13.3 Spin-orbit coupling

Spin-orbit splittings can be calculated by setting up (and diagonalizing) spin-orbit matrices between scalar-relativistic states. The latter have to be calculated and stored within CI calculations:


In all-electron calculations, one proceeds with the calculation of SO integrals


(For ECP calculation, this is not needed.)

Generating and processing of SO matrices is done with


where keyword3 is ls or ecp for all-electron or ECP calculations, respectively. If ls is given (recommended), epcs will be used for all atoms that hold ecps, and and all-electron treatment for the remaining atoms. If ecp is given, spin-orbit only includes the contributions of the ecps. Alternatively, one can also use AFLS (same as or AMFI) or ALS. ALS means that a one-center approximation is used for the excited configurations, but a full LS calculation is done in the internal configuration space. With AFLS|AMFI the once-center approximation is also used for the internal space.

An example input with ECPs is

{multi;wf,sym=2;wf,sym=3;wf,sym=5}  !2P states, state averaged
{ci;wf,sym=2;save,5101.2}           !2Px state
{ci;wf,sym=3;save,5102.2}           !2Py state
{ci;wf,sym=5;save,5103.2}           !2Pz state
{ci;hlsmat,ls,5101.2,5102.2,5103.2} !compute and diagonalize SO matrix

The corresponding input for an all-electron calculation is

{multi;wf,sym=2;wf,sym=3;wf,sym=5}  !2P states, state averaged
{lsint}                             !Compute spin-orbit 2-electron integrals
{ci;wf,sym=2;save,6101.2}           !2Px state
{ci;wf,sym=3;save,6102.2}           !2Py state
{ci;wf,sym=5;save,6103.2}           !2Pz state
{ci;hlsmat,ls,6101.2,6102.2,6103.2} !compute and diagonalize SO matrix

molpro@molpro.net 2018-11-18