Dario De Fazio

Hyperquantization algorithm. I. Theory for triatomic systems

In this paper we present the theoretical concepts and methodology of the hyperquantization algorithm for the three body quantum mechanical problem. Within the framework of the hyperspherical approach to reaction dynamics, we use angular momentum algebra (or its generalization, e.g., including Hahn coefficients which are orthonormal polynomials on a set of grid points which span the interaction region) to compute matrix elements of the Hamiltonian operator parametrically in the hyperradius. The particularly advantageous aspects of the method proposed here is that no integrals are required and the construction of the kinetic energy matrix is simple and universal: salient features are the block tridiagonal structure of the Hamiltonian matrix and a number of symmetry properties. The extremely sparse structure is a further advantage for the diagonalization required to evaluate the adiabatic hyperspherical states as a function of the hyperradius. Numerical implementation is illustrated in the following paper by...

Hyperquantization algorithm. II. Implementation for the F+H2 reaction dynamics including open-shell and spin-orbit interactions

This work focuses on numerical aspects and performances of the hyperquantization algorithm, presented in the preceding paper, for a prototypical atom–diatom reaction. Here we provide also the extensions which allow the treatment of excited electronic surfaces. Test calculations have been carried out on the reaction F+H2 at a total nuclear angular momentum equal to zero, the fine structure of the fluorine atom being also explicitly taken into account. The technique presented is shown to be simple and effective for applications to reactive scattering problems, and the results are competitive with those obtained applying other current methods, especially in the strong triatomic interaction region.

Lifetime of reactive scattering resonances: Q-matrix analysis and angular momentum dependence for the F+H2 reaction by the hyperquantization algorithm

We report a study on the behavior with total angular momentum J of several resonances occurring at collision energies below or slightly above the reaction barrier in the F+H2-->HF+H reaction. Resonance positions and widths are extracted from exact time-independent quantum mechanical calculations using the hyperquantization algorithm and Smiths Q-matrix formalism which exploits complete S-matrix information. The results confirm previous work but provide much greater insight. Identification of quasi-bound states responsible for the resonances based on adiabatic models for the long-range atom-molecule interactions both in the entrance and exit channels, is successful except for the feature occurring at the lowest energy, which is found to overlap with an exit-channel resonance for J approximately 7. The two features are analyzed as overlapping resonances and their excellent Lorentzian fits, with well-behaved J-dependences of positions and widths, support the interpretation of the low-energy feature as a resonance to be associated to the triatomic transition state of the reaction. Resonance role on the reactive observables (integral cross sections and angular distributions) is investigated. The mechanism leading to forward scattering in the reactive differential cross section is commented, while the effects on rate constants, as well as the sensitivity of the resonance pattern to modification of the potential energy surface, are fully discussed elsewhere.

Direct evaluation of the lifetime matrix by the hyperquantization algorithm: narrow resonances in the F + H2 reaction dynamics and their splitting for nonzero angular momentum.

We propose a new method for the direct and efficient evaluation of the Felix Smiths lifetime Q matrix for reactive scattering problems. Simultaneous propagation of the solution to a set of close-coupled equations together with its energy derivative allows one to avoid common problems pertinent to the finite-difference approach. The procedure is implemented on a reactive scattering code which employs the hyperquantization algorithm and the Johnson-Manolopoulos [J. Comput. Phys. 13, 455 (1973); J. Chem. Phys 85, 6425 (1986)] propagation to obtain the complete S matrix and scattering observables. As an application of the developed formalism, we focus on the total angular momentum dependence of narrow under-barrier resonances supported by van der Waals wells of the title reaction. Using our method, we fully characterize these metastable states obtaining their positions and lifetimes from Lorentzian fits to the largest eigenvalue of the lifetime matrix. Remarkable splittings of the resonances observed at J>0 are rationalized in terms of a hyperspherical model. In order to provide an insight on the decay mechanism, the Q-matrix eigenvectors are analyzed and the dominant channels populated during the decomposition of metastable states are determined. Possible relevance of the present results to reactive scattering experiments is discussed.

Reactivity enhanced by under-barrier tunneling and resonances: the F+H2→HF+H reaction

Accurate quantum mechanical rate constants (all contributing partial waves, fine energy grid Boltzmann averaging) for the title reaction are obtained by the hyperquantization algorithm, covering the range from above room temperature down to the cold regime (few K). The good agreement with available experiments down to � 200 K, obtained by blending ab initio description of the transition state and molecular beam scattering experimental characterization of the entrance channel, establishes the reliability of the approach to describe deviations from Arrhenius behavior at those low temperatures where quantum mechanics can induce specific selectivity in chemical reactivity 2003 Elsevier Science B.V. All rights reserved.

