Deformed potential surface

Figure 33 Deformed potential surface for terminally blocked alanine at t = 10 A2. The position of the unique minimum is indicated by point M.206...

Figure 34 Deformed potential surface for terminally blocked alanine at t = 0.295 A2. The unique minimum of the t — 10 A2 map of Figure 33 has moved to the intermediate position I, but (even though other minima appear) there is no problem in identifying point I with the position of the global minimum in the map of Figure 32.206...

It is conceivable that the twisting motion experiences internal friction, by which is meant the occurrence of bumps or barriers in the potential surface along which the DNA deforms. This would cause y to exhibit a temperature (T) dependence differing from that due to the viscosity of water. Experimental results 4"1 give no indication of such anomalous T dependence, as shown subsequently. 

When the electrostatic properties are evaluated by AF summation, the effect of the spherical-atom molecule must be evaluated separately. According to electrostatic theory, on the surface of any spherical charge distribution, the distribution acts as if concentrated at its center. Thus, outside the spherical-atom molecule s density, the potential due to this density is zero. At a point inside the distribution the nuclei are incompletely screened, and the potential will be repulsive, that is, positive. Since the spherical atom potential converges rapidly, it can be evaluated in real space, while the deformation potential A(r) is evaluated in reciprocal space. When the promolecule density, rather than the superposition of rc-modified non-neutral spherical-atom densities advocated by Hansen (1993), is evaluated in direct space, the pertinent expressions are given by (Destro et al. 1989)... 

Process ability Surface area, surface free energy, crystal defects, and deformation potential affect compressibility and machineability on high-speed tableting machines with reduced compression dwell times Particle size distribution and shape affect flow properties, efficiency of dry mixing process, and segregation potential Compressibility, flow ability, and dilution potential affect the choice of direct compression as a manufacturing process... 

Fully relaxed single-bond torsional potentials of oligothiophenes 16 (n = 0-2) under the interaction of the parallel external electric field (EF) constructed by point charges have been evaluated with semi-empirical AMI and PM3 calculations <2004SM(145)253>. Consistent evolutions of the torsional potential surfaces have been observed for three lineal oligothiophenes (Figure 43) as the EF increases. In particular, the equilibrium molecular geometries are deformed toward planar conformations, and the torsional barriers around the central bond are elevated. These... 

For interaction with long wavelength, low-energy phonons the deformation potential approximation, frequently in use for covalent compounds with spherical energy surfaces E = E(k), leads to the form45 88)... 

Fig. 2.4. Warped Mexican-hat type of potential surface for Jahn-Teller distortion of octahedral MXs molecule. The symmetry of the two-dimensional deformation space is 3 m, and displacements along the mirror iines correspond to distortions of the octahedron that preserve tetragonal symmetry (elongated or compressed octahedron)...

In addition, an incremental (deformation) potential 5w is produced by the re-distribution of masses which again is factorized by a number, the second Love number k, on the earth s surface... 

This vanishes at the Fermi surface, therefore the deformation potential coupling to a single isotropic band does not influence elastic constants (see sect. 3.2). It leads to an observable effect for... 

Equation (102) shows that MAQO can provide important information about the electronic parameters (extremal Fermi surface cross-sectional area, effective masses, electronic relaxation times) and about the electron-phonon interaction (strain derivatives of the cross-sectional area for different symmetry strains). With the help of this technique, combined with de Haas-van Alphen susceptibility measurements, one can put the deformation potential interaction and the temperature dependence of the elastic constants, discussed above in sect. 3.2, on a solid basis. In the following we discuss some compounds. 

The effective mass ratios measured are of the order of one. The deformation potential coupUng constants vary between 0.5 x 10 K and 3.8 x 10 K. That deduced from the temperature dependence is 10 K. From the band structure for LaAg it was conjectured that the phase transition in the LaAgIn compounds could be due to a nesting feature of the Fermi surface, which gives large electron-phonon matrix elements for the observed M-point phonons (Knorr et al. 1980, Niksch et al. 1987). 

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