Cross-contamination of the fitting parameters in multidimensional tunneling treatments.

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.

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

A new hybrid-model fitting program for methylamine-like molecules has been developed, on the basis of an effective Hamiltonian in which the ammonia-like inversion motion is treated using a tunneling formalism, whereas 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 C(3v)) 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.

A microwave study of hydrogen-transfer-triggered methyl-group rotation in 5-methyltropolone.

We present here the first experimental and theoretical study of the microwave spectrum of 5-methyltropolone, which can be visualized as a seven-membered "aromatic" carbon ring with a five-membered hydrogen-bonded cyclic structure at the top and a methyl group at the bottom. The molecule is known from earlier studies in the literature to exhibit two large-amplitude motions, an intramolecular hydrogen transfer and a methyl torsion. The former motion is particularly interesting because transfer of the hydrogen atom from the hydroxyl to the carbonyl group induces a tautomerization in the molecule, which then triggers a 60° internal rotation of the methyl group. Measurements were carried out by Fourier-transform microwave spectroscopy in the 8-24 GHz frequency range. Theoretical analysis was carried out using a tunneling-rotational Hamiltonian based on a G(12)(m) extended-group-theory formalism. Our global fit of 1015 transitions to 20 molecular parameters gave a root-mean-square deviation of 1.5 kHz. The tunneling splitting of the two J=0 levels arising from a hypothetical pure hydrogen-transfer motion is calculated to be 1310 MHz. The tunneling splitting of the two J=0 levels arising from a hypothetical pure methyl top internal-rotation motion is calculated to be 885 MHz. We have also carried out ab initio calculations, which support the structural parameters determined from our spectroscopic analysis and give estimates of the barriers to the two large-amplitude motions.

Direct spectral evidence of single-axis rotation and ortho-hydrogen-assisted nuclear spin conversion of CH3F in solid para-hydrogen.

Observation of two weak absorption lines from the E (K = 1) level and one intense feature from A (K = 0) for degenerate modes nu(4) and nu(6) of CH(3)F provides direct spectral evidence that CH(3)F isolated in p-H(2) rotates about only its symmetry axis, and not about the other two axes. An interaction between A and E vibrational levels caused by the partially hindered spinning rotation is proposed. Conversion of nuclear spin between A and E components of CH(3)F is rapid when p-H(2) contains some o-H(2), but becomes slow when the proportion of o-H(2) is much decreased.

Dynamical structure of peptide molecules.

In view of the importance of the peptide linkage in structural biology, we have carried out intensive investigations on peptide molecules consisting of a peptide linkage with one or two substituents in the gas phase by Fourier transform microwave spectroscopy, paying special attention to the internal rotation of the substituents relative to the central linkage framework. We have found that, in sharp contrast with the stiff structure around the central C-N bond of the linkage, the internal rotations of the substituents are of low frequency and thus of large amplitude and are extremely susceptible to their local environment such as the presence of other substituents.

Two-dimensional tunneling Hamiltonian treatment of the microwave spectrum of 2-methylmalonaldehyde.

The molecule 2-methylmalonaldehyde (2-MMA) exists in the gas phase as a six-membered hydrogen-bonded ring [HO-CH=C(CH(3))-CH=O] and exhibits two large-amplitude motions, an intramolecular hydrogen transfer and a methyl torsion. The former motion is interesting because the transfer of the hydrogen atom from the hydroxyl to the carbonyl group induces a tautomerization in the ring, i.e., HO-CH=C(CH(3))-CH=O-->O=CH-C(CH(3))=CH-OH, which then triggers a 60 degrees internal rotation of the methyl group attached to the ring. The microwave spectra of 2-MMA-d0, 2-MMA-d1, and 2-MMA-d3 were studied previously by Sanders [J. Mol. Spectrosc. 86, 27 (1981)], who used a rotating-axis-system program for two-level inversion problems to fit rotational transitions involving the nondegenerate A(+) and A(-) sublevels to several times their measurement uncertainty. A global fit could not be carried out at that time because no appropriate theory was available. In particular, observed-minus-calculated residuals for the E(+) and E(-) sublevels were sometimes as large as several megahertz. In the present work, we use a tunneling-rotational Hamiltonian based on a G(12) (m) group-theoretical formalism to carry out global fits of Sanders' 2-MMA-d0 and 2-MMA-d1 [DO-CH=C(CH(3))-CH=O] spectra nearly to measurement uncertainty, obtaining root-mean-square deviations of 0.12 and 0.10 MHz, respectively. The formalism used here was originally derived to treat the methylamine spectrum, but the interaction between hydrogen transfer and CH(3) torsion in 2-MMA is similar, from the viewpoint of molecular symmetry, to the interaction between CNH(2) inversion and CH(3) torsion in methylamine. These similarities are discussed in some detail.

