Quantum dynamics overview

An overview of the time-dependent wavepacket propagation approach for four-atom reactions together with the construction of ab initio potential energy surfaces sufficiently accurate for quantum dynamics calculations has been presented. Today, we are able to perform the full-dimensional (six degrees-of-freedom) quantum dynamics calculations for four-atom reactions. With the most accurate YZCL2 surface for the benchmark four-atom reaction H2 + OH <-> H+H2O and its isotopic analogs, we were able to show the following ... 

Quantum dynamics on graphs became an issue also in the context of quantum information. Aharonov et.al (1993) pointed out that a random quantum walk on one dimensional chains can be faster than the corresponding classical random walk. Since then, a whole field has emerged dealing with quantum effects on graphs with properties superiour to the corresponding classical operations. For an introductory overview and further references, see Kempe (2003). 

In this chapter, we are concerned with various theoretical formulations that allow us to treat nonadiabatic quantum dynamics in a classical description. To introduce the main concepts, we first give a brief overview of the existing methods and then discuss their application to ultrafast molecular photoprocesses. 

This overview has also considered the advantages and disadvantages of a description using first principles dynamics. Its application to many-atom systems undergoing electronic transitions is a very active and challenging subject of molecular quantum dynamics. 

For the past several years we have been developing and applying quantum dynamics (QD) and quantum-classical molecular dynamics (QCMD) methods, which are based on the explicitly time-dependent Schroedinger equation. For an overview of the models and simulation results see e.g.4 and the references cited... 

With this brief overview of classical theories of unimolecular reaction rate, one might wonder why classical mechanics is so useful in treating molecular systems that are microscopic, and one might question when a classical statistical theory should be replaced by a corresponding quantum theory. These general questions bring up the important issue of quantum-classical correspondence in general and the field of quantum chaos [27-29] (i.e., the quantum dynamics of classically chaotic systems) in particular. For example, is it possible to translate the above classical concepts (e.g., phase space separatrix, NHIM, reactive islands) into quantum mechanics, and if yes, how What is the consequence of... 

To calculate numerically the quantum dynamics of the various cations in time-dependent domain, we shall use the multiconfiguration time-dependent Hartree method (MCTDH) [79-82, 113, 114]. This method for propagating multidimensional wave packets is one of the most powerful techniques currently available. For an overview of the capabilities and applications of the MCTDH method we refer to a recent book [114]. Additional insight into the vibronic dynamics can be achieved by performing time-independent calculations. To this end Lanczos algorithm [115,116] is a very suitable algorithm for our purposes because of the structural sparsity of the Hamiltonian secular matrix and the matrix-vector multiplication routine is very efficient to implement [6]. 

The thirty three papers in the proceedings of QSCP-Xni are divided between the present two volumes in the following manner. The first volume, with the subtitle Conceptual and Computational Advances in Quantum Chemistry, contains twenty papers and is divided into six parts. The first part focuses on historical overviews of significance to the QSCP workshop series and quantum chemistry. The remaining five parts, entitled High-Precision Quantum Chemistry, Beyond Nonrelativistic Theory Relativity and QED, Advances in Wave Function Methods, Advances in Density Functional Theory, and Advances in Concepts and Models, address different aspects of quantum mechanics as applied to electronic structure theory and its foundations. The second volume, with the subtitle Dynamics, Spectroscopy, Clusters, and Nanostructures, contains the remaining thirteen papers and is divided into three parts Quantum Dynamics and Spectroscopy, Complexes and Clusters, and Nanostructures and Complex Systems. ... 

Abstract. This paper presents an overview of the time-dependent quantum wavepacket approach to chemical reaction dynamics. After a brief review of some early works, the paper gives an up-to-date account of the recent development of computational methodologies in time-dependent quantum dynamics. The presentation of the paper focuses on the development of accurate or numerically exact time-dependent methods and their specific applications to tetraatomic reactions. After summarizing the current state-of-the-art time-dependent wavepacket approach, a perspective on future (development is provided. 

In the present contribution I have attempted to give a condensed overview over our work on the quantum dynamics on vibronically coupled PES, considering pedagogic, historic, and systematic aspects in a balanced way. Time-independent and time-dependent phenomena have been addressed. While the examples discussed were necessarily not exhaustive, a set of representative cases has been selected which should cover the most important aspects and their interrelations. In particular, the quantum nature of the phenomena is apparent whenever the discrete level structure of the vibronically coupled states plays a role. Also regarding electronic... 

A brief overview of energy calculations and molecular dynamics approaches currently used to model the dynamics of atomic or molecular clusters has been presented. The discussion has been limited to methods in which the nuclear dynamics are classical. Much effort is currently devoted to the field of quantum dynamics, but such an approach is still limited to systems composed of a few nuclei and a small number of electrons. 

