MOLPRO

19 THE MCSCF PROGRAM MULTI 138
or CI wavefunctions. This method is applicable only if the orbital mixing is negligible. For
CASSCF wavefunctions this can be achieved by maximizing the overlap of the active orbitals
with those of a reference geometry, at which the wavefunctions are assumed to be diabatic (e.g.
for symmetry reasons). The orbital overlap is maximized using using the new DIAB command
in the MCSCF program. Only the active orbitals are transformed.
This procedure works as follows: first, the orbitals are determined at the reference geometry.
Then, the calculations are performed at displaced geometries, and the ”diabatic” active orbitals,
which have maximum overlap with the active orbitals at the reference geometry, are obtained
by adding a DIAB directive to the input:
Old form (Molpro96, obsolete):
DIAB,orbref, orbsav, orb1,orb2,pri
New form:
DIAB,orbref [,TYPE=orbtype] [,STATE=state] [,SPIN=spin] [,MS2=ms2] [,SAVE=orbsav]
[,ORB1=orb1, ORB2=orb2] [,PRINT=pri] [,METHOD=method]
Here orbref is the record holding the orbitals of the reference geometry, and orbsav is the record
on which the new orbitals are stored. If orbsav is not given (recommended!) the new orbitals
are stored in the default dump record (2140.2) or the one given on the ORBITAL directive
(see section 19.5.3). In contrast to earlier versions of MOLPRO it is possible that orbref and
orbsav are the same. The specifications TYPE, STATE, SPIN can be used to select specific
sets of reference orbitals, as described in section 4.11. orb1, orb2 is a pair of orbitals for which
the overlap is to be maximized. These orbitals are specified in the form number.sym, e.g. 3.1
means the third orbital in symmetry 1. If orb1, orb2 are not given, the overlap of all active
orbitals is maximized. pri is a print parameter. If this is set to 1, the transformation angles for
each orbital are printed for each Jacobi iteration. method determines the diabatization method.
method=1 (default): use Jacobi rotations; method=2: use block diagonalization. Both methods
yield very similar results. method=2 must only be used for CASSCF wavefunctions. method=-1
and method=-2: as the positive values, but AO overlap matrix of the current geometry is used.
This minimizes the change of the MO coefficients, rather than maximizing the overlap to the
neighbouring orbitals.
Using the defaults described above, the following input is sufficient in most cases:
DIAB,orbref
Using Molpro98 is is not necessary any more to give any GEOM and DISPL cards. The
displacements and overlap matrices are computed automatically (the geometries are stored in
the dump records, along with the orbitals).
The diabatic orbitals have the property that the sum of orbital and overlap contributions in the
non-adiabatic coupling matrix elements become approximately zero, such that the adiabatic
mixing occurs only through changes of the CI coefficients. This allows to determine the mixing
angle directly from the CI coefficients, either in a simple way as described for instance in J.
Chem. Phys. 89, 3139 (1988), or in a more advanced manner as described by Pacher, Cederbaum,
and Köppel in J. Chem. Phys. 89, 7367 (1988). Recently, an automatic procedure, as
described in J. Chem. Phys. 102, 0000, (1999) has been implemented into MOLPRO. This is
available in Version 99.1 and later and is described in section 38.
Below we present an example for the first two excited states of H 2 S, which have B 1 and A 2
symmetry in C 2v , and A ′′ symmetry in C S . We first perform a reference calculation in C 2v symmetry,
and then determine the diabatic orbitals for displaced geometries in C S symmetry. Each
subsequent calculation uses the previous orbitals as reference. One could also use the orbitals