The input for MRPT/CASPT2 is similar to MRCI, but the following commands are used.

rs2 !second-order multireference perturbation theory rs3 !third-order multireference perturbation theory rs2c !second-order multireference perturbation theory !with a more contracted configuration space.

In case of `rs2` and `rs3`, exactly the same configuration spaces as
in the MRCI are used. In this case the excitations with two electrons in the
external orbital space are *internally contracted*. The total number of correlated
orbitals is restricted to 16 for machines with 32-bit integers and to 32 for
machines with 64-bit integers.

In the `rs2c` case certain additional configuration classes involving internal
and semi-internal excitations are also internally contracted (see
J. Chem. Phys. **112**, 5546 (2000)). This is exactly as in the `mrcic` case (see above).
This method is much more
efficient than `rs2` and more suitable for large cases. In particular, in this case
only the number of *active* orbitals is restricted to 16 or 32 on 32 and 64 bit
machines, respectively, and any number of closed-shell (inactive) orbitals can be
used (up to a maximum as defined by a program parameter).

Note that the RS2 and RS2c methods yield slightly different results. In both cases
the results also slightly differ from those obtained with the method of
of Roos et al. (J. Chem. Phys. **96**, 1218 (1992)), as
implemented in MOLCAS, since in the latter case *all* configuration spaces
are internally contracted. This introduces some bottlenecks that are not present
in MOLPRO.

Restricted active space (RASPT2) or general MRPT2 calculations can be performed using
the `restrict` and/or `select` directives as explained in section
for MCSCF and CASSCF.

MRPT2 and CASPT2 calculations often suffer from so-called intruder state problems,
leading to a blow-up of the wavefunction and no convergence. This problem can
often be avoided by using *level shifts*. These
shifts can be specified on the `rs2` and `rs2c` cards:

`rs2,shift=`*value*
`rs2c,shift=`*value*

The energy is approximately corrected for the shift as proposed by Roos and Andersson.
(Chem. Phys. Lett. **245**, 215 (1995)).

Alternatively (or in addition, the IPEA shift proposed by
G. Ghigo, B. O. Roos, and P.A. Malmqvist, Chem. Phys. Lett. **396**, 142 (2004) can be used:

`rs2,ipea=`*value*

It is also possible to use modified zeroth-order Hamiltonians; see reference manual for further details.

Energy gradients are available for `rs2`, including multi-state treatments.
Currently, gradients are not yet available for `rs2c`.

molpro@molpro.net 2018-09-21