Sextic centrifugal distortion constants of polyatomic molecules

Detailed expressions, in terms of fundamental molecular parameters, are given for the sextic centrifugal distortion constants for a general polyatomic molecule. The calculation of these expressions is based on the Watson molecular vibrational-rotational hamiltonian using third and fourth-order ordinary perturbation theory. Numerical examples are given for the H₂S, SO₂ and NH₃ molecules. The calculated and observed sextic constants for these molecules are in good agreement.     

Sextic centrifugal distortion constants of ozone

Theoretical expressions for the sextic centrifugal distortion constants of triangular triatomic molecules, as given by Sumberg and Parker, have been evaluated for the ozone molecule. For this calculation, the harmonic frequencies and cubic anharmonic potential constants determined by Barbe, Secroun, and Jouve were used. The calculated distortion constants were compared to complete sets of measured distortion constants recently determined by Maki, and by Barbe et al. Even though the measured constants range over more than four orders of magnitude, we find that the theory reproduces the relative magnitudes and the algebraic signs of the constants quite well. Absolute quantitative agreement is considerably better than order-of-magnitude.     

Calculated sextic centrifugal distortion constants of polyatomic molecules

By a perturbation treatment of the vibration-rotation Hamiltonian, expressions are derived for the sextic centrifugal distortion constants of a polyatomic molecule in terms of the basic molecular parameters. The calculation can be simplified by reordering the terms in the perturbation expansion. The theoretical expressions for the sextic distortion constants contain the cubic anharmonic potential constants, for which they are a possible source of information. The formulas are applied to molecules of various types of symmetry, and numerical results are computed for sulfur dioxide, ammonia and methane from published anharmonic force fields. The agreement with the observed distortion constants is good for SO₂ and reasonable for NH₃, but poor for CH₄. These results probably reflect the present state of knowledge of the cubic potentials of these three molecules.     

An approximation method for evaluating centrifugal distortion constants in XY2 bent symmetric nonhydride molecules

An approximation method is preser ted for an easier evaluation of centrifugal distortion constants τ_αβγδ in XY₂ bent symmetric ronhydride molecules, employing the known extremal properties of the intramolecular force constants. The formulas for τ_αβγδ thus obtained involve only atomic masses, geometry and normal vibrational frequencies of the molecule. The centrifugal distortion constants calculated under this approximation compare very well with experimental values obtained from the microwave spectrum.     

Calculation of centrifugal distortion constants for diatomic molecules from RKR potentials

Expressions are developed for computing the centrifugal distortion constants D_v, H_v, and L_v directly from the Rydberg-Klein-Rees rotationless potential of a diatomic molecule. These expressions involve summations over integrals of the wavefunctions of all neighboring vibrational levels. Application is made to the X¹Σ⁺ state of CO and the $\text{X}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state of O₂. In these applications, we have neglected the contributions of the continuum wavefunctions. For higher vibrational levels, particularly those near the dissociation limit, this approximation would be expected to fail. For the lowest vibrational levels of an electronic state, this method gives the same results for D_v, H_v, and L_v as the Dunham relations. However, for intermediate vibrational levels the present method is an improvement since expressions for only a few coefficients of the Dunham expansion are available. The use of D_v and H_v values calculated from Rydberg-Klein-Rees potentials in an iterative improvement of the reduction of spectroscopic data is described.     

