Rigid-rotator dynamics, calculations

We have carried out converged rigid-rotator dynamics calculations for four potentials ... 

Consider a quantity of some liquid, say, a drop of water, that is composed of N individual molecules. To describe the geometry of this system if we assume the molecules are rigid, each molecule must be described by six numbers three to give its position and three to describe its rotational orientation. This 6N-dimensional space is called phase space. Dynamical calculations must additionally maintain a list of velocities. 

Let us first consider the case of a long n-alkane molecule in the solid crystalline phase. From lattice dynamical calculations it is known that collective librational phonons (about the chain axis) exist in the lattice, some giving rise to scattering and/or absorption in infrared [70]. Let us take a n-alkane molecule with an even number of carbon atoms which belongs to the C h point group. The rigid rotation about its axis is of Bg species, the same as the Raman active d mode. When the... 

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. 

A more realistic model for the secondary relaxation needs to consider motions of a molecular group (considered as a rigid object) between two levels. The group may contain N atoms with the scattering length h, at positions r (i=lj ). The associated motion may consist of a rotation aroimd an arbitrary axis, e.g. through the centre of mass depicted by a rotational matrix Q and a displacement by a translational vector . In order to evaluate the coherent dynamic structure factor, scattering amphtudes of the initial (1) and final (2) states have to be calculated ... 

The earliest molecular dynamics simulations using realistic potentials were of atoms interacting under the Lennard-Jones potential. In such calculations the only forces on the atoms are those due to non-bonded interactions. It is rather more difficult to simulate molecules because the interaction between two non-spherical molecules depends upon their relative orientation as well as the distance between them If the molecules are flexible then there will also be intramolecular interactions, which give rise to changes in conformation. Clearly, the simplest model is to treat the species present as rigid bodies with no intramolecular conformational freedom. In such cases the dynamics of each molecule can often be considered in terms of translations of its centre of mass and rotations about its centre of mass. The force on the molecule equals the vector sum of all the forces acting at the... 

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