Igor N. Kozin

Calculating energy levels of isomerizing tetra-atomic molecules. II. The vibrational states of acetylene and vinylidene

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.

Bifurcation in rotational spectra of nonlinear AB2 molecules

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...

Monodromy in the spectrum of a rigid symmetric top molecule in an electric field

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.

Calculating energy levels of isomerizing tetra-atomic molecules. I. The rovibrational bound states of Ar2HF

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.

Variational calculation of highly excited rovibrational energy levels of H2O2.

Results are presented for highly accurate ab initio variational calculation of the rotation-vibration energy levels of H2O2 in its electronic ground state. These results use a recently computed potential energy surface and the variational nuclear-motion programs WARV4, which uses an exact kinetic energy operator, and TROVE, which uses a numerical expansion for the kinetic energy. The TROVE calculations are performed for levels with high values of rotational excitation, J up to 35. The purely ab initio calculations of the rovibrational energy levels reproduce the observed levels with a standard deviation of about 1 cm(-1), similar to that of the J = 0 calculation, because the discrepancy between theory and experiment for rotational energies within a given vibrational state is substantially determined by the error in the vibrational band origin. Minor adjustments are made to the ab initio equilibrium geometry and to the height of the torsional barrier. Using these and correcting the band origins using the error in J = 0 states lowers the standard deviation of the observed-calculated energies to only 0.002 cm(-1) for levels up to J = 10 and 0.02 cm(-1) for all experimentally known energy levels, which extend up to J = 35.

Ro-vibrational spectra of C2H2 based on variational nuclear motion calculations

A published ab initio-based potential energy surface and newly constructed dipole moment surface of acetylene have been used to compute vibrational band intensities. The line intensity calculations employed the variational nuclear motion code WAVR4 for computation of wave functions and energy levels, and a newly developed code DIPOLE4 for computation of dipole transitions. Owing to the high computational cost of J > 0 transitions using direct variational methods only J = 0 and J = 1 states and transitions have been computed variationally. The intensities of J > 1 transitions were extrapolated from J = 0 and J = 1 using Hönl–London coefficients. The resulting effective rotational constants B and transition intensities are compared with experimental data for the (3ν4 + ν5) combination band, the ν3 and the ν5 fundamental band. The prospects of using this procedure for extensive calculations of a hot line list, important for cool stars and extrasolar planets are discussed.

Relative equilibria of D(2)H(+) and H(2)D(+)

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 momentumJ 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.