Collinear collisions in a double-morse well

We discuss the fraction of chaotic trajectories in a bound system near the dissociation limit, and the fraction of apparent chaos in scattering trajectories above that energy. Both depend in an oscillatory manner on the coupling parameter δ = m/(m + M), which means that not the coupling as such is responsible for more or less chaos. Rather, two different kinds of resonance condition determine what counts as chaos in the bound and scattering cases. The second resonance condition, determining more or less easy passage through the well for scattering trajectories, determines also the average lifetime and the RRKM-ness of unimolecular complex decay. They depend also in an oscillatory way on the mass ratio.     

Relaxation in a double potential well

Kinetic equations are deduced for the density matrix describing the relaxation in a two-level system interacting with a heat reservoir. It is assumed that the frequency of transition between the levels is small relative to the characteristic frequency of fluctuation in the reservoir; the interaction may be of any strength. The equations are used to discuss the relaxation in such a system.     

Trapping of a particle in a short-range harmonic potential well

Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed.     

Optical potential calculations for molecular collisions

The Feshbach optical formalism is applied to elastic, nonreactive atom-diatom scattering on a single potential energy surface. The optical potential depends on GQ, the resolvent of E-QHQ, where Q projects onto open as well as closed channels. A method for generating GQ is developed which goes beyond the free-space approximation by partitioning the radial part of the intermolecular separation into a set of intervals, on each of which the projected interaction QVQ is represented by a constant diagonal form. The resulting GQ is used in calculations on a model collinear system. The calculations are carried out with various approximations on the full nonlocal optical potential equation for Pψ Emphasis is placed on two of these, one of which is characterized by a local homogeneous equation for Pψ, and the other by a local inhomogeneous equation for Pψ.     

Trapping of positronium in a size-dependent spherical square well potential

The real trapping potential energy U(r) of positronium in vacancy-type holes and self-sustaining bubbles in liquids is replaced by a spherical square well potential of finite energy depth U_m and the scaling procedure proposed by Yu et al. is applied. Available data for the ortho-positronium lifetime in molecular crystals and in liquids are re-examined and a unique relation is found between the potential energy depth U_m and the calculated radius R of the trapping site. The general form of a surface-enhanced real potential energy U(r) which is compatible with the behaviour of U_m is proposed.     

Combining transition state calculations with quasiclassical trajectory calculations: II. Collinear collisions involving vibrationally excited reagents

Conventional quasiclassical trajectory simulations of collinear reactive collisions, A + BC (v = 0, 1 and 2) → AB + C, have been compared with trajectories integrated forward and backward in time from points along a dividing line S^* in the strong interaction zone. Calculations have been performed on three different potential energy surfaces, ranging from a strongly attractive surface with a 1 kcal mol⁻¹ barrier to a strongly repulsive surface with a 10 kcal mol⁻¹ barrier, and for all combinations of light (1 amu) and heavy (35 amu) atoms. Two methods of selecting S^* have been examined. The first, based on defining vibrationally adiabatic states orthogonal to the minimum energy path by an approximate analysis, works well for many combinations of potential energy surface and atomic masses. However, a better method is to use pods (periodic orbiting dividing surfaces) for which the action over one cycle of the pods motion is equal to (v + 1/2)h. In only a few cases, where the pods cross the minimum energy path after substantial curvature in the latter, is the agreement between the two sets of calculations less than very good. The results confirm that reagent vibrational motion is in many cases strongly adiabatic up to S^* (i.e. the transition state), and suggest that similar combined calculations on three-dimensional systems should provide a substantial saving in computer effort compared with conventional quasiclassical trajectory methods.     

Intermolecular potential for thermal H2O-He collisions

Theoretical potentials for rotational excitation of H2O by He were constructed via several methods, all of which start with a large basis set SCF interaction. The semiempirical Hartree-Fock with damped dispersion (HFD) model adds a damped long-range attraction with parameters adjusted to fit experimental total differential cross sections. Purely ab initio potentials add correlation energies obtained via perturbation theory (MP2 and MP4) or a variational method (ICF1). Scattering calculations were performed on all surfaces to compare with available beam scattering and pressure broadening data and to assess sensitivity of state-to-state rates to uncertainties in the potential. From comparison with the limited experimental data, the ICF1 surface appears to be marginally better than the MP4 surface. Thermal rates calculated from this surface should be accurate to better than 50%, at least for the larger, more important rates.     

