sign of spin orbit matrix elements?

millard alexander mha at mha-ibm4.umd.edu
Wed Jan 3 16:55:28 GMT 2001

```dear molpro users and molpro experts:

i am determining the spin-orbit matrix elements for an atom in a 2P
state (Aluminum).  when i calculate the matrix elements by hand,
i find that the <py | lx sx | pz-bar > matrix element is i*a/2, where a
is the spin-orbit constant, and, similarly, the
<pz |ly sy |px-bar> matrix element is i*a/2

when i run the following molpro input file

***,almrci
memory,1,m
file,1,al.i,scratch
file,3,al.wf,new

basis={spd,al,vdz}

ncalc=0
geometry={x,y;a1,al}
saveorb=3514.3

int;-;pri,-1
lsint
rhf;occ,5,1,1;wf,13,1,1;start,2410.3;save,2411.3;
!orbprint
multi;occ,6,2,2;closed,3,1,1;
wf,13,1,1;wf,13,2,1;wf,13,3,1
orbprint
natorb,,ci

e1A1mc(ncalc)=energy(1)
e2A1mc(ncalc)=energy(2)
e1B2mc(ncalc)=energy(3)
ci;occ,6,2,2;closed,3,1,1
wf,13,1,1;state,1
ref,2
ref,3
save,3164.1
e1A1ci(ncalc)=energy(1)
e1A1d(ncalc)=energd(1)
ci;occ,6,2,2;closed,3,1,1
wf,13,2,1;state,1
save,3174.1
ref,1
ref,3
e1B2ci(ncalc)=energy(1)
e1B2d(ncalc)=energd(1)
ci;occ,6,2,2;closed,3,1,1
wf,13,3,1;state,1
save,3184.1
ref,1
ref,2
e1B1ci(ncalc)=energy(1)
e1B1d(ncalc)=energd(1)
ci;tranls,3174.1,3184.1,1,1,lsz
set,lsz_xy,trlsz
ci;tranls,3184.1,3174.1,1,1,lsz
set,lsz_yx,trlsz
ci;tranls,3164.1,3174.1,1,-1,lsy
set,lsy_zxb,trlsy
ci;tranls,3174.1,3164.1,1,-1,lsy
set,lsy_xzb,trlsy
ci;tranls,3164.1,3184.1,1,-1,lsx
set,lsx_zyb,trlsx
ci;tranls,3184.1,3164.1,1,-1,lsx
set,lsx_yzb,trlsx
show,ls*
---

i get

LSZ_XY                 =         -.00013559
LSZ_YX                 =          .00013559
LSY_ZXB                =         -.00013559
LSY_XZB                =          .00013559
LSX_ZYB                =          .00013559
LSX_YZB                =         -.00013559

which corresponds to the opposite signs than i would predict
for the matrix elements of lxsx and lysy, but the correct
signs for the matrix elements of lzsz.

perhaps i am making an error?

any insight would be appreciated.

millard alexander

--
Millard Alexander, Distinguished University Professor
Department of Chemistry and Biochemistry
University of Maryland, College Park, MD 20742-2021
tel:  1.301.405.1823     fax:  1.301.314.9121
email:  mha at mha-ibm4.umd.edu
www:  http://www-mha.umd.edu/~mha

```