7.3 State-averaged MCSCF

In order to compute excited states it is usually best to optimize the energy average for all states under consideration. This avoids root-flipping problems during the optimization process and yields a single set of compromise orbitals for all states.

The number of states to be optimized in a given symmetry is specified on a state directive, which must follow directly after the wf directive, e.g.,

wf,16,1,0;state,2 !optimize two states of symmetry 1

It is also possible to optimize states of different symmetries together. In this case several wf / state directives can follow each other, e.g.,

wf,16,1,0;state,2 !optimize two states of symmetry 1
wf,16,2,0;state,1 !optimize one states of symmetry 2

etc. Optionally also the weights for each state can be specified, e.g.

wf,16,1,0;state,2;weight,0.2,0.8   !optimize two states of symmetry 1
                                   !first state has weight 0.2,
                                   !second state weight 0.8

By default, the weights of all states are identical, which is normally the most sensible choice. The following example shows a state-averaged calculation for $\rm O_2$, in which the valence states ($^3\Sigma_g^-$, $^1\Delta_g$) are treated together.

***,O2
print,basis,orbitals
geometry                   !geometry specification, using z-matrix
o1
o2,o1,r
end

r=2.2 bohr                 !bond distance

basis=vtz                  !triple-zeta basis set

{hf                        !invoke RHF program
wf,16,4,2                  !define wavefunction: 16 electrons, symmetry 4, triplet
occ,3,1,1,,2,1,1           !number of occupied orbitals in each symmetry
open,1.6,1.7}              !define open shell orbitals

{casscf                    !invoke CASSCF program
wf,16,4,2                  !triplet Sigma-
wf,16,4,0                  !singlet delta (xy)
wf,16,1,0}                 !singlet delta (xx - yy)

Note that averaging of states with different spin-multiplicity, as in the present examples, is possible only for CASSCF, but not for more restricted RASSCF or MCSCF, wavefunctions.