Rigid-rotator interaction potential

These results demonstrate that as defined by Eq. [32] is a formal dihedral potential that couples the 1-4 atoms, because the sum of these interactions over all nonbonded rotating pairs is exactly the total torsional potential (for a rigid rotation). Because of the relationships given in Eqs. [31] and [32], V"dAB) and V.,(AB) are called the differential and integrated dihedral potentials, respectively. 

Inspection of the optimized geometry indicates that dimerization of the car-bene center of 31b is hindered but still attained, as the facing methyl groups can rotate about one another in order to minimize the interaction potential during dimerization. The relatively easy isolation of the dimer of 31b supports this view. On the other hand, in 39, the flexible motion of bulky and rigid three-dimensional bicyclic substituents during the dimerization is not attained. 

Here is the reduced mass of the coUisional system, B is the rotational constant of the diatom (rigid rotor approximation assumed), j and J are the operators for rotational angular momentum of the diatom and total angular momentum, respectively, and V is the interaction potential. The BF z-axis is chosen to lie along the ion-diatom center of mass vector R, such that Q is the projection of both J and j along the BF z-axis. 

The rotational spectrum of a molecule with internal rotation (torsion) is modified due to torsion-rotation interaction. The interpretation of this modification allows the determination of the internal rotation potential barrier [59Lin, 68Dre, 84Gorj. The molecule is generally taken to be rigid except for this torsional degree of freedom. However, special methods have been developed to include interactions with molecular vibrations. 

Spectral densities are calculated within the framework of the theoretical model for the dynamical evolution of the system. In the SRLS approach a two-body Smoluchowski equation describes the time evolution of the density probability of two relaxation processes (at different time scales) coupled by an interaction potential. In the application of this model to the description of protein dynamics, the two relaxing processes are interpreted as the slow global tumbling of the whole protein and the relatively fast local motion of the spin probe, the local motion of the N- H bond in our case. Both processes are described as rigid rotators the motion of which is coupled by a potential correlating their reorientation, and it is interpreted as providing the local ordering that the molecule imposes on the probe. 

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

Theory. The theory of collision-induced absorption profiles of systems with anisotropic interaction [43, 269] is based on Arthurs and Dalgamo s close coupled rigid rotor approximation [10]. Dipole and potential functions are approximated as rigid rotor functions, thus neglecting vibrational and centrifugal stretching effects. Only the H2-He and H2-H2 systems have been considered to date, because these have relatively few channels (i.e., rotational levels of H2 to be accounted for in the calculations). The... 

CA may be considered to have the following structural factors controlling the rigidity of the molecule an interdependent rotational potential, which controls the unperturbed dimension in solution, by (1) the steric interactions between neighboring pyranose rings with and without substituent groups, (2) the intramolecular hydrogen bonds... 

In one specific model the potential well arises from the interaction of the molecule with its nearest ndghbours. These are taken to form a more or less rigid cage which rotates without surface slip in a continuum whose viscous, or dscoelastic, properties are those of the bulk fluid. In this sort of model we note that the exchange of momentum between molecule and cage does not permit the random motions, of molecule with respect to cage and of cage with respect to bulk medium, to be imcorrelated. 

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