Selectivity: An Electron Density Perspective

Ríos‐Gutiérrez, Mar; Miranda‐Quintana, Ramón Alain

doi:10.1002/9783527829941.ch10

Cited by 1 publication

(2 citation statements)

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“…The so-called Parr function is equal to the change in the magnetization (polarization) density that occurs when the number of electrons is increased (or decreased) but the spin polarization of the system is chosen to be minimized, ,− P + ( r ) = ρ S ( N 0 + 1 , S min false( N 0 + 1 false) ; r ) − ρ S ( N 0 , S min false( N 0 false) ; r ) P − ( r ) = ρ S ( N 0 , S min false( N 0 false) ; r ) − ρ S ( N 0 − 1 , S min false( N 0 − 1 false) ; r …”

Section: Methodsmentioning

confidence: 99%

“…The so-called Parr function is equal to the change in the magnetization (polarization) density that occurs when the number of electrons is increased (or decreased) but the spin polarization of the system is chosen to be minimized, ,− Here S min ( N ) denotes the choice of spin polarization that minimizes the energy of the system for a given number of electrons. In previous computational applications of the Parr function, it was always assumed that the reference state was a singlet, so S min ( N 0 ) = 0 and ρ S ( N 0 , S min ( N 0 ); r ) = 0.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Methodsmentioning

confidence: 99%

“…The so-called Parr function is equal to the change in the magnetization (polarization) density that occurs when the number of electrons is increased (or decreased) but the spin polarization of the system is chosen to be minimized, ,− Here S min ( N ) denotes the choice of spin polarization that minimizes the energy of the system for a given number of electrons. In previous computational applications of the Parr function, it was always assumed that the reference state was a singlet, so S min ( N 0 ) = 0 and ρ S ( N 0 , S min ( N 0 ); r ) = 0.…”

Section: Methodsmentioning

confidence: 99%