Analysis of the microwave spectrum of hydrazine

Microwave measurements in the interval from 6 to 133 GHz, consisting of 444 rotational transitions in the vibrational ground state of hydrazine with J ≤ 31 and K_a ≤ 6 were fit to an effective rotational Hamiltonian containing 9 asymmetric rotor constants, 14 NH₂ inversion parameters, and 1 internal rotation parameter, with an overall standard deviation of the fit of 0.40 MHz. This set of parameters contains: (i) the three rotational constants; (ii) tunneling splitting constants for NH₂ inversion at one end of the molecule, for NH₂ inversion at both ends of the molecule, and for internal rotation through the trans barrier; (iii) two K-type doubling constants affecting the K = 1 levels; (iv) an a-type Coriolis interaction with matrix elements linear in K; and (v) various centrifugal distortion corrections to the above parameters. A consistent group theoretical formalism was used to label the energy levels and to select terms in the phenomenological rotational Hamiltonian. The Hamiltonian matrix, which is set up in a tunneling basis set, is of dimension 16×16 and contains only ΔK_a = 0 matrix elements, asymmetric rotor effects being taken into account on the diagonal by terms from a Polo expansion in bⁿ. Hyperfine splittings and barrier heights are not discussed.     

Microwave spectra of dimethylsulfide-d6, (CD3)2S,ground and excited torsional states

The microwave spectra of the molecular isotope (CD₃)₂S in the ground state and the first and second excited states of methyl top torsion (internal rotation) and of CSC deformation as well as the ground-state spectra of the ¹³C and ³⁴S substituted forms have been measured. The rotational constants and centrifugal distortion and rotation-vibration interaction constants could be determined. The rotational lines in the excited torsional states (1₁, 1₂, 2₁, 2₂, 2₃) were found to be split into quartets due to the interaction between molecular rotation and methyl top internal rotation. The experimental multiplet splittings were fitted to those calculated from a rotation-internal rotation Hamiltonian in order to obtain values for the internal rotation barrier V₃ and the top-top interaction potential coefficients V₁₂ and V′₁₂. V₁₂ was too highly correlated with V₃ for a separate determination. The values following from the least-squares adjustment are discussed.     

A rotational Hamiltonian for the ground vibrational state of hydrazine

A Hamiltonian matrix suitable for fitting rotational energy levels of the hydrazine molecule in its ground vibrational and electronic states was obtained. This matrix is of dimension 16 × 16, where the 16 functions labeling the rows and columns consist of the two members of a near-prolate asymmetric rotor doublet (with given | K_a |) for the eight different, but chemically equivalent, conformers which the molecule can reach by various combinations of -NH₂ inversion at either end of the molecule, and internal rotation about the NN bond. The matrix is derived in a phenomenological fashion, by applying group theoretical arguments to a model in which tunneling among the various frameworks is assumed to be very slow compared with the vibrational frequencies. A comprehensive treatment of the large-amplitude vibrational potential surfaces and associated tunneling pathways has not been carried out, nor have quartic (J⁴) centrifugal distortion effects been considered in a systematic fashion. Preliminary fits indicate that the model developed can be used to fit the hydrazine microwave data in a consistent fashion, and a full treatment of such data has been undertaken.     

A reduced form of the spin-spin centrifugal distortion Hamiltonian for orthorhombic asymmetric top molecules

The spin-spin centrifugal distortion Hamiltonian for an asymmetric top molecule in a given vibrational level of an open-shell electronic state with S ? 1 may contain more parameters than can be determined from the observed energy levels. This paper describes the reduction of the Hamiltonian by means of a unitary transformation to a form suitable for fitting to observed energies. It is established that there are six determinable spin-spin centrifugal distortion parameters for a molecule of orthorhombic symmetry; the corresponding matrix elements are derived for both Hund’s case (a) and case (b) coupling schemes.     

Correlation diagrams for quasi-symmetric top molecules with a single rotor

The rotation-bending-internal rotation Hamiltonian for quasi-symmetric top molecules with a single rotor [A. Wierzbicki, J. Koput, and M. Kr?glewski, J. Mol. Spectrosc.99, 102–115 (1983)] is used to calculate the correlation diagrams between the energy levels of the SiH₃NCO-type molecules in the symmetric and asymmetric top limits, and to predict various features of the microwave spectrum through trial calculations. The height of the barrier to linearity was varied from 0 to 6500 cm^?1. For the barriers 0, 31, and 139 cm^?1, the effects of hindered internal rotation are studied and several (Δl = 3, Δk = 0) resonances are found. In some cases almost all the microwave transitions from a given vibrational state can be perturbed.     

