Correlation tables between irreps for f orbitals

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?

• 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). Feb 13, 2022 at 14:21
• – Tyberius
Feb 13, 2022 at 16:06

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