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 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.     

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.     

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.     

用从头算方法研究GeCl2分子的非谐振力场和光谱常数

用从头算方法的MP2和CCSD（T）方法结合cc-pVTZ基组计算了二氯化锗同位素（⁷⁰GeCl₂、⁷²GeCl₂和⁷⁶GeCl₂）分子的平衡结构、光谱常数和非谐振力场.二氯化锗的几何结构、转动常数、振转相互作用常数、谐频、非谐振常数、四次和六次离心畸变常数、三次和四次力常数的计算结果与实验结果符合较好,二氯化锗分子的同位素效应较小,可能的原因是Ge同位素的质量变化相对较小.两种方法计算的结果均与实验结果符合,但CCSD（T）方法比MP2计算结果的偏差稍大一些,可能的原因是CCSD（T）方法在描述过共价Cl原子的电子相关时不够充分.     

Van Vleck transformation as an alternative to the contact transformation: Non-linear molecules off resonance

The projector formulation for the Van Vleck transformation has been applied to the Wilson-Howard Hamiltonian (i.e., the Hamiltonian for the vibration-rotation energy of rigid molecules). Formal expressions are obtained for γ and q constants, for the linear vibrational dependence of quartic and for the sextic centrifugal distortion constants.     

PO2自由基的光谱常数和非谐力场的理论研究

利用B3PW91、B3LYP和B3P86方法以及cc-pvQz和6-311++G(3df,3pd)基组计算了PO2自由基的光谱常数。先将计算的平衡几何结构、转动常数、谐频和基频、四次离心畸变常数和六次离心畸变常数与已有的相应实验或理论数据进行了比较。在此基础上,从理论上预测了非谐性常数、振转相互作用常数、科里奥利耦合常数、三次和四次力常数。计算结果表明,B3PW91/G理论水平得到的PO2自由基的光谱常数是可靠的。     

Classical and quantum oscillators of sextic and octic anharmonicities

Classical oscillators of sextic and octic anharmonicities are solved analytically up to the linear power of λ (anharmonic constant) by using Taylor series method. These solutions exhibit the presence of secular terms which are summed up for all orders. The frequency shifts of the oscillators for small anharmonic constants are obtained. It is found that the calculated shifts agree nicely with the available results to-date. The solutions for classical anharmonic oscillators are used to obtain the solutions corresponding to quantum anharmonic oscillators by imposing fundamental commutation relations between position and momentum operators.     

Sextic force field of nitrous oxide

The sextic force field in the curvilinear internal coordinates has been studied for the nitrous oxide molecule from the spectroscopic data of ¹⁴N₂¹⁶O, ¹⁴N¹⁵N¹⁶O, and ¹⁵N¹⁴N¹⁶O. The bands below 6600 cm⁻¹ have been used. The force constants in the internal coordinates are converted to those in dimensionless normal coordinates by two successive transformations. The vibration Hamiltonian matrix for each symmetry species of a given isotopic species has been constructed from the harmonic oscillator basis functions, and it is then diagonalized numerically to give the vibrational energy levels and the wavefunctions. The latter have been used for the evaluation of ratational constants. The least-squares refinement has been very successful in the present study, and it is shown that the general quartic force field supplemented by the quintic and sextic stretching diagonal force constants estimated from the Morse function, provided that the terms up to sextic are kept in the dimensionless normal coordinate space, well reproduces the spectroscopic constants such as the vibrational levels, rotational constants, l-type doubling constants, and centrifugal distortion constants. The spectroscopic constants of the isotopic molecules which are excluded from the refinement process are also in good agreement with the computed ones. The bond dissociation energies of the NN and NO bonds estimated from the present results have been critically examined.     

The harmonic force fields of methylene chloride and dichlorosilane from combined microwave and infrared data

The harmonic force fields of methylene chloride and dichlorosilane have been obtained by combining the vibrational wavenumbers and centrifugal distortion constants of several isotopic species. Although enough data were available from earlier work for dichlorosilane, it was first necessary for methylene chloride to determine its distortion constants from microwave spectra. Transitions were measured up to J = 80 and J = 90 for CH₂Cl₂ and CD₂Cl₂, respectively, and the analysis gave accurate rotational constants, and quartic and sextic distortion constants. Ground-state effective, substitution, ground-state average and approximate equilibrium structures have been obtained for both molecules.     

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.     

An Improved Anharmonic Potential for CHF3

We have investigated the potential energy surface of CHF₃theoretically using standard quantum chemical methods. The harmonic force field was obtained by an MP2 calculation, while the cubic and quartic components have been evaluated at the SCF level in Cartesian coordinates. Finally we scaled the geometry and the potential in symmetry coordinates to reproduce the experimental ground state rotational constants, fundamentals, overtones, and quartic and sextic centrifugal distortion constants of two isotopomers.     

