[molpro-user] How to calculate accurate spin-orbit splitting in sodium

[Guenter Klatt]

Dear Molpro users,

I'm having a problem with the result of a simple test calculation on a sodium 
atom. From my understanding the 2P state of sodium is split by spin-orbit 
coupling, which leads to the famous Na doublet at 16,956 cm-1 and 16,973 
cm-1,
i.e. a splitting by 17 wavenumbers.

My test calculation for the Na atom at CASSCF/MRCI levels yields  splittings 
of only 11.8 cm-1 (CAS) and 10.3 cm-1 (MRCI), respectively. Could you please 
suggest ways of improving agreement with experiment? I have attached my input 
file below.

Thanks very much for any help,

Gunter Klatt, University of Heidelberg

***,SO calculation for the Na atom
geometry={na}
basis={spd,na,vtz}                                 !use uncontracted basis

{rhf;occ,3,1,1,,1;wf,11,1,1}                      !rhf for 2S state

{multi;occ,3,2,2,0,2                                  !casscf
frozen,0,0,0,0,0
closed,0,0,0,0,0                                            
wf,11,1,1;wf,11,2,1;wf,11,3,1;wf,11,5,1}        !2S and 2P states

{ci;wf,11,1,1;save,3042.1;noexc}                 !save casscf wavefunctions
{ci;wf,11,2,1;save,3062.1;noexc}
{ci;wf,11,3,1;save,3072.1;noexc}
{ci;wf,11,5,1;save,3082.1;noexc}

{ci;wf,11,1,1;save,4010.1}                  !mrci calculations for 2S state
{ci;wf,11,2,1;save,4042.1}                  !mrci calculations for 2P states
{ci;wf,11,3,1;save,4062.1}                  !mrci calculations for 2P states
{ci;wf,11,5,1;save,4082.1}                  !mrci calculations for 2P states

lsint                                                   !compute SO integrals

text,2P states, casscf
{ci;hlsmat,ls,3062.1,3072.1,3082.1;print,hls=2}   !Only 2P states, casscf

text,2P states, mrci
{ci;hlsmat,ls,4042.1,4062.1;print,hls=2}          !Only 2P states, mrci

text,2S, 2P states, casscf
{ci;hlsmat,ls,3042.1,3062.1,3072.1,3082.1;print,hls=2} !All states, casscf

text,2S, 2P states, mrci 
ci;hlsmat,ls,4010.1,4042.1,4062.1;print,hls=2} !All states, mrci
---