The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach

Eric Cancès (1, 2) , Gabriel Stoltz (1, 2) , Mathieu Lewin (1, 2, 3)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum
3 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We present here a formulation of the electronic ground-state energy in terms of the second order reduced density matrix, using a duality argument. It is shown that the computation of the ground-state energy reduces to the search of the projection of some two-electron reduced Hamiltonian on the dual cone of $N$-representability conditions. Some numerical results validate the approach, both for equilibrium geometries and for the dissociation curve of N$_2$.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Eric Cancès, Gabriel Stoltz, Mathieu Lewin. The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach. Journal of Chemical Physics, 2006, 125, pp.064101. ⟨hal-00132412⟩