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

Peterson, Kirk kipeters at wsu.edu
Fri Sep 13 17:54:44 BST 2013

Dear Gunter,

you could certainly try correlating the outer-core 2p electrons (and adding some extra tight p functions to the basis set). This should increase the splitting.  While Molpro can't actually do it,
it might be that the Gaunt interaction is needed for the most accurate result (check out the Dirac program).

best wishes,


On Sep 13, 2013, at 5:38 AM, Guenter Klatt <Guenter.Klatt at pci.uni-heidelberg.de> wrote:

> 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
> ---
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