21.7 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 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.,

`RS2,MIX=`*nstates*, `ROOT=`*ioptroot*

where .

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 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

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