Molecular dynamics quantum mechanical treatment

In principle, the ideal description of a solution would be a quantum mechanical treatment of the supermolecule consisting of representative numbers of molecules of solute and solvent. In practice this is not presently feasible, even if only a single solute molecule is included. In recent years, however, with the advances in processor technology that have occurred, it has become possible to carry out increasingly detailed molecular dynamics or Monte Carlo simulations of solutions, involving hundreds or perhaps even thousands of solvent molecules. In these, all solute-solvent and solvent-solvent interactions are taken into account, at some level of sophistication. 

Baer, M. (1983). Quantum mechanical treatment of electronic transitions in atom-molecule collisions, in Molecular Collision Dynamics, ed. J.M. Bowman (Springer, Berlin Heidelberg). 

It should be recalled that the calculation of solvent effects on optical activity presents some unique problems. A chiral solute induces a chiral structure of the surrounding solvent, even when the individual solvent molecules are achiral. This means that the solvent participates in the observed optical effect not only by a modification of the geometric structure and electronic density of the solute, but that part of the observed OR or circular dichroism arises from the chiral solvent shell rather than from the solute molecule as such. This is not accounted for by the PCM, and can be rendered only by an explicit quantum mechanical treatment of at least the first solvent shell, or preferably by molecular dynamics simulations. 

Mary Jo Nye enumerates the topics treated in the Journal as molecular spectroscopy and molecular structures, the quantum mechanical treatment of electronic structure of molecules and crystals and the problem of chemical binding, the kinetics of chemical reactions from the standpoint of basic physical principles, the thermodynamic properties of substances and calculation by statistical mechanical methods, the structure of crystals, and surface phenomena. M.J. Nye, From Chemical Philosophy to Theoretical Chemistry. Dynamics of Matter and Dynamics of Disciplines (Berkeley University of California Press 1993), 254. Many of these were considered by Barriol, as we will see later in this chapter. 

So far, no exact 6D quantum dynamics calculation has been reported for diatomic dissociation on surface. But with modern computer power, such numerical endeavor will undoubtly be realized soon. We also note here recent mixed quantum/classical studies of Jackson who treated three COM coordinates classically and three internal molecular coordinates quantum mechanically for H2/Cu(100) (120). Such treatment seems quite promising for more complex systems. 

In reality, of course, atoms obey quantum mechanics rather than classical mechanics. As you will discover in other chapters in this book, great advances have been made recently in the quantum mechanical treatment of molecular systems. However, one should realize just how much care has to go into the selection of correct coordinates and the necessity to choose appropriate systems for quantum mechanical study. For arbitrarily large systems, or for systems containing several heavy atoms, quantum methods are not yet readily applicable. It is in such cases that classical mechanical approaches can be utilized with profit. Furthermore, even in systems for which quantum mechanical treatments are now feasible, comparisons with classical data often help researchers to isolate those phenomena which arise solely in the quantum mechanics, yielding fundamental insight into the two different dynamics. In the classical approach, the motion of each atom is calculated by numerically solving the classical differential equations of motion (1), either second order with respect to time in the positions, x (Newton s law), or,... 

Van Kampen N (1981) Appl Sci Res 37 67-75, for a quantum mechanical treatment see Bruch LW, GoeW CJ (1981) J Chem Phys 74 4040-4047 Bird RB, Ottinger HC (1992) Ann Rev Phys Chem 43 371-406 Bird RB, Stewart WE, Lightfoot EN (1960) Transport phenomena Wiley, New York Dahler JS, Scriven LE (1961) Nature 192.3 37 (No 4797) Dahler JS (1965) chap 15 In Seeger RJ, Temple G (eds) Research frontiers in fluid dynamics Wiley-Interscience, New York Hirschfelder JO, Curtiss CF, Bird RB (1964) Molecular theory of gases and liquids Wiley, New York [Second printing with corrections and added notes]... 

The large mass of a nucleus compared to that of an electron permits an approximate separation of the electronic and nuclear motion. Molecules are complicated quantum objects and this separation greatly simplifies their quantum mechanical treatment. It also allows us to visualize the dynamics of molecules and provides the essential link between quantum mechanics and traditional chemistry. We should be aware that even the notion of molecular electronic states is a consequence of the approximate separability of the electronic and nuclear motion. Without this separability the introduction of molecular electronic states would be relatively useless and just a mathematical construction. 

The field of applications of molecular quantum dynamics covers broad areas of science not only in chemistry but also in physics and biology. Historically, due to the fact that the full quantum-mechanical simulation of molecular processes is limited to small systems, molecular quantum dynamics has given rise mainly to important applications of astrophysical and atmospheric relevance. In the interstellar medium or the Earth atmosphere, molecules are generally in the gas phase. Since many accurate spectroscopic data are available, these media have provided various prototype systems to study quantum effects in molecules and to calibrate the theoretical methods used to simulate these effects. In this context, it is not surprising that much theoretical effort is still directed toward modeling the full quantum-mechanical treatment of small molecules. Among others, one can cite the studies of the spectroscopy of water [159-161], and of the spectroscopy, photodissociation. 

A general and alternative approach can be proposed in order to establish the number of topological constraints ndx, T, P) for any thermodynamic condition using Molecular Dynamics (MD). In both MD s versions, classical or First Principles (FPMD) using the Car-Parrinello scheme, Newton s equation of motion is solved for a system of N atoms or ions, representing a given material. Forces are either evaluated from a model interaction potential which has been fitted to recover some materials properties, or directly calculated from the electronic density in case of a quantum mechanical treatment using density functional theory (DFT). 

The molecular beam and laser teclmiques described in this section, especially in combination with theoretical treatments using accurate PESs and a quantum mechanical description of the collisional event, have revealed considerable detail about the dynamics of chemical reactions. Several aspects of reactive scattering are currently drawing special attention. The measurement of vector correlations, for example as described in section B2.3.3.5. continue to be of particular interest, especially the interplay between the product angular distribution and rotational polarization. 

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

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