Molecular correlation time definition

Indeed, 13C spin-lattice relaxation times can also reflect conformational changes of a protein, i.e. helix to random coil transitions. This was demonstrated with models of polyamino acids [178-180], in which definite conformations can be generated, e.g. by addition of chemicals or by changes in temperature. Thus effective molecular correlation times tc determined from spin-lattice relaxation times and the NOE factors were 24-32 ns/rad for the a carbons of poly-(/f-benzyl L-glutamate) in the more rigid helical form and about 0.8 ms/rad for the more flexible random coil form [180],... 

Bloembergen et al. (S) have presented a relationship between the correlation time for molecular rotation in liquids and the relaxation times assuming that relaxation takes place via mechanism (i) of Section II,A,3. Although the theory can be at best semiquantitative when applied to the protons of water molecules adsorbed on silica gel, values of the nuclear correlation time have been calculated 18) from the T data. These correlation times as a function of x/m show a definite change of slope near a monolayer coverage. This result, if corroborated by data on other solids, may provide a rather unique method for the determination of monolayer coverage. 

In order to implement the relaxation calculations some additional definitions should be provided i) the nuclear spin interactions acting as relaxation mechanisms and ii) a molecular model motion, including iii) the distribution of correlation times at which the motion is occurring. These features will depend on aspects such as the temperature, the physical state of the sample, and the magnitude of the external applied magnetic field, among others. A more detailed analysis of such relaxation mechanisms can be found in References [4,8,25,26]. 

The chemical world is often divided into measurers and makers of molecules. This division has deep historic roots, but it artificially impedes taking advantage of both aspects of the chemical sciences. Of key importance to all forms of chemistry are instruments and techniques that allow examination, in space and in time, of the composition and characterization of a chemical system under study. To achieve this end in a practical manner, these instruments will need to multiplex several analytical methods. They will need to meet one or more of the requirements for characterization of the products of combinatorial chemical synthesis, correlation of molecular structure with dynamic processes, high-resolution definition of three-dimensional structures and the dynamics of then-formation, and remote detection and telemetry. 

In order to extract some more information from the csa contribution to relaxation times, the next step is to switch to a molecular frame (x,y,z) where the shielding tensor is diagonal (x, y, z is called the Principal Axis System i.e., PAS). Owing to the properties reported in (44), the relevant calculations include the transformation of gzz into g x, yy, and g z involving, for the calculation of spectral densities, the correlation function of squares of trigonometric functions such as cos20(t)cos20(O) (see the previous section and more importantly Eq. (29) for the definition of the normalized spectral density J((d)). They yield for an isotropic reorientation (the molecule is supposed to behave as a sphere)... 

Abstract The theoretical basis for the quantum time evolution of path integral centroid variables is described, as weU as the motivation for using these variables to study condensed phase quantum dynamics. The equihbrium centroid distribution is shown to be a well-defined distribution function in the canonical ensemble. A quantum mechanical quasi-density operator (QDO) can then be associated with each value of the distribution so that, upon the application of rigorous quantum mechanics, it can be used to provide an exact definition of both static and dynamical centroid variables. Various properties of the dynamical centroid variables can thus be defined and explored. Importantly, this perspective shows that the centroid constraint on the imaginary time paths introduces a non-stationarity in the equihbrium ensemble. This, in turn, can be proven to yield information on the correlations of spontaneous dynamical fluctuations. This exact formalism also leads to a derivation of Centroid Molecular Dynamics, as well as the basis for systematic improvements of that theory. 

The physical properties and chemical reactivity of molecules may be and often are drastically changed by a surrounding medium. In many cases specific complexes are formed between the solvent and solute molecules whereas in other cases only the non-bonded intermolecular interactions are responsible for the solvational effects. By one definition, the environmental effects can be divided into two principally different types, i.e. to the static and dynamic effects. The former are caused by the coulombic, exchange, electronic polarization and correlation interactions between two or more molecular species at fixed (close) distances and relative orientation in space. The dynamic interactions are due to the orientational relaxation and atomic polarization effects, which can be accounted for rigorously only by using time-dependent quantum theory. 

Comparative structural analysis of sodium channel genes has permitted the development of testable hypotheses concerning the neurotoxin recognition properties of the sodium channel protein. However, specific elements of the deduced structure have not yet been definitively correlated with the molecular recognition of sodium channel-directed neurotoxins by discrete binding domains. It is, thus, not possible at the present time to know which pharmacological properties are determined by the sodium channel protein per se and which are determined by interactions between it and crucial features of its membrane environment. Clearly, it will be necessary to analyze the effects of specific modifications of sodium channel structure in a defined membrane environment in order to address these and other questions relating to sodium channel function. 

Compared to crystalline materials, the production and handling of amorphous substances are subject to serious complexities. Whereas the formation of crystalline materials can be described in terms of the phase rule, and solid-solid transformations (polymorphism) are well characterised in terms of pressure and temperature, this is not the case for glassy preparations that, in terms of phase behaviour, are classified as unstable . Their apparent stability derives from their very slow relaxations towards equilibrium states. Furthermore, where crystal structures are described by atomic or ionic coordinates in space, that which is not possible for amorphous materials, by definition, lack long-range order. Structurally, therefore, positions and orientations of molecules in a glass can only be described in terms of atomic or molecular distribution functions, which change over time the rates of such changes are defined by time correlation functions (relaxation times). 

As mentioned above, the nuclei are assumed to be fixed and are thus nothing more than sources of an external electrostatic potential in which the electrons move. If there is no magnetic field external to the molecule under consideration, and if external electric fields are time-independent, we arrive at the so-called electrostatic limit of relativistic density functional theory. Note that most molecular systems fall within this regime. In this case, one can prove the relativistic Hohen-berg-Kohn theorem using the charge density, p(r) = J f), only. This leads to a definition of an exchange-correlation functional -Exc[p( )]... 

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