Molecular ensemble approach

Master equation methods are not tire only option for calculating tire kinetics of energy transfer and analytic approaches in general have certain drawbacks in not reflecting, for example, certain statistical aspects of coupled systems. Alternative approaches to tire calculation of energy migration dynamics in molecular ensembles are Monte Carlo calculations [18,19 and 20] and probability matrix iteration [21, 22], amongst otliers. 

This volume focuses on the variety of phenomena associated with the above-mentioned systems. The discussion has both experimental and theoretical components. It is desirable to consider all these processes within the framework of a unified theoretical approach. Such an approach is possible because the most important physico-chemical phenomena in such media are accompanied by the rearrangement of intra- and inter-molecular coordinates and consequently, a surrounding molecular ensemble. Some powerful mathematical tools are presented for such processes describing the theory of radiationless multi-vibrational transitions. Thus, the first part of the volume addresses the following issues ... 

These remarks apply to a molecular ensemble free of strong internal or external fields and associated potential terms V. With the imposition of this extra variable, the challenge to analytical theory becomes more difficult to meet and there is a need for a clear and complementary method of approaching the problem numerically using computer simi tion. ... 

Molecular dynamics simulations entail integrating Newton s second law of motion for an ensemble of atoms in order to derive the thermodynamic and transport properties of the ensemble. The two most common approaches to predict thermal conductivities by means of molecular dynamics include the direct and the Green-Kubo methods. The direct method is a non-equilibrium molecular dynamics approach that simulates the experimental setup by imposing a temperature gradient across the simulation cell. The Green-Kubo method is an equilibrium molecular dynamics approach, in which the thermal conductivity is obtained from the heat current fluctuations by means of the fluctuation-dissipation theorem. Comparisons of both methods show that results obtained by either method are consistent with each other [55]. Studies have shown that molecular dynamics can predict the thermal conductivity of crystalline materials [24, 55-60], superlattices [10-12], silicon nanowires [7] and amorphous materials [61, 62]. Recently, non-equilibrium molecular dynamics was used to study the thermal conductivity of argon thin films, using a pair-wise Lennard-Jones interatomic potential [56]. 

A first contribution to J-p is caused by the bonding between two atoms which constitute one molecule. This direct intra-molecular interaction between the atoms is taken into considerations as a f -bond. In addition there are intra-molecular interactions of indirect nature between the both atoms of a molecule. These atoms affect each other indirectly by n point interactions with all remaining atoms and combinations of atoms. The so-called intra-molecular pair cavity function y (ryw) expresses the ensemble of all indirect interactions which appear between the atoms of a molecule in f-bonds [13] and establishes the searched correlation function for all indirect interactions between the atoms inside a molecule. TTie molecular DFT approach evaluates the cluster expansion to calculate y (rjvr) using TPT. This approximation takes into account only presentations with vertices n <— 2, for what reason it is called the single chain approximation (TPT1)[12]. [7,8]... 

To exemplify a molecular similarity method, we employed here a 3D shape-based molecular similarity approach using OpenEye scientific software (OpenEye). A set of 27 molecules (Amoore, 1971) were compared to benzaldehyde (query molecule). The representation used here is based on the volume of each molecule. A conformational ensemble is built for the molecules in the database, whereas the conformation of the query remains fixed (the chemical nature of benzaldehyde does not entail different conformers, though in many cases the conformation of the query molecules might be complex and crucial). After the conformers of each molecule in the data set are built, each one of them is compared with the query and a similarity value is computed. For the particular program employed here (ROCS), the similarity is quantified as a score formed by two terms, one takes into account the chemical nature of the molecules while the other relies on molecular shape, such score is referred to as combo score. The maximum similarity value is 2 which can only be obtained from the comparison of a molecule with itself in the exact same conformation (perfect match). The normalized values (from 0 to 1) for the odor and combo score similarities are compared in the graph shown in Fig. 2.4. As can be observed, as the combo score increases, the odor similarity to benzaldehyde also increases. This correlation shows that part of the odor similarity was captured by the molecular... 

There are two main approaches used to simulate polymer materials molecular dynamics and Monte Carlo methods. The molecular dynamics approach is based on numerical integration of Newton s equations of motion for a system of particles (or monomers). Particles follow dctcr-ministic trajectories in space for a well-defined set of interaction potentials between them. In a qualitatively different simulation technique, called Monte Carlo, phase space is sampled randomly. Molecular dynamics and Monte Carlo simulation approaches are analogous to time and ensemble methods of averaging in statistical mechanics. Some modern computer simulation methods use a combination of the two approaches. 

We show how the response of a molecule to an external oscillating electric field can be described in terms of intrinsic properties of the molecules, namely the (hyper)polarizabilities. We outline how these properties are described in the case of exact states by considering the time-development of the exact state in the presence of a time-dependent electric field. Approximations introduced in theoretical studies of nonlinear optical properties are introduced, in particular the separation of electronic and nuclear degrees of freedom which gives rise to the partitioning of the (hyper)polarizabilities into electronic and vibrational contributions. Different approaches for calculating (hyper)polarizabilities are discussed, with a special focus on the electronic contributions in most cases. We end with a brief discussion of the connection between the microscopic responses of an individual molecule to the experimentally observed responses from a molecular ensemble... 

The conformation of a gas-phase molecule can be derived by minimizing the strain energy Eqs. (1.1.23)—(1.1.26). A powerful simulation tool for the collective behavior of a molecular ensemble is molecular dynamics (MD) [11], In the classical approach, the total instantaneous energy of a molecular system, E(tot) is again a sum of terms as in Eqs. (1.1.23)—(1.1.26). Note that the above functional forms assume that the electronic structure is not significantly perturbed, that is, E(elec-tronic) = constant. 

We present a theoretical study of the oxidation reaction of NOj to NOj by dioxygen in the cages of sodalite. The combined Blue Moon Ensemble and Car Parrinello Molecular Dynamics approaches were used. 

Other approaches than the luminophore-spacer-receptor paradigm exist, illustrated in the preceding examples, for designing a molecular system for sensing analytes in solution. An efficient one—the chemosensing ensemble approach—is reminiscent of the antibody-based competition test in immunoassays. According to this approach. 

Unfortunately, statistical mechanics is not familiar even for the large majority of chemists and chemical engineers. Moreover, fundamental equations in statistical mechanics cannot often be solved rigorously for complex systems and the introduction of approximation becomes necessary to obtain useful results for real systems. In any theoretical approach for molecular ensemble, we must confront with so-called many-body problems and two-body approximations must be applied. Even in the frameworks of this approximation, our knowledge on the intermolecular interaction, which is necessary in statistical mechanical treatment is still poor. 

We have already pointed out that statistical mechanical method is indispensable in molecular ensemble design . Full account of molecular simulation is given in some books and will not be reproduced here. Two types of approaches can be classified in applying fliis method. 

In typical SCF LCAO MO calculations, the lone pairs of the valence and inner electronic shells can strongly affect the overall IT descriptors of the chemical bonds. Elimination of such lone-pair contributions in the resultant IT bond indices requires an ensemble (flexible input) approach [9,10,55]. In this scheme of determining the IT bond descriptors of diatomic fragments in molecules, the joint (bond) probabilities of two AO centered on different atoms constitute the input probabilities of the molecular information channel. Indeed, such probabilities reflect the simultaneous participation of the given pair of basis functions in interatomic chemical bonds so that this ensemble approach effectively projects out the spurious contributions attributable to inner-shell and outer-shell AO, which are excluded from mixing into the... 

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