Energy short-range interaction

The second excitation mechanism, impact scattering, involves a short range interaction between the electron and the molecule (put simply, a collision) which scatters the electrons over a wide range of angles. The usefiil feature of impact scattering is that all vibrations may be excited and not only the dipole active ones. As in Raman spectroscopy, the electron may also take an amount of energy hv away from excited molecules and leave the surface with an energy equal to Eq + hv. 

The classical kinetic theoty of gases treats a system of non-interacting particles, but in real gases there is a short-range interaction which has an effect on the physical properties of gases. The most simple description of this interaction uses the Lennard-Jones potential which postulates a central force between molecules, giving an energy of interaction as a function of the inter-nuclear distance, r. 

According to Allen and Tildesley, the standard recipe to evaluate Af/ in step one of the algorithm described in Sec. IIIB involves computing the energy of atom i with all the other atoms before and after the move (see p. 159 of Ref. 25, italics by the present author) as far as simple fluids are concerned. The evaluation of Af/ can be made more efficient in this case by realizing that for short-range interactions U can be split into three contributions... 

In Eq. (31) we should note that U r represents the interaction energy per primary solvent molecule. Then the number of solvent molecules that can be interact directly with an ion in phase 5" (= O or W) is denoted as N. Accordingly, the contribution of the short-range interactions to the solvation energy of the ion phase S (i.e., transfer... 

The local conformational preferences of a PE chain are described by more complicated torsion potential energy functions than those in a random walk. The simulation must not only establish the coordinates on the 2nnd lattice of every second carbon atom in the initial configurations of the PE chains, but must also describe the intramolecular short range interactions of these carbon atoms, as well as the contributions to the short-range interactions from that... 

The Forster resonance energy transfer can be used as a spectroscopic ruler in the range of 10-100 A. The distance between the donor and acceptor molecules should be constant during the donor lifetime, and greater than about 10 A in order to avoid the effect of short-range interactions. The validity of such a spectroscopic ruler has been confirmed by studies on model systems in which the donor and acceptor are separated by well-defined rigid spacers. Several precautions must be taken to ensure correct use of the spectroscopic ruler, which is based on the use of Eqs (9.1) to (9.3) ... 

Another feature that is still puzzling scientists is the role of the soft mode in structural order-disorder transitions. As already mentioned in Sect. 3 the energy U in theoretical treatments is based predominantly on short-range interactions and often the local fields are replaced by a mean field to mimic some long-range properties. In the solid solution D-RADP-x the FE soft mode suffers from the lack of translational invariance, so that only for x < 0.32 sufficient coherence can be achieved to provide a successful contribution to... 

A number of techniques have been employed to model the framework structure of silica and zeolites (Catlow Cormack, 1987). Early attempts at calculating the lattice energy of a silicate assumed only electrostatic interactions. These calculations were of limited use since the short-range interactions had been ignored. The short-range terms are generally modelled in terms of the Buckingham potential,... 

Parameters required for the description of polyesters I are taken from a recent paper (Abe, A, J. Am. Chem. Soc. 1984, 106, 14) which dealt with the dipole moments of dialkyl esters of dicarboxylic acids. Since the ester groups are all assumed to be in the trans configuration, short-range interactions between consecutive rigid cores are unimportant. As for the rotation around the O-C — C-C bond, the six-state scheme (termed model I in the above paper) is employed. The statistical weight parameter a representing the relative importance of the reversed ester conformations with respect to the normal ones is set equal to unity. The three-state scheme (termed model II) proposed alternatively in the above reference is examined for chains with n = 5 and 6 for comparison. In this model the C O /CC eclipsed form is assumed to be intrinsically more stable than the C 0 /CH form a stabilzation energy E( 1) of 5.0 kj mol-1 is adopted. 

Allowing for rotation about the Ca—C bond (/.e., variation of ijr) and for some degree of freedom about the peptide bond [i.e., small variation of ro), the characteristic ratios of the form / (crs) and form II [trans) poly(L-proline) chain are calculated by a Monte Carlo method in which the conformational energies are used as weighting factors. The Monte Carlo method enabled short-range interactions (beyond those involved in a single residue) to be taken into account. 

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