Thermodynamic and structural properties of a fluid with a rectangular well potential

Thermodynamic and structural properties of a system with a rectangular well potential are investigated in the supercritical region using the approximate Martynov-Sarkisov (MS) integral equation for the binary distribution function. It is shown that, in contrast to other approximations, in particular the Percus-Yevick equation (PY) and hypernetted chain approximation (HNC), the MS equation describes the limits of existence of the homogeneous phase.Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino. State University of New York, Mt. Sinai Medical Center, USA. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 2, pp. 88–95, March–April, 1993.     

Shannon information entropy for a hyperbolic double‐well potential

We use the ansatz method to obtain the symmetric and antisymmetric solutions of a hyperbolic double‐well potential by solving the Heun differential equation. The Shannon entropy is studied. The position S_x and momentum S_p information entropies for the low‐lying two states N = 1, 2 are calculated. Some interesting features of the information entropy densities ρ_s(x) and ρ_s(p) as well as the probability density ρ(x) are demonstrated. We find that ρ(x) is equal or greater than 1 at positions for the allowed potential‐depth values of U₀ = 595.84 (symmetric case) and U₀ = 1092.8 (antisymmetric case). This arises from the fact that most of the density is less than 1, the curve has to rise higher than 1 to have a total area of 1 as required for all probability distributions. We find that the position information entropy S_x decreases with the potential strength but the momentum entropy S_p is contrary to the S_x. The Bialynicki‐Birula–Mycielski inequality is also tested and found to hold for these cases. © 2015 Wiley Periodicals, Inc.     

Quantum tunneling process for double well potential

Quantum tunneling effects of Gaussian wave packet in one‐ and two‐dimensional double well potentials are investigated using quantum Liouville equation for time evolution of Wigner distribution in phase space. It is shown that a trajectory‐based solution of this problem can be constructed by the entangled trajectory ensemble simulating the evolving quantum state. Quantum effects arise in this approach as a breakdown of the statistical independence of the trajectory ensemble. © 2014 Wiley Periodicals, Inc.     

Perturbation theory for liquids with a hard sphere plus square well potential

Numerical data have been obtained for a series of perturbation theory in the form of Barker-Henderson discrete representation. A hard sphere liquid (864 particles) was modeled by the Monte Carlo method for 106 values of occupancy from the range η = 0.005–0.530 (step 0.005); the well width was varied from 0 to 1.5 hard sphere diameters. For each occupancy, averaging was done over 60·10⁶ ensembles. Approximating analytical expressions are given as functions of well density and width for the first three terms of the free energy decomposition. For reduced temperature T* = 1.0, the standard error in the free energy calculation (three orders of perturbation theory if the above expressions are used) is of the order of ±0.001. Analysis of four-particle correlations revealed peaks at distances of 1.35 Å and 1.65 Å (η = 0.53) in the high-density region of hard sphere liquids, which are absent in crystals and dense liquids. It is analyzed whether the results are useful for realization of WCA theory of simple liquids in second order perturbation theory.     

Extended diffusion in a double well potential: Transition from classical to quantum regime

The transition between the classical and quantum regimes in the diffusion of a particle in a 2-4 double-well potential is treated via the strong collision model in the high-temperature limit. Both the classical and semiclassical position correlation functions, their spectra, and correlation times are evaluated using the memory function formalism. It is shown that even in the high temperature limit, marked classical-quantum transition effects appear in the observables when collisions are rare.     

A simple and effective technique to locate quasi-degeneracy in a symmetric double well potential

Perturbation theory based model can be used to locate the quasi-degeneracy in an arbitrary double well potential. This method, extensively explain the effect of the coupling term on pair of states called quasi-degenerate. This model helps us to calculate the energy of the pair of quasi-degenerate states using appreciably small basis. Dispersion equation corresponding to the split energy levels are presented in a very explicit form. Numerical calculation shows that the proposed method can give extremely accurate results for symmetric double-well potentials.     

Classical dependence of polarization on potential energy surface in rotationally inelastic collisions

Quasiclassicol trajectory calculations have been performed for model potential energy surfaces to investigate polarization in (j,m_j) → (j',m_j) integral cross sections For j = 0, it was found that the occurrence of polarization requires an attractive well, and that it be in the collinear configuration Results for j≠ 0 are also presented.     

