MOLPRO

37 NON ADIABATIC COUPLING MATRIX ELEMENTS 272
program, using the NOEXC option. The transition density matrix is stored using the DM directive
of the CI program.
2.) Compute the wavefunctions at the (positively) displaced geometry and store the CI wavefunction
in a second record.
3.) If the second-order (three-point) method is used, step (2) is repeated at a (negatively) displaced
geometry.
4.) Compute the transition density matrices between the states at the reference geometry and
the displaced geometr(ies). This is done with the TRANS directive of the CI program.
5.) Finally, the DDR program is used to assemble the matrix element. Using the first-order
two-point method, only a single input line is needed:
DDR, dr, orb1, orb2, trdm2
where dr is the geometry increment used as denominator in the finite difference method, orb1
is the record holding the orbitals of the reference geometry, orb2 is the record holding the
orbitals of the displaced geometry, and trdm2 is the record holding the transition density matrix
computed from the CI-vectors at R and R+DR.
If central differences (three points) are used, the input is as follows:
DDR,2*dr
ORBITAL,orb1,orb2,orb3
DENSITY,trdm1,trdm2,trdm3
where dr, orb1, orb2 are as above, and orb3 is the record holding the orbitals at the negatively
displaced geometry.
trdm1, trdm2, trdm3 are the records holding the transition densities γ(R|R), γ(R|R + DR), and
γ(R|R − DR), respectively.
If more than two states are computed simultaneously, the transition density matrices for all pairs
of states will be stored in the same record. In that case, and also when there are just two states
whose spatial symmetry is not 1, it is necessary to specify for which states the coupling is to be
computed using the STATE directive:
STATE,state 1 , state 2
where state i is of the form istate.isym (the symmetries of both states must be the same, and it is
therefore sufficient to specify the symmetry of the first state).
As an example the input for first-order and second-order calculations is given below. The calculation
is repeated for a range of geometries, and at the end of the calculation the results are
printed using the TABLE command.
In the calculation shown, the ”diabatic” CASSCF orbitals are generated in the two CASSCF
calculations at the displaced geometries by maximizing the overlap with the orbitals at the reference
geometry. This is optional, and (within the numerical accuacy) does not influence the
final results. However, the relative contributions of the orbital, overlap and CI contributions to
the NACME are modified. If diabatic orbitals are used, which change as little as possible as
function of geometry, the sum of overlap and orbital contribution is minimized, and to a very
good approximation the NACME could be obtained from the CI-vectors alone.