I have been learning some basics of molpro and quantum chemistry, however I am deeply confused now.
As a very simple example, I want to compute the energy of a carbon atom using D2h group
For its ground state, if I give this input:
occ,2,1,1,0,0,0,0,0 closed,1,0,0,0,0,0,0,0 wf,6,4,2
The reason why I used this input is that I want to compute a specific electron configuration which has one alpha electron in the 2px orbital and the other alpha electron in 2py
And my understanding for this input text is that:
2 Ag irreps (for 1s and 2s orbital) and 1 B3u (for 2px) and 1 B2u(for 2py), then the total symetry is B3u*B2u=B3g which coresponds to the number 4 in my WF input, both electrons are spin-up so S=2 for WF input
Is this the correct way to do it? Following this thought I changed my input to
occ,2,0,1,0,1,0,0,0 closed,1,0,0,0,0,0,0,0 wf,6,7,2
occ,2,1,0,0,1,0,0,0 closed,1,0,0,0,0,0,0,0 wf,6,6,2
for the configuration where the 2 aplha electrons are in 2py+2pz and 2px+2pz orbitals.
These 3 inputs actually returned me exactly the same energy which makes sense to me if I think in the way that B1g B2g and B3g should be the same for a single atom because it doesn't matter how I pick my x y and z for a sphere.
However then i tried have those 2 electrons paird in just one orbitals, then there will be 3 possible configurations which are just a pair of electrons in one of the three p orbitals. Here I am confused, beacuse if I think like that there is no difference which axis I should call it as my z axis (as in there is no difference of x y and z axis in the case of an atom) then then the px/pz/pz should give me the same value of energy, which it is the case what molpro tells me, but when we write out the term symbol shouldn't that be like when the electrons are both in px or py orbital then the term is 1D, and when the electrons are both in pz then it is a 1S term? According to the energy level of carbon, 1D and 1S should not be have the same energy, so there is a conflict obviously, what did I miss here? I am pretty sure that I was not using the software in a correct way, but what should be the rigorous way of specifying a electron configuration in molpro?