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Molecular two-electron reduced density matrices (2-RDMs) are computed variationally without the many-electron wave function by constraining the 2-RDM with a set of three-particle N -representability conditions known as three-positivity conditions. These constraints restrict four distinct three-particle probability distributions, which can be defined for any N -particle system, to be nonnegative. The variational calculation of the 2-RDM with full three-positivity conditions is implemented with the first-order semidefinite programming algorithm D.A. Mazziotti , Phys. Rev. Lett. 93 , 213001 ( 2004 ) . We also derive and implement a generalization of the T 2 representability condition, which is a subset of the three-positivity conditions. Energies and 2-RDMs are computed for several molecules as well as the nitrogen molecule at both equilibrium and nonequilibrium geometries. The ground-state energies for nitrogen are within 0.0015 a.u. of the values from full configuration interaction at all internuclear distances.
Physical Review A – American Physical Society (APS)
Published: Sep 1, 2006
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