Essentials of Computational Chemistry

210 7 INCLUDING ELECTRON CORRELATION IN MO THEORY
E
frozen HF
virtual orbitals
enforced empty
no more than
n excitations
in permitted
Complete active space
all possible
occupation
schemes allowed
no more than
n excitations
out permitted
enforced doubly
occupied
frozen HF
occupied orbitals
restricted
active
space
Figure 7.3 Possible assignment of different orbitals in a completely general MCSCF formalism.
Frozen orbitals are not permitted to relax from their HF shapes, in addition to having their occupation
numbers of zero (virtual) or two (occupied) enforced
While all of the above details are useful for making calculations more efficient, they still
are not necessarily very helpful in evaluating just which orbitals should be included in any
given space. Typically, a certain amount of trial and error is required in the selection of an
active space. After selection of a given active space and convergence of the MCSCF wave
function, one should inspect the occupation numbers of the active orbitals. A reasonable
rule of thumb is that any orbital having an occupation number greater than 1.98 or less
than 0.02 is not important enough to include in the CAS space, and should be removed to
avoid instability. In addition, of course, it may be wise to add some orbitals not previously
considered to see if their occupation numbers justify inclusion in the active space. And,