appearance on visualization) is not, it can be switched by an appropriate command
with one initially in the active space but irrelevant to the calculation. Figure8.10
shows the two MOs in the active space of our CASSCF(2,2) calculation, localized
by the NBO method (in this case, with the Boys method the ordinal numbers of
the relevant orbitals was unclear, due to the their not being nicely localized). The
occupancy is revealed by visualization with an appropriate program or, less conve-
niently, inspection of printed output, which shows that the bonding-type C 1 /C 4 MO
number 16 is formally occupied by two electrons and the antibonding-type MO
number 17 is formally vacant. Note that this species has 32 electrons. If, say, the
MO resembling MO 16 here had been MO 10 and MO 16 had been a C–H bonding
orbital, ten and 16 could be switched – see below for cyclopentane. The point is that
we want to perform a CI calculation using the relevant orbitals.
Step 3 is a geometry optimization. Appropriate keywords might be CASSCF
(2,2)/6-31G, specifying a CASSCF(2,2) procedure (a limited CI optimization)
using the 6-31G basis, which will normally be the smallest chosen. Other key-
words might dictate the information to be taken from step 2 and how to calculate
the initial Hessian (e.g., use a semiempirical calculation) for the optimization.
Figure8.11compares our CASSCF(2,2)/6-31G C2hrelative minimum (no imagi-
nary frequencies – see below) with the C2hCASSCF(4,4)/6-31G minimum of
Doubleday [ 61 ].
Step 4 is a frequency calculation on the geometry from step 3, again using the
CASSCF(2,2)/6-31G method. The program might allow this step to automatically
follow the optimization. In most cases the frequency calculation is desirable, to
characterize the nature of the optimized structure as a minimum or some kind of
saddle point, and to obtain thermodynamic data like zero point energy and enthalpy
and free energy (Sections 2.5 and 5.5.2.1b).
One further step is desirable for obtaining relative energies, namely performing
on the CASSCF(2,2)/6-31G geometry a calculation designed to treat electron
correlation better than was done by the CASSCF calculation. Recall that Hartree–
Fock (also called SCF) calculations treat electron correlation only very approximately
(Section 5.4.1). In a typical CASSCF calculation most of the electrons, i.e. those
MO 16, formally doubly occupied MO 17, formally unoccupiedFig. 8.10 Visualization of the relevant MOs, 16 and 17, for the active space of a CASSCF(2,2)
calculation on 1,4-butanediyl: the algorithm will recognize the active space as consisting of the
two frontier orbitals (HOMO and LUMO; the molecule has 32 electrons); we ensure by visual
inspection that these are the two MOs that are localized on the end carbons. If a desired orbital is
not a frontier orbital to start with, it can be switched with one (see text). NBO localization was used
here. Calculated with the HF/STO-3G basis and localized by the NBO method
542 8 Some “Special” Topics