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Unformatted text preview: I Above, ρ ( r ; q i ) is the charge distribution about atom i for total charge q i I The simplest model for this charge is a point charge, which leads to U ij ( r ij ; q i , q j ) = q i q j / r ij (10) I In the potential of Streitz and Mintmire, an atomicchargedensity of the following form is assumed ρ i ( r ; q i ) = Z i δ ( r r i ) + ( q i Z i ) f i ( r r i ) (11) I Here, Z i is an effective core charge which should satisfy the condition < Z i < Z i with Z i being the total nuclear charge of the atom I Function f i describes the radial distribution of the valence charge in space I The Coulomb interaction integral between the charge densities ρ a and ρ b is [ ρ a  ρ b ] = Z d 3 r 1 Z d 3 r 2 ρ a ( r 1 ) ρ b ( r 2 ) r 12 (12) I Correspondingly the nuclearattraction integral is [ a  ρ b ] = Z d 3 r ρ a ( r )  r r a  (13) I The atomicdensity distribution is modeled as a simple exponential of the form f i (  r r i  ) = ( ξ 3 i /π ) exp ( 2 ξ i  r r i  ) (14) I This distribution could be constructed from Slater 1 s orbitals I However, the choice was made based on mathematical convenience I This model could be extended by implementing a distribution which is not spherical in space (constructed from, e.g., p and d orbitals), as authors speculate in the article I The potential applies the idea of electronegativity equilibration...
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 Winter '12
 Kotakoski
 Electrostatics, Electric charge, Fundamental physics concepts, qi qj, charge qi, partial charge qi

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