Sextic centrifugal distortion constants: interplay of density functional and basis set for accurate yet feasible computations

Quantum-chemical calculations assist the analysis of laboratory spectra, and often provide the only means to determine spectroscopic data that cannot be accessed experimentally. Accurate predictions of vibrational and rotational spectroscopic parameters are required for applications in the field of high-resolution molecular spectroscopy. While the accuracy issue of the quantum-chemical calculation of vibrational properties and of equilibrium structures has been addressed in the literature, the same is not true for centrifugal distortion constants that however play an essential role for the interpretation of remote sensing data. In this work, the performance of several model chemistries, rooted mainly in density functional theory, in computing sextic centrifugal distortion constants is assessed employing a benchmark set of molecules of both atmospheric and astrochemical relevance. The Jensen’s (aug-)pcs-n basis sets, different flavours of Dunning’s triple-ζ basis sets and the SNSD basis set, are employed in conjunction with different functionals, and their predictions are benchmarked against experimental and theoretical data at the coupled cluster level of theory. This study also demonstrates the reliability of the calculation of sextic centrifugal distortion constants within the Gaussian16 rev. B.01 program package. Reliable predictions of the sextic centrifugal distortion constants for the gauche- and trans-conformers of ethyl-mercaptan are also presented.     

Parametric approach to centrifugal distortion constants: Application to bent symmetric XY2-type molecules

A method to generate all the mathematically possible values of the centrifugal distortion constants of a molecule compatible with its vibration frequencies is developed. Application of the method to the XY₂-bent symmetric-type molecules enables mapping of the τ_αβγδ constants as a function of a single parameter. The use of the method in defining the limits as well as in refining the experimental values of τ_αβγδ constants is discussed. The method also opens up a route to fix the force constants unambiguously employing the τ_αβγδ constants as additional data. The numerical example of SeO₂ molecule is given to illustrate the general procedure.     

Planarity relations for the sextic centrifugal distortion constants of triangular triatomic molecules

Four linearly independent linear combinations of the ten sextic centrifugal distortion coefficients of triangular triatomic molecules are presented. These combinations are formed in such a way that the resulting expressions depend only on the equilibrium geometry and the harmonic force field parameters of the molecule, quantities which are ordinarily known to considerably better precision than the sextic constants. The relations obtained thus constitute a set of planarity constraints on the ten sextic coefficients which arise in connection with the Nielsen-Amat expansion of the Darling-Dennison Hamiltonian. The planarity expressions can be utilized to effect a reduction of the sextic portion of the Hamiltonian.     

The centrifugal distortion constants of disulfur monoxide

The microwave spectrum of the molecular transient disulfur monoxide, S₂O, has been reexamined and the microwave measurements have been extended into the millimeterwave region. From the present data, the following ground-state rotational constants and quartic distortion constants have been obtained (MHz):

$\text{A = 41915.44,}\text{B = 5059.07,}\text{C = 4507.19}$

$\text{δ}{}_{\mathrm{J}}\text{= 1.895 X 10}{}^{\mathrm{?}}\text{, δ}{}_{\mathrm{JK}}\text{= ?3.192 X 10}{}^{\mathrm{?2}}\text{,}\text{δ}{}_{\mathrm{K}}\text{= 1.197 X 10}{}^0$

$\text{δ}{}_{\mathrm{J}}\text{= 3.453 X 10}{}^{\mathrm{?4}}\text{and δ}{}_{\mathrm{K}}\text{= 1.223 X 10}{}^{\mathrm{?2}}$

The centrifugal distortion constants obtained from the rotational spectrum are used to discuss the vibrational spectrum of disulfur monoxide.     

Recalculation of sextic centrifugal distortion constants of ozone

A complete set of sextic centrifugal distortion constants of ozone is calculated by evaluating the theoretical expressions developed by Sumberg and Parker, and also by evaluating the theoretical expressions developed by Aliev and Watson. Comparison with experimentally determined constants shows that similar and satisfactory agreement is obtained with either set of theoretical expressions. The set of calculated sextic constants previously published by Chan and Parker and based on the theoretical expressions of Sumberg and Parker is shown to contain an error. The source of the error is discussed.     

