Gaussian overlap model

G. Ayton and G. Patey, A Generalized Gaussian Overlap Model for Fluids of Anisotropic Particles, J. Chem. Phys. 102 (1995) 9040 ... 

Thus, the Gaussian overlap model generates a strength parameter e and a range parameter a that are determined by the relative orientation of the two molecules. These two parameters may now be used in any of a variety of two-parameter potentials that have been proposed to describe atomic interactions. For example, we may use e(ui, U2) and o-(Ui, O2, r) in the Lennard-Jones (12-6) potential... 

A working alternative to the ISM for the short-ranged interaction is the Gaussian overlap model [24]. The energy and length parameters are defined in terms of the overlap of Gaussian cores. 

As the SIBFA approach relies on the use of distributed multipoles and on approximation derived form localized MOs, it is possible to generalize the philosophy to a direct use of electron density. That way, the Gaussian electrostatic model (GEM) [2, 14-16] relies on ab initio-derived fragment electron densities to compute the components of the total interaction energy. It offers the possibility of a continuous electrostatic model going from distributed multipoles to densities and allows a direct inclusion of short-range quantum effects such as overlap and penetration effects in the molecular mechanics energies. 

In the deconvolution using Gaussian peak model, all peaks have a deviation of less than 1%. These are even close to 0%, regardless of whether the peaks overlap. 

Figure 6. Predicted interchain radial distribution function for a hard-core polyethylene melt described by three single-chain models atomistic RIS at 430 K, overlapping (lid = 0.5) SFC model with appropriately chosen aspect ratio and site number density (see text), and the Gaussian thread model (shifted horizontally to align the hard core diameter with the value of rld = l).

Model correlation functions. Certain model correlation functions have been found that model the intracollisional process fairly closely. These satisfy a number of physical and mathematical requirements and their Fourier transforms provide a simple analytical model of the spectral profile. The model functions depend on the choice of two or three parameters which may be related to the physics (i.e., the spectral moments) of the system. Sears [363, 362] expanded the classical correlation function as a series in powers of time squared, assuming an exponential overlap-induced dipole moment as in Eq. 4.1. The series was truncated at the second term and the parameters of the dipole model were related to the spectral moments [79]. The spectral model profile was obtained by Fourier transform. Levine and Birnbaum [232] developed a classical line shape, assuming straight trajectories and a Gaussian dipole function. The model was successful in reproducing measured He-Ar [232] and other [189, 245] spectra. Moreover, the quantum effect associated with the straight path approximation could also be estimated. We will be interested in such three-parameter model correlation functions below whose Fourier transforms fit measured spectra and the computed quantum profiles closely see Section 5.10. Intracollisional model correlation functions were discussed by Birnbaum et a/., (1982). 

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