The calculation of van der Waals vibrational and rotational states of atom-large molecule complexes, with Ar-fluorene as an example

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Abstract
We introduce a method to calculate the van der Waals vibrational and rotational states of complexes which consist of an atom bound to a large aspherical molecule. A hamiltonian is derived using a body fixed frame, the orientation of which is determined by the molecule only. The cartesian components of the vector which connects the atom with the centre of mass of the molecule, are used as vibrational coordinates. The van der Waals vibrational states are then obtained as a linear combination of harmonic oscillator product (LCHOP) functions. The rotational constants are calculated by second order van Vleck perturbation theory. The method is tested on Ar-fluorene. The uncertainties in the structures which are determined by a rigid molecular model for the rotational constants, are typically of the order of the vibrational amplitudes. For the ground state the latter are ≈ 0·3 Å for the motion of Ar along the fluorene plane and ≈ 0·1 Å for the motion of Ar perpendicular to the plane. At energies below 27 cm-1, the van der Waals states of this complex can be labelled with mode quantum numbers. At energies above 45 cm-1, we enter a chaotic region, which is characterized by a strong coupling between the modes.

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