Microwave spectra and centrifugal distortion constants of oxetane

The microwave spectra of oxetane (trimethylene oxide) and its three symmetrically deuterated isotopic species have been observed on a Hewlett-Packard microwave spectrometer from 26.5 to 40 GHz. For the parent species, the β-d₂ and the αα′-d₄ species, about 300 lines have been assigned for each molecule, and for the d₆ species more than 600 lines have been assigned. The assignments range from v = 0 to v = 5 in the puckering vibration; although they are mostly Q transitions, either 3 or 4 R transitions have been observed for each vibrational state.The spectra have been interpreted using an effective rotational hamiltonian for each vibrational state, including five quartic distortion constants according to Watson's formulation, and a variable number of sextic distortion constants; in general, the lines are fitted to about ± 10 kHz. The distortion constants show an anomalous zig-zag dependence on the puckering vibrational quantum number, similar to that first observed for the rotational constants by Gwinn and coworkers. This is interpreted according to a simple modification of the standard theory of centrifugal distortion, involving the double minimum potential function in the puckering coordinate.     

The centrifugal distortion constant DK of symmetric top molecules

The centrifugal distortion constant D_K of a symmetric top molecule has proved a very elusive parameter to estimate by spectroscopic analysis. Values of D_K have been calculated for the molecules BF₃, SO₃, NH₃, PH₃, AsH₃, NF₃, PF₃, AsF₃, CH₃D, SiH₃D, GeH₃D, CH₃F, CH₃Cl, CH₃Br, CH₃I, CH_eCN, CH₃CCH, H₂C₃H₂, cyclo-C₃H₆, and isotopic modifications thereof, in terms of their quadratic force constants. In all cases the force constants used are reliably determined by existing spectroscopic data. Where direct comparison is possible, good agreement with experimental D_K values is found, and the calculated constants are considered reliable to ± 5%. The constants are intended to be of assistance in future spectroscopic and structural studies on the molecules listed. Structural applications to methyl iodide, silane, and cyclopropane are considered.     

A planarity relation for sextic centrifugal distortion constants

The relations between the molecular parameters of a planar molecule are used to derive a planarity relation for the sextic centrifugal distortion constants from the recently published expressions [Aliev and Watson, J. Mol. Spectrosc.61, 29 (1976)]. This relation, which contains only the rotational constants and the quartic and sextic distortion constants, is strictly valid only for the equilibrium constants, but will be useful as a constraint in the fitting of rotational energies if the experimental error is larger than the vibrational defect. The planarity relation is compared with the observed constants for the SO₂, O₃, NO₂, H₂O, and H₂S molecules. There appears to be a significant defect for SO₂ and for H₂O and its isotopes. The defect for SO₂ may be too large to be genuine, and possibly results from truncation of the Hamiltonian at the sextic terms.     

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.     

Upper and lower bounds of quartic centrifugal distortion constants

Expressions are obtained for the maximum and minimum possible values of the equilibrium centrifugal distortion constants τ_αβγδ for a molecule with given structure and vibrational frequencies. The method of calculation, based on Lagrangian multipliers, is also applied to the empirical centrifugal constants (such as D_J, D_JK, D_K, or Δ_J, Δ_JK, Δ_K, δ_J, δ_K) employed in fitting the rotational structure of spectra. These formulas make it possible to test whether a set of observed centrifugal constants is consistent with the rotational constants and vibrational frequencies. When inconsistencies arise, they are probably due to zero-point vibrational effects. By means of a second method employing inequalities, simpler formulas are derived for wider bounds. These are useful in calculating approximate values of the constants, as a preliminary to deciding which terms to include in the rotational Hamiltonian of any particular molecule.     

The centrifugal distortion constants for the molecule of thiane

The microwave spectrum of thiane has been studied in the 8- to 18-GHz region. Thirty five new rotational lines of the ground vibrational state with J up to 41 have been measured and assigned. These lines and a previous set reported by R. W. Kitchin, T. B. Malloy, Jr., and R. L. Cook [J. Mol. Spectrosc.57, 179–188 (1975)] have been used for the determination of the centrifugal distortion constants in Watson's model by means of a least-squares fitting method.