. Ghigo, B. O. Roos, and P.A. Malmqvist,
Chem. Phys. Lett. 396, 142 (2004) can be used. The implementation is not exactly identical to
the one in MOLCAS, since in our program the singly external configurations are not (RS2) or
only partially (RS2C) contracted. In Molpro, the shift is implemented as follows:
1
2 D ppε is added to the occupied part of the Fock matrix; in addition, 2ε is added as a general
shift (not corrected). ε is the value specified with the IPEA option (default 0). A value of
0.20-0.25 is recommended. This removes intruder state problems to a large extent and usually
improves the results. Note that the method is not exactly orbital invariant, and pseudo-canonical
orbitals should be used (see CANONICAL option in MULTI).
It is possible to use SHIFT and IPEA simultaneously, but it does not make sense to use one of
the G-options together with IPEA.
21.6 Integral direct calculations
RS2, RS2C, and RS3 calculations with very large basis sets can be performed in integral-direct
mode. The calculation will be direct if a global DIRECT or GDIRECT card appears earlier in the
input. Alternatively, (mainly for testing) DIRECT can be specified as an option on the RSn[C]
card:
RS2 [,Gn] [,SHIFT=shift] [,DIRECT]
RS2C [,Gn] [,SHIFT=shift] [,DIRECT]
21.7 CASPT2 gradients
P. Celani and H.-J. Werner, J. Chem. Phys. 119, 5044 (2003))
CASPT2 analytic energy gradients are computed automatically if a FORCE or OPTG command
follows (see sections 41 and 42). Analytical gradients are presently only available for RS2
calculations (not RS2C), and only for the standard Ĥ (0) (not G1, G2 etc). Gradients can be
computed for single-state calculations, as well as multi-state MS-MR-CASPT2 (see section
21.3.
In single state calculations, the gradient is automatically computed for the state computed in
CASPT2/RSPT2 (i.e., using STATE,1,2 the second state in the symmetry under consideration
is computed, see section 21.2). The program works with state-averaged MCSCF (CASSCF)
orbitals, and no CPMCSCF directive is needed. It is necessary that the state under consideration
is included in the preceding (state-averaged) MCSCF/CASSCF. The RS2 gradient program
can also be used to compute state-averaged MCSCF/CASSCF gradients by using the NOEXC
directive.
In a multi-state MS-MR-CASPT2 calculation, the state for which the gradient is computed must
be specified using the ROOT option (default ROOT=1), i.e.,
RS2,MIX=nstates, ROOT=ioptroot
where 1 ≤ ioptroot ≤ nstates.
Level shifts can be used. By default, the exact gradient of the level-shift corrected energy is
computed. For a non-zero shift, this requires to solve the CASPT2 Z-vector equations, which
roughly doubles the computational effort. In single state calculations it is possible to ignore
the effect of the level shift on the gradient and not to solve the Z-vector equation. This variant,
which is described in the above paper, may be sufficiently accurate for many purposes. It is
invoked using the IGNORE option, e.g.