Next: Density-matrix minimization Up: Contents Previous: Density-matrix formulation

Density-matrix representation

$\rho({\bf r},{\bf r'}) = \displaystyle{\sum_{\alpha \beta} \phi_{\alpha} ({\bf r}) P^{\alpha \beta} \phi_{\beta}^{\ast}({\bf r'})}$

Exploit the short range of the DM: $\rho({\bf r},{\bf r'}) \rightarrow 0 ~\sf {as}~ \left\vert {\bf r} - {\bf r'} \right\vert \rightarrow \infty$

by making:

i.e. imposing: $\rho({\bf r},{\bf r'}) = 0 ~\sf {when}~ \left\vert {\bf r} - {\bf r'} \right\vert > r_{\rm {cut}}$

Peter D. Haynes 2001-11-09