Vibration-Rotational Spectroscopy and Molecular Dynamics

The following sections are included:

• INTRODUCTION

• FOREWORD

• PREFACE

• CONTENTS

Three recent developments in the experimental methods for the study of transient molecules are discussed in some detail: (1) production of transient molecules, by either electric discharge or laser vaporization, in a supersonic jet incorporated in a Fourier–transform microwave spectrometer, (2) Fourier–transform microwave spectroscopy, and (3) kinetic spectroscopy. Among many results reported, the following molecules are mentioned as examples: hydrocarbon radicals (ethynyl CCH, vinyl C₂H₃, ethyl C₂H₅, propargyl C₃H₃, allyl C₃H₅), molecules with a carbon chain (HC₉N, C_nS with n = 3,4, C_nO with n = 2–9, HC_nO with n = 3, 4, HC_nS with n = 3, 4, HCCN, C₂N), FeCO, rare gas-OH complexes, and then accompanies implication of these and other studies to astronomy. Two types of applications of kinetic spectroscopy are added: O(¹D₂)+CH₄ reaction and diagnosis of the silane discharge plasma.

The significance of ab initio calculations at different levels for the determination of molecular parameters and the prediction of rotationally resolved infrared and microwave/millimeterwave spectra is outlined. The fruitful interplay of theoretical and experimental studies, mostly by high resolution Fourier Transform infrared spectroscopy, is demonstrated for the reactive and short-lived species FCCF and FCCCl. The predictive potential of ab initio calculations enabled the detection and characterization of the novel, hitherto unknown monohalogenophosphines PH₂X (X = F, Cl, Br, I).

A theory is discussed in detail of the unitary transformations of the effective rotation and vibration-rotational Hamiltonians of axially symmetric molecules leading to correlation-free reduced forms of these Hamiltonians. Various aspects are discussed of the use of reduced Hamiltonians in fitting the highly accurate data of the rotational and vibration-rotational spectroscopy for the ground as well as excited vibrational molecular states. Advances in measuring techniques in the sub-millimeter-wave spectroscopy and in one-dimensional and two-dimensional microwave Fourier transform spectroscopy are described and their applications are presented on numerous examples of the determination of molecular parameters for the ground and excited vibrational states. The high precision and accuracy of the submillimeter-wave and especially microwave Fourier transform spectroscopy make it possible to verify theoretical conclusions and to use novel approaches like fitting the experimental data with unitary equivalent sets of parameters.

The following sections are included:

• Introduction

• Intensities of Hot Bands
  • Formulas
  • Discussion
  • Intensity and Visibility of Hot Bands

• Applications of Hot Bands to Vibrational Problems

• Vibrational Characteristics of Hot Bands
  • Symmetry of Vibrational Levels
  • Vibrational Frequencies
  • Selection Rules

• Rovibrational Characteristics of Hot Bands
  • Symmetry of Rovibrational Levels
  • Rovibrational Structure of Hot Bands
  • Intensities and Nuclear Spin Statistics
    • For C_3ν molecules
    • For D_3h molecules
    • For D_2d molecules
    • Other symmetry groups
  • Frequency Expressions and Appearance of Hot Bands in C_3ν Molecules
  • A⁺A^- Splittings in Hot Bands of C_3ν Molecules
  • Hot Bands of D_2d Molecules
  • Hot Bands of D_3h Molecules

• Determination of A₀(C₀) with the Help of Hot Bands
  • Introduction
  • Principle of the Determination of A₀ with the Help of Hot Bands
  • Examples of Determinations
  • Comparison of Two Methods

• Hot Bands Used to Access Dark or Hidden States
  • The Missing Fundamental in FCl¹⁸O₃
  • Vibrational Levels Inaccessible by Direct Transitions
  • Rotational Levels Inaccessible by Direct Transitions from the Ground State
  • States Inaccessible by Direct Transitions for Accidental Reasons
    • CD₃CN
    • Propyne
    • Use of LSCD from Degenerate States
    • H₃Si⁷⁹Br
    • PF₃
    • CH₃NC
    • CF₃Cl
    • CF₃Br and CF₃I
    • SPF₃

