Biomedical subjects

JT Hougen

Publications and source records attributed to JT Hougen.

5 recordsLinked to original sources

PubMed2000

Contact Transformations and Determinable Parameters in Spectroscopic Fitting Hamiltonians.

In recent least-squares fits of torsion-rotation spectra of acetaldehyde and methanol it was found possible to adjust more fourth-order parameters than would be expected from traditional contact-transformation considerations. To investigate this discrepancy between theory and practice we have carried out numerical fitting experiments on the simpler three-dimensional (three-Eulerian-angle) asymmetric rotor problem, using J </= 20 unitless energy levels generated artificially from a full orthorhombic Hamiltonian with quadratic through octic operators in the angular momentum components. Results are analyzed using the condition number kappa of the least-squares matrix, which is a measure of its invertibility in the presence of round-off and other errors. When kappa is very large, parameters must be removed from the fit until kappa becomes acceptably small, corresponding to procedures which lead to reduced Hamiltonians in molecular spectroscopy. We find that under certain circumstances kappa can be decreased to an acceptable level for Hamiltonians which are only partially reduced when compared to Watson A and S reductions. Some insight into this behavior is obtained from classical mechanics and from the concept of delayed contact transformations. Transferring this numerical and algebraic understanding to the more complicated four-dimensional methyl-top internal rotor problem supports the empirical observation that presently existing data sets for methanol and acetaldehyde are most efficiently fit using partially reduced Hamiltonians and further suggests that expanding the methanol data set to transitions involving levels of higher J, K, and v(t) would favor even more strongly the use of partially reduced fourth-order Hamiltonians.

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PubMed2000

Approximate Selection Rules for |K| = 1-0 and 1-1 Tunneling-Rotation Transitions in the Methanol Dimer.

Approximate K = 0 and |K| = 1 tunneling-rotation eigenfunctions for the four A, four E, and one G symmetry species present in the methanol dimer, derived from molecular parameters obtained previously from a least-squares fit to transition frequencies involving K = 0 and 1 levels, are used to clarify some apparent contradictions associated with traditional b- and c-type transition designations in the E and G tunneling-rotational states of this dimer. These approximate eigenfunctions also predict strong and weak line intensities which are consistent with the pattern of strong a-, b-, and c-type transitions observed, thus supporting our previous separate K-state analysis based only on energy level differences. Some of the predicted weaker |K| = 1 a-type transitions should be experimentally observable with more signal averaging. Copyright 2000 Academic Press.

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PubMed1999

Global Analysis of a-, b-, and c-Type Transitions Involving Tunneling Components of K = 0 and 1 States of the Methanol Dimer.

Spectral data on K = 0 and 1 levels of the methanol dimer available from previous and present Fourier transform microwave measurements have been interpreted globally, using a group-theoretically derived effective Hamiltonian and corresponding tunneling matrix elements to describe the splittings arising from a large number of tunneling motions. In the present work, 302 new measurements (40 K = 1-1 and 262 K = 1-0 transitions) were added to the previous data set to give a total of 584 assigned transitions with J </= 6. As a result of the rather complete K = 0, 1 data set for J </= 4, the lone-pair exchange tunneling splittings were obtained experimentally. Matrix element expansions in J(J + 1) used in the previous K = 0 formalism were modified to apply to K > 0, essentially by making a number of real coefficients complex, as required by the generalized internal-axis-method tunneling formalism. To reduce the number of adjustable parameters to an acceptable level in both the K = 0 and K = 1 effective Hamiltonians (used in separate K = 0 and K = 1 least-squares fits), a rather large number of assumptions concerning probably negligible parameters had to be made. The present fitting results should thus be considered as providing assurance of the group-theoretical line assignments as well as a nearly quantitative global interpretation of the tunneling splittings, even though they do not yet unambiguously determine the relative contributions from all 25 group-theoretically inequivalent tunneling motions in this complex, nor do they permit quantitative extrapolation to higher K levels. Copyright 1999 Academic Press.

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PubMed1999

Linestrengths of Torsion-Rotation Transitions of Methanol for J </= 22, K </= 14, and upsilont </= 2 from Hamiltonian-Based Calculations.

Linestrengths have been obtained for methanol based on matrix elements of the dipole moment operator evaluated in a set of torsion-rotation eigenfunctions. The latter were obtained from the parameters and effective Hamiltonian giving the best spectral fit available for a data set containing J </= 20, K </= 14, and upsilont </= 1 microwave and far infrared transitions. The dipole moment function was represented as a Fourier expansion in the torsional angle gamma. Values for the permanent components µa and µb were obtained from experiment; values for their cos 3gamma variation and for the sin 3gamma variation of µc were obtained from quantum chemistry molecular orbital calculations. The approach described allows calculation of the linestrength for any transition which satisfies the general selection rule A1 left and right arrow A2 or E left and right arrow E. A complete set of such linestrengths for all methanol torsion-rotation transitions involving levels with J </= 22, K </= 14, and upsilont </= 2, and with intensities and frequencies above the rather small cutoff limits of 10(-6) D2 and 1 kHz, respectively, together with individual contributions from the permanent and gamma-varying dipole moment components, have been tabulated and are available on request (ftp.monash.edu.au/pub/chem/1998a). Copyright 1999 Academic Press.

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PubMed1998

Some Properties and Uses of Torsional Overlap Integrals

The first diagonalization step in a rho-axis-method treatment of methyl-top internal rotation problems involves finding eigenvalues and eigenvectors of a torsional Hamiltonian, which depends on the rotational projection quantum number K as a parameter. Traditionally the torsional quantum number vt = 0, 1, 2···is assigned to eigenfunctions of given K in order of increasing energy. In this paper we propose an alternative labeling scheme, using the torsional quantum number vT, which is based on properties of the K-dependent torsional overlap integrals . In particular, the quantum number vT is assigned in such a way that torsional wavefunctions |vT, K> vary as slowly as possible when K changes by unity. Roughly speaking, vT = vt for torsional levels below the barrier, whereas vT is more closely related to the free-rotor quantum number for levels above the barrier. Because of the latter fact, we believe vT will in general be a physically more meaningful torsional quantum number for levels above the barrier. The usefulness of overlap integrals for qualitative prediction of torsion-rotation band intensities and for rationalizing the magnitudes of perturbations involving some excitation of the small-amplitude vibrations in an internal rotor problem is also discussed. Copyright 1998 Academic Press. Copyright 1998Academic Press

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