Because electrons are indistinguishable with pairwise interactions, the energy of any many-electron molecule can be written as a functional of a two-electron quantity?the two-electron reduced density matrix (2-RDM). Three approaches to the direct calculation of the 2-RDM will be discussed: (i) the variational 2-RDM method [1], (ii) the parametric 2-RDM method [2], and (iii) the solution of the contracted (CSE), or anti-Hermitian contracted (ACSE), Schr�dinger equation [3]. First, the variational 2-RDM method minimizes the energy as a functional of the 2-RDM constrained by N-representability conditions. We can accurately approximate strong electron correlation at a cost that scales polynomially with system size. Second, the parametric 2-RDM method, a variant of the variational method, improves upon the accuracy of the coupled cluster singles-doubles at a computational cost that scales like configuration interaction singles-doubles. We can efficiently treat problems with moderate multi-reference correlation as in single-bond dissociation and diradicals. Third, the ACSE method solves for the 2-RDM through a cumulant-based reconstruction of the 3-RDM from the 2-RDM. With the ACSE both strongly correlated ground- and excited-state energies can be computed at a cost that grows quadratically with the number of active orbitals. Additionally, we will show how to use RDM theory to perform measurement-driven reconstruction of quantum processes [4]. In quantum process reconstruction quantum information about many-particle systems is extracted from experimental data in the form of 1- or 2-RDMs.[1] D. A. Mazziotti, Phys. Rev. Lett. 108 , 263002 (2012).[2] C. A. Schwerdtfeger, A. Eugene DePrince III, and D. A. Mazziotti, J. Chem. Phys. 134 , 174102 (2011).[3] G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80 , 022507 (2009).[4] J. J. Foley IV and D. A. Mazziotti, Phys. Rev. A 86  , 012512 (2012).

Electronic structure and processes in many dimensions from two-electron reduced density matrices

246th National Meeting (2013)

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