• Conclusion

• Acknowledgements

• References

It is now an established, experimentally verified fact that in the vibrational states of the H₂Se molecule, at high J and K_a values the rotational energies form four-member groups of nearly degenerate levels, so-called energy clusters. Realistic quantum mechanical calculations have shown that the H₂S and H₂Te molecules exhibit similar effects. The present paper is concerned with the theoretical description of the energy clusters, mostly by variational calculations, i.e., calculations of the rotation-vibration energies by diagonalization of a matrix representation of the rotation-vibration Hamiltonian. Initially, we discuss the prediction of the four-fold clusters by classical and semi-classical theory, and we show how these predictions are borne out by experiment and by quantum mechanical calculations. Analysis of rotation-vibration wavefunctions obtained from variational calculations provides a simple picture of the rotational motion in the cluster states: The molecule rotates around one of its two bonds in a clockwise or an anticlockwise manner. The two choices for the bond, and the two choices for the sense of the rotation provide a total of four equivalent situations corresponding to a four-fold energy cluster. In the present paper, we use H₂Te as "example molecule", but the discussion can readily be extended to the lighter analogues H₂S and H₂Se. Finally, we briefly discuss our present knowledge about the high-J, high-K_a rotational energy spectrum of H₂O, for which no clusters have been observed experimentally.

The problem of relative phases of molecular wavefunctions, and their bearing on non-diagonal matrix elements, is discussed. Special attention is given to the definition of relative phases in different sets of ro-vibronic basis functions, inclusive of spin, related to each other by vector coupling. The phase dependence of the transformation matrices between such different sets, and of the matrix elements of certain relevant operators, is also emphasized.

This requires to a certain extent the re-formulation of the basic algebra of the spherical tensorial sets, in order to account for general phases of both basis functions and tensor operator components.

Phase conventions which render the matrix elements of all possible terms of the vibration-rotation Hamiltonian simultaneously real are finally suggested.

Large amplitude motions in molecules have been the subject of a large number of studies. The purpose of this paper is not to describe these motions extensively but rather to concentrate on the comparison of the effects of a one-dimensional large amplitude motion on two molecules, namely H₂O₂ and HNO₃. For H₂O₂ the motion is the torsion of the two equal halves O–H rotors around the O–O bond. During this motion the molecule passes through two barriers corresponding to the trans- and cis-planar configurations. As a consequence, one observes both a splitting (trans-barrier) and a staggering (cis-barrier) of the levels and it is necessary to use a double extension of the permutation-inversion group of the molecule to establish the symmetry properties and selection rules. For HNO₃, the motion is the torsion of the O–H bond relative to the much heavier , radical, and the molecule passes from one planar equilibrium configuration to an equivalent one. This torsion induces a splitting of the levels and the use of the permutation-inversion group of the molecule is required to understand its spectroscopic properties. This paper describes in detail the effects of the large amplitude motion both in H₂O₂ and HNO₃, discussing also the influence of the numerous vibration-torsion resonances affecting the excited states.

A general method for constructing permutation-inversion groups and their extensions for molecules containing two coaxial rotors is presented. Precise techniques are given for construction of irreducible representations, and their systematic labeling is proposed. Species of the dipole moment, tensor of polarizability, and total angular momentum operators are determined. General infrared and Raman selection rules, classifications of rotorsional, rotational, and torsional wavefunctions are derived. Nuclear spin statistical weights are determined in general. Theory is illustrated for the and complexes.

Radiative association processes play an important role in the formation of interstellar molecules by gas phase ion-molecule reactions. Due to experimental difficulties, only a few radiative association reactions have been studied in the laboratory. Therefore, most processes of interstellar importance must have their rates obtained by theoretical methods. Especially statistical approaches were applied in the past in the attempt to predict the association rates of larger molecular complexes. A full understanding, however, of the different possible reaction mechanisms and their dynamics can only be provided by detailed quantum-mechanical studies. Such rigorous ab initio calculations of the radiative association formation of noble gas hydride ions XH⁺ (X =He,Ne,Ar) are described here to discuss the requirements and limitations of this approach. Rate coefficients of all possible radiative association reactions resulting from X + H⁺ and from X⁺ + H collisions are calculated over a wide temperature range. For this purpose, the potential energy and electric dipole moment functions of the corresponding ground electronic and the first excited and states are determined at the configuration interaction level of theory and the electronic transition dipole moment functions between the two ¹Σ⁺ states are evaluated using the state interaction method of Malmqvist and Roos. From the potential energy functions, all rotation-vibration bound and rotationally quasi-bound levels are obtained for each electronic state. In the present diatomic systems the only efficient formation occurs in the two-state process in which radiative stabilization is achieved through transitions from the initial quasibound levels of the excited ùΣ⁺ state to the bound rotation-vibration levels of the ground electronic state. The temperature dependence of the corresponding rate coefficients show the typical behavior with a maximum at low temperatures and a rapid fall-off when temperatures rise above 100 K. In case of the HeH⁺ system, potential functions obtained from previous highly accurate directly correlated wavefunction calculations are used to assess the reliability of the present results.

The following sections are included:

• INDEX