Internal rotation and spin conversion of CH3OH in solid para-hydrogen.

The quantum solid para-hydrogen (p-H2) has recently proven useful in matrix isolation spectroscopy. Spectral lines of compounds embedded in this host are unusually narrow, and several species have been reported to rotate in p-H2. We found that a p-H2 matrix inhibits rotation of isolated methanol (CH3OH) but still allows internal rotation about the C-O bond, with splittings of the E/A torsional doublet in internal rotation-coupled vibrational modes that are qualitatively consistent with those for CH3OH in the gaseous phase. This simplified high-resolution spectrum further revealed the slow conversion of nuclear spin symmetry from species E to species A in the host matrix, offering potential insight into nuclear spin conversion in astrophysical sources.

Anomalous splittings of torsional sublevels induced by the aldehyde inversion motion in the S1 state of acetaldehyde.

The G6 group-theoretical high-barrier formalism developed previously for internally rotating and inverting CH3NHD is used to interpret the abnormal torsional splittings in the S1 state of acetaldehyde for levels 14(0-)15(0), 14(0-)15(1), and 14(0-)15(2), where 14(0-) denotes the upper inversion tunneling component of the aldehyde hydrogen and 15 denotes the methyl torsional vibration. This formalism, derived using an extended permutation-inversion group G6m, treats simultaneously methyl torsional tunneling, aldehyde-hydrogen inversion tunneling and overall rotation. Fits to the rotational states of the four pairs of inversion-torsion vibrational levels (14(0+)15(0A,E), 14(0-)15(0A,E)), (14(0+)15(1A,E), 14(0-)15(1A,E)), (14(0+)15(2A,E), 14(0-)15(2A,E)), and (14(0+)15(3A,E), 14(0-)15(3A,E)) are performed, giving root-mean-square deviations of 0.003, 0.004, 0.004, and 0.004 cm(-1), respectively, which are nearly equal to the experimental uncertainty of 0.003 cm(-1). For torsional levels lying near the top of the torsional barrier, this theoretical model, after including higher-order terms, provides satisfactory fits to the experimental data. The partially anomalous K-doublet structure of the S1 state, which deviates from that in a simple torsion-rotation molecule, is fitted using this formalism and is shown to arise from coupling of torsion and rotation motion with the aldehyde-hydrogen inversion.

Torsional Splittings in Small-Amplitude Vibrational Fundamental States of Methanol-Type Molecules.

Group-theoretical methods are used to show that inverted torsional splittings in fundamental levels of small-amplitude vibrations of methanol-like molecules can be parameterized and understood in terms of the energy level patterns induced when a pair of high-barrier torsionally split components of given v(t) and (t)A+(t)E symmetry species in the molecular symmetry group G(6) is allowed to interact with small-amplitude vibrational modes of symmetry (v)E. Such doubly degenerate (v)E vibrational modes arise rather naturally in G(6) (isomorphic with the point-group C(3v)) for those methyl-group vibrations in point-group-C(s) asymmetric tops such as CH(3)-CHO that are analogs of the degenerate methyl-group stretch, bend, and rocking vibrations in point-group-C(3v) symmetric tops such as CH(3)-C identical withC-H. The present group-theoretical treatment is somewhat different from, but (as a comparison of model parameters shows) still fundamentally similar to, the recent local mode explanation of inverted torsional splittings in the C-H stretching fundamental region in methanol. Copyright 2001 Academic Press.