Electron Nuclear Dynamics Theory Research Articles

Statistical-law formulas for zero- to two-electron-transfer probabilities in proton-molecule and proton cancer therapy reactions from electron nuclear dynamics theory.

We present the first quantum-mechanical derivation of statistical-law formulas to calculate zero- to two-electron transfers (ETs) in proton-molecule reactions. The original statistical derivation assumed that the n-ET probabilities of N electrons in a shell obey an N-trial binomial distribution with success probability equal to an individual one-ET probability; the latter was heuristically identified with the number of transferred electrons from the integrated charge density. The obtained formulas proved accurate to calculate ET cross sections in proton-molecule and proton cancer therapy (PCT) reactions. We adopt the electron nuclear dynamics (END) theory in our quantum-mechanical derivation due to its versatile description of ETs via a Thouless single-determinantal state. Since non-orthogonal Thouless dynamical spin-orbitals pose mathematical difficulties, we first present a derivation for a model system with N ≥ 2 electrons where only two with opposite spins are ET active; in that scheme, the Thouless dynamical spin-orbitals become orthogonal, a fact that facilitates a still intricate derivation. In the end, we obtain the number of transferred electrons from the Thouless state charge density and the ETs probabilities from the Thouless state resolution into projectile-molecule eigenstates describing ETs. We prove that those probabilities and numbers of electrons interrelate as in the statistical-law formulas via their common dependency on the Thouless variational parameters. We review past ET results of proton-molecule and PCT reactions obtained with these formulas in the END framework and present new results of H+ + N2O. We will present the derivation for systems with N > 2 electrons all active for ETs in a sequel.

Some coherent-states aspects of the electron nuclear dynamics theory: past and present

Past and present coherent-states (CS) efforts with the electron nuclear dynamics (END) theory at its simplest level (SL-END) are reviewed. END is a time-dependent, variational, non-adiabatic, direct-dynamics method that describes simultaneously the nuclei and electrons of a molecular system. Within that characterization, SL-END adopts a classical-mechanics description for the nuclei and a quantum single-determinantal representation for the electrons. From its very inception, SL-END has been associated with the CS theory. CS sets are continuous and over-complete sets that satisfy the resolution of identity with a positive measure. Different CS sets can play an astonishing number of roles within SL-END that have several practical consequences. Originally, SL-END utilized the canonical and Thouless CS sets to correctly represent the nuclear and electronic parts of the SL-END wavefunction, respectively, thus defining a proper phase space for the SL-END dynamical equations. Later, canonical and rotational CS sets were used for reconstructing quantum vibrational and quantum rotational descriptions from the SL-END classical nuclear dynamics. That development proved essential to calculate state-resolved properties in ion-molecule and atom-molecule collisions with SL-END. Present CS efforts include a time-dependent Kohn-Sham density-functional-theory direct-dynamic method in the END framework and a CS approach to the charge-equilibration model inter alia.

Nonadiabatic evolution of electronic states by electron nuclear dynamics theory

AbstractThe problem of how to determine the nonadiabatic content of any given dynamic process involving molecular motion is addressed in the context of Electron Nuclear Dynamics (END) theory. Specifically, it is proposed to cast the dynamic END wave function into the language of static electronic configurations with time dependent complex‐valued amplitudes. This is achieved by adiabatic transport of an electronic basis along the classical nuclear trajectories of the studied molecular system, as yielded by END simulation. Projecting the dynamic wave function on this basis yields a natural distinction between adiabatic and nonadiabatic components of the motion considered. Tracing the evolution of the leading configurations is shown to be a helpful device for clarifying the physical nature of electronic excitation processes. For illustration of these concepts, dynamic configuration analysis is applied to the scattering of a proton by a lithium atom. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Abstraction and exchange mechanisms for the D2+NH3+ reaction at hyperthermal collision energies

Minimal Electron Nuclear Dynamics theory is applied to D2+NH3+ reaction at collision energies from 6 to 16 eV in the center-of-mass frame. This method for direct nonadiabatic dynamics describes the electrons with a family of complex determinantal wave functions in terms of nonorthogonal spin orbitals and treats the nuclei as classical particles. There are no geometrical constraints imposed on this six-atom system. Emphasis is put on the details of the abstraction and exchange reaction mechanisms for ground-state reactants. Comparisons are made to recent molecular-beam experiments.

Rovibrational analysis of molecular collisions using coherent states

A generalization of the Prony method, which fits a set of complex exponentials to a time dependent signal, is presented. This generalized Prony method is applied to analyze rovibrational dynamics of products in a theoretical treatment of molecular collisions. Employing suitable coherent states an a posteriori quantum analysis can be performed on molecular trajectories with classical nuclei obtained with electron nuclear dynamics theory. Illustrative calculations are presented for state resolved cross sections of proton collisions with water molecules and compared to results from crossed beam experiments.

