Interactive Tool for Visualization of Adiabatic Adjustment in APH Coordinates for Computational Studies of Vibrational Motion and Chemical Reactions

The adiabatically-adjusting principal-axes hyperspherical (APH) coordinates reviewed in this letter are one of the best coordinate sets developed for computational treatment of spectroscopy and dynamics of triatomic molecules. Unfortunately, it is not so easy to understand and interpret them, compared to other simpler coordinates, like valence coordinates or Jacobi coordinates. To address this issue, we developed a desktop application called APHDemo. This tool visualizes the process of adjustment of the APH coordinates to the shape of a triatomic molecule during molecular vibrations or chemical reaction, and helps to understand their physical meaning without going into complicated math

Theoretical Study of Ozone Forming Recombination Reaction and Anomalous Isotope Effect Associated with It

The ozone forming recombination reaction stands out among many chemical processes that take place in the atmosphere. This reaction is responsible for the reconstruction of ozone layer, which protects life on Earth from harmful ultra-violate radiation and is a source of so-called anomalous isotope effect in ozone. The reaction was intensively studied, but at a very basic level. There were only couple of papers where the recombination rate coefficient was computed and found to roughly agree with the experimental data. In this dissertation, the recombination process in ozone is approached using new and efficient method, which includes several modern techniques. The rovibrational scattering resonances of O3 are characterized by solving three-dimensional time-independent Schrödinger equation in symmetric-top approximation. The widths (or lifetimes) of scattering resonances are computed using complex absorbing potential. The high efficiency is achieved by using convenient vibrational coordinates, optimal grid for dissociative coordinate and construction of small Hamiltonian matrix in locally optimal basis. The symmetry of the problem is also utilized by implementing a symmetry-adapted basis for one of vibrational coordinates. Stabilization of scattering resonances is described approximately, using mixed quantum/classical theory, for which an efficient frozen rotor approximation is developed. The rate coefficient of ozone recombination, predicted here for unsubstituted ozone, 48O3, as well as its pressure and temperature dependencies, agrees very well with experimental data. The isotope effects, one related to zero-point energy and another to symmetry, are studied for a limited number of rotational excitations and for two isotopologues 50O3 and 52O3 (singly and doubly substituted with 18O). Both effects were found to be in the right direction and of right order of magnitude. The width of scattering resonances control these isotope effects. The approach is universal and can be applied to any other similar system, for example, S3

A quantum and semiclassical study of dynamical resonances in the C + NO-->CN + O reaction

Accurate quantum mechanical reactive scattering calculations were performed for the collinear C+NO-->CN+O reaction using a polynomial-modified London Eyring Polanyi Sato (PQLEPS) potential energy surface (PES), which has a 4.26 eV deep well in the strong interaction region, and a reference LEPS PES, which has no well in that region. The reaction probabilities obtained for both PESs show signatures for resonances. These resonances were characterized by calculating the eigenvalues and eigenvectors of the collision lifetime matrix as a function of energy. Many resonances were found for scattering on both PESs, indicating that the potential well in the PQLEPS PES does not play the sole role in producing resonances in this relatively heavy atom system and that Feshbach processes occur for both PESs. However, the well in the PQLEPS PES is responsible for the differences in the energies, lifetimes, and compositions of the corresponding resonance states. These resonances are also interpreted in terms of simple periodic orbits supported by both PESs (using the WKB formalism), to further illustrate the role played by that potential well on the dynamics of this reaction. The existence of the resonances is associated with the dynamics of the long-lived CNO complex, which is much different than that of systems having an activation barrier. Although these results were obtained for a collinear model of the reaction, its collinearly-dominated nature suggests that related resonant behavior may occur in the real world

Microscopic derivation of multi-channel Hubbard models for ultracold nonreactive molecules in an optical lattice

Recent experimental advances in the cooling and manipulation of bialkali dimer molecules have enabled the production of gases of ultracold molecules that are not chemically reactive. It has been presumed in the literature that in the absence of an electric field the low-energy scattering of such nonreactive molecules (NRMs) will be similar to atoms, in which a single $s$-wave scattering length governs the collisional physics. However, in Ref. [1], it was argued that the short-range collisional physics of NRMs is much more complex than for atoms, and that this leads to a many-body description in terms of a multi-channel Hubbard model. In this work, we show that this multi-channel Hubbard model description of NRMs in an optical lattice is robust against the approximations employed in Ref. [1] to estimate its parameters. We do so via an exact, albeit formal, derivation of a multi-channel resonance model for two NRMs from an ab initio description of the molecules in terms of their constituent atoms. We discuss the regularization of this two-body multi-channel resonance model in the presence of a harmonic trap, and how its solutions form the basis for the many-body model of Ref. [1]. We also generalize the derivation of the effective lattice model to include multiple internal states (e.g., rotational or hyperfine). We end with an outlook to future research.Comment: 19 pages, 4 figure

