MOLPRO

40 SPIN-ORBIT-COUPLING 292
integrals. The default value for PREFAC is TWOINT/100, and the default value for TWOINT
is 10 −7 . In the case when no integrals are precomputed, these thresholds can be specified as
options for HLSMAT or TRANLS cards, see below.
The input for spin-orbit ECPs is described in section 12. Of course, in ECP-LS calculations the
LSINT card is not needed.
40.3 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
record2.file
bra2ms
ket2ms
lsop
Record holding the bra-wavefunction.
Record holding the ket-wavefunction. Both records must have been
generated using the SAVE directive of the MRCI program.
2 × M S value of the bra-wavefunction.
2 × M S value of the ket-wavefunction.
Cartesian component of the Spin-orbit Hamiltonian.
This can be one of LSX, LSY, or LSZ in all electron calculations, and
ECPLSX, ECPLSY, or ECPLSZ in ECP calculations. Starting from the
MOLPRO version 2008.1, more types are available which control the
approximation level. These are described in section 40.4.
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
20), 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 ∆M S = ±1 for the LSX and LSY operators, and ∆M S = 0
for the LSZ operator. Note that 2M 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.
40.4 Approximations used in calculating spin-orbit integrals and matrix elements
Recently, more sophisticated approximations were introduced to simplify spin-orbit calculations
for larger molecules. These are controlled by specifying the spin-orbit operator type lsop as
follows (we omit suffixes X, Y, Z which specify the component):