The electronic temperature and the effective chemical potential parameters of an atom in a molecule. A Fermi–Dirac semi-local variational approach

Franco‐Pérez, Marco

doi:10.1039/d1cp04071e

Cited by 3 publications

(1 citation statement)

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“…The external potential is, in the simplest case, defined by the electrostatic potential that the nuclei, with charges Z A and positions R A , assert on the electrons, v ( r ) = prefix∑ A = 1 N normala normalt normalo normalm normals prefix− Z A false| boldr − boldR A false| but any other potential that is not produced by the electrons themselves (e.g., from an external electric field) could also be included. , Given an external potential, the number of electrons suffices to specify the state of the system assuming that the spin/excitation-level of the system corresponds to a nondegenerate ground state. However, (conceptual) DFT can be extended to include finite-temperature effects, − time-dependent effects, − excited states, − external forces, − or other auxiliary variables. − For simplicity, in this paper, we use a time-independent zero-temperature ground-state approach. We will furthermore assume that the ground state does not have spatial degeneracy.…”

Section: Introductionmentioning

confidence: 99%

Spin-Polarized Conceptual Density Functional Theory from the Convex Hull

Richer,

Heidar-Zadeh,

Ríos-Gutiérrez

et al. 2024

J. Chem. Theory Comput.

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We present a new, nonarbitrary, internally consistent, and unambiguous framework for spin-polarized conceptual density-functional theory (SP-DFT). We explicitly characterize the convex hull of energy, as a function of the number of electrons and their spin, as the only accessible ground states in spin-polarized density functional theory. Then, we construct continuous linear and quadratic models for the energy. The nondifferentiable linear model exactly captures the simplicial geometry of the complex hull about the point of interest and gives exact representations for the conceptual DFT reactivity indicators. The continuous quadratic energy model is the paraboloid of maximum curvature, which most tightly encloses the point of interest and neighboring vertices. The quadratic model is invariant to the choice of coordinate system (i.e., {N, S} vs {N α, N β}) and reduces to a sensible formulation of spin-free conceptual DFT in the appropriate limit. Using the quadratic model, we generalize the Parr functions {P +(r), P –(r)} (and their derivatives with respect to number of electrons) to this new spin-polarized framework, integrating the Parr function concept into the context of (spin-polarized) conceptual DFT, and extending it to include higher-order effects.

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