MOLPRO

40 SPIN-ORBIT-COUPLING 291
k,1.2,0.032828,0.231204;}
geometry={li;h,li,r}
int;
{hf;wf,4,1}
{multi
occ,4,0,0,0
closed,0,0,0,0
natorb,,ci,save=3500.2}
{multi;maxiter,20
vb}
optg
---
40 SPIN-ORBIT-COUPLING
40.1 Introduction
Spin-orbit matrix elements and eigenstates can be computed using either the Breit-Pauli (BP) operator
or spin-orbit pseudopotentials (ECPs). The state-interacting method is employed, which
means that the spin-orbit eigenstates are obtained by diagonalizing Ĥ el +Ĥ SO in a basis of eigenfunctions
of Ĥ el . The full Breit-Pauli SO-operator can be used only for MCSCF wavefunctions.
For MRCI wavefunctions, the full BP operator is used for computing the matrix elements between
internal configurations (no electrons in external orbitals), while for contributions of external
configurations a mean-field one-electron fock operator is employed. The error caused by
this approximation is usually smaller than 1 cm −1 .
The program allows either the computation of individual spin-orbit matrix elements for a given
pair of states, or the automatic setting-up and diagonalization of the whole matrix for a given
set of electronic states. In the latter case, matrix elements over one-electron operators are also
computed and transformed to the spin-orbit eigenstates (by default, the dipole matrix elements
are computed; other operators can be specified on the GEXPEC or EXPEC cards, see section
6.13). Since it may be often sufficient to compute the spin-orbit matrix elements in a smaller
basis than the energies, it is possible to replace the energy eigenvalues by precomputed values,
which are passed to the spin-orbit program by the MOLPRO variable HLSDIAG.
40.2 Calculation of SO integrals
The one-and two-electron spin-orbit integrals over the BP Hamiltonian can be precomputed and
stored on disk using the command
LSINT [,X] [,Y] [,Z] [,ONECENTER] [;TWOINT,twoint;] [;PREFAC,prefac;]
X, Y, and Z specify the components to be computed. If none of these is given, all three are evaluated.
The advantage of precomputing the integrals is that they can then be used in any number
of subsequent SO calculations, but this may require a large amount of disk space (note that there
are 6 times as many integrals as in an energy calculation). If the LSINT card is not given, the
integrals are computed whenever needed. The keyword ONECENTER activates the one-center
approximation for one- and two- electron spin-orbit integrals. This can reduce drastically the
computing time for large molecules. TWOINT and PREFAC can be used to control the accuracy
of spin-orbit integrals. These thresholds are similar to TWOINT and PREFAC for standard