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arXiv · 2010.09639

Dissociation limit in Kohn-Sham density functional theory

Sören Behr·Benedikt R. Graswald
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Abstract

We consider the dissociation limit for molecules of the type $X_2$ in the Kohn-Sham density functional theory setting, where $X$ can be any element with $N$ electrons. We prove that when the two atoms in the system are torn infinitely far apart, the energy of the system convergences to $\min \limits_{α\in [0,N]} \big( I^{X}_α + I^{X}_{2N-α} \big)$, where $I^{X}_α$ denotes the energy of the atom with $α$ electrons surrounding it. Depending on the "strength" of the exchange this minimum might not be equal to the symmetric splitting $2I^{X}_{N}$. We show numerically that for the $H_2$-molecule with Dirac exchange this gives the expected result of twice the energy of a H-atom $2 I^{H}_1$.

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Sören Behr, Benedikt R. Graswald. 2021-07-28. Dissociation limit in Kohn-Sham density functional theory. https://arxiv.org/abs/2010.09639

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