Missing state of nsnp ^3P

Dirac experts,

This is an old question that we meet when we work for Al+ by using the old version of MRCC.

For Al+, we find that one mj component of Al+ ³P₁ is missing. This calculation is implemented under C2v , which has two spatial symmetry i.e., symm=1, and 2. By using nsing=1 and ntrip=3, we obtain four roots for each symm, which can be assigned by referring to NIST data. One root is ns^{2 1}S₀ , and the other three roots are nsnp ³P.

In details,
symm=1:
root1--1S0, root2--37182.93 (³P₀), root3--37376.71 (³P₂), root4--37376.71(³P₂)

symm=2:
root1--1S0, root2--37247.25 (³P₁), root3--37376.71 (³P₂), root4--37376.71(³P₂)

For ³P₁, there should be two components mj=0 and mj=1. Therefore, the above results lack one mj component for ³P₁. We cannot find reason so far. Could you suggest us, thank you very mcuh!

Attached is fort.56 that we used. We find that the MINP file is of the same role with fort.56, therefore we use fort.56 to define our calculation directly.

fort.57.symm1:
1
1 1 7 6 1.0
1
1 1 8 6 1.0
1
1 1 9 6 1.0

fort.57.symm2
1
1 1 64 6 1.0
1
1 1 65 6 1.0
1
1 1 66 6 1.0



Best regards,

Yanmei

Dear Yanmei,
Even if you have a good initial guess, it is not guaranteed that the iterative procedure will converge to the desired roots.
The simplest solution is to use the brute-force trial vector generation, that is, to run CCS for, lets say, 50 roots, and then restart the CCSD, CCSDT, etc. calculation selecting the desired roots. See note 7 for the description of keyword rest in the manual. Even in this case it is not guaranteed that you get all Mj states.
But what is the application for which you need all the Mj states?

Dear Kallay,
Thank you for your suggestion. We will try.
For a state with nonzero j, we need all Mj component to give the the tensor/scalar polarizability of this state.
Best regards,
Yanmei

Dear Yanmei,
But what approach do you follow for the calculation of polarizabilities? I would simply calculate them by numerical differentiation wrt the electric field. Then you don't need all the Mj components.

Dear Kallay,
We follow your work [PRA 83, 030503 (2011)] and our work published in PRA 88, 052518 (2013).

I don't understand your say "you don't need all the Mj components". Under the electrio field, ^3P_1 state will break into mj=0 and mj=+/1 components. What we fit is the specific components. We need all the three components to give the polarizability of ^3P_1.

Best regards,

Yanmei