[molpro-user] 5d basis function definitions

[Will Glover]

Thanks for responding, but to clarify for the list archives, what you said below is not quite correct.  The correct correspondence, given by Peter is:
l=2,m=-2  xy
     m=-1  yz
     m=0   3z^2-r^2
     m=1   xz
     m=2   x^2-y^2

This can be confirmed by running a MolPro calculation on an atom with d-functions in D2h symmetry and seeing which d-function corresponds to which irreducible representation.

Thanks again,
-- 
Will

--- On Mon, 3/22/10, Papp Attila <pappati at phys.unideb.hu> wrote:

> From: Papp Attila <pappati at phys.unideb.hu>
> Subject: Re: [molpro-user] 5d basis function definitions
> To: molpro-user at molpro.net
> Date: Monday, March 22, 2010, 4:08 AM
> Quoting Will Glover <will_glover at yahoo.com>:
> 
> 
> Hi Will
> 
> The d type orbitals correspond to the spherical harminics
> with l=2. In  
> order to get real functions from this complex functions, we
> can use  
> linear combinations of them:
> 
> Y(m=-1)+Y(m=1)--> d1+ ( that is just the sum of the
> spherical  
> harmonics with |m|=1)
> 
> Y(m=-1)-Y(m=1)--> d1- ( that is just the differnce of
> the |m|=1 )
> 
> Y(m=-2)+Y(m=2)--> d2+ ( that is just the sum of the
> spherical  
> harmonics with m=|2|)
> 
> Y(m=-2)-Y(m=2)--> d2- ( that is just the differnce of
> the |m|=2 )
> 
> Y(m=0)--> d0 (It's already real)
> 
> This is the MOLPRO convention for the D orbitals.
> 
> Re your question:
> 
> d(zz) = d0
> d(yz)=d1+
> d(xz)=d1-
> d(xy)=d2-
> d(xx-yy)=d2+
> 
> You can find a more precise descripton about the real
> spherical harmonics:
> 
> http://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics_with_l_.3D_2
> 
> regards
> 
> ~Attila
> 
> 
> > Hi all,
> > Apologies if this is a trivial question - I searched
> the manual and   
> > web to no avail.  Could someone translate
> MolPro's 5d basis types:   
> > d0, d2-, d1+, d2+, d1- into dxy, dyz, dxz, dx2y2, dz2
> for me please?
> >
> > Many thanks,
> > --
> > Will
> >
> >
> >
> >
> > _______________________________________________
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> > Molpro-user at molpro.net
> > http://www.molpro.net/mailman/listinfo/molpro-user
> >
> 
> 
> 
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