33.3 Calculation of individual SO matrix elements

Individual spin-orbit matrix elements can be computed within the MRCI program using

TRANLS,record1.file, record2.file, bra2ms, ket2ms, lsop;

where

record1.file

Record holding the bra-wavefunction.

record2.file

Record holding the ket-wavefunction. Both records must have been generated using the SAVE directive of the MRCI program.

bra2ms

$2 \times M_S$ value of the bra-wavefunction.

ket2ms

$2 \times M_S$ value of the ket-wavefunction.

lsop

Cartesian component of the Spin-orbit Hamiltonian.
This can be one of ${\tt LSX}$, ${\tt LSY}$, or ${\tt LSZ}$ in all electron calculations, and ${\tt ECPLSX}$, ${\tt ECPLSY}$, or ${\tt ECPLSZ}$ in ECP calculations.

Since the spin-orbit program is part of the MRCI program, the TRANLS card must be preceded by a [MR]CI card. For the case that the matrix elements are computed for MCSCF wavefunctions, one has to recompute and save the CI-vectors using the MRCI program (see chapter 17), using the NOEXC directive to avoid inclusion of any further excitations out of the MCSCF reference function. If in the MRCI step several states of the same symmetry are computed simultaneously using the STATE directive, the matrix elements are computed for all these states. Note that the OCC and CLOSED cards must be the same for all states used in a TRANLS calculation.

The selection rules for the $M_S$ values are $\Delta M_S = \pm 1$ for the LSX and LSY operators, and $\Delta M_S=0$ for the LSZ operator. Note that $2 M_S$ has to be specified, and so the selection rules applying to the difference of the input values are 0 or 2.

In all-electron SO calculations the value of the calculated spin-orbit matrix element is saved (in atomic units) in the MOLPRO variables TRLSX, TRLSY and TRLSZ for the $x$, $y$, and $z$ components respectively. For ECP-LS calculations the variables TRECPLSX, TRECPLSY, and TRECPLSZ are used. Note that for imaginary matrix elements (i.e., for the $x$ and $z$ components of the SO Hamiltonian) the matrix elements are imaginary and the stored real values have to be multiplied by $i$. If matrix elements for several states are computed, all values are stored in the respective variable-arrays with the bra-states running fastest.