Nonuniqueness of magnetic fields and energy derivatives in spin-polarized density functional theory Journal Articles uri icon

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abstract

  • The effect of the recently uncovered nonuniqueness of the external magnetic field B(r⃑) corresponding to a given pair of density n(r⃑) and spin density ns(r⃑) on the derivative of the energy functional of spin-polarized density functional theory, and its implications for the definition of chemical reactivity descriptors, is examined. For ground states, the nonuniqueness of B(r⃑) implies the nondifferentiability of the energy functional Ev,B[n,ns] with respect to ns(r⃑). It is shown, on the other hand, that this nonuniqueness allows the existence of the one-sided derivatives of Ev,B[n,ns] with respect to ns(r⃑). Although the N-electron ground state can always be obtained from the minimization of Ev,B[n,ns] without any constraint on the spin number Ns=∫ns(r⃑)dr⃑, the Lagrange multiplier μs associated with the fixation of Ns does not vanish even for ground states. μs is identified as the left- or right-side derivative of the total energy with respect to Ns, which justifies the interpretation of μs as a (spin) chemical potential. This is relevant not only for the spin-polarized generalization of conceptual density functional theory, the spin chemical potential being one of the elementary reactivity descriptors, but also for the extension of the thermodynamical analogy of density functional theory for the spin-polarized case. For higher-order reactivity indices, B(r⃑)’s nonuniqueness has similar implications as for μs, leading to a split of the indices with respect to Ns into one-sided reactivity descriptors.

publication date

  • October 21, 2009