MOLPRO

21 MULTIREFERENCE RAYLEIGH SCHRÖDINGER PERTURBATION THEORY 166
Gn Use modified zeroth order Hamiltonian, see section 21.4
SHIFT=value Level shift, see section 21.5
IPEA=value
MIX=nstates
ROOT=ioptroot
SAVEH=record
INIT
IGNORE
IPEA shift proposed by G. Ghigo, B. O. Roos, and P.A. Malmqvist,
Chem. Phys. Lett. 396, 142 (2004), see section 21.5.
Invokes multi-state (MS-CASPT2) treatment using nstates states.
See section 21.3 for more details.
Root number to be optimized in geometry optimization. This
refers to the nstates included in the MS-CASPT2. See section
21.7 for more details.
Record for saving the effective Hamiltonian in MS-CASPT2
calculations. If this is not given, a default record will be used
(recommended).
(logical) Initializes a MS-CASPT2 with single state reference
functions, see section 21.3
(logical) Flags an approximate gradient calculation without CP-
CASPT2; see section 21.7 for details.
In addition, all valid options for MRCI can be given (see Sect. 20).
21.1 Introduction
Multireference perturbation calculations are performed by the MRCI program as a special case.
For RS2 (CASPT2,RASPT2) only matrix elements over a one-electron operator need to be
computed, and therefore the computational effort is much smaller than for a corresponding
MRCI. For RS3 (CASPT3) the energy expectation value for the first-order wavefunction must
be computed and the computational effort is about the same as for one MRCI iteration. The
RS2 and RS3 programs use the same configuration spaces as the MRCI, i.e., only the doubly
external configurations are internally contracted.
A new version of the program has been implemented in which also subspaces of the singly external
and internal configuration spaces are internally contracted (see reference given above).
This program, which is called using the keyword RS2C, is more efficient than RS2, in particular
for large molecules with many closed-shell (inactive) orbitals. It is recommended to use this
program for normal applications of second-order multireference perturbation theory (CASPT2,
RASPT2). Note that it gives slightly different results than RS2 due to the different contraction
scheme. It should also be noted that neither RS2 or RS2C are identical with the CASPT2 of
Roos et al. [J. Chem. Phys. 96, 1218 (1992)], since certain configuration subspaces are left
uncontracted. However, the differences are normally very small. The last point that should be
mentioned is that the calculation of CASPT2/RASPT2 density matrices (and therefore molecular
properties) is presently possible only with the RS2 command and not with RS2C.
The results of multireference perturbation theory may be sensitive to the choice of the zerothorder
Hamiltonian. This dependence is more pronounced in second-order than in third-order.
Several options are available, which will be described in the following sections. It may also
happen that (Ĥ (0) − E (0) ) in the basis of the configuration state functions becomes (nearly)
singular. This is known as ”intruder state problem” and can cause convergence problems or
lead to a blow-up of the wavefunction. Often, such problems can be eliminated by including
more orbitals into the reference wavefunction, but of course this leads to an increase of the CPU
time. The use of modified Fock operators (see below) or level shifts, as proposed by Roos and