Microwave spectrum of dimethylallene : Centrifugal distortion analysis

The rotational absorption lines of the molecule dimethylallene in the vibrational ground state deviate from a rigid rotor pattern by shifts due to centrifugal distortion and by shifts and splittings due to methyl top internal rotation. By enlarging the number of previously measured lines it has been possible to apply successfully a Watson-type centrifugal distortion formula and to analyze the resulting “effective rigid rotor” rotational constants for the remaining contributions due to internal rotation and centrifugal distortion. Care has been taken to calculate or at least estimate the separate contributions and compare their magnitudes.     

Vibration-rotation interaction in HCNO caused by accidental resonances and enhanced by the quasilinearity of the molecule

The recent assignment of the vibrational spectrum of the quasilinear molecule HCNO revealed several near coincidences between vibrational energy levels involving the two bending modes, ν₄ (skeletal bending mode) and ν₅ (HCN-bending mode), and the lowest-lying stretching mode, ν₃ (NO stretching mode). By considering the correlation between the energy levels of a linear and a bent molecular model of HCNO, it is seen that resonance interactions which would be of third or higher order in a linear molecule Hamiltonian would be of first or second order in the Hamiltonian of a bent molecule, and thus might be significant in the quasilinear molecule HCNO. In this way we were able to identify the type of observed interaction occurring between three pairs of nearly coincident levels, (00010, 00002), (00020, 00012), and (00100, 00004). Anomalous centrifugal distortion effects had been observed and reported earlier for the pure rotational transitions arising from molecules in the 00010, 00020, and 00002 levels. Rotational transitions arising from molecules in the 00004 and 00100 vibrational states of HCNO and the 00100 state of DCNO are reported here for the first time. For two pairs of levels, (00010, 00002) and (00100, 00004), we could determine the magnitude of the coefficients of the interaction matrix elements from an analysis of the centrifugal distortion effects.     

The effects of vibration-rotation interaction on the quadrupole hyperfine structure of molecular rotational levels

By using a contact transformation method similar to that commonly employed when determining higher-order corrections to the harmonic oscillator and rigid rotor energy levels of molecules, analogous centrifugal distortion and anharmonic corrections to the nuclear quadrupole coupling energies have been obtained for molecules containing one quadrupolar nucleus. The J, K dependence and v, l dependence of these higher-order corrections to the quadrupole hyperfine energies can be cast in a form which is remarkably similar to the form taken for ordinary vibrational and rotational energy corrections, a result which was not evident from earlier partial treatments of this general problem. Results are obtained here for asymmetric top, symmetric top, spherical top, and linear molecules.     

Vibration-rotation Hamiltonian for asymmetric Cs molecules adapted to very strong Coriolis resonance : Application to the microwave reinvestigations of the ν7 and ν9 states of HCOOH and DCOOH

Formic acid is a C_s asymmetric top molecule exhibiting an exceptionally strong Coriolis resonance between its ν₇ and ν₉ vibrational states. The usual molecular model composed of two Watson Hamiltonians coupled by linear and quadratic vibration-rotation coupling terms does not allow satisfactory interpretations of such rotational spectra by microwave spectroscopy. In this case, it is necessary to perform a more complete development of the vibration-rotation coupling part of the standard Hamiltonian operator. The first part of this paper gives details of these developments, yielding a new molecular model adapted to very strong Coriolis resonance for C_s asymmetric top molecules. This new model consists of two Watson Hamiltonians developed up to the sextic centrifugal distortion coefficients and linked by 10 coupling constants. In the second part of this paper, this model has been successfully tested on H¹²COOH and D¹²COOH. From careful microwave reinvestigations of the ν₇ and ν₉ states of these two molecules, numerous new important rotational lines of various μ_b type and intervibrational transitions of μ_c type have been assigned. Various tests are performed to estimate the quality of the results. A critical discussion of the numerical investigation revealed the limits of the new molecular model proposed for strong Coriolis resonance.     

