Hans‐Dieter Meyera

Bio: Hans‐Dieter Meyera is an academic researcher. The author has contributed to research in topics: Equations of motion & S-matrix. The author has an hindex of 1, co-authored 1 publications receiving 623 citations.

A classical analog for electronic degrees of freedom in nonadiabatic collision processes

Abstract: It is shown how a formally exact classical analog can be defined for a finite dimensional (in Hilbert space) quantum mechanical system. This approach is then used to obtain a classical model for the electronic degrees of freedom in a molecular collision system, and the combination of this with the usual classical description of the heavy particle (i.e., nuclear) motion provides a completely classical model for the electronic and heavy particle degrees of freedom. The resulting equations of motion are shown to be equivalent to describing the electronic degrees of freedom by the time‐dependent Schrodinger equation, the time dependence arising from the classical motion of the nuclei, the trajectory of which is determined by the quantum mechanical average (i.e., Ehrenfest) force on the nuclei. Quantizing the system via classical S‐matrix theory is shown to provide a dynamically consistent description of nonadiabatic collision processes; i.e., different electronic transitions have different heavy particle trajectories and, for example, the total energy of the electronic and heavy particle degrees of freedom is conserved. Application of this classical model for the electronic degrees of freedom (plus classical S‐matrix theory) to the two‐state model problem shows that the approach provides a good description of the electronic dynamics.

Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids

Abstract: From a discretization of the path integral formulation of quantum mechanics, it is possible to relate equilibrium quantum many body theory to classical statistical mechanics. In this paper, we significantly extend and analyze this well known isomorphism in terms of the equilibrium theory of classical molecular fluids composed of flexible polyatomic species. We show how quantum influence functionals are isomorphic to classical cavity distribution functions. The former describe the influence of surrounding media on the dynamics of quantal degrees of freedom, and the latter describe environmental effects for classical models of flexible molecules and chemical equilibria. The connection allows the use of classical theories to perform nonperturbative calculations of influence functionals which treat the influence functionals and many body correlation functions in a self‐consistent fashion. We illustrate the computational advantages of the method by studying its predictions for a hard sphere model of liquid helium above the l transition. The nature of quantum indistinguishability of identical particles (i.e., quantum exchange) is treated in our theory in terms of an exact isomorphism with chemical equilibria. This connection allows the treatment of exchange in condensed phases in terms of the classical law of mass action, and provides a computational advance over existing methods for interacting systems. By picturing exchange in terms of classical association equilibrium, we arrive at a view (hinted at long ago by Feynman and by Penrose and Onsager) in which the Bose condensation is related to an equilibrium polymeric sol–gel transition. Thus, below the l transition, the correlations in liquid helium are equivalent to those in a classical fluid containing a finite concentration of macroscopic polymers. We stress how the path integral aspect of the isomorphism leads to useful geometrical interpretations of quantum phenomena. For example, tunneling phenomena can be viewed in terms of solitonic (or instantonic) configurations or flexible chain molecules. With this picture, we show how the isomorphism can be employed to understand both adiabatic and nonadiabatic solvent effects on chemical bonding. For concreteness, we provide a detailed analysis of a particular model of the chemical bond for which a partial summation over intermediate quantum paths leads to an Ising model problem in the isomorphism. While applications like this are presented in the form of qualitative illustrations, a variety of methods can be employed to produce quantitative results. We sketch how these calculations can be performed for various problems, making connections with methods like the renormalization group (RG) technique. The classical isomorphism together with the modern theory of classical polyatomic systems provides a powerful framework for quantitative solutions of condensed matter quantum mechanical problems.

Ab Initio Multiple Spawning: Photochemistry from First Principles Quantum Molecular Dynamics

Abstract: The ab initio multiple spawning (AIMS) method is a time-dependent formulation of quantum chemistry, whereby the nuclear dynamics and electronic structure problems are solved simultaneously. Quantum mechanical effects in the nuclear dynamics are included, especially the nonadiabatic effects which are crucial in modeling dynamics on multiple electronic states. The AIMS method makes it possible to describe photochemistry from first principles molecular dynamics, with no empirical parameters. We describe the method and present the application to two molecules of interest in organic photochemistryethylene and cyclobutene. We show that the photodynamics of ethylene involves both covalent and ionic electronic excited states and the return to the ground state proceeds through a pyramidalized geometry. For the photoinduced ring opening of cyclobutene, we show that the disrotatory motion predicted by the Woodward−Hoffmann rules is established within the first 50 fs after optical excitation.

The Semiclassical Initial Value Representation: A Potentially Practical Way for Adding Quantum Effects to Classical Molecular Dynamics Simulations

Abstract: The semiclassical (SC) initial value representation (IVR) provides a potentially practical way for adding quantum mechanical effects to classical molecular dynamics (MD) simulations of the dynamics of complex molecular systems (i.e., those with many degrees of freedom). It does this by replacing the nonlinear boundary value problem of semiclassical theory by an average over the initial conditions of classical trajectories. This paper reviews the background and rebirth of interest in such approaches and surveys a variety of their recent applications. Special focus is on the ability to treat the dynamics of complex systems, and in this regard, the forward−backward (FB) version of the approach is especially promising. Several examples of the FB-IVR applied to model problems of many degrees of freedom show it to be capable of describing quantum effects quite well and also how these effects are quenched when some of the degrees of freedom are averaged over (“decoherence”).

Ring-Polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space

Abstract: This article reviews the ring-polymer molecular dynamics model for condensed-phase quantum dynamics. This model, which involves classical evolution in an extended ring-polymer phase space, provides a practical approach to approximating the effects of quantum fluctuations on the dynamics of condensed-phase systems. The review covers the theory, implementation, applications, and limitations of the approximation.

Modeling the Kinetics of Bimolecular Reactions

Abstract: A review of the theoretical and computational modeling of bimolecular reactions is given. The review is divided into several sections which are as follows: gas-phase thermal reactions; gas-phase state-selected reactions and product state distributions; and condensed-phase bimolecular reactions. The section on gas-phase thermal reactions covers the enthalpies and free energies of reaction, kinetics, saddle points and potential energy surfaces, rate theory for simple barrier reactions and bimolecular reactions over potential wells. The section on gas-phase state-selected reactions focuses on electronically adiabatic reactions and electronically nonadiabatic reactions. Finally, the section on condensed-phase bimolecular reactions covers reactions in liquids, reactions on surfaces and in solids and tunneling at low temperature.