Vibration-rotation Interaction Research Articles

Submillimeter-wave spectroscopy of HN 2+ and DN 2+ in the excited vibrational states

The pure rotational transitions of HN 2 + and DN 2 + in the first excited vibrational states for all the fundamental vibrational modes have been observed in the range of 300–750 GHz. The molecular constants determined are much more accurate compared with those obtained from the infrared spectroscopy. The equilibrium rotational constants, B e = 46832.45 (71) MHz for HN 2 + and B e = 38708.38 (58) MHz for DN 2 +, have been determined by correcting for the higher-order vibration–rotation interaction effects, γ ij , obtained by an infrared investigation. The equilibrium bond lengths are derived from these equilibrium rotational constants: r e (H–N) = 1.03460 (14) Å and r e (N–N) = 1.092698 (26) Å.

Formalism of Quantum Number Polynomials

Theoretical aspects of the recent perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. By the example of a biatomic molecule, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Hermann-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established.

Semispectroscopic and Quantitative Structure−Property Relationship Estimates of the Equilibrium and Vibrationally Averaged Structure and Dipole Moment of 1-Buten-3-yne

Systematic quantum chemical calculations have been performed to obtain precise estimates of the equilibrium and vibrationally averaged molecular structure and electric dipole moment of vinylacetylene (VA, 1-buten-3-yne). Anharmonic (cubic and semi-diagonal quartic) MP2/cc-pVTZ force fields in normal coordinates were computed to account for anharmonic vibrational effects, including zero-point contributions to the rotational constants and the electric dipole moment. A simultaneous weighted least-squares structural refinement was performed, resulting in the best semispectroscopic estimate of the re structure of VA. The refinement was based on experimentally measured ground-state rotational constants of two isotopologs of VA corrected to equilibrium values using MP2/cc-pVTZ vibration-rotation interaction constants and all-electron CCSD(T)/aug-cc-pVTZ structural constraints. The semispectroscopic re structure of VA agrees excellently with the high-level CCSD(T)/aug-cc-pVTZ ab initio structure. The most dependable, CCSD(T)/cc-pVQZ//CCSD(T)/aug-cc-pVTZ equilibrium electric dipole moment of VA, in D, is mua= 0.4088, mub= 0.0004, and muc= 0. The vibrationally corrected a-component of 0.4214 D is in excellent agreement with one of the available experimental values. The present analysis shows that mub is negligible even after vibrational correction. A simple quantitative structure-property relationship (QSPR) model resulted in a highly similar estimate, 0.45 D, for the electric dipole moment of VA.

Vibration-rotation interactions between overtone and combination levels of asymmetric-top molecules: Application to the infrared spectroscopy of formaldehyde and ketene

The conventional vibration-rotation Hamiltonian for an asymmetric-top molecule is rewritten by expanding the elements of the inverse inertial tensor about the equilibrium molecular geometry. The approach allows the identification of terms in the Hamiltonian that couple states differing by two, three, or four vibrational quanta and hence the calculation of dimensioned Coriolis xi coupling coefficients for interacting fundamental, overtone, and combination levels. The matrix elements that result from the application of the expanded Hamiltonian depend upon the harmonic vibrational wave numbers, equilibrium moments of inertia, Coriolis zeta parameters, and the derivatives of the elements of the inertial tensor matrix with respect to each of the normal coordinates. The Coriolis coupling coefficients may be calculated through evaluation of the summations that result from the appropriate terms. The validity of the approach is demonstrated through the calculation of coupling coefficients for interacting levels in formaldehyde and ketene. The uncertainty in the calculated values of the coupling coefficients is typically better than +/-6%, although the values calculated for interactions that involve low-frequency vibrational modes are less reliable. Comparisons are made between the calculated values and experimental results.

Ground-state constants, ab initio anharmonic force field, and equilibrium structure of F 2BOH

The millimeterwave spectra of F 2 10BOH and F 2 11BOH (difluorohydroxyborane) have been measured in their ground vibrational state. Accurate rotational and centrifugal distortion constants have been determined. The equilibrium geometry and anharmonic force fields have been calculated at the CCSD(T) level of theory. The ab initio centrifugal distortion constants and rotation–vibration interaction constants are compared to the experimental values. Some discrepancies are found and discussed. Particularly, it is explained why the semi-experimental structure is not reliable. The best equilibrium structure is: r e (BF cis) = 132.29 pm, r e (BF trans) = 131.29 pm, r e (BO) = 134.48 pm, r e (OH) = 95.74 pm, ∠ e (FBF) = 118.36°, ∠ e ( F cisBO) = 122.25°, and ∠ e (BOH) = 113.14°.