Microwave spectroscopy of furfural in vibrationally excited states

The results of microwave spectrum investigation of the excited vibrational states of furfural in the frequency range between 49 and 149 GHz are reported. In total 15 excited vibrational states (9 for trans-furfural and 6 for cis-furfural) were assigned and analyzed. Six of the 15 investigated states were assigned for the first time. Accurate values of rigid rotor and quartic centrifugal distortion constants of asymmetric top Hamiltonian have been determined for 13 excited states. Also for some states several sextic and octic level constants were needed in order to fit the data within experimental accuracy. The v_t = 3 and v_s = 1, v_a = 1 states of trans-furfural were found to be strongly perturbed and only rotational transitions with low K_a values can be reliably identified in this study.     

The rotational a-type sepctra of 15N-labeled diazirine,H2CN2

The rotational a-type spectra of isotopically enriched diazirine isotopomers, H₂¹²C¹⁴N¹⁵N and H₂¹²C¹⁵N₂, have been recorded in the region between 8 and 300 GHZ; the latter isotopomer has been observed for the first time. Using Watson's A-reduced Hamiltonian, the rotational constants and the quartic and some sextic centrifugal distortion constants have been determined for the ground vibrational states.     

Characteristic patterns in microwave spectra of quasi-symmetric top molecules of the WH3XYZ type

Characteristic patterns in microwave spectra of quasi-symmetric top molecules of the WH₃XYZ type are discussed in terms of the quasi-symmetric top model accounting for the large-amplitude WXY bending motion, and internal and overall rotation. The molecules SiH₃NCS, SiH₃NCO, CH₃NCS, CH₃NCO, and CH₃SCN, exemplifying the symmetric, quasi-symmetric, and asymmetric top molecules, are considered. The correlation parameter γ_v is defined to quantify the position of a WH₃XYZ molecule between the two symmetric and asymmetric top limiting cases. The quasi-symmetric top model is compared to the usual approach to the rotational-vibrational problem of symmetric top molecules.     

Analysis and fit of the Fourier-transform microwave spectrum of the two-top molecule N-methylacetamide

The jet-cooled Fourier-transform microwave spectrum of N-methylacetamide (CH₃NHC(O)CH₃), a molecule containing two methyl tops with relatively low barriers to internal rotation, has been recorded and fit to nearly experimental uncertainty. Measurements were carried out between 10 and 26 GHz, with the nitrogen quadrupole splittings resolved for many transitions. The permutation-inversion group for this molecule is G₁₈ (not isomorphic to any point group), with irreducible representations A₁, A₂, E₁, E₂, E₃, and E₄. One of these symmetry species and the usual three asymmetric rotor quantum numbers J_KaKc were assigned to each torsion-rotation level involved in the observed transitions. F values were assigned to hyperfine components, where . Transitions involving levels of A₁ and A₂ species could be fit to an asymmetric rotor Hamiltonian. The other transitions were first fit separately for each symmetry species using a Pickett-like effective rotational Hamiltonian. Constants from these fits show a number of additive properties which can be correlated with sums and differences of effects involving the two tops. A final global fit to 48 molecular parameters for 839 hyperfine components of 216 torsion-rotation transitions involving 152 torsion-rotation levels was carried out using a newly written two-top computer program, giving a root-mean-square deviation of observed-minus-calculated residuals of 4 kHz. This program was written in the principal axis system of the molecule and uses a free-rotor basis set for each top, a symmetric-top basis set for the rotational functions, and a single-step diagonalization procedure. Such an approach requires quite long computation times, but it is much less prone to subtle programming errors (a consideration felt to be important since checking the new program against precise fits of low-barrier two-top molecules in the literature was not possible). The two internal rotation angles in this molecule correspond to the Ramachandran angles ψ and φ often defined to describe polypeptide folding. Barriers to internal rotation about these two angles were found to be 73 and 79 cm⁻¹, respectively. Top-top coupling in both the kinetic and potential energy part of the Hamiltonian is relatively small in this molecule.     

Forbidden rotational spectra of axially symmetric polar molecules

In this paper we consider the rotational transitions induced by centrifugal distortion in polar or quasipolar symmetric top molecules belonging to the point groups C_n and C_nv (n ≥ 3). It is shown that in this series only the molecules of point groups C₃, C_3v, C₄, and C_4v may possess rotational spectra induced by first-order centrifugal distortion. A general expression is given for the effective dipole moment operator and for its matrix elements. The peak absorption coefficients for some of the strongest ΔK = 3 transitions of the CH₃D molecule have been calculated and compared with the peak absorption coefficients of allowed transitions.     

