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.     

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.     

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.     

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.     

Sextic centrifugal distortion constants of axially symmetric molecules

Expressions in terms of molecular parameters are obtained for the sextic centrifugal distortion constants H_J, H_JK, H_KJ, and H_K of axially symmetric molecules. A numerical example for the NH₃ molecule is given which shows that the sextic distortion of NH₃ is normal. It is emphasized that the observed sextic distortion constants provide additional information on the cubic anharmonic potential coefficients.     

Microwave spectrum of propionitrile: Determination of the quartic and sextic centrifugal distortion constants

The ground state rotational spectrum of propionitrile has been reinvestigated between 8 and 250 GHz. A total of 218 transitions with J ≤ 48 and K ≤ 21 have been assigned. These data have been analyzed in terms of a reduced Hamiltonian similar to, but different from that proposed by Watson. All the determinable constants up to the sextic terms have been significantly determined. The rotational constants are (in MHz):

$\text{A}{}^{\mathrm{\prime }}\text{= 27 663.683, B}{}^{\mathrm{\prime }}\text{= 4714.187 8, and C}{}^{\mathrm{\prime }}\text{= 4235.085.2}$

     

Determination of the cubic force field of nitrosyl fluoride by vibration-rotation α constants and sextic centrifugal distortion constants

Summary The rotational spectra of ONF in the (100), (010) and (001) excited vibrational states were observed and the corresponding vibrationratation α constants determined. A centrifugal-distortion analysis of 156 ground-state rotational transitions yielded accurate values of all the sextic centrifugal-distortion constants. Both vibration-rotation α constants and sextic centrifugal-distortion constants were used to determine, by least-squares methods, the cubic part of the general valence force field of nitrosyl fluoride. Anab initio calculation provided reliable constraints for the three cubic terms of the potential-energy function which are not directly determinable by the available experimental data. Supporting organizations: C.N.R. and M.P.I.     

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 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.     

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.     

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.     

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.     

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.     

The microwave spectrum and centrifugal distortion constants of propiolic acid

The microwave spectra of propiolic acid and propiolic acid-d have been measured up to J = 30. These have enabled accurate evaluation of the rotational and centrifugal distortion constants for each species. The measured frequencies are presented, along with some predictions of transitions unmeasured in the present work, but of potential use in radioastronomy.     

The microwave spectrum and centrifugal distortion constants of vinyl fluoride

The rotational spectrum of vinyl fluoride up to J = 40 has been assigned and measured in the frequency region 8–37 GHz. Both a- and b-type transitions were observed. These measurements have been combined with those made in other frequency regions to calculate refined rotational constants and to obtain all quartic and some sextic centrifugal distortion constants. A comparison is made between the quartic centrifugal distortion constants measured here and those calculated from vibrational data.