International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'
Analytic energy gradients, excited states, and pure-state N-representability in v2RDM-driven CASSCFEugene DePrince
The direct variational optimization of the ground-state two-electron reduced-density matrix (2-RDM) can routinely be achieved via semidefinite programming techniques. The resulting variational 2-RDM (v2RDM) approach can be used to realize polynomially-scaling complete active space self-consistent field (CASSCF) computations applicable to active spaces comprised of 50 electrons in 50 orbitals, or more . Analytic energy gradients for v2RDM-CASSCF are readily available, and excited-state information can be extracted from the time-evolution of the one-electron RDM  or within the framework of the extended random phase approximation (ERPA) [3,4]. However, within the ERPA, a proper treatment of excitations from degenerate ground states requires the application of pure-state N-representability conditions [5,6].
 J. Fosso-Tande, T.-S. Nguyen, G. Gidofalvi, and A. E. DePrince, III, J. Chem. Theory Comput. 12 2260-2271 (2016).
 D. B. Jeffcoat and A. E. DePrince, III, J. Chem. Phys. 141 214104 (2014).
 K. Chatterjee and K. Pernal, J. Chem. Phys. 137 2041009 (2012).
 H. van Aggelen, B. Verstichel, G. Acke, M. Degroote, P. Bultinck, P. W. Ayers, and D. V. Neck, Comput. Theor. Chem. 1003 50-54 (2013).
 M. Altunbulak and A. Klyachko, Commun. Math. Phys. 282 287 (2008).
 A. E. DePrince, III, J. Chem. Phys. 145 164109 (2016).