Potential energy spherical truncation

In order to limit the total number of interactions exp>erienced by each molecule in a computer simulation, the potential energy is usually truncated so that a molecule s interaction range is finite. For example, the ordinary (spherical) Lennard-Jones potential is truncated at about 2.5cr the interactions between all molecules separated by more than this distance are weak enough to be neglected. In order to maintain conservation of energy, an anisotropic potential function should be truncated at an equipotential surface. However, if the potential is not too anisotropic, truncation at a fixed distance leads to only minor effects on energy conservation. ... 

In the implementation of the Ewald summation according to Eq. 20, the value of the potential energy is controlled by three parameters a, the upper limit of m (ntcut), and the upper limit of n (ncut). At equal truncation error in the two spaces, the summation in the real space is often Umited to interactions involving only the nearest image (m = 0), and consequently a spherical cutoff distance i cut < in the real space can be applied. Moreover, the number of replicas in reciprocal space can be reduced by applying a spherical cutoff of n according to jnj < cut. 

The water-water intermolecular interaction is described by the TIP4P potential. The ethane molecule consists of two interaction sites, each of which interacts with each other via Lennard-Jones (LJ) potential. The reference of ethane molecule is spherical and is of LJ type interaction with size and energy parameters of 4.18 A and 1.72 kj/mol. The LJ parameters for methyl group of ethane are 3.78 A and 0.866 kj/mol. For the water-guest interaction, the Lorentz-Berthelot rule is assumed. The interaction potentials for all pairs of molecules are truncated smoothly at... 

The angular dependence of the coefficients C R, < a. < b) can be expressed in a closed form. The relevant formulae are obtained by asymptotic expansion of the polarization series truncated at some finite order. In practice such an asymptotic expansion is best performed by evaluating the polarization energies (as given by equations 9, 18, and 21) using the multipole expansion of the electrostatic potential l/ ri — r2. The latter expansion can be written in terms of either the Cartesian or the spherical tensors. The spherical formulation appears to be more popular because it leads much more easily to closed formulae and only this formulation will be considered in this article. Denoting by (r) the regular solid harmonic r Cim(0,), where Cim 0,) is the spherical harmonic in the Racah normalization and with the Condon and Shortley phase, one can write ... 

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