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Describing dissociation in variational second order density matrix theory

A correct description of dissociating bonds is even more challenging to methods based on the density or first or second order density matrices than to wave function based techniques. Density and density matrix based techniques typically yield dissociated states with fractional charges instead of correct integer charges. Such non-physical fractionally charged dissociated states also occur in variational second order density matrix theory[1] under the necessary but not sufficient P-, Q- and G-condition for Nrepresentability. Additional N-representability constraints are needed to correct them. To this end, we introduced linear constraints on the energy of atomic subspaces in the molecule. This work focuses on the implementation of such subspace constraints, more specifically on the identification of the tightest set of subspace constraints, their scale-up to bigger molecules and their relationship to size-consistency. These issues are discussed in relation to the potential energy surface of the F3 - ion. First of all, the subspace constraints enforce size-consistency and a correct dissociation, but do not improve the accuracy of the method at short bond lengths, where they are not active. They only become active when one or more bonds are stretched. Furthermore, while only a small number of subspace constraints suffices to obtain the correct dissociation, the constraints are geometry dependent. They are therefore quite laborious to apply to large potential energy surfaces ​
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