First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules
Department of Chemistry and the James Franck Institute,
The University of Chicago, Chicago, IL 60637, USA. firstname.lastname@example.org
The ground-state energy and properties of any many-electron atom or molecule may be rigorously computed by variationally computing the two-electron reduced density matrix rather than the many-electron wavefunction. While early attempts fifty years ago to compute the ground-state 2-RDM directly were stymied because the 2-RDM must be constrained to represent an N-electron wavefunction, recent advances in theory and optimization have made direct computation of the 2-RDM possible. The constraints in the variational calculation of the 2-RDM require a special optimization known as a semidefinite programming. Development of first-order semidefinite programming for the 2-RDM method has reduced the computational costs of the calculation by orders of magnitude [Mazziotti, Phys. Rev. Lett. 93 (2004) 213001]. The variational 2-RDM approach is effective at capturing multi-reference correlation effects that are especially important at non-equilibrium molecular geometries. Recent work on 2-RDM methods will be reviewed and illustrated with particular emphasis on the importance of advances in large-scale semidefinite programming.
Mathematics Subject Classification: 90C22 / 81Q05 / 52A40
Key words: Semidefinite programming / electron correlation / reduced density matrices / N-representability conditions.
© EDP Sciences, SMAI, 2007