[molpro-user] 5d basis function definitions

[Papp Attila]

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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