Variational density matrix optimization using semidefinite programming

programming Brecht Verstichel, ∗ Helen van Aggelen, Dimitri Van Neck, Paul W. Ayers, and Patrick Bultinck Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium Department of Chemistry, McMaster University, Hamilton, Ontario, L8S 4M1, Canada Abstract We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N -representable density matrix leads to matrix-positivity constraints on the density matrix. We then formulate this in a standard semidefinite programming form, after which two interior point methods are discussed to solve the SDP. As an example we show the results of an application of the method on the isoelectronic series of Beryllium.