## 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:

{ci;...;save,record1.file}
...
{ci;...;save,
recordn.file}

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

lsint

(For ECP calculation, this is not needed.)

Generating and processing of SO matrices is done with

{ci;hlsmat,keyword3,record1.file,..,recordn.file}

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

```***,Br
geometry={br}
basis=vtz-pp
{rhf;wf,sym=5}
{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

```***,Br
dkroll=1
geometry={br}
basis=vtz-dk
{rhf;wf,sym=5}
{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