Rotational-vibrational polarizability operator for nonlinear X2Y molecules: Application to the calculation of the Raman spectrum of the H2O molecule

For nonlinear X2Y molecules, an expression for the transformed polarizability operator is obtained with an accuracy of up to the second order of the theory of perturbation. This operator is applied to the calculation of the intensities of Raman lines of the H2O molecule. The corrections to the polarizability of the molecule associated with the vibrational-rotational interaction are shown to considerably change the integral intensity of a pure rotational band. The dependence of the average polarizability of the molecule on the vibrational quantum number V2, describing deformation vibrations, is estimated.

First stretching overtone of BiH3: an extreme local-mode case for XH3-type molecule?

The first stretching overtone region of short-lived, formerly inaccessible BiH3 near 3405 cm(-1) has been measured by Fourier-transform infrared spectroscopy with a resolution of 0.0066 cm(-1). Only the 2nu1(A1)/nu1+nu3(E) band system has been observed. Rotational analysis, with transitions reaching J'max=14, has revealed almost perfect local-mode behavior for the upper states denoted as (200A1/E) in the local-mode notation. Ratios of vibration-rotation interaction parameters q(eff)/alpha(eff)(BB) and r(eff)/alpha(eff)(BC), and the appropriate rotational constant differences, are in good agreement with theoretical local-mode limit values. A simple stretching vibrational model reproduces the observed vibrational term values well, and the potential parameters obtained are close to true values.

Calculation of the Combination Scattering Spectrum of the H2O Molecule Based on the Effective Polarizability Operator

This paper presents a procedure for calculation of the combination scattering spectrum of a nonlinear molecule of the X2Y type which is based on a transformed polarizability operator taking into account the vibration-rotation interaction in the molecule to within the second order of the perturbation theory. The matrix elements of the operator are determined and classified by molecule symmetry type. The combination scattering spectrum of the H2O molecule is calculated in the region of the 2v2 band. The second derivative of the average polarizability of the H2O molecule with respect to the normal coordinate q2, associated with deformation vibrations, and the vibrational dependence of the average polarizability of the H2O molecule on the deformation quantum number v2 are estimated.

Spectroscopic Parameters of High Overtones of the Vibrations of Molecules

Based on the fundamental equation from the vibration theory of molecules and the operation of direct product of matrices and its properties for eigenvalues and eigenvectors, an equation of overtone vibrations for any high order has been obtained whose solution yields the matrices of vibration modes. Correlations determining changes in the structure parameters, just as expressions for the matrices of the coefficients of kinematic interaction and force constants, and for the parameters of vibrational-rotational interaction have been presented. Using the formulas obtained, the electro-optical parameters of water molecules H2O and isotopes H217O and H218O have been calculated for overtones of up to the sixth order within the framework of the semiempirical quantum-chemical CNDO/2 method using the method of numerical differentiation by spline functions.

Vibrational Spectroscopic Database on Acetylene, X̃ 1Σg+ (12C2H2, C212D2, and C213H2)

Information on the vibrational energy states in acetylene (12C2H2, C212D2, and C213H2) is gathered: spectroscopic constants (vibrational frequencies and anharmonicities, vibration-rotation interaction parameters), observed vibrational energy states and complete sets of predicted vibrational energies and predicted principal rotational constants Bv for states of C212H2, C212D2, and C213H2 up to 15000, 10000, and 12000 cm−1, respectively. Statistical parameters (partition functions and integrated number of states) deduced from these predicted spectroscopic data are provided for the three isotopomers. The equilibrium geometrical structure is determined to be re(CH)=106.138(35) pm and re(CC)=120.292(13) pm from constants available for C212H2, C212D2, C213H2, and C212HD.

