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Order of d,f,g orbitals

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Author Post
Member
Registered: Mar 2018
Posts: 2
Hi,

I'm trying to post-process the qchem data. I want to know the ordering of the d,f,g gaussian orbitals that's used within qchem, for both spherical and cartesian forms. For example, for the 6d orbitals, how the xx,xy,xz,yy,yz,zz ordered for the cartesian case. Likewise, how the "m" quantum numbers are ordered for the spherical case.

Thanks,
Bikash
Member
Registered: May 2016
Posts: 7
Hi Bikash,

To my knowledge (as of ~3 years ago, not sure if it has changed), it is different if you print in Molden format than regular Q-Chem format with print_orbitals=1.
In Q-Chem, the order is:
Spherical:
d(xy)
d(yz)
d(z2)
d(xz)
d(x2-y2)

f(y(3x2-z2))
f(xyz)
f(yz2)
f(z3)
f(xz2)
f(z(x2-y2))
f(x(x2-3y2))

g(xy(x2-y2))
g(zy3)
g(z2xy)
g(z3x)
g(z4)
g(z3y)
g(z2(x2-y2))
g(zx3)
g(x4+y4)

Cartesian:
d(x2)
d(xy)
d(y2)
d(xz)
d(yz)
d(z2)

f(x3)
f(x2y)
f(xy2)
f(y3)
f(x2z)
f(xyz)
f(y2z)
f(xz2)
f(yz2)
f(z3)

g(x4)
g(x3y)
g(x2y2)
g(xy3)
g(y4)
g(x3z)
g(x2yz)
g(y3z)
g(x2z2)
g(xyz2)
g(y2z2)
g(xz3)
g(yz3)
g(z4)

But if you choose to print in Molden format, here is the ordering:
Spherical:
d(z2)
d(xz)
d(yz)
d(x2-y2)
d(xy)

f(z3)
f(xz2)
f(yz2)
f(z(x2-y2))
f(xyz)
f(x(x2-3y2))
f(y(3x2-z2))

g(z4)
g(z3y)
g(z3x)
g(z2(x2-y2))
g(z2xy)
g(zx3)
g(zy3)
g(x4+y4)
g(xy(x2-y2))

Cartesian:
d(x2)
d(y2)
d(z2)
d(xy)
d(xz)
d(yz)

f(x3)
f(y3)
f(z3)
f(xy2)
f(x2y)
f(x2z)
f(xz2)
f(yz2)
f(y2z)
f(xyz)

g(x4)
g(y4)
g(z4)
g(x3y)
g(xy3)
g(xz3)
g(y3z)
g(xz3)
g(yz3)
g(x2y2)
g(x2z2)
g(x2yz)
g(y2z2)
g(xyz2)

All the best,
Samer
Member
Registered: Mar 2018
Posts: 2
Many thanks, Samer! I'll give the above ordering a try and see if things are consistent.

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