Interaction potential dihedral angle

According to the namre of the empirical potential energy function, described in Chapter 2, different motions can take place on different time scales, e.g., bond stretching and bond angle bending vs. dihedral angle librations and non-bond interactions. Multiple time step (MTS) methods [38-40,42] allow one to use different integration time steps in the same simulation so as to treat the time development of the slow and fast movements most effectively. 

Note that Fig. 3.55 is the more exact counterpart of Fig. 4 in Brunck and Weinhold, note 71. Note also that the full potential barrier includes contributions from gauche-type interactions at other dihedral angles. In this context, it is interesting that an idealized cosine-like dependence of the o cc-o ch overlap (or Fock-matrix element), namely... 

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... 

June et al. (85) presented united-atom calculations for butane and for hexane in silicalite, whereby the bond and dihedral angles of the alkanes were allowed to vary. In addition, the calculation of hexane took account of an additional intramolecular Lennard-Jones potential for nonbonded atoms more than three bonds apart (which prevents the alkane crossing over itself). The interaction parameters for the alkane molecules were taken from Ryckaert and Bellmans (3), and those governing the interaction of the alkanes with the zeolite from a previous study of the low-occupancy sorption of alkanes in silicalite (87). Variable loadings of alkanes were considered from 1 to 8 molecules per unit cell were considered, and calculations were allowed to run for 500 ps for diffusion at 300 K. 

The applicability of the reaction-rate formula in the intermediate-friction regime to the interpretation of conformational changes of bi-naphtyl in solution has been discussed.47 The intramolecular motion is governed by a bistable potential depending on a single variable, which is identified with the dihedral angle between the naphthalene moieties in binaphtyl. The influence of hydrodynamic interactions and coupling with the other coordinates of the molecules also are evoked. 

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