19.5.9 Diabatic orbitals

In order to construct diabatic states, it is necessary to determine
the mixing of the diabatic states in the adiabatic wavefunctions.
In principle, this mixing can be obtained by integration of the
non-adiabatic coupling matrix elements. Often, it is much easier
to use an approximate method, in which the mixing is determined
by inspection of the CI coefficients of the MCSCF 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 19.5.4).
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 42.

Below we present an example for the first two excited states of HS,
which have and symmetry in , and symmetry in
. We first perform a reference calculation in symmetry,
and then determine the diabatic orbitals for displaced geometries in
symmetry. Each subsequent calculation uses the previous orbitals
as reference. One could also use the orbitals of the calculation
as reference for all other calculations. In this case one would have to take
out the second-last input card, which sets `reforb=2141.2`.

See section 42 for the automatic generation of diabatic energies.

molpro@molpro.net 2018-12-14