Accuracy of spectroscopic constants of diatomic molecules from ab initio calculations

The basis-set convergence of cc-pVXZ basis sets is investigated for the MP2 and CCSD equilibrium bond distances and harmonic frequencies of BH, HF, CO, N2, and F2 by comparing with explicitly correlated R12 results. The convergence is, in general, smooth but slow—for example, for harmonic frequencies at the quadruple-zeta level, the basis-set error is typically 7 cm−1; at the sixtuple-zeta level, it is about 2 cm−1. For most constants, the convergence can be accelerated by using a two-point linear extrapolation procedure. Equilibrium bond distances, harmonic frequencies, anharmonic contributions, vibration-rotation interaction constants, and rotational constants for the vibrational ground state have been calculated for the same set of molecules using standard wave function and basis-set levels of ab initio theory. The accuracy of the calculated constants has been established by carrying out a statistical analysis of the deviations with respect to experiment. The largest errors for bond distances and harmonic frequencies calculated at the core-corrected CCSD(T)/cc-pV6Z level are 0.4 pm and 13.4 cm−1, respectively. Much smaller errors occur for the anharmonic contributions.

The equilibrium structure of trans-glyoxal from experimental rotational constants and calculated vibration–rotation interaction constants

A total of six high-resolution FT-IR spectra for trans-glyoxal-d2, trans-glyoxal-d1 and trans-glyoxal-13C2 were recorded with a resolution ranging from 0.003 to 0.004 cm−1. By means of a simultaneous ground state combination difference analysis for each of these isotopologues using the Watson Hamiltonian in A-reduction and Ir-representation the ground state rotational constants are obtained. An empirical equilibrium structure is determined for trans-glyoxal using these experimental ground state rotational constants and vibration–rotation interaction constants calculated at the CCSD(T)/cc-pVTZ level of theory. The least-squares fit yields the following structural parameters for trans-glyoxal: re(C–C) = 1.51453(38) Å, re(C–H) = 1.10071(26) Å, re(CO) = 1.20450(27) Å, αe(CCH) = 115.251(24)°, and αe(HCO) = 123.472(19)° in excellent agreement with theoretical predictions at the CCSD(T)/cc-pVQZ level of theory.

Molecular dynamics simulations of the orientational motion of liquid chloroform at 298 K and 220K

Molecular dynamics simulations of liquid chloroform at 298 K and 220 K, using established optimized potential parameters and run on single-processor workstations, are employed to compute the first- and second-order Legendre polynomial, single-molecule orientational correlation functions describing the tumbling motion of the carbon-hydrogen bond direction. The results of the simulated Raman correlation functions compare well with their experimental counterparts from previously reported Fourier-transformed band contours of two totally symmetric vibration-rotation modes of the liquid. Simulated angular momentum, angular velocity, and intermolecular torque correlation functions are shown, and helped to characterize the insignificance of free orientational mobility within the system. Perturbation effects from rotation-vibration interaction and collision-induced intensities are present, but their effects on the correlation results are not sufficiently high to be of major significance.

Role of intramolecular interactions in Raman spectra of N 2 and O 2 molecules

The effect of vibration–rotation interactions and anharmonicities on the polarizabilities matrix elements, Raman scattering cross-sections, and depolarization degrees of N 2 and O 2 molecules for vibrational transitions v→ v, v+1, v+2, v+3 have been investigated.

The Algebraic Cluster Model: Three-Body Clusters

A new method is introduced to study three-body clusters. Triangular configurations with D3h point-group symmetry are analyzed. The spectrum, transition form factors, and B(Eλ) values of 12C are investigated. It is concluded that the low-lying spectrum of 12C can be described by three alpha-particles at the vertices of an equilateral triangle, but not as a rigid structure. Large rotation–vibration interactions, Coriolis forces, and vibration–vibration interactions are needed. Other interpretations, such as the harmonic oscillator and a soft deformed oscillator with SO(6) hyperspherical symmetry, appear to be excluded by electron scattering data.

Molecular equilibrium structures from experimental rotational constants and calculated vibration–rotation interaction constants

A detailed study is carried out of the accuracy of molecular equilibrium geometries obtained from least-squares fits involving experimental rotational constants B0 and sums of ab initio vibration–rotation interaction constants αrB. The vibration–rotation interaction constants have been calculated for 18 single-configuration dominated molecules containing hydrogen and first-row atoms at various standard levels of ab initio theory. Comparisons with the experimental data and tests for the internal consistency of the calculations show that the equilibrium structures generated using Hartree–Fock vibration–rotation interaction constants have an accuracy similar to that obtained by a direct minimization of the CCSD(T) energy. The most accurate vibration–rotation interaction constants are those calculated at the CCSD(T)/cc-pVQZ level. The equilibrium bond distances determined from these interaction constants have relative errors of 0.02%–0.06%, surpassing the accuracy obtainable either by purely experimental techniques (except for the smallest systems such as diatomics) or by ab initio methods.

