44.4 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):

`LS`- Standard spin-orbit calculations.
`ALS`- The one-center approximation is used for one- and two-electron spin-orbit integrals.
`FLS`- The effective Fock-matrix approximation is used for the internal part too.
`AFLS|AMFI`- The one-center approximation is used for one- and two-electron spin-orbit integrals, and the effective Fock-matrix approximation for the internal part.
`ECPLS`- Effective core potentials are used for all atoms at which they are defined; contributions of all other atoms are neglected (see below).

In case that the effective Fock matrix is used for all contributions, and no spin-orbit
integrals are pre-calculated and stored on disk (i.e., the `LSINT` command is not given), the Fock
matrices are evaluated in direct mode and no integrals are stored on disk. When this is
combined with the one-center approximation (AMFI), the computing and I/O times are drastically reduced,
and this makes spin-orbit calculations quite fast even for larger molecules.

Also, the treatment of ECP-type of spin-orbit interaction has been changed and now
allows for treating both ECP and non-ECP atoms in one calculation. Thus,
in molecules containing both heavy and light atoms, the
heavy atoms can be described using ECPs and the light atoms using all-electron basis sets.
If the operator type is `LS`, `ALS`, `FLS`, or `AFLS`, then for the atoms having an
ECP spin-orbit operator defined in the basis input the ECP operator is used, while the full
BP-operator is used for all other atoms (couplings are neglected). Both one-center and AMFI approximations can be used in this case.
If, on the other hand, one specifies
the operator type as `ECPLS`, then the behavior is the same as in the
previous versions, i.e., only the ECP contributions are considered and the contributions from
all other atoms are neglected.

molpro@molpro.net 2019-01-15