Fully relaxed

Example If a drug molecule interacts with a receptor molecule through hydrogen bonds, then yon might restrain the distance between the donor and acceptor atoms involved in the hydrogen bonds. During a molecular dynamics simulation, these atoms would slay near an ideal value, while the rest of the molecular system fully relaxes. 

The lower bound 0 in the integration refers to the time at which the first contact is made after attaining the fully relaxed state. The upper bound / is the actual time spent in the loading experiment when the load P(i) is recorded. 

First, the stability of the fitted Llo structure relative to other crystal structure with the same composition can be studied. In the present case we calculated the cohesive energies of fully relaxed B2 and structure 40 compounds and found 4.41eV and 4.50 eV, respectively. These are both lower than the cohesive energy of the Llo structure. Structure B19 was also investigated but relaxation always transformed this structure into Llo. 

Fig. 13. Calculated 2H solid echo spectra for log-Gaussian distributions of correlation times of different widths. Note the differences of the line shapes for fully relaxed and partially relaxed spectra. The centre of the distribution of correlation times is given as a normalized exchange rate a0 = 1/3tc. For deuterons in aliphatic C—H bonds the conversion factor is approximately 4.10s sec-1...

Fig. 21. Deuteron NMR spectra for the phenyl groups in polycarbonate (amorphous film, drawn from solution at room temperature, Mw 30000, Mw/M = 1 -8). Left column fully relaxed spectra. Right column partially relaxed spectra corresponding to the mobile groups only...

At this point, it is important to notice that in general, the sum of the contributions do not match exactly AE as higher order terms are present. The difference between the sum of contributions and AE is denoted 8E. Concerning the variational schemes, SE is generally small in the CSOV (or RVS) approach thanks to the antisymmetry conservation and not present in the Ziegler scheme as the Eoi term is taking into account a fully relaxed wavefunction. It is not the case for the KM scheme which... 

In the case of polymer samples, it is expected that, at the temperatures and frequencies at which the rheological measurements were carried out, the polymer chains should be fully relaxed and exhibit characteristic homo-polymer-like terminal flow behavior (i.e., the curves can be expressed by a power-law of G oc co2 and G" oc co). 

A different view of the OMT process is that the molecule, M, is fully reduced, M , or oxidized, M+, during the tunneling process [25, 26, 92-95]. In this picture a fully relaxed ion is formed in the junction. The absorption of a phonon (the creation of a vibrational excitation) then induces the ion to decay back to the neutral molecule with emission (or absorption) of an electron - which then completes tunneling through the barrier. For simplicity, the reduction case will be discussed in detail however, the oxidation arguments are similar. A transition of the type M + e —> M is conventionally described as formation of an electron affinity level. The most commonly used measure of condensed-phase electron affinity is the halfwave reduction potential measured in non-aqueous solvents, Ey2. Often these values are tabulated relative to the saturated calomel electrode (SCE). In order to correlate OMTS data with electrochemical potentials, we need them referenced to an electron in the vacuum state. That is, we need the potential for the half reaction ... 

For this purpose we freeze each monomer in its geometry in the complex, so that only changes in z ntermolecular potential energy are involved. The binding energies V(A, B) thus differ slightly from those with respect to fully relaxed monomers. 

Here, the relaxed softness matrix Srel groups the equilibrium, fully relaxed responses in the subsystem numbers of electrons, following the displacements in the chemical potentials of their (separate) electron reservoirs, the relaxed geometric softness matrix... 

Schneider and co-workers (159) attempted to rescue the Grant-Cheney approach, at least for methyl substituents. They refined it by using a modified potential for the repulsive force (186) along with fully relaxed molecular structures as determined by force-field calculations. This indeed led to a satisfactory correlation of yg-SCS(CH3) with repulsive interactions in methylcyclohexane and some methylbicyclo[2.2.1]heptanes (159). Schneider s treatment, however, implies that a signal shift originates not only from steric H-H repulsion but includes effects from secondary carbon-framework distortions (85,159). 

Equation (4.68) with a = 0 applies for linear or nicked circular DNAs. When r = r, the (initially) supercoiled DNA is predicted to experience no deformational strain, as it is fully relaxed, and to bind the same amount of dye as its linear counterpart with the same concentration of free dye. Under these conditions, the supercoiled and linear DNA/chloroquine complexes are expected to exhibit identical local structures, rigidities, and deformational dynamics. This important corollary to the standard model was untested till recently.(53)... 