Millimeterwave rotational spectrum and internal rotation in o-chlorotoluene

The millimeterwave rotational spectrum of o-chlorotoluene is investigated in the frequency region 150-250 GHz. Many rotational lines show splitting due to internal rotation of the methyl group. The analysis of the internal rotation splitting allows us to determine with precision the potential barrier to internal rotation of the methyl group. However, it is found that the moment of inertia of the methyl top is probably much smaller than usually assumed, which significantly affects the value of the barrier. Accurate centrifugal distortion constants are obtained for the ground states of ³⁵Cl and ³⁷Cl isotopologues as well as for an excited vibrational state.     

On the determination of the reduced rotational operator for polyatomic molecules

Irreducible tensorial sets are used for constructing the reduced rotational Hamiltonian of the molecule, i.e., for obtaining the Hamiltonian with independent rotational, centrifugal distortion, and resonance parameters. General formulas are obtained which allow one to do this, and are valid for molecules of any symmetry. As an illustration of the general results, molecules of T_d symmetry are considered.     

The microwave spectrum of cis-2-pentene

The microwave spectrum of cis-2-pentene has been shown to originate from molecules in the skew-conformation (dihedral angle φ = 119 ± 3°). From A-E doublet splittings the barrier to internal rotation about the C₁C₂ axis was found to be 280 ± 4 cm^?1; furthermore the dipole moment components and centrifugal distortion constants are reported. In excited states of the C₃C₄ torsion the spectra exhibit further splittings; these are due to tunneling between the two equivalent skew-conformations through a barrier of 210 ± 20 cm^?1.     

The large-amplitude motions in quasi-symmetric top molecules with internal C3v rotors: The vibration-torsion-rotation Hamiltonian of a two-top molecule

An expression for the vibration-torsion-rotation Hamiltonian of a molecule with triatomic nonrigid frame and two internal C_3v rotors has been derived. Three large-amplitude motions, namely skeletal bending and two torsions, are removed from the vibrational problem and are considered together with the rotational problem. The Hamiltonian obtained is applicable to any two-C_3v-top molecule with triatomic linear or bent frame. The zeroth-order skeletal bending-torsion-rotation Hamiltonian is derived and the method of solving the corresponding Schrödinger equation is discussed. The Hamiltonian obtained with only slight modifications is shown to be applicable to any single-C_3v-top molecule with a quasi-linear tetratomic nonrigid frame or to the problem of the large-amplitude bending motion in a pentatomic quasi-linear molecule.     

Analysis of Coriolis perturbations in the high-resolution infrared spectra of arsine (AsH3)

Numerical methods for the analysis of high-resolution infrared spectra of symmetric top molecules perturbed by Coriolis interactions between degenerate and nondegenerate vibrational levels are discussed in the second order of approximation. Application to the high-resolution infrared spectra of the AsH₃ molecule in the region of the fundamentals ν₁, ν₃ and ν₂, ν₄ yields considerably improved values of the molecular constants of AsH₃, including the band origins rotational constants, Coriolis coupling constants, centrifugal distortion constants, and the parameter of the K-type doubling effect.     

The microwave spectra of ortho-fluorotoluene with the asymmetric internal rotors CH2D and CD2H

The rotational spectra of αd₁- and αd₂-ortho-fluorotoluene in the ground state of the methyl group torsion have been measured. The evaluation of the spectra has been based on the theory for the internal rotation of an asymmetric internal top formulated earlier by several authors. The barrier potential being threefold symmetric (V₃), each torsional level consists of three nondegenerate substates, designated as sy and ±asy. The sy-state is assigned to the conformation with the unique methyl hydrogen isotope within the molecular heavy-atom plane (sy-rotamer), while the ±asy-states belong to the respective out-of-plane conformation (asy-rotamer). In the torsional ground state the level spacing between the ±asy substates is very small and numerous accidental close degeneracies are present between the rotational level systems based on these torsional substates. The rotational levels involved are strongly perturbed by the coupling between molecular overall rotation and internal rotation. Large deviations from a rigid rotor spectrum and (+) ? (?) intersystem (“tunneling”) transitions are observed. The spectrum of the asy-rotamer can be well reproduced by a “two-dimensional” Hamiltonian containing 11 “rotational constants,” 9 of which are determined by a fit to the spectrum. Several are sufficiently barrier-dependent to derive V₃. We obtain (in cal/mole) 567 ± 48 for αd₁-ortho-fluorotoluene, 711 ± 40 for the αd₂-isotope. The deviations from 649 cal/mole for the normal isotope are appreciable, probably indicating shortcomings of the semirigid model. The sy-rotamer presents a rigid rotor spectrum.