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 45 and 46). Analytical gradients are presently only available for RS2 calculations (not RS2C), and only for the standard (not G1, G2 etc). Gradients can be computed for single-state calculations, as well as multi-state MS-MR-CASPT2 (see section 21.3. However, only states with the same symmetry and spin and the same number of electrons as in the optimized state can be included in the preceding SA-CASSCF (CONFIG,DET must not be given in the CASSCF).
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.,
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.
Any publications employing the CASPT2 gradients should cite the above paper. A citation for MS-CASPT2 gradient method is P. Celani and H.-J. Werner, to be published.
CASPT2 geometry optimizations for HO:
This produces the Table
METHOD R_OPT THETA_OPT E_OPT rs2,analytical,ignore 1.8250 102.1069 -76.22789382 rs2,analytical,exact 1.8261 102.1168 -76.22789441 rs2,numerical 1.8261 102.1168 -76.22789441 rs2c,numerical 1.8260 102.1187 -76.22787681
MS-CASPT2 geometry optimization for the second excited state if HO:
This produces the table
METHOD R_OPT THETA_OPT E_OPT rs2,analytical 2.4259 96.7213 -75.81630628 rs2,numerical 2.4259 96.7213 -75.81630628