Pseudorotational dynamics of H3+ and Li3+

AbstractThe origin of the pseudoprecession phenomenon is investigated through a computational study of the time evolution of H3+ and Li3+ by electron nuclear dynamics theory. In particular, the pseudorotation of both molecules is shown to induce a spatial rotation, which in turn leads to Coriolis coupling of the two orthogonal nuclear shape deformation modes. This effect is rooted in an anisotropy of the molecular ground state potential energy surface that is caused by the interaction between the D3h ground state and a twofold degenerate first excited state. Computations are performed for a variety of vibrational energies. In addition, the impact of the anharmonicity of the ground state potential surface on the shape deformation modes and the coupling between them is discussed. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Direct differential-cross-section calculations for ion-atom and atom-atom collisions in the keV range

The direct differential cross section and the total cross section for scattering of 0.5-, 1.5-, and 5.0-keV ${\mathrm{H}}^{+},$ H, and He projectiles by He and Ne targets over the laboratory scattering angle range $0.01\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}10.0\ifmmode^\circ\else\textdegree\fi{}$ are studied using the electron nuclear dynamics theory, which treats the simultaneous dynamics of all electrons and nuclei. Emphasis is put on the quantum effects of the forward peak scattering. Comparison of the present results with available experimental data shows very good agreement.

Pseudoprecession of triatomic systems by electron nuclear dynamics theory

A variety of dynamic effects related to the pseudorotation of triatomic singly charged species is explored using the electron nuclear dynamics (END) theory. The concepts relevant to the motion studied are developed through the analysis of the simplest molecular species capable of pseudorotation, namely H\documentclass{article}\pagestyle{empty}\begin{document}$_{3}^{+}$\end{document}. It is shown that the wave function for this system leads to anharmonicities in the ground-state potential surface, which make the limiting case of circular pseudorotation unattainable. Initial asymmetries between the vibrational modes of the molecule are demonstrated to induce a rotational mode that in turn couples the vibrational degrees of freedom by action of the Coriolis force. Two different dissociation channels open up for the case of large initial momenta: \documentclass{article}\pagestyle{empty}\begin{document}$\mathrm{H_{3}^{+}\to H^{+}+H+H}$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$\mathrm{H_{3}^{+}\to H^{+}+H_{2}}$\end{document}. The latter mechanism is associated with periodic spin exchange between the two bonding H atoms, which introduces a purely electronic time scale into the process besides the nuclear one and thus represents a typical nonadiabatic process. The Jahn–Teller system C\documentclass{article}\pagestyle{empty}\begin{document}$_{3}^{+}$\end{document} exhibits a range of new motional phenomena. In particular, a characteristic frequency shift between the two orthogonal vibrational coordinates is observed, resulting from the anisotropy in the curvature of the C2v minimum of C\documentclass{article}\pagestyle{empty}\begin{document}$_{3}^{+}$\end{document}. It is shown that the Jahn–Teller parameters of the system can in principle be determined from electron nuclear dynamics simulations. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 966–988, 2000

Quantum dynamical studies of H 3

The Electron nuclear dynamics theory is used to study various processes involving the disintegration of an H 3 unit from an initial state of equilateral geometry that is associated with a degeneracy of the electronic system. The electronic wavefunction is initially defined as representation of either of the D 3h doublet components; the corresponding dynamical features are considered in terms of nuclear trajectories for both cases. Disintegration out of a rotating state is shown to yield periodic electronic spin exchange between two bonding H atoms, which is interpreted as a signature of non-adiabatic behavior. Possible applications of this phenomenon in the study of molecular dissociation are discussed.

Electron nuclear dynamics of charge-transfer collisions of protons with atomic oxygen

The electron nuclear dynamics theory is applied to the study of proton collisions with ground-state oxygen atoms at collision energies of 0.5, 1.0, and 1.5 keV. Total electron transfer cross sections are calculated in reasonable agreement with recent expe

Electron nuclear dynamics of H + + H 2O collisions

Proton water collisions at 46 eV in the center of mass frame are studied within the electron nuclear dynamics theory (END). The electronic degrees of freedom are described with a coherent state formulation of determinantal wavefunctions. The nuclei are treated as classical particles but full nonadiabatic couplings are retained. The equations of motion are formulated in a generalized phase space and bypass the use of preconstructed potential energy surfaces. Differential cross sections for inelastic and electron transfer reactions as well as energy transfer are compared with experiment.