Rovibrational Molecular Hamiltonian in Mixed Bond-Angle and Umbrella-Like Coordinates

Abstract

A new exact quantum mechanical rovibrational Hamiltonian operator for molecules exhibiting large amplitude inversion and torsion motions is derived. The derivation is based on a division of a molecule into two parts: a frame and a top. The nuclei of the frame only are used to construct a molecular system of axes. The inversion motion of the frame is described in the umbrella-like coordinates, whereas the torsion motion of the top is described by the nonstandard torsion angle defined in terms of the nuclear vectors and one of the molecular axes. The internal coordinates chosen take into account the properties of the inversion and torsion motions. Vibrational s and rotational Omega vectors obtained for the introduced internal coordinates determine the rovibrational tensor G defined by simple scalar products of these vectors. The Jacobian of the transformation from the Cartesian to the internal coordinates considered and the G tensor specify the rovibrational Hamiltonian. As a result, the Hamiltonian for penta-atomic molecules like NH2OH with one inverter is presented and a complete set of the formulas necessary to write down the Hamiltonian of more complex molecules, like NH2NH2 with two inverters, is reported. The approach considered is essentially general and sufficiently simple, as demonstrated by derivation of a polyatomic molecule Hamiltonian in polyspherical coordinates, obtained by other methods with much greater efforts.

The structure of phenol-Arn (n=1,2) clusters in their S and S1 states

“…In addition, high-level quantum chemical calculations of the potential energy surface in the S 0 state yield a -bonded global minimum, and it is unclear at present whether the H-bonded structure is a shallow local minimum or a transition state. [17][18][19][20] Comparison of rotational constants derived from a rotational band contour fit of the S 1 origin spectrum with ab initio rotational constants obtained at the MP2 / 6-31G͑d , p͒ level also support a -bonded ͑1 ͉ 0͒ geometry for n =1. 21 Meerts et al 6 presented the fully rotationally resolved electronic spectrum of the 7D-phenol-Ar 1 cluster, without a detailed structural analysis.…”

Vibrational levels of formaldehyde: Calculations from new high precision potential energy surfaces and comparison with experimental band origins

“…The internal coordinates (I) and (II) are non-orthogonal sets while (III) is an orthogonal coordinate set. The kinetic energy operator of the nuclei (using the notation from ref [53]) in the laboratory frame r starts from the CH 1 H 2 center of mass. Figure 1 shows these three sets of the internal vectors.…”

An Optimized Algebraic Basis for Molecular Potentials

“…The substantial improvement of the variational accuracy of the bound-state spectra computed on a OGQNSB with respect to the unoptimized QNSB permits, in practice, calculations of a given accuracy on a significantly smaller basis size to be made. While this improvement is practically irrelevant to the solution of the one-dimensional vibrational problem of diatomics, it is of great importance for the application of this method to the calculation of the spectra based on the ab initio multidimensional potential surfaces of polyatomic molecules, as is currently pursued in quantum chemical research. − In particular, the OGQNSB approach can be incorporated easily into most present-day Morse-coordinate-based codes for computing vibrational spectra of polyatomic molecules. ,,− We are also currently developing a custom implementation of a generalization of the expansion in eq 1 to the polyatomic case, to be solved in a multidimensional OGQNSB.…”