A related observation is that fully relaxed supercoiled DNA/dye complexes are somehow different from nicked circular DNA/dye complexes in the presence of the same concentration of free dye, where the binding ratios should be the same. This is readily seen in gel electrophoresis in the presence of sufficient dye concentration so that at least one, but not all, of the topoisomers is positively supercoiled. The slowest moving, presumably fully relaxed, topoisomer migrates significantly faster than the nicked circle, and this difference increases with the amount of dye present. This is not observed with chloroquine, perhaps because the effect is too small. However, it is readily apparent in the original gels of Keller0 61) in which ethidium was used to unwind the topoisomers. We have confirmed this effect for ethidium and have observed similar behavior for proflavine, 9-aminoacridine, and quinacrine. 

The iFi terms are the fluorescence lifetimes of fractional contributions a, and the xRJ indicate decay constants due to solvent relaxation (or other excited-state processes) of fractional contribution Pj. The negative sign is indicative of a relaxation process (red shift). Usually, the relaxation process is approximated to a single relaxation time x R by assuming an initial excited state and a final fully relaxed state (see, e.g., Ref. 128). A steady-state fluo-... 

Striped (SI) and from a hexagonal incommensurate (HI) phase. The structure and the corresponding schematic diffraction patterns are shown in Fig. 31 the diffraction patterns have been calculated for fully relaxed walls, i.e. the SI and the HI phase are in fact uniaxially and uniformly compressed phases, respectively. By inspection of Fig. 31 it is obvious that the various incommensurate structures can easily be identified by their characteristic diffraction patterns. 

Fig. 31. Schematics of (a) real lattice and (b), (c) the (n,n) and (n,2n) diffraction features of incommensurate layers. SI - striped incommensurate, HI - hexagonal incommensurate, HIR -hexagonal incommensurate rotated. All phases are assumed to be fully relaxed. O denotes the (93 X 93)R30° commensurate and the incommensurate structures.

The analysis in the last paragraph has shown that the incommensurate Xe layer on Pt(lll) at misfits of about 6% is a striped phase with fully relaxed domain walls, i.e. a uniaxially compressed layer. For only partially relaxed domain walls and depending on the extent of the wall relaxation and on the nature of the walls (light, heavy or superheavy) additional statellites in the (n, n) diffraction patterns should appear. Indeed, closer to the beginning of the C-I transition, i.e. in the case of a weakly incommensurate layer (misfits below 4%) we observe an additional on-axis peak at Qcimm + e/2 in the (2,2) diffraction pattern. In order to determine the nature of the domain walls we have calculated the structure factor for the different domain wall types as a function of the domain wall relaxation following the analysis of Stephens et al. The observed additional on-axis satellite is consistent with the occurrence of superheavy striped domain wails the observed peak intensities indicate a domain wall width of A=i3-5Xe inter-row distances. With... 

Figure 3.3 The tetragonal distortion in a coherent epilayer, (a) fully relaxed, and (b) constrained to match the substrate...

The fully relaxed lattice parameter of the layer, is the value that we need to use in Vegard s law to find the composition of the epilayer. 

Find the unit cell of layer material in the fully relaxed (i.e. bulk) condition from materials databases. For alloys of more than one material, Vegard s law is applied to the lattice parameters, Poisson ratios and stmcture factors. Find the susceptibility of the layers (the extremely small change in susceptibility when a layer is strained may be ignored). 

If a specimen is heavily dislocated it may be impossible to distinguish peaks in double-crystal rocking curves. Figure 7.5 shows a five-layer Si-Ge specimen grown with 0.5 //m thick layers, with the Ge content in each layer respectively 10, 20, 30, 40 and 50% the aim being to produce a moderate amount of relaxation at each layer so that the top layer is fully relaxed 50% Ge but without excessive threading dislocations. This was achieved—the dislocation density was... 

In the spirit of Eq. 3.39 and neglecting the ongoing decay of Schain(Q>0 due to local reptation, from the heights of the achieved plateaus we may obtain a first estimate for the amount of confinement. Identifying the plateau levels with a Debye-Waller factor describing the confinement we get d=44 A, a value that is a lower estimate for the true tube diameter since S ° (Q,t) is not fully relaxed. The horizontal bars in Fig. 3.16 are the predictions from this Debye-Waller factor estimate. 

Figure 4. Conformational map for dihydropyran. Because of the double bond, 4 atoms are always almost coplanar and a limited number of conformations is probable. The energy contours are at 2 kcal/mol intervals, starting 1 kcal/mol above the minima. The favored conformations are half-chairs, and the easiest paths of transition between the two are through the boat forms. The symmetry of this energy map applies only to dihydropyran, and not to derivatives which cause increases and decreases in the sizes of the allowed (low-energy) areas. This map was calculated with MMP2(85) at increments of 0.1 A shift of the two non-planar atoms. Three of the carbon atoms were held in a plane while C6 and 01 were held at specific distances above and below the plane. Otherwise, the structure was fully relaxed at each increment. The reader may enjoy plotting the indicated path of conformational interchange (pseudorotation) on a copy of Figure 3.

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