An Improved Anharmonic Force Field of Difluoromethanimine, F2C NH

The anharmonic force field of difluoromethanimine, F₂C NH, has been reinvestigated theoretically using a coupled-cluster singles and doubles approach, augmented for structural optimization and harmonic force field by a contribution of connected triple excitations, CCSD(T). The cubic and quartic force constants have been obtained by numerical derivatives computed from analytical quadratic force constants calculated by second-order Møller-Plesset perturbation theory, MP2. The quadratic force constants and the equilibrium structure of F₂C NH have then been scaled by a global least-squares fitting procedure to the spectroscopic data and parameters experimentally determined for this molecule. This force field, obtained in the internal coordinates space and therefore valid for all isotopomers of difluoromethanimine, yields a complete set of spectroscopic molecular constants providing a critical assessment of the experimental rotational and centrifugal distortion constants, fundamentals, overtones, and combination bands determined so far for F₂C NH. In addition, the final force field can be used to make predictions of all important vibrational and rotational parameters which should be accurate and useful for new spectroscopic investigations.     

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.     

VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory

Vibrational levels of polyatomic molecules are analysed with Van Vleck perturbation theory to connect experimental energy levels to computed molecular potential energy surfaces. Vibrational matrix elements are calculated from a quartic potential function via second-order Van Vleck perturbation theory, a procedure that treats both weak and strong interactions among vibrational states by approximately block-diagonalising the vibrational Hamiltonian. A clear and complete derivation of anharmonic and resonance constants as well as general expressions for both on- and off-diagonal matrix elements of the transformed Hamiltonian is presented. The equations are written in partial fraction form and as a constant multiplied by a harmonic oscillator matrix element to facilitate removing the effect of strongly interacting resonant states both in analytical formulae and in computer code. The derived equations are validated numerically, and results for the isotopomers of formaldehyde (H₂CO, HDCO, D₂CO) are included. The implications of the equations on zero-point energy calculations and experimental fits are discussed. The VPT2+K method is defined by these results for use in fitting and calculating vibrational energy levels.     

The anharmonic force fields of PH3, PHF2, PF3, PH5, and H3PO

The cubic and quartic force fields of the title compounds are determined from ab initio SCF calculations using 6-31G^** and TZP/TZ2P basis sets. The computed geometries, vibration-rotation interaction constants, l-doubling constants, anharmonicity constants, and vibrational wavenumbers are compared with the available experimental data, especially for PH₃ and PF₃. Many experimentally unknown spectroscopic constants are predicted. A scaling procedure based on calculated harmonic and anharmonic force fields is proposed for predicting the vibrational wavenumbers of unknown molecules such as PH₅.     

Calculation of spectroscopic parameters and vibrational overtones of methanol

A high-level quartic ab initio potential energy surface of methanol has been used to calculate spectroscopic constants of the ¹²CH₃OH molecule. These include coefficients of quartic anharmonic resonance terms, Darling-Dennison constants, for stretching states. A model expressed in terms of dimensionless normal coordinates has been employed in the calculation of O—H and C—H stretching vibrational states in high-overtone regions. Both cubic Fermi and quartic Darling-Dennison anharmonic coupling terms have been included in the model in order to take into account strong resonances between different states. The nonlinear least-squares method has been used to optimize some of the model parameters employing experimental term values of ¹²CH₃OH as data. Vibrational assignments are suggested for the first C—H stretching overtone region.     

Vibrations of excited molecules at combination and difference frequencies

In the context of the theory of molecular vibrations, by applying the direct product operation of matrices, an equation for the vibrations of vibrationally excited molecules at combination and difference frequencies is obtained. From the solution of this equation, elements of vibration patterns and expressions that can be used for the study of changes in the molecular structural parameters and the coefficients of kinematic interactions are determined. The formulas obtained are applied to the calculation of the anharmonic electro-optical parameters of the molecules of water H₂O and its two isotopes H₂ ¹⁷O and H₂ ¹⁸O. These calculations are performed in terms of the semiempirical quantum-chemical CNDO/2 method and by numerical differentiation of dipole moment functions by employing a cubic spline approximation.     

The rotational spectrum of acrylonitrile in excited states of the two low-frequency CCN bending vibrational modes

The strongest vibrational satellites in the rotational spectrum of acrylonitrile have been assigned and frequencies of μ_a- and μ_b-type transitions in the frequency range 27–184 GHz are reported for the first two excited states in the lowest frequency in-plane CCN bending vibrational mode and the first excited state in the out-of-plane CCN bending mode. The values of the rotational constants, the quartic and sextic centrifugal distortion constants, and one octic centrifugal distortion constant are determined for each of these states. Less extensive results are also presented for the third quantum of the in-plane bend. The data set for the ground state has been extended by a number of new measurements and the improved ground state constants are used in a discussion of changes in rotational and centrifugal distortion constants with vibrational state where all constants associated with P_zⁿ and P²P_z⁽ⁿ⁻²⁾ terms in the Hamiltonian are found to reflect the common origin of the two CCN bends.     

Anharmonic potential function of formaldehyde

By using a simple anharmonic potential including 25 higher-order constants, the vibrational frequencies, vibration-rotation interaction constants, and centrifugal distortion constants of formaldehyde were calculated to agree well with the observed values. The harmonic part of the potential gives favorable signs of compliance constants for the C_2v-type dissociations into the methylene radical and into carbon monoxide, as well as for the C_s-type dissociation into the formyl radical. The cubic constants have adequate signs to predict the changes of quadratic constants on the dissociation of the CH or the CO bonds. From the Morse parameter of the CH bond, the heat of dissociation for the process H₂CO → CO + 2H is calculated to be 137 kcal/mole.