Exact quantum calculations of the kinetic isotope effect: Cross sections and rate constants for the F+HD reaction and role of tunneling

In this paper we present integral cross sections (in the 5-220 meV collision energy range) and rate constants (in the 100-300 K range of temperature) for the F+HD reaction leading to HF+D and DF+H. The exact quantum reactive scattering calculations were carried out using the hyperquantization algorithm on an improved potential energy surface which incorporates the effects of open shell and fine structure of the fluorine atom in the entrance channel. The results reproduce satisfactorily molecular beam scattering experiments as well as chemical kinetics data for both the HF and DF channels. In particular, the agreement of the rate coefficients and the vibrational branching ratios with experimental measurements is improved with respect to previous studies. At thermal and subthermal energies, the rates are greatly influenced by tunneling through the reaction barrier. Therefore exchange of deuterium is shown to be penalized with respect to exchange of hydrogen, and the isotopic branching exhibits a strong dependence on translational energy. Also, it is found that rotational excitation of the reactant HD molecule enhances the production of HF and decreases the reactivity at the D end, obtaining insight on the reaction stereodynamics.

Exact state-to-state quantum dynamics of the F + HD --> HF(v' = 2) + D reaction on model potential energy surfaces.

In this paper, we present the results of a theoretical investigation on the dynamics of the title reaction at collision energies below 1.2 kcal/mol using rigorous quantum reactive scattering calculations. Vibrationally resolved integral and differential cross sections, as well as product rotational distributions, have been calculated using two electronically adiabatic potential energy surfaces, developed by us on the basis of semiempirical modifications of the entrance channel. In particular, we focus our attention on the role of the exothermicity and of the exit channel region of the interaction on the experimental observables. From the comparison between the theoretical results, insight about the main mechanisms governing the reaction is extracted, especially regarding the bimodal structure of the HF(v = 2) nascent rotational state distributions. A good overall agreement with molecular beam scattering experiments has been obtained.

The A+BC reaction by the hyperquantization algorithm: the symmetric hyperspherical parametrization for J > 0

Abstract The methodology of the hyperspherical coordinate approach to triatomic reactions is presented, special emphasis being given to the extension of the hyperquantization algorithm in the symmetric parametrization to the general case of nonzero total angular momentum. The discrete analogs of hyperspherical harmonics, i.e. functions orthonormal on a lattice of points covering the interaction region, are used as basis sets to compute the adiabatic hyperspherical states parametrically dependent on the hyperradius which serve as effective potentials for reactive scattering. The relevant aspects of the method are that no integrals have to be calculated and the Hamiltonian matrix is sparse and can be evaluated analytically, using angular momentum coupling theory. A survey of numerical results and extensions is given.

The He + H2+ → HeH+ + H reaction: Ab initio studies of the potential energy surface, benchmark time-independent quantum dynamics in an extended energy range and comparison with experiments

In this work we critically revise several aspects of previous ab initio quantum chemistry studies [P. Palmieri et al., Mol. Phys. 98, 1835 (2000); C. N. Ramachandran et al., Chem. Phys. Lett. 469, 26 (2009)] of the HeH(2)(+) system. New diatomic curves for the H(2)(+) and HeH(+) molecular ions, which provide vibrational frequencies at a near spectroscopic level of accuracy, have been generated to test the quality of the diatomic terms employed in the previous analytical fittings. The reliability of the global potential energy surfaces has also been tested performing benchmark quantum scattering calculations within the time-independent approach in an extended interval of energies. In particular, the total integral cross sections have been calculated in the total collision energy range 0.955-2.400 eV for the scattering of the He atom by the ortho- and para-hydrogen molecular ion. The energy profiles of the total integral cross sections for selected vibro-rotational states of H(2)(+) (v = 0,...,5 and j = 1,...,7) show a strong rotational enhancement for the lower vibrational states which becomes weaker as the vibrational quantum number increases. Comparison with several available experimental data is presented and discussed.

Probabilities for the F+H2→HF+H reaction by the hyperquantization algorithm: alternative sequential diagonalization schemes

This work reports on the performances of the hyperquantization algorithm in the symmetric hyperspherical coordinate representation for the F+H2 reaction. The use of alternative sequential diagonalization schemes has greatly reduced the computing time and memory requirements, making the technique very efficient and competitive for applications to atom–diatom reactions for the entire range of hyperradial variable ρ. The effectiveness of the sequential diagonalization-truncation depends on the topology of the potential energy surface, which varies along different ranges of the hyperradius. The appearance at ρ≈4 a0 of the ridge line on the potential energy surface, which separates the reactant and product valleys, marks the transition between the regions of preferential applicability of two alternative ways to perform sequentially the diagonalization of the fixed-ρ Hamiltonian matrix. Reaction probabilties for total zero angular momentum are reported and compared with previous calculations.