8.2 Multireference perturbation theory, CASPT2, CASPT3

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:


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:


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 2018-12-18