renormalizations of the polarization sets done by MOLPRO on the MOLDEN input file

[Dave Moore]

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Dear Sirs,

	I am trying to use the MOLDEN files created by MOLPRO for
visualization and manipulation of the molecular orbitals and
densities.  I am checking my program by using the CUBE functionality
of MOLPRO.  What I have found is that, as long as there are only s-
and p-type orbitals in the basis set, my program gives precisely the
same results as MOLPRO.  However, as soon as I add a polarization
set, the results are different.  In trying to track down this
discrepancy, I discovered (using orbprint) that the MO coefficients
in the MOLDEN file are not the same as those in the MOLPRO file. 
Since MOLDEN can only deal with cartesian (6D, 10F) polarization
functions, I thought that specifying CARTESIAN in the MOLPRO input
would fix this problem, but it doesn't ... the MO coefficients are
still different between the MOLPRO output file and the MOLDEN file
(the particulars are given below).
	Thus it seems that MOLPRO is expecting MOLDEN to use a different
normalization condition for its polarization sets, but I cannot find
documentation on it anywhere.  I would appreciate any details you can
offer about the renormalizations of the polarization sets done by
MOLPRO on the MOLDEN input file (for either the SPHERICAL or
CARTESIAN cases, or both).  There does not seem to be any information
about this in the MOLPRO manual or on the MOLDEN website.  Thank you
in advance for your assistance.

Dave Moore
Chemistry Dept.
UNC Chapel Hill


Specific discrepancies between MOLPRO and MOLDEN MO coeffients:

1)  When using the CARTESIAN keyword in MOLPRO, it seems logical to
me that the coefficients should not change at all between MOLPRO and
MOLDEN, since MOLDEN also uses the cartesian (6D, 10F) polarization
functions.  However this is not the case, MOLPRO divides the xx, yy
and zz coefficients by sqrt(27.0) or 3**(1.5), before writing them to
the MOLDEN file, while leaving the xy, xz and yz coefficients are
unchanged.  I have tried to figure out the origin of this
transformation without success (so far).  If both programs (MOLDEN
and MOLPRO) are using normalized Gaussian primitives for their d-type
basis functions, I do not understand how this can be correct.

2)  When using CARTESIAN polarization functions, the f-orbitals
coefficients are also changed between the MOLPRO and MOLDEN files. 
Coefficients for primitives with an axis repeated 3 times (e.g. xxx),
are divided by sqrt(3375.0) or 15**(1.5), and coefficients for
primitives with an axis repeated twice are divided by sqrt(27.0)
(same as for the d-orbitals).  Once again I do not understand the
origin of this term, if normalized gaussian primitives are being used
in both places.

3)  When SPHERICAL polarization functions are used in MOLPRO, there
are again some discrepancies between the coefficients in the MOLPRO
and MOLDEN files.  Of course here there must be some transformation
between the 5D representation used in MOLPRO and the 6D 
representation used in MOLDEN, but I do not understand how it is
determined.  I have not completely finished my analysis, but I have
figured out the following correlations between the coefficients in
the MOLPRO and MOLDEN files so far:

MOLPRO		MOLDEN
d0	-->		dzz*sqrt(27.0)
d1+   -->		dxz
d1-	-->		dyz
d2-	-->		dxy
d2+	-->		a1*dxx + a2*dyy, 
where a1 and a2 are coefficients I have not yet determined	

I do not understand these correlations, because the transforms I am
used to are (for example):
d1+ = a*dxz + a*dyz
d1- = a*dxz - a*dyz
where a is a normalization coefficient.
but instead MOLPRO seems to be using d1+=dxz and d1-=dyz, which could
certainly be correct, but is nonstandard (I think).  Finally, the
factor of 3**(1.5) on the dzz coefficient is again confusing.

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