Molecular dynamics simplified picture

A simplified picture of molecular dynamics might be very helpful to an experimentalist in designing a control strategy. It is very difficult to visualize the motion of an Al-atom molecule in a full (3N - 6)-dimen-sional configuration space. A reduced dimension picture would serve as a stepping stone to insight. 

In Section VILA a strongly idealized picture was described. The dielectric response of an oscillating nonrigid dipole was found in terms of collective vibrations of two charged particles. Now a more specific picture pertinent to an idealized water structure will be considered. Namely, we shall briefly consider thermal motions of a dipole as (i) pure rotations in Fig. 56b and (ii) pure translations in Fig. 58a. Item (i) presents the major interest for us, since we would like to roughly estimate on the basis of a molecular dynamics form of the absorption band stipulated by rotation of a dipole. Of course, even in terms of a simplified scheme, the internal rotations of a molecule should also be accompanied by its translations, so the Figs. 56a and 56b should somehow interfere. However, in Section IX.B.l we for simplicity will neglect this interference. This assumption approximately holds, since, as will be shown in Section IX.B.2, the mean frequencies of these two types of motion substantially differ. 

The As calculations (Equation (3.95)) were based on the Poisson equation, solved for a five-zone model (Section 3.5.4, Inhomogeneous Media) in which the solute (zone 1) was surrounded by four dielectric zones (2-5). A simplified schematic picture is given in Figure 3.26, but in the actual calculations, the zone boundaries were based on structures obtained from classical molecular dynamics (MD) simulations (with inclusion of a few thousand TIP3P water molecules and Na+ counterions to neutralize the negative charge from the DNA). Each zone was assigned optical and static dielectric constants (sxk and e0k, k = 1, 5). For the solute (zone 1), = e0k = 1.0 was adopted. For zones 2,3,... 

We employ a classical description of the dynamical consequences of such a quantum object as the hydrogen bond. This concerns, for instance, the vibration of HB molecules. The price we pay for such an approach is that several fitted model parameters (e.g., force constants) are not related explicitly to the molecular structure of our object. Note that in the MD simulation method, based on application of various effective potentials, the classical theory is also often used [33-35]. Avery detailed analysis of the problems pertinent to the two-fractional (mixed) models of water is given in the latter work (review) with respect to various (mostly steady-state) properties of water. In the context of our work, the use of a classical mixed model is justified by a possibility of considering a simplified picture of two-state molecular motion allowing a relatively simple analytical calculation of the complex permittivity s(v) given in Section II. 

In a simplified picture of the molecular dynamics in the isotropic (liquid) phase and in solid phase, it is commonly assumed that in an isotropic liquid the constituent molecules have freedom of translational and rotational mobility. A solid phase on the other hand, is considered as a state with a high degree of molecular translational and rotational immobilization. Thus at the phase transition, on going from the solid phase to the isotropic phase, molecules are liberated and enabled to move. Traditionally, we refer to this as melting of the translational and rotational degrees of freedom (on going from the solid phase to the isotropic phase, e.g. by warming up a sample)... 

Recently, Neue [54] published another paper on an application of WT in dynamic NMR spectroscopy which could simplify the analysis of the free induction decay (FID) signal. Dynamic NMR spectroscopy is a technique used to measure rate parameters for a molecule [55]. The measured resonance frequencies represent the spatial coordinates of spins. Any motion, such as bond rotation and other molecular gymnastics, may change these frequencies as a function of time. The localization property of WT gives a better picture... 

The goal of extending classical thermostatics to irreversible problems with reference to the rates of the physical processes is as old as thermodynamics itself. This task has been attempted at different levels. Description of nonequilibrium systems at the hydrodynamic level provides essentially a macroscopic picture. Thus, these approaches are unable to predict thermophysical constants from the properties of individual particles in fact, these theories must be provided with the transport coefficients in order to be implemented. Microscopic kinetic theories beginning with the Boltzmann equation attempt to explain the observed macroscopic properties in terms of the dynamics of simplified particles (typically hard spheres). For higher densities kinetic theories acquire enormous complexity which largely restricts them to only qualitative and approximate results. For realistic cases one must turn to atomistic computer simulations. This is particularly useful for complicated molecular systems such as polymer melts where there is little hope that simple statistical mechanical theories can provide accurate, quantitative descriptions of their behavior. 

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