In a CASSCF wavefunction the occupied orbital space is divided
into a set of *inactive* or *closed-shell* orbitals
and a set of *active* orbitals. All inactive orbitals are doubly
occupied in each Slater determinant. On the other hand, the
active orbitals have varying occupations, and all possible Slater
determinants (or CSFs) are taken into account which can be
generated by distributing the
electrons in all possible
ways among the active orbitals, where
is the number of
closed-shell (inactive) orbitals, and is the total number of
electrons. Thus, it corresponds to a full CI in the active space.

The CASSCF program is invoked using the

`casscf`

Aliases for this command are `mcscf` or `multi`.
This command is optionally followed by further input defining
the wavefunction.
The inactive orbital space is defined using
the `closed` directive.

`closed`,

where is the number of doubly occupied (inactive) orbitals in
irreducible representation . The total number of occupied
orbitals is specified using the `occ` directive, as in Hartree-Fock.

`occ`,

where . The number of active orbitals in irreducible representations is
then . Note that the inactive orbitals are always the first in
each symmetry, i.e., inactive and active spaces cannot be mixed.
The number of electrons, as well as the symmetry
of the wavefunction and the total spin is specified using the `wf`
directive, as explained already for open-shell HF:

`wf`,

where is the symmetry of the total wavefunction (the direct product of the symmetries of all occupied spin orbitals), and defines the spin (0=singlet, 1=doublet, 2=triplet etc).

From the above it follows that the number of active electrons is

(1) |

By default, the inactive space consists of all inner-shell orbitals, and the active space of all valence orbitals which are obtained from the atomic valence orbitals (full valence active space). The default number of electrons equals the sum of nuclear charges, the default wavefunction symmetry is 1 and singlet. The default starting guess for the orbitals is taken from the most recent orbital optimization, e.g., Hartree-Fock. The simplest input for a CASSCF calculation for formaldehyde is therefore

***,formaldehyde print,orbitals,civector !this is optional: print the occupied orbitals !and the CI vector !by default, only coefficients larger than 0.05 !are printed. angstrom geometry={ !define the nuclear coordinates C O , C , rco H1 , C , rch , O , hco H2 , C , rch , O , hco , H1 , 180 } rco=1.182 Ang rch=1.102 Ang hco=122.1789 Degree basis=vdz !Select basis set hf !Perform HF calculation casscf !Perform CASSCF calculation, !using the HF orbitals as starting guess.

In this case, the carbon and oxygen orbitals are inactive, and the
carbon and oxygen , as well as the hydrogen orbitals are active.
This corresponds to the following input, which could be given after
the `casscf` directive:

{casscf closed,2 !2 inactive orbitals in Symmetry 1 (a1) occ,7,2,3 !7a1, 2b1, 3b2 occupied orbitals wf,16,1,0} !16 electrons, Symmetry 1 (A1), singlet

Thus, there are five , two , and three active orbitals. This
yields 3644 CSFs or 11148 Slater determinants. *Note that the wf
directive must be given after the occ and closed ones.* A
shorter expansion results if the orbital of oxygen is made
inactive. In this case the input would be

{casscf closed,3 !3 inactive orbitals in Symmetry 1 (a1) occ,7,2,3 !7a1, 2b1, 3b2 occupied orbitals wf,16,1,0} !16 electrons, Symmetry 1 (A1), singlet

and now only 1408 CSFs or 4036 Slater determinants are generated.

molpro@molpro.net 2018-11-16