Zhengji Zhao – Optimization Online

Large-scale semidefinite programs in electronic structure calculation

Published: 2005/02/25

Bastiaan J. Braams

Basic Sciences Applications, Semi-definite Programming computational chemistry, large-scale optimization, n-representability, parallel computing, reduced density matrix, semidefinite programming

Employing the variational approach having the two-body reduced density matrix (RDM) as variables to compute the ground state energies of atomic-molecular systems has been a long time dream in electronic structure theory in chemical physics/physical chemistry. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual … Read more

The Reduced Density Matrix Method for Electronic Structure Calculations and the Role of Three-Index Representability Conditions

Published: 2003/10/16

Basic Sciences Applications, Convex Optimization, Semi-definite Programming large scale semidefinite programming

The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used $P$, $Q$ and $G$ conditions. The additional conditions (called $T1$ and $T2$ here) are implicit in work of R.~M.~Erdahl [Int.\ J.\ Quantum Chem.\ {\bf13}, 697–718 (1978)] and extend the well-known three-index diagonal … Read more