The study of the rotational spectrum of the H2O⋯HF dimer in the equilibrium gas phase in the range 180–350GHz by continuously frequency scanning microwave spectrometer with backward-wave oscillator and acoustic detection of absorption is described. The results of analyzing of the most intense spectral series are given. The assignment of some spectral series observed earlier is corrected. Data on the Coriolis interaction between the ground and excited vibrational states are obtained and spectroscopic constants of the dimer are significantly refined.

A general, full-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is further developed. The resulting computer program may be run in serial and parallel modes and is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the isomerizing acetylene/vinylidene system is presented. Large-scale calculations using a coordinate system based on orthogonal satellite vectors have been performed in six dimensions and vibrational term values and wave functions for acetylene and vinylidene states up to approximately 23 000 cm(-1) above the potential minimum have been determined. This has permitted the characterization of acetylene and vinylidene states at and above the isomerization barrier. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than in any variational calculations reported hitherto for this system. Comparison of the calculated density of states with that determined empirically suggests that our calculations are the most realistic achieved for this system to date. Indeed more states have been converged than in any previous study of this system. Calculations on lower lying excited states of acetylene based on HC-CH diatom-diatom coordinates give nearly identical results to those based on orthogonal satellite vectors. Comparisons are also made with calculations based on HH-CC diatom-diatom coordinates.

Two methods of evaluating matrix elements of a function in a polynomial basis are considered: the expansion method, where the function is expanded in the basis and the integrals are evaluated analytically, and the numerical method, where the integration is performed directly using numerical quadrature. A reduced grid is proposed for the latter which makes use of the symmetry of the basis. Comparison of the two methods is presented in the context of evaluation of matrix elements in a non-direct product basis. If high accuracy of all matrix elements is required then the expansion method is the best choice. If however the accuracy of high order matrix elements is not important (as in variational ro-vibrational calculations where one is typically interested only in the lowest eigenstates), then the method based on the reduced grid offers sufficient accuracy and is much quicker than the expansion method.

We demonstrate how relative equilibria of a vibrating molecule, which are families of principal periodic orbits otherwise known as nonlinear normal modes, can be used to describe the global polyad structure of vibrational energy levels. The classical action integral n (E) computed along these orbits at different energies E corresponds to the polyad quantum number n so that the energy E (n) of different relative equilibria describes the splitting of n-polyads. Further information on the internal polyad structure can be driven from the stability analysis of relative equilibria. We use the ozone molecule as a concrete example where n-polyads or “hyperpolyads” should be distinguished from the well-known polyads of the 1:1 stretching mode resonance; the stretching polyads are structural elements of hyperpolyads. We give dynamical interpretation of the relation between relative equilibria and n-polyads based on the normal form reduction in the limit of small vibrations near the equilibrium.

A general computational method for the accurate calculation of rotationally and vibrationally excited states of tetraatomic molecules is developed. The resulting program is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. The program offers a choice of coordinate systems based on Radau, Jacobi, diatom-diatom and orthogonal satellite vectors. The method includes all six vibrational dimensions plus three rotational dimensions. Vibration-rotation calculations with reduced dimensionality in the radial degrees of freedom are easily tackled via constraints imposed on the radial coordinates via the input file.

We show that for rigid symmetric top molecules in electric fields the phenomenon of monodromy arises naturally as a “defect” in the lattice of quantum states in the energy-momentum diagram. This makes it impossible to use either the total angular momentum or a pendular quantum number to label the states globally. The monodromy is created or destroyed by classical Hamiltonian Hopf bifurcations from relative equilibria. These phenomena are robust and should be observable in quasi-symmetric top molecules with field strengths ℰ satisfying μE/b>4.5, where μ is the dipole moment and b the rotational constant perpendicular to the symmetry axis of the molecule.

A general, six-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is developed. The resulting program is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the Ar2HF van der Waals trimer is presented in which the HF intramolecular stretching coordinate is separated out adiabatically and is not treated explicitly. Vibrational term values up to about 100 cm−1 with absolute convergence to better than 0.1 cm−1 are reported. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than hitherto. States that sample Ar–Ar–HF linear configurations and approach Ar–HF–Ar linear configurations are characterized for the first time. Results for total angular momentum J=0 and 1 provide the first accurate calculations of rotational constants for this system. The rotational constants for the HF bending states of Ar2HF in the ground and first vibrationally excited states of the HF monomer are in good agreement with experiment, confirming the accuracy of the potential used in this work.

