Rotational-translational

Translation and rotation Translation, rotation, torsion Translation, rotation, torsion, vibration... 

E. Rotational, Translational, and Vibrational Contributions to the Correlation Funetion... 

Some SpartanView procedures are identical to SpartanBuild procedures and are not described m detail In particular the same mouse button keyboard combinations are used to rotate translate and scale models Also the same menu commands are used to change the model display and obtain geometry data Please refer back to the SpartanBuild instructions for help with these operations... 

Rotate translate and scale the ac tive model using the same mouse and keyboard operations as those used with SpartanBuild... 

The scroll bar slides back and forth, and the "step" label is updated during the animation. You can rotate, translate, and scale the model at any point during the animation. 

Robustness. The relative ordering of the triangular episodes in a trend is invariant to scaling of both the time axis and the function value. It is also invariant to any linear transformation (e.g., rotation, translation). Finally it is quite robust to uncertainties in the real value of the signal (e.g., noise), provided that the extent of a maximal episode is much larger than the period of noise. 

Many competing effects can contribute to ligand-receptor binding free energies changes in rotational, translational, conformational, and vibrational entropy of the... 

Continuum models are being increasingly used to study protein-ligand recognition [115]. Most studies have considered series of similar ligands or protein mutants and focussed on binding free energy differences. This leads to partial cancelation of some troublesome contributions, especially rotational/translation/vibrational entropy... 

Currently, we evaluate the vibrational/rotational/translational entropy of the solute molecules using normal mode and classical statistical analyses. Although the use of a quasiharmonic analysis, as suggested by Schlitter24... 

The special class of transformation, known as symmetry (or unitary) transformation, preserves the shape of geometrical objects, and in particular the norm (length) of individual vectors. For this class of transformation the symmetry operation becomes equivalent to a transformation of the coordinate system. Rotation, translation, reflection and inversion are obvious examples of such transformations. If the discussion is restricted to real vector space the transformations are called orthogonal. 

It has been shown frequently that without the presence of strong intermolecular interactions, discotic molecules are highly mobile in the liquid crystalline state.1 They undergo both lateral as well as rotational translations, resulting in the absence of positional order. Similarly, such discotics also freely rotate in the columnar aggregates they form in solution. This lack of positional order in the columns accounts for the absence of chiral or helical supramolecular order. We will demonstrate this characteristic using results obtained for triphenylenes. 

It is now possible to design the experiments using molecular beams and laser techniques such that the initial vibrational, rotational, translational or electronic states of the reagent are selected or final states of products are specified. In contrast to the measurement of overall rate constants in a bulk kinetics experiment, state-to-state differential and integral cross sections can be measured for different initial states of reactants and final states of products in these sophisticated experiments. Molecular beam studies have become more common, lasers have been used to excite the reagent molecules and it has become possible to detect the product molecules by laser-induced fluorescence . These experimental studies have put forward a dramatic change in experimental study of chemical reactions at the molecular level and has culminated in what is now called state-to-state chemistry. 

The above experimental results largely relate to spectroscopic techniques, which do not give direct information about the spatial scale of the molecular motions. The size of the spatial heterogeneities is estimated by indirect methods such as sensitivity of the dynamics to the probe size or from the differences between translational and rotational diffusion coefficients (rotation-translation paradox). It might be expected that the additional spatial information provided by neutron scattering could help to discriminate between the two scenarios proposed. 

Proper rotational operations are represented by the n-fold rotation axes n 1000 (n = 2, 3,4, 6). Rotation-inversion axes such as the 2 axis are improper rotation operations, while screw axes and glide planes are combined rotation-translation operations. 

An early application of this type of analysis was to decompose Pio/v( ) into its rotational, translational and their cross-correlation subspectra. It was shown through this decomposition that electrostatic solvation spectra for dipole and charge perturbations are dominated by rotational dynamics. More generally, it was shown how the range and symmetry of AP and molecular properties such as masses and moments of inertia are related to the relative contributions of rotational and translational degrees of freedom to SD. INM analysis has also proved useful in comparing the molecular mechaitisms contributing to short-time dynamics observed in different experiments,such as SD, optical Kerr ef-... 

Figure 3. Comparison of normalized MM influence spectra for SD (left panel) and OKE (rightpanel) in room-temperature acetonitrile. The SD spectrum isfor a perturbation in the partial charges of a dipolar diatom in with Br2-like nonelectrostatic potential parameters. Both spectra are decomposed into rotational, translational and rot.-trans. cross correlation components. The imaginary-requency portions of the spectra are plotted along the negative real axis. The SD results arefrom Ref. and the OKE results from Ref.

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