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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?

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  • $\begingroup$ You can use a table, but I'm not sure if it will give you the optimal configuration for that highly complicated triatomic. I think you'll have to try several and then pick the one that gives you the best results (for example, lowest CISD energies). $\endgroup$ Commented Feb 13, 2022 at 14:21
  • $\begingroup$ Related: molpro.net/info/2015.1/doc/manual/node165.html $\endgroup$
    – Tyberius
    Commented Feb 13, 2022 at 16:06

1 Answer 1

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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 $B_{2u} \bigoplus B_{3u}$

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