Relative equilibria of molecules are classical trajectories corresponding to steady rotations about stationary axes during which the shape of the molecule does not change. They can be used to explain and predict features of quantum spectra at high values of the total angular momentum J in much the same way that absolute equilibria are used at low J. This paper gives a classification of the symmetry types of relative equilibria of AB(2) molecules and computes the relative equilibria bifurcation diagrams and normal mode frequencies for D(2)H(+) and H(2)D(+). These are then fed into a harmonic quantization procedure to produce a number of predictions concerning the structures of energy level clusters and their rearrangements as J increases. In particular the formation of doublet pairs is predicted for H(2)D(+) from J approximate to 26.

We present a global study of how the relative equilibria of the H3+ ion change as the angular momentum J increases. A relative equilibrium is a classical trajectory for which the molecule rotates about a stationary axis without changing its shape. The study confirms previous results which show that the geometry of the minimum energy relative equilibria changes from an equilateral triangle to a symmetric linear configuration at around J=47. The series of bifurcations and stability changes that accompany this transition is presented in detail. New results include the discovery that the rotating equilateral triangle remains linearly stable for a large range of angular momentum values beyond the point where it ceases to be a minimum of the total energy. A third type of relative equilibrium, a rotating isosceles triangle, is also found to be linearly stable in the approximate range J=0–34. Both the equilateral and isosceles triangle configurations lose stability via Hamiltonian–Hopf bifurcations. The frequencies and symmetry species of the normal modes of the stable relative equilibria are computed and harmonic quantization is used to predict how the symmetries of the lowest lying quantum states will change as J increases. Energy level clustering due to tunneling between symmetry-equivalent relative equilibria is described.

Relative equilibria of molecules are classical trajectories corresponding to steady rotations about stationary axes during which the shape of the molecule does not change. They can be used to explain and predict features of quantum spectra at high values of the total angular momentum J in much the same way that absolute equilibria are used at low J. This paper gives a classi® cation of the symmetry types of relative equilibria of AB2 molecules and computes the relative equilibria bifurcation diagrams and normal mode frequencies for D2H ‡ and H2D ‡ . These are then fed into a harmonic quantization procedure to produce a number of predictions concerning the structures of energy level clusters and their rearrangements as J increases. In particular the formation of doublet pairs is predicted for H2D ‡ from J o 26.

The rotational energy level structures of quasi-spherical top molecules is investigated through the analysis of systems of stationary points on classical rotational energy surface. The series of simplest typical bifurcations of stationary points are given, as a quasi-spherical molecule evolves to the spherical top limit due to rotational excitation or molecular isotopomerisation. In this way the correlation between asymmetric and spherical top rotation energy multiplets is studied for A4 and AB4 molecules and corresponding isotopomers. It is demonstrated that the correlation depends on the point symmetry of the asymmetric top molecule. Slight symmetry breaking from C2v point symmetry down to Cs results in the appearance of imperfect bifurcations [M. Golubitsky and D.G. Schaeffer, ‘Singularities and Groups in Bifurcation Theory’, vol. 1, Springer-Verlag, 1984]. The effect of imperfect bifurcation and its manifestation in molecular rotational spectra are discussed.

The present work reports anab initioMRD-CI calculation of the dipole moment surfaces for the electronic ground state of the H2Te molecule. Using theab initioresults, we calculate the vibrational transition moments, and we simulate the far-infrared spectrum of H2Te by means of the MORBID program system. We obtain the equilibrium value of the dipole moment from theab initiocalculation as 0.377 Debye based on our initial theoretical treatment which was employed over a wide range of molecular geometries. However, the use of an improved AO basis at the equilibrium geometry of H2Te lowers this result to 0.298 Debye. The comparison of our simulated far-infrared spectrum with the experimental spectrum suggests that this value is too large, and that the correct value is certainly larger than 0.19 Debye and very probably smaller than 0.26 Debye. From theab initiodata, we predict many vibrational transition moments for H2Te, D2Te, and HDTe. We hope that these results will be of assistance in the interpretation of the rotation–vibration spectrum of these molecules.

