A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules

The rovibrational spectrum of trideutero‐methane has been measured at resolutions mostly close to the Doppler limit on an interferometric Fourier transform spectrometer from the lowest fundamental vibration to high overtones of the CH stretching vibration (wave numbers from 900 to 12 000 cm−1). The CH chromophore spectrum is fully assigned and interpreted by means of the tridiagonal Fermi resonance Hamiltonian for the coupled CH stretching and bending vibrations. The Hamiltonian predicts and also fits the visible spectrum up to 19 000 cm−1 measured by Scherer et al., Perry et al., and Campargue et al. The effective tridiagonal Hamiltonian is derived ab initio by means of MRD‐CI and full CI calculations of the potential surface of methane, a variational vibrational calculation in a normal coordinate subspace of the coupled CH stretching and bending motions and an approximate similarity transformation to tridiagonal form. Fits of the experimental results by the tridiagonal and the variational Hamiltonian le...

Vibrational spectrum and potential energy surface of the CH chromophore in CHD3

The dissociative recombination of an ${\mathrm{H}}_{3}^{+}$ ion after it is struck by a low-energy electron is important for understanding observations of ${\mathrm{H}}_{3}^{+}$ in diffuse interstellar clouds. At the same time, it is the simplest triatomic ion and for this reason its theoretical description can serve as a prototype for other polyatomic ions. Meanwhile, experimental determinations of the recombination rate have varied widely, which has resulted in some controversy and confusion. Until recently, it seemed unlikely that this problem could be resolved by theoretical studies because the mechanism of ${\mathrm{H}}_{3}^{+}$ dissociative recombination remained unclear. A recent study, however [Kokoouline et al., Nature (London) 412, 891 (2001)], provided evidence that the inclusion of the Jahn-Teller coupling can produce a dissociative recombination rate that overlaps the range of experimental observations. Here, we propose a theoretical description of the coupling between nuclear and electronic degrees of freedom in a polyatomic molecule, which describes the competition between autoionization and predissociation of the Rydberg states formed after an incident electron is captured. The method treats the vibrational and rotational excitations of the ion, accounts for all symmetry restrictions imposed by the geometry of the molecule, including vibrational, rotational, and electronic and nuclear-spin symmetries. The framework combines the multichannel quantum-defect theory, the adiabatic hyperspherical approach, and the techniques of outgoing-wave Siegert pseudostates. The proposed method can be applied to studies of dissociative recombination of other triatomic ions, including all the degrees of freedom quantum mechanically. Our calculations of the cross section and the recombination rate confirm that the Jahn-Teller effect is responsible for the large rate in ${\mathrm{H}}_{3}^{+}.$ Theoretical results for dissociative recombination of ${\mathrm{H}}_{3}^{+}$ are in agreement with storage-ring experiments.

Unified theoretical treatment of dissociative recombination of D3h triatomic ions: Application to H3+ and D3+

We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs the evolution from reactants to products in high dimensional systems. In the classical case this is the standard Poincare–Birkhoff normal form. In the quantum case we develop a normal form based on the Weyl calculus and an explicit algorithm for computing this quantum normal form. The classical normal form allows us to discover and compute the phase space structures that govern classical reaction dynamics. From this knowledge we are able to provide a direct construction of an energy dependent dividing surface in phase space having the properties that trajectories do not locally 're-cross' the surface and the directional flux across the surface is minimal. Using this, we are able to give a formula for the directional flux through the dividing surface that goes beyond the harmonic approximation. We relate this construction to the flux–flux autocorrelation function which is a standard ingredient in the expression for the reaction rate in the chemistry community. We also give a classical mechanical interpretation of the activated complex as a normally hyperbolic invariant manifold (NHIM), and further describe the structure of the NHIM. The quantum normal form provides us with an efficient algorithm to compute quantum reaction rates and we relate this algorithm to the quantum version of the flux–flux autocorrelation function formalism. The significance of the classical phase space structures for the quantum mechanics of reactions is elucidated by studying the phase space distribution of scattering states. The quantum normal form also provides an efficient way of computing Gamov–Siegert resonances. We relate these resonances to the lifetimes of the quantum activated complex. We consider several one, two and three degree-of-freedom systems and show explicitly how calculations of the above quantities can be carried out. Our theoretical framework is valid for Hamiltonian systems with an arbitrary number of degrees of freedom and we demonstrate that in several situations it gives rise to algorithms that are computationally more efficient than existing methods.

http://iopscience.iop.org/article/10.1088/0951-7715/21/1/R01/pdf

Wigner's dynamical transition state theory in phase space: classical and quantum

Solid hydroxide research of the last twenty years is reviewed with regard to bonding and structure of hydroxide ions in solid materials. This article is focussed on new results on hydrogen bonding and other intermolecular interactions including cooperative, anticooperative, and synergetic effects, H/D isotope effects, and phase transitions due to order-disorder reorientational motions of the OH− ions. The results of the main techniques used for structure determination as well as for spectroscopic and physical measurements of solid hydroxides, viz. X-ray and neutron scattering, infrared and Raman spectroscopy, NMR and NQR studies etc., are discussed.

A. Čejchan

Papers

The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H3+

Vibrational dynamics of hydrogen bonds: The system OH−·H2O

A new Morse-oscillator based Hamiltonian for H3+: Explicit expressions for some vibrational matrix elements