Theoretical study of weakly bound vibrational states of the sodium trimer : numerical methods; prospects for the formation of Na3 in an ultracold gas

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Time-Dependent Quantum Reactive Scattering in Hyperspherical Coordinates

We present a time-dependent hyperspherical, wave packet method for calculating three atom state-to-state S-matrix elements.The wave packet is propagated in time using adiabatically adjusting, principal axes hyperspherical (APH) coordinates that treat all arrangement channels equivalently, allowing the simultaneous analysis of the products in all three arrangement channels.We take advantage of the symmetry of the potential energy surface and decompose the initial wave packet into its component irreducible representations, propagating each component separately.Each packet is analyzed by projecting it onto the hyperspherical basis at a fixed, asymptotic hyperradius, andirreducible representation dependent S-matrix elements are obtained by matching the hyperspherical projections to symmetry-adapted Jacobi coordinate boundary conditions.We obtain arrangement channel-dependent S-matrix elements as linear combinations of the irreducible representation dependent elements.We derive and implement a new three-dimensional Sylvester-like algorithm that reduces the number of multiplications required to apply the Hamiltonian to the wave packet, dramatically increasing the computational efficiency.A convergence study is presented to show the behavior of the results as the initial parameters are varied and to determine the values of those parameters that give accurate results.State-to-state H+H2 and F+H2 results for zero total angular momentum are presented and show excellent agreement with time-independent benchmark results

Quantum mechanical hydrogen-hydrogen collisional cross section calculation for astrophysics

The purpose of this work is to perform a quantum mechanical calculation of the collisional state-to-state cross sections for H-H2 required for astrophysical modeling. Previous quantum and semi-classical cooling rates computed from cross sections have shown unexplained discrepancies. This attempts to clarify the situation and provide reliable cross sections to the astrophysical community. As a side benefit of this calculation geometric phase effects in the H-H2 collision dynamics are investigated at higher energies than previously attempted. Cooling is critical to the formation of the first objects formed in the early universe, and other diverse phenomenon of interest to astrophysics. For instance, in order to collapse into objects, the gravitational potential energy of primordial density fluctuations must be radiated away. The most abundant element in the universe is hydrogen, and cooling processes involving hydrogen are important in several contexts

Quantum theory of chemical reactions in the presence of electromagnetic fields

We present a theory for rigorous quantum scattering calculations of probabilities for chemical reactions of atoms with diatomic molecules in the presence of an external electric field. The approach is based on the fully uncoupled basis set representation of the total wave function in the space-fixed coordinate frame, the Fock-Delves hyperspherical coordinates and adiabatic partitioning of the total Hamiltonian of the reactive system. The adiabatic channel wave functions are expanded in basis sets of hyperangular functions corresponding to different reaction arrangements and the interactions with external fields are included in each chemical arrangement separately. We apply the theory to examine the effects of electric fields on the chemical reactions of LiF molecules with H atoms and HF molecules with Li atoms at low temperatures and show that electric fields may enhance the probability of chemical reactions and modify reactive scattering resonances by coupling the rotational states of the reactants. Our preliminary results suggest that chemical reactions of polar molecules at temperatures below 1 K can be selectively manipulated with dc electric fields and microwave laser radiation.Comment: Accepted for publication in J. Chem. Phy

Three Dimensional Atom-Diatom Reactive Scattering Calculations Using Symmetrized Hyperspherical Coordinates

The focus of this thesis is the use of symmetrized hyperspherical coordinate techniques in the accurate calculation of differential cross sections for the reactive collision of an atom with a diatomic molecule in three-dimensional space. A single set of symmetrized hyperspherical coordinates treats all regions of configuration space in an equivalent inelastic scattering problem which is conceptually and computationally easier to handle. The work described here represents the first successful application of any accurate hyperspherical coordinate methodology to atom-diatom reactive scattering in three-dimensional space. This methodology has permitted the calculation of zero total angular momentum (J = 0) partial wave transition probabilities and associated phases over a significantly larger range of collision energies (up to 1.6 eV total energy) than previously possible for the system H + H₂. The numerical stability of the treatment is sufficiently high to permit the first lifetime matrix analysis of the resonance structure of H + H₂ based on scattering matrices from our accurate calculations. This analysis reveals a series of 6 resonance states in the J = 0 partial wave, some of which have not been seen before. The symmetrized hyperspherical coordinate methodology is presented in detail. A selection of surface functions and scattering results for J = 0 H + H₂ using the LSTH potential energy surface are presented and discussed. In addition, a small number of results from the Porter-Karplus potential energy surface are also given.</p