Dynamics Averages

Hi) The use of quantum methods to obtain correct statistical static (but not dynamic) averages for heavy quantum particles. In this category path-integral methods were developed on the basis of Feynman s path... 

You ch oosc Ih c viilucs Lo avcriigc iii Ih e Molten kir Dynamics Averages dialog hox. As you run a molecular dynamics simulaLion, IlyperChem stores data m a CSV lile. This file has the same name as the IIIN file containing the molecular system, plus the extension. fov. If the molecular system is not yet stored in a IIIX file, IlyperChem uses the filename chem.csv. 

I o averageu torsion, select the fouratoms of the torsion, name the torsion tor, for exam pie, and then select tor as Lh e quan tity Lo be averaged from the Molecular Dynamics. Averages dialog box. 

Averages or plotted values at regular time intervals. You specify an Average/Graph period in the Molecular Dynamics Averages dialog box. 

To average or plot a structural quantity, the structural quantity must first be selected and named by the normal process for creating named selections (select the atoms and then use the menu item Select/Name Selection to give the selected atoms a name). Erom then on the Molecular Dynamics Averages dialog box will show these named selections as possible candidates to be averaged or plotted in addition to energetic quantities described above. 

The single average value that is reported for this quantity in the Molecular Dynamics averages dialog box is the limit reached by the plotted values at i=N, i.e. the RMS value of x ... 

Dynamic average. An average over a single point in phase space at all times. 

For the silica gel (Figure 3A), the solution was removed slightly less effectively, and more Cs was left (ca. 0.0020 atoms/A2). The spectral behavior is quite similar to that of boehmite, except that there is a peak due to surface Cs coordinated by only water molecules and not in contact with the surface oxygens (so-called outer sphere complexes)at 30% RH. Complete dynamical averaging among sites at frequencies greater than ca. 10 kHz occurs at 70% RH and greater. 

For kaolinite the sample permeability was very low and the solution was poorly removed. The spectra (Figure 3C) are consequently complex, containing peaks for inner and outer sphere complexes, CsCl precipitate from resMual solution (near 200 ppm) and a complex spinning sideband pattern. Spectral resolution is poorer, but at 70% RH for instance, inner sphere complexes resonate near 16 ppm and outer sphere complexes near 31 ppm. Dynamical averaging of the inner and outer sphere complexes occurs at 70% RH, and at 100% RH even the CsCl precipitate is dissolved in the water film and averaged. 

On increasing the temperature all the protons become equivalent by dynamic averaging. 

The rotation of the fluorophores is a factor that affects the energy transfer. Only maximal rotational freedom will permit tda estimation. There is no way to predict this factor. Therefore the dynamic averaged value of k2 is considered 2/3. This prediction induces a certain error in the calculation of distances (see Chap. 1). 

S. K. Schiferl and D. C. Wallace, Statistical Errors in Molecular Dynamics Averages, J. 

When the molecules are free to rotate at a rate that is much faster than the deexcitation rate of the donor (isotropic dynamic averaging), the average value of k2 is 2/3. In a rigid medium, the square of the average of k is 0.476 for an ensemble of acceptors that are statistically randomly distributed about the donor with respect to both distance and orientation (this case is often called the static isotropic average). 

This section deals with a single donor-acceptor distance. Let us consider first the case where the donor and acceptor can freely rotate at a rate higher than the energy transfer rate, so that the orientation factor k2 can be taken as 2/3 (isotropic dynamic average). The donor-acceptor distance can then be determined by steady-state measurements via the value of the transfer efficiency (Eq. 9.3) ... 

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