Correlation tables between irreps for f orbitals

Question

I want to define occupied orbitals in terms of IRREPs for tungsten which has f orbitals. The highest possible point group for $\ce{WF2}$ in MOLPRO is $D_{2\mathrm h}$. Unfortunately, one can't write $\Phi_{u}$ as a direct sum of IRREPS in $D_{2\mathrm h}$. How can I solve this?

Answer 1

The simplest way to check the correlation between $f$-type basis functions in a high-symmetry point group (say $D_{\infty h}$) and in its Abelian subgroup (say $D_{2h}$) or any other subgroup is to compare their character tables from http://symmetry.jacobs-university.de/

$D_{\infty h}$ http://symmetry.jacobs-university.de/cgi-bin/group.cgi?group=1001&option=4

$D_{2h}$ http://symmetry.jacobs-university.de/cgi-bin/group.cgi?group=602&option=4

Here's how the correlation looks like for the 7 spherical $f$-type functions.

Correlation table

basis functions	$D_{2h}$	$D_{\infty h}$
$z^3$	$B_{1u}$	$\Sigma_u^+$
$xz^2$	$B_{3u}$	$\Pi_u$
$yz^2$	$B_{2u}$	$\Pi_u$
$y(3x^2-y^2)$	$B_{3u}$	$\Phi_u$
$x(x^2-3y^2)$	$B_{2u}$	$\Phi_u$
$xyz$	$A_u$	$\Delta_u$
$z(x^2-y^2)$	$B_{1u}$	$\Delta_u$

So, you can write $\Phi_u$ as $B_{2u} \bigoplus B_{3u}$