Theoretical studies molecular dynamics

P.-O. Westlund, T. Larsson, and O. Teleman, Paramagnetic Enhanced Proton Spin-Lattice Relaxation in the Ni " " Hexa-aquo Complex. A Theoretical and Molecular Dynamics Simulation Study of the Bloembergen-Morgan Decomposition Approach, Mol. Phys., 78 (1993), 1365-1384. 

Although it turned out that a number of essential features concerning dynamics of molecular liquids can be well captured by the theory of the previous subsection (see Secs. 3 and 5), an intense investigation through experimental, theoretical, and molecular-dynamics simulation studies for simple liquids has revealed that the microscopic processes underlying various time-dependent phenomena cannot be fully accounted for by a simplified memory-function approach [18, 19, 20]. In particular, the assumption that the decay of memory kernels is ruled by a simple exponential-type relaxation must be significantly revised in view of the results of the kinetic framework developed for dense liquids (see Sec. 5.1.4). This motivated us to further improve the theory for dynamics of polyatomic fluids. 

Small metal clusters are also of interest because of their importance in catalysis. Despite the fact that small clusters should consist of mostly surface atoms, measurement of the photon ionization threshold for Hg clusters suggest that a transition from van der Waals to metallic properties occurs in the range of 20-70 atoms per cluster [88] and near-bulk magnetic properties are expected for Ni, Pd, and Pt clusters of only 13 atoms [89] Theoretical calculations on Sin and other semiconductors predict that the stmcture reflects the bulk lattice for 1000 atoms but the bulk electronic wave functions are not obtained [90]. Bartell and co-workers [91] study beams of molecular clusters with electron dirfraction and molecular dynamics simulations and find new phases not observed in the bulk. Bulk models appear to be valid for their clusters of several thousand atoms (see Section IX-3). 

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],... 

The input to a minimisation program consists of a set of initial coordinates for the system. The initial coordinates may come from a variety of sources. They may be obtained from an experimental technique, such as X-ray crystallography or NMR. In other cases a theoretical method is employed, such as a conformational search algorithm. A combination of experimenfal and theoretical approaches may also be used. For example, to study the behaviour of a protein in water one may take an X-ray structure of the protein and immerse it in a solvent bath, where the coordinates of the solvent molecules have been obtained from a Monte Carlo or molecular dynamics simulation. 

Another principal difficulty is that the precise effect of local dynamics on the NOE intensity cannot be determined from the data. The dynamic correction factor [85] describes the ratio of the effects of distance and angular fluctuations. Theoretical studies based on NOE intensities extracted from molecular dynamics trajectories [86,87] are helpful to understand the detailed relationship between NMR parameters and local dynamics and may lead to structure-dependent corrections. In an implicit way, an estimate of the dynamic correction factor has been used in an ensemble relaxation matrix refinement by including order parameters for proton-proton vectors derived from molecular dynamics calculations [72]. One remaining challenge is to incorporate data describing the local dynamics of the molecule directly into the refinement, in such a way that an order parameter calculated from the calculated ensemble is similar to the measured order parameter. 

In this situation computer simulation is useful, since the conditions of the simulation can be chosen such that full equihbrium is established, and one can test the theoretical concepts more stringently than by experiment. Also, it is possible to deal with ideal and perfectly flat surfaces, very suitable for testing the general mechanisms alluded to above, and to disregard in a first step all the complications that real substrate surfaces have (corrugation on the atomistic scale, roughness on the mesoscopic scale, surface steps, adsorbed impurities, etc.). Of course, it may be desirable to add such complications at a later stage, but this will not be considered here. In fact, computer simulations, i.e., molecular dynamics (MD) and Monte Carlo (MC) calculations, have been extensively used to study both static and dynamic properties [11] in particular, structural properties at interfaces have been considered in detail [12]. 

Using the first-principles molecular-dynamics simulation, Munejiri, Shimojo and Hoshino studied the structure of liquid sulfur at 400 K, below the polymerization temperature [79]. They found that some of the Ss ring molecules homolytically open up on excitation of one electron from the HOMO to the LUMO. The chain-like diradicals S " thus generated partly recombine intramolecularly with formation of a branched Sy=S species rather than cyclo-Ss- Furthermore, the authors showed that photo-induced polymerization occurs in liquid sulfur when the Ss chains or Sy=S species are close to each other at their end. The mechanism of polymerization of sulfur remains a challenging problem for further theoretical work. 

The first reaction filmed by X-rays was the recombination of photodisso-ciated iodine in a CCI4 solution [18, 19, 49]. As this reaction is considered a prototype chemical reaction, a considerable effort was made to study it. Experimental techniques such as linear [50-52] and nonlinear [53-55] spectroscopy were used, as well as theoretical methods such as quantum chemistry [56] and molecular dynamics simulation [57]. A fair understanding of the dissociation and recombination dynamics resulted. However, a fascinating challenge remained to film atomic motions during the reaction. This was done in the following way. 

The availability of thermodynamically reliable quantities at liquid interfaces is advantageous as a reference in examining data obtained by other surface specific techniques. The model-independent solid information about thermodynamics of adsorption can be used as a norm in microscopic interpretation and understanding of currently available surface specific experimental techniques and theoretical approaches such as molecular dynamics simulations. This chapter will focus on the adsorption at the polarized liquid-liquid interfaces, which enable us to externally control the phase-boundary potential, providing an additional degree of freedom in studying the adsorption of electrified interfaces. A main emphasis will be on some aspects that have not been fully dealt with in previous reviews and monographs [8-21]. 

For nonequilibrium statistical mechanics, the present development of a phase space probability distribution that properly accounts for exchange with a reservoir, thermal or otherwise, is a significant advance. In the linear limit the probability distribution yielded the Green-Kubo theory. From the computational point of view, the nonequilibrium phase space probability distribution provided the basis for the first nonequilibrium Monte Carlo algorithm, and this proved to be not just feasible but actually efficient. Monte Carlo procedures are inherently more mathematically flexible than molecular dynamics, and the development of such a nonequilibrium algorithm opens up many, previously intractable, systems for study. The transition probabilities that form part of the theory likewise include the influence of the reservoir, and they should provide a fecund basis for future theoretical research. The application of the theory to molecular-level problems answers one of the two questions posed in the first paragraph of this conclusion the nonequilibrium Second Law does indeed provide a quantitative basis for the detailed analysis of nonequilibrium problems. 

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