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6.3 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

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.

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