md2011-10-note_Part_3

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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 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...
View Full Document

{[ snackBarMessage ]}

Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online