md2011-10-note_Part_3

# md2011-10-note_Part_3 - I Above ρ r q i is the charge...

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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 atomic-charge-density 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 nuclear-attraction integral is [ a | ρ b ] = Z d 3 r ρ a ( r ) | r- r a | (13) I The atomic-density 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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md2011-10-note_Part_3 - I Above ρ r q i is the charge...

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