Anisotropic contribution to the van der Waals and the Casimir-Polder energies for CO₂ and CH₄ molecules near surfaces and thin films

In order to understand why carbon dioxide (CO$_2$) and methane (CH$_4$) molecules interact differently with surfaces, we investigate the Casimir-Polder energy of a linearly polarizable CO$_2$ molecule and an isotropically polarizable CH$_4$ molecule in front of an atomically thin gold film and an amorphous silica slab. We quantitatively analyze how the anisotropy in the polarizability of the molecule influences the van der Waals contribution to the binding energy of the molecule.