A Hybrid Program for Fitting Rotationally Resolved Spectra of Floppy Molecules with One Large-Amplitude Rotatory Motion and One Large-Amplitude Oscillatory Motion

Abstract

A new hybrid-model fitting program for methylamine-like molecules has been developed, based on an effective Hamiltonian in which the ammonia-like inversion motion is treated using a tunneling formalism, while the internal-rotation motion is treated using an explicit kinetic energy operator and potential energy function. The Hamiltonian in the computer program is set up as a 2×2 partitioned matrix, where each diagonal block contains a traditional torsion-rotation Hamiltonian (as in the earlier program BELGI), and the two off-diagonal blocks contain tunneling terms. This hybrid formulation permits the use of the permutation-inversion group G6 (isomorphic to C3v) for terms in the two diagonal blocks, but requires G12 for terms in the off-diagonal blocks. The first application of the new program is to 2-methylmalonaldehyde. Microwave data for this molecule were previously fit using an all-tunneling Hamiltonian formalism to treat both large-amplitude-motions. For 2-methylmalonaldehyde, the hybrid program achieves the same quality of fit as was obtained with the all-tunneling program, but fits with the hybrid program eliminate a large discrepancy between internal rotation barriers in the OH and OD isotopologs of 2-methylmalonaldehyde that arose in fits with the all-tunneling program. This large isotopic shift in internal rotation barrier is thus almost certainly an artifact of the all-tunneling model. Other molecules for application of the hybrid program are mentioned.

The excited-state structure, vibrations, lifetimes, and nonradiative dynamics of jet-cooled 1-methylcytosine

“…Kleiner and Hougen have proposed an approach for solving 2D-coupled motions in systems with a methyl rotor and a double-minimum oscillatory motion such as ring inversion. 66 Whereas their approach is optimal for eigenvalues far below the barrier, 66 we need eigenvalues also above the butterfly barrier of ∼400 cm −1 . The problem is additionally complicated by the additional involvement of the NH 2 inversion mode because besides the up-down and up-up minima in Figure 9 there are also the down-up and down-down minima.…”

Cross-contamination of the fitting parameters in multidimensional tunneling treatments

“…Another method is presented in Ref. [12], where a hybrid formalism is described in which the internal rotation motion is treated using an explicit potential function, while the hypothetical pure hydrogen transfer motion is treated by a tunneling formalism. Fits to microwave transitions [2] using a computer program based on this formalism gave barrier heights of V 3 = 302.4 cm −1 and 315.4 cm −1 , respectively, for the -OH and -OD isotopologs.…”

“…The method of Ref. [12] thus reduces the discrepancy from its pure tunneling value [2] of 90 cm −1 to the significantly smaller value of 13 cm −1 .…”

Understanding (coupled) large amplitude motions: the interplay of microwave spectroscopy, spectral modeling, and quantum chemistry

“…A few models for complicated interactions arising in individual molecules have been also developed based on group theoretical approaches, e.g. studies on the rotatory-wagging coupled motions in 2-methylmalonaldehyde, a methylamine-like molecule, by Kleiner and Hougen using the hybrid model [25].…”