Vacuum, dihedral angle

Here the atoms in the system are numbered by i, j, k, l = 1,..., N. The distance between two atoms i, j is ry, q is the (partial) charge on an atom, 6 is the angle defined by the coordinates (i, j, k) of three consecutive atoms, and 4> is the dihedral angle defined by the positions of four consecutive atoms, e0 is the dielectric permittivity of vacuum, n is the dihedral multiplicity. The potential function, as given in equation (6), has many parameters that depend on the atoms involved. The first term accounts for Coulombic interactions. The second term is the Lennard-Jones interaction energy. It is composed of a strongly repulsive term and a van der Waals-like attractive term. The form of the repulsive term is chosen ad hoc and has the function of defining the size of the atom. The Ay coefficients are a function of the van der Waals radii of the... 

Figure 1. History of the dihedral angle C3-C4-C5-05 calculated from a typical molecular dynamics simulation of a a-D-glucopyranose in the conformation in vacuum. (Reproduced from Ref. 9. Copyright 1986 American Chemical Society.)...

Fig.9 Potential energy (a) and dipole moment (b) of HFIP vs dihedral angle in vacuum (black) and within a PCM (red)... 

To determine the surface energy of the solid A in equilibrium with its own vapour, dihedral angle ]/° of grain boundary grooves in vacuum or a neutral gas. Then, assuming that the grain boundary energy of solid A in contact with liquid B is not affected by adsorption of B, (jgV is obtained from the equation ... 

The vacuum potential results, corresponding to the limit of zero viscosity, are shown in Fig. 41a. At zero viscosity, the dihedral angle 41 oscillates with a period of approximately 0.63 ps. When the conditions are changed to represent water at 300 K (i.e., the solvent-modified potential-of-mean-force surface is used and r) = 1.0 cP), the dominant effect is that the dihedral motion has a periodicity of about 3.7 ps (see Fig. 41b). The solvent influence observed in these simulations is consistent with an earlier molecular dynamics study of... 

Figure 41. Solvent viscosity effects on low-frequency motions of alanine dipeptide. The normalized spectral density for the dihedral angle is plotted versus frequency (ps 1) for (a) dynamics on a vacuum potential surface (see Fig. 58a) (6) dynamics with a potential of mean force (see Fig. 58b) in a solvent of viscosity, y = 1.0 cP (c) dynamics with a potential of mean force (see Fig. 586) in a solvent of viscosity, ij > 1.0 cP.

Figure 59. Probability distribution for the alanine dipeptide in the (, 1/9 dihedral-angle space at 300 K (a) vacuum potential surface (b) solvent-modified potential surface.

We examine structural and dynamic aspects of both the dipep-tlde solute and the aqueous solvent. For the dlpeptide, primary emphasis Is placed on the Internal motions. The size and dynamical character of fluctuations relative to the average structure are Investigated In vacuum and In the presence of solvent. The dlpeptide vibrational degrees of freedom have frequencies varying from approximately 50 (dihedral angle torsions) to 3500 cm ... 

Figure 4. Time correlation function and spectral density for fluctuations in the dihedral angle, x (Figure I). Top in solution bottom under vacuum. The functions shown dotted at the top are obtained from a Langevin equation ("see text).

Fig. 3 Energy difference taken with MRCCSDT[2 + 2] around 90° dihedral angle of the ethylene molecule. Methods apphed are CAS(2,2) and subsequent Fermi-vacuum-dependent perturbative corrections, averaged according to Eqs. (15) or (17). Abbreviations DK and EN refer to the partitioning (see text)...

Describe possible microstructural ehanges with annealing time (from Oh to 00 h) of an oxide polycrystal which was fully densified by hot pressing in a vacuum. Assume that the dihedral angle is 75°. 

Use data in Table 4.3 to estimate the dihedral angles for the intersections of both a high-angle grain boundary and an incoherent twin boundary with the surface of Cu if it is annealed at high temperature in vacuum. 

Fig. 26.6 MP2/aug-cc-pVTZ total energy profiles upon variation of selected C-C-O-C dihedral angles in the molecules with alkyl and hydroxyl periphery in vacuum V2 denotes the anti- gauche barrier, V3 stands for transition from gauche to eclipsed conformation...

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