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David A. Mazziotti (damazzuchicago.edu) Abstract: The energy and properties of a manyelectron atom or molecule may be directly computed from a variational optimization of a twoelectron reduced density matrix (2RDM) that is constrained to represent manyelectron quantum systems. In this paper we implement a variational 2RDM method with a representability constraint, known as the $T_2$ condition. The optimization of the 2RDM is performed with a firstorder algorithm for semidefinite programming [Mazziotti, Phys. Rev. Lett. \textbf{93}, 213001 (2004)] which, because of its lower computational cost in comparison to secondorder methods, allows the treatment of larger basis sets. We also derive and implement a spin and symmetryadapted formulation of the $T_2$ condition that significantly decreases the size of the largest block in the $T_2$ matrix. The $T_2$ condition, originally derived by Erdahl [Int. J. Quantum Chem. \textbf{13}, 697 (1978)], was recently applied via a secondorder algorithm to atoms and molecules [Zhao et al., J. Chem. Phys. \textbf{120}, 2095 (2004)]. While these calculations were restricted to molecules at equilibrium geometries in minimal basis sets, we apply the 2RDM method with the $T_2$ condition to compute the electronic energies of molecules in both minimal and nonminimal basis sets at equilibrium as well as nonequilibrium geometries. Accurate potential energies curves are produced for BH, HF, and N$_{2}$. Results are compared with the 2RDM method without the $T_2$ condition as well as several wavefunction methods. Keywords: semidefinite programming, molecular electronic structure, reduced density matrices Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Physical Review A (submitted 2005). Download: [PDF] Entry Submitted: 09/16/2005 Modify/Update this entry  
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