Question about calculate transition electric field


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Dear all,

   I want to calculate transition electric field:
where b and a represent two electronic states, ρba(r) is the transition density.
   I modify the nwdft/lr_tddft/tddft_analysis.F, and I calculate H2O as an example.
But I read the code of calculating transition dipole moment as an example. I find in source file tddft_analysis.F, when ipol = 1 for closed shell molecule, the quantity should times dsqrt(2.0d0), not 2.0, for spin up and spin down.


1294 if (ipol.eq.1) then
1295 do i=1,20
1296 tmom(i)=tmom(i)*dsqrt(2.0d0)
1297 enddo


I think it should be an simple problem, but I still can not understand why should it be like:
1296 tmom(i)=tmom(i)*2.0d0
for two spin statistics.

Can any one give me an simple hint of this question?