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Date: Tue, 26 Feb 2008 10:05:26 -0500
To: nwchem-users@emsl.pnl.gov
From: JR Schmidt <jordan.schmidt@yale.edu>
Subject: Re: [NWCHEM] Spherical p-type orbitals
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Thank you for the replies.  Since the original question was a bit 
vague, let me clarify my motivation.

In particular, I am interested in looking at a singlet-D oxygen atom 
(as a part of a larger system).  For various reasons I explicitly 
need a single-reference method.  If I am not mistaken, the p-orbital 
configuration for singlet-D oxygen should look like (using the 
notation Yl,m for the spherical harmonics),

(Y1,-1)^2(Y1,0)^2 (or other degenerate combinations)

Thus, in principle it looks like one can create a 'reasonable' 
single-reference description of singlet-D oxygen using spherical 
harmonic basis functions.  However since Y1,0 = pz and Y1,-1 = px - i 
* py this state cannot be cannot be written in terms of px and py 
with purely real coefficients.

For completeness, you CAN get a good description of singlet-D oxygen 
(using real coefficients) with two references if you don't care about 
L_z, by adding up two degenerate singlet-D states with different L_z:

(Y1,-1)^2(Y1,0)^2 + (Y1,1)^2(Y1,0)^2 = [px^2pz^2] - [py^2pz^2]

If you do a CISD using the Cartesian basis functions, this is 
qualitatively what you get.

Unfortunately, it looks like my original question was a bit off the 
mark in that even the 'spherical' basis functions are not normal 
spherical harmonics, but solid harmonics (i.e. the combinations of 
Yl,m +/-Yl,-m that are taken to be purely real) and thus this WOULD 
give identical results with the Cartesian basis functions for the 
case of p-orbitals.  It looks like I would need to use a special 
purpose code capable of dealing with spherical harmonics to do what I 
am looking for.  (To reiterate, this is to be part of a larger 
system, thus making many of the workarounds that have been suggested 
untenable).

Thanks again for your replies,
JR Schmidt