Collision-induced absorption in the ν2 fundamental band of CH4. I. Determination of the quadrupole transition moment

An experimental value for the quadrupole transition moment of the ν2 fundamental band of CH4 has been determined by fitting the collision-induced enhancement spectrum of CH4 with Ar as the perturber. The observed quadrupole-induced absorption increases linearly with the Ar density, ρAr, and is comparable to the allowed dipole intensity due to Coriolis interaction with the ν4 band at approximately 125 amagats. Ignoring vibration-rotation interaction and Coriolis interaction,, we equate the measured slope of the integrated intensity versus ρAr to the theoretical expression for the quadrupole-induced absorption, and obtain the value |〈0|Q|ν2〉|=0.445 ea02 for the quadrupole transition matrix element. A theoretical value 〈0|Q|ν2〉=0.478 ea02 has been determined by large-scale ab initio calculations and, considering both the theoretical approximations and experimental uncertainties, we regard the agreement as good, thus confirming our interpretation of the enhancement as due to the quadrupole collision-induced mechanism.

Microwave spectra and molecular structures of (Z)-pent-2-en-4-ynenitrile and maleonitrile.

Accurate equilibrium structures have been determined for (Z)-pent-2-en-4-ynenitrile (8) and maleonitrile (9) by combining microwave spectroscopy data and ab initio quantum chemistry calculations. The microwave spectra of 10 isotopomers of 8 and 5 isotopomers of 9 were obtained using a pulsed nozzle Fourier transform microwave spectrometer. The ground-state rotational constants were adjusted for vibration-rotation interaction effects calculated from force fields obtained from ab initio calculations. The resultant equilibrium rotational constants were used to determine structures that are in very good agreement with those obtained from high-level ab initio calculations (CCSD(T)/cc-pVTZ). The geometric parameters in 8 and 9 are very similar; they also do not differ significantly from the all-carbon analogue, (Z)-hex-3-ene-1,5-diyne (7), the parent molecule for the Bergman cyclization. A small deviation from linearity about the alkyne and cyano linkages is observed for 7-9 and several related species where accurate equilibrium parameters are available. The data on 7-9 should be of interest to radioastronomy and may provide insights on the formation and interstellar chemistry of unsaturated species such as the cyanopolyynes.

Isotropic Raman line shapes of N2 and O2 along their liquid–gas coexistence lines

Isotropic Raman line shapes provide information about molecular interactions, structure, and dynamics. Such line shapes have been measured experimentally along the liquid–gas coexistence lines for both nitrogen and oxygen. We extend previous theoretical studies of nitrogen Raman line shapes by including in a systematic way the dependence of the bond lengths and dispersion and repulsive force parameters on vibrational coordinates. In so doing we include the effects of vibration-rotation and resonant vibrational intermolecular interactions. The dispersion and repulsive force parameter dependences are crucial for obtaining a quantitative description (and even the correct sign) of the line shift. Using a recently developed intermolecular potential, we perform similar calculations for oxygen. For both oxygen and nitrogen agreement with experimental Raman line shifts and line widths along the liquid–gas coexistence lines is reasonably good. One interesting feature of our results is that the dependence of the dispersion and repulsive force parameters on the vibrational coordinates is developed in such a way as to be directly useful in calculations of vibrational lifetimes.

Density functional theory predictions of anharmonicity and spectroscopic constants for diatomic molecules

The reliability of density functional theory and other electronic structure methods is examined for anharmonicities and spectroscopic constants of the ground electronic states of several diatomic molecules. The equilibrium bond length re, harmonic vibrational frequency ωe, vibrational anharmonicity ωexe, rotational constant Be, centrifugal distortion constant D̄e, and vibration-rotation interaction constant αe have been obtained theoretically for BF, CO, N2, CH+, and H2. Predictions using Hartree–Fock, coupled-cluster singles and doubles (CCSD), coupled cluster singles and doubles with perturbative triples [CCSD(T)], and various density functional methods (S-VWN, BLYP, and B3LYP) have been made using the 6-31G*, aug-cc-pVDZ, and aug-cc-pVTZ basis sets and compared to experimental values. Density functional theory predictions of the spectroscopic constants are reliable (particularly for B3LYP) and often perform as well as the more expensive CCSD and CCSD(T) estimates.