This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.
 Winter '12
 Kotakoski

Click to edit the document details