Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Cross-contamination of the fitting parameters in multidimensional tunneling treatments

Published

Author(s)

Jon T. Hougen, Nobukimi Ohashi

Abstract

In this paper we examine the two-dimensional tunneling formalism used previously to fit the hydrogen-transfer and internal-rotation splittings in the microwave spectrum of 2 methylmalonaldehyde in an effort to determine the origin of various counterintuitive results concerning the isotopic dependence of the internal-rotation splittings in that molecule. We find that the cause of the problem lies in a “parameter contamination” phenomenon, where some of the numerical magnitude of splitting parameters from modes with large tunneling splittings “leaks into” the parameters of modes with smaller tunneling splittings. We show that such parameter contamination, which greatly complicates the determination of barrier heights from the least-squares-fitted splitting parameters, will be a general problem in spectral fits using the multi-dimensional tunneling formalism, since it arises from subtle mathematical features of the non-orthogonal framework functions used to set up the tunneling Hamiltonian. Transforming to a physically less intuitive orthonormal set of basis functions allows us to give an approximate numerical estimate of the contamination of tunneling parameters for 2- methylmalonaldehyde by combining a dominant tunneling path hypothesis with results recently given for the hydrogen-transfer--internal-rotation potential function for this molecule.
Citation
Journal of Molecular Spectroscopy
Volume
342

Keywords

large-amplitude motions, least-squares fits, multidimensional tunneling, parameter contamination, rotational levels, tunneling splittings large-amplitude motions, least-squares fits, multidimensional tunneling, parameter contamination, rotational levels, tunneling splittings large-amplitude motions, least-squares fits, multidimensional tunneling, parameter contamination, rotational levels, tunneling splittings large-amplitude motions, least-squares fits, multidimensional tunneling, parameter contamination, rotational levels, tunneling splittings large-amplitude motions, least-squares fits, multidimensional tunneling, parameter contamination, rotational levels, tunneling splittings

Citation

Hougen, J. and Ohashi, N. (2017), Cross-contamination of the fitting parameters in multidimensional tunneling treatments, Journal of Molecular Spectroscopy, [online], https://doi.org/10.1016/j.jms2017.04.015 (Accessed June 15, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created April 29, 2017, Updated November 10, 2018