Collinear collision of an atom with a homonuclear diatomic molecule

The problem of collinear scattering of an atom from a homonuclear diatomic molecule is formulated in terms of a first-order nonlinear matrix differential equation for the variable coefficient of reflection. For a homonuclear molecule when the target Hamiltonian is invariant under the parity transformation, only transitions between even states or odd states are possible. This selection rule reduces the number of open or closed channels that contribute to the reflection and transmission coefficients. But for numerical calculation, under the conditions of the problem, one can approximate the target Hamiltonian by the Hamiltonian of a displaced harmonic oscillator. In this approximation, the reflectional symmetry of the Hamiltonian is not preserved and transitions between any two levels of the target are possible. To simplify the problem further, the interaction between the projectile and the target is assumed to be a sum of two Gaussian terms. For this combination of the potentials the many-channel interaction can be expressed analytically. By fitting the Lennard–Jones potential with a sum of two Gaussian potentials and solving the matrix differential equation, transition probabilities are obtained for the He? H₂ collision. The numerical results are compared with the results found by Secrest and Johnson, and by Clark and Dickinson.     

Exact solutions of an asymmetric double well potential

Journal of Mathematical Chemistry - The analytical solutions of an asymmetric double well potential $$V(x)=a, x^2-b, x^3+c, x^4$$ are found to be a triconfluent Heun function $$H_{T}(alpha ,...     

Collinear two-photon excitation of indium rydberg states in a fast atomic beam

The 29p-Rydberg state of neutral indium was produced by double resonant two-photon excitation in a fast atomic beam and detected via field ionization in a longitudinal electric field.     

Semiclassical path integral theory of a double‐well potential in an electric field

A recently published methodology based on semiclassical path integral (SCPI) theory was implemented in the case of a model of a double‐well potential perturbed by a static electric field, with application to the inversion frequency of NH₃. This model was chosen as an idealized case for testing of the present approach, as well as for quantum mechanical models that might be applied in the future. The calculations were concerned with the variation of the frequency of inversion as a function of field strength, F, and of distance, x_f (from the symmetric point x_o = 0), where the field is “felt.” It is found that this variation occurs sharply in very small regions of values of these parameters, and the system switches from internal oscillation to diffusion to the continuum. The fact that the theory is in analytic form allows the extraction of results and conclusions not only at the full SCPI level, but also at the Jeffreys–Wentzel–Kramers–Brillouin (JWKB) level. Comparison shows that the discrepancy sets in as the field strength increases, in accordance with the well‐known limitations of the JWKB method regarding its dependence on the degree of variation of the potential as a function of position. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

共线散射体系A+BC的平-振能量传递──无限维李代数处理方法

利用无限维李代数方法处理了在BC分子能谱中含有二级与三级非简谐项的散射体系A＋BC的平-振能量传递问题，获得了散射过程的含有主要动力学参量的跃迁矩阵元和跃迁几率的解析表达式     

Direct versus resonances mediated F+OH collisions on a new 3A" potential energy surface

A theoretical study of the F(2P) + OH(2Pi) --> HF(1Sigma+) + O(3P) reactive collisions is carried out on a new global potential energy surface (PES) of the ground 3A" adiabatic electronic state. The ab initio calculations are based on multireference configuration interaction calculations, using the aug-cc-pVTZ extended basis sets of Dunning et al. A functional representation of the PES shows no nominal barrier to reaction, contrary to previous results by others. Wave packet and quasiclassical trajectory calculations have been performed for this PES to study the F + OH(v = 0,j) reactive collision. The comparison was performed at fixed and constant values of the total angular momentum from 0 to 110 and relative translational energy up to 0.8 eV. The reaction presents a dynamical barrier, essentially due to the zero-point energy for the bending vibration near the saddle point. This determines two different reaction mechanisms. At energies higher than approximately 0.125 eV the reaction is direct, while below that value it is indirect and mediated by heavy-light-heavy resonances. Such resonances, also found in the simulations of the photodetachment spectrum of the triatomic anion, manifest themselves in the quasiclassical simulations, too, where they are associated to periodic orbits.