These experiments stimulated theoretical work by us (9-14), independently by Schinke and co-workers (15-17), and recently both groups (18) to rigorously model this unimolecular dissociation. Ab /wiYio-based potential energy surfaces were constructed by these groups, and used in quantum dynamics calculations to obtain the real energies and widths of the HOCl resonances for OH-overtones. The results of our calculations and their interpretation will be reviewed below. However, before describing that work, we present a short overview of the theory and calculation of unimolecular resonances. 

The study of quautum effects associated with nuclear motion is a distinct field of chemistry, known as quantum molecular dynamics. This section gives an overview of the methodology of the field for fiirtlier reading, consult [1, 2, 3, 4 and 5,]. 

For larger systems, various approximate schemes have been developed, called mixed methods as they treat parts of the system using different levels of theory. Of interest to us here are quantuin-seiniclassical methods, which use full quantum mechanics to treat the electrons, but use approximations based on trajectories in a classical phase space to describe the nuclear motion. The prefix quantum may be dropped, and we will talk of seiniclassical methods. There are a number of different approaches, but here we shall concentrate on the few that are suitable for direct dynamics molecular simulations. An overview of other methods is given in the introduction of [21]. 

Most of the AIMD simulations described in the literature have assumed that Newtonian dynamics was sufficient for the nuclei. While this is often justified, there are important cases where the quantum mechanical nature of the nuclei is crucial for even a qualitative understanding. For example, tunneling is intrinsically quantum mechanical and can be important in chemistry involving proton transfer. A second area where nuclei must be described quantum mechanically is when the BOA breaks down, as is always the case when multiple coupled electronic states participate in chemistry. In particular, photochemical processes are often dominated by conical intersections [14,15], where two electronic states are exactly degenerate and the BOA fails. In this chapter, we discuss our recent development of the ab initio multiple spawning (AIMS) method which solves the elecronic and nuclear Schrodinger equations simultaneously this makes AIMD approaches applicable for problems where quantum mechanical effects of both electrons and nuclei are important. We present an overview of what has been achieved, and make a special effort to point out areas where further improvements can be made. Theoretical aspects of the AIMS method are... 

In chapter 1, Profs. Cramer and Truhlar provide an overview of the current status of continuum models of solvation. They examine available continuum models and computational techniques implementing such models for both electrostatic and non-electrostatic components of the free energy of solvation. They then consider a number of case studies with particular focus on the prediction of heterocyclic tautomeric equilibria. In the discussion of the latter they focus attention on the subtleties of actual chemical systems and some of the danger in applying continuum models uncritically. They hope the reader will emerge with a balanced appreciation of the power and limitations of these methods. In the last section they offer a brief overview of methods to extend continuum solvation modeling to account for dynamic effects in spectroscopy and kinetics. Their conclusion is that there has been tremendous progress in the development and practical implementation of useful continuum models in the last five years. These techniques are now poised to allow quantum chemistry to have the same revolutionary impact on condensed-phase chemistry as the last 25 years have witnessed for gas-phase chemistry. 

Nanosecond Absorption Spectroscopy Absorption apparatus, 226, 131 apparatus, 226, 152 detectors, 226, 126 detector systems, 226, 125 excitation source, 226, 121 global analysis, 226, 146, 155 heme proteins, 226, 142 kinetic applications, 226, 134 monochromators/spectrographs, 226, 125 multiphoton effects, 226, 141 nanosecond time-resolved recombination, 226, 141 overview, 226, 119, 147 probe source, 226, 124 quantum yields, 226, 139 rhodopsin, 226, 158 sample holders, 226, 133 singular value decomposition, 226, 146, 155 spectral dynamics, 226, 136 time delay generators, 226, 130. 

After an overview of the main papers devoted to chaos in lasers (Section I.A) and in nonlinear optical processes (Section I.B), we present a more detailed analysis of dynamics in a process of second-harmonic generation of light (Section II) as well as in Kerr oscillators (Section III). The last case we consider particularly in the context of coupled nonlinear systems. Finally, we present a cumulant approach to the problem of quantum corrections to the classical dynamics in second-harmonic generation and Kerr processes (Section IV). 

The purpose of this chapter is a detailed comparison of these systems and the elucidation of the transition from regular to irregular dynamics or from mode-specific to statistical behavior. The main focus will be the intimate relationship between the multidimensional PES on one hand and observables like dissociation rate and final-state distributions on the other. Another important question is the rigorous test of statistical methods for these systems, in comparison to quantum mechanical as well as classical calculations. The chapter is organized in the following way The three potential-energy surfaces and the quantum mechanical dynamics calculations are briefly described in Sections II and III, respectively. The results for HCO, DCO, HNO, and H02 are discussed in Sections IV-VII, and the overview ends with a short summary in Section VIII. 

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