We report here how we have incorporated the effects of a nonzero total electron spin in the MORBID Hamiltonian and computer program [P. Jensen, J. Mol. Spectrosc. 128, 478-501 (1988); J. Chem. Soc. Faraday Trans. 2 84, 1315-1340 (1988); in "Methods in Computational Molecular Physics" (S. Wilson and G. H. F. Diercksen, Eds.), Plenum Press, New York, 1992] for calculating the rovibronic energies of a triatomic molecule directly from the potential energy function. The spin-spin and spin-rotation Hamiltonian terms, given in a form depending on the vibrational coordinates, have been expressed in terms of isotope-independent functions and added to the MORBID rotation-vibration Hamiltonian. The eigenvalues of the resulting Hamiltonian are obtained in a variational procedure. This method is tested on the methylene radical CH2 in the X ; 3 B 1 electronic ground state for which we describe simultaneously the splittings due to electron spin for the isotopomers 12 CH2 , 12 CD2 , and 13 CH2 . For these molecules, experimental data are available, and we compare the results of least-squares fits to these data with predictions from ab initio theory.

A microscopic theory is proposed for bifurcation in the rotational spectra of nonlinear AB 2 -type molecules. The theory is based on a study of small-amplitude vibrational and precessional motion near the stationary states of a rotating molecule. Bifurcation leads to the formation of fourfold clusters of levels in the upper parts of the rotational multiplets, disruption of the symmetry of the molecule, and a transition from normal to local valence vibrations. The role of the centrifugal force of inertia in the development of these effects is clarified. Bifurcation and the accompanying phenomena are studied in the hydride molecules H 2 O, H 2 S, H 2 Se, and H 2 Te using empirical molecular potentials.

A classical microscopic theory of rovibrational motion at high angular momenta in symmetrical nonlinear molecules AB2 is derived within the framework of small oscillations near the stationary states of a rotating molecule. The full-dimensional analysis including stretching vibrations has confirmed the existence of the bifurcation predicted previously by means of the rigid-bender model [see B. I. Zhilinskii and I. M. Pavlichenkov, Opt. Spectrosk. (USSR) 64, 413 (1988)]. The formation of fourfold energy clusters resulting from the bifurcation has been experimentally verified for H2Se and it has been demonstrated in fully-dimensional quantum mechanical calculations carried out with the MORBID computer program. We show in the present work that apart from the level clustering, the bifurcation produces physically important effects including molecular symmetry-breaking and a transition from the normal mode to the local mode limit for the stretching vibrations due to the centrifugal forces. The application of the present theory with realistic molecular potentials to the H2Te, H2Se, and H2S hydrides results in predictions of the bifurcation points very close to those calculated previously. However for the lighter H2O molecule we find that the bifurcation occurs at higher values of the total angular momentum than obtained in previous estimations. The present work shows it to be very unlikely that the bifurcation in H2O will lead to clustering of energy levels. This result is in agreement with recent variational calculations.

In the present work, we study the spectrum of the H2Te molecule in the submillimeter-wave and far infrared region. An important aim of this investigation is the further experimental characterization of the anomalous "four-fold cluster effect" exhibited by the rotational energy levels in the vibrational ground state of H2Te. The spectrum in the region 90-472 GHz was measured with a source-modulated millimeter-wave spectrometer and that between 600 and 1600 GHz with a far-infrared sideband spectrometer. The far infrared spectrum from 30 to 360 cm-1 was measured with a Bruker IFS 120 HR interferometer attached to a 3 m long cell. We have assigned 224 submillimeter-wave lines and 1695 FIR lines. These observed data were supplemented by a large number of ground state combination differences derived from rotation-vibration bands of H2Te, and the resulting large data set was analyzed by means of a modified Watson Hamiltonian. Accurate sets of rotational and centrifugal distortion constants for all eight tellurium isotopomers were obtained.

1. A.F. Krupnov. in Modern Aspects of Microwave Spectroscopy'', G.W. Chantry, Ed, Academic Press, L, (1979) 217-256. 2. G. Winnewiser, A.F. Krupnov, M.Yu. Ttretyakov, M. Liedtke, F. Lewen, A.H. Saleck, R Schieder, A.P. Shkaev and S.V. Volokhov, J. Mol. Spectrosc. 165, 294 (1994). $^{\ast}$On leave of absence from N. Novgorod.