22.7 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 39 and 40). Analytical gradients are presently only available for RS2 calculations (not RS2C), and only for the standard $\hat H^{(0)}$ (not G1, G2 etc). Gradients can be computed for single-state calculations, as well as multi-state MS-MR-CASPT2 (see section 22.3.

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 22.2). 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 $1 \le ioptroot \le nstates$. The program works with state-averaged MCSCF (CASSCF) orbitals, and no CPMCSCF directive is needed. The RS2 gradient program can also be used to compute state-averaged MCSCF/CASSCF gradients using the NOEXC directive.

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.

RS2,SHIFT=0.2,IGNORE
OPTG

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.

Example:

CASPT2 geometry optimizations for H$_2$O:

h2o_caspt2_opt.com

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 $^3B_2$ state if H$_2$O:

h2o_mscaspt2_opt.com

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