[molpro-user] On phase convention

Apostolos Kalemos kalemos at chem.uoa.gr
Fri Feb 10 09:20:18 GMT 2012

Dear molpro authors,

A couple of simple questions that are of some importance when Spin-Orbit 
(SO) calculations are performed.

1. What is the phase convention in the definition of the spherical 
harmonics? Do the authors follow the same convention as e.g.
in Merzbacher's book,  (-1)^m.... 3rd ed. p. 248, eq. (11.78)? The 
entire SO matrix is given in the zeroth order basis set (cartesian 
If I want to transform some matrix elements back to the Omega basis set 
do I have to use the expressions |Lamda=+1> = - 1/sqrt(2) (x + iy) and 
|Lamda=+2> =1/sqrt(5) [(x^2-y^2) + 2ixy] ?

2. As you all know the Omega states come out doubly degenerate (+/-). 
These are linear combinations of the zeroth order basis set. Four some 
reasons some of the eigenvectors of the SO matrix
come out as linear combinations of these degenerate "+" and "-" |Omega| 
states that makes difficult (or even impossible) to put labels on my 
points and eventually to the entire potential curve.
Is there anything that I can do in order to get it correctly?

Thanks in advance
A. Kalemos

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