Fractional electron number, temperature, and perturbations in chemical reactions

2016 ◽  
Vol 18 (22) ◽  
pp. 15070-15080 ◽  
Author(s):  
Ramón Alain Miranda-Quintana ◽  
Paul W. Ayers
Keyword(s):  
Density Functional Theory ◽  
Chemical Reactions ◽  
Density Functional ◽  
Mathematical Framework ◽  
Electron Number ◽  
Conceptual Density Functional Theory ◽  
Functional Theory

The mathematical framework of conceptual density functional theory is extended to use the eigenstates and eigenvalues of perturbed subsystems. This unites, justifies, and extends, several previously proposed models.

scholarly journals What Do We Learn from the Classical Turning Surface of the Kohn-Sham Potential as Electron Number Is Varied Continuously?

2019 ◽  
Author(s):  
Tim Gould ◽  
Benjamin Libereles ◽  
John P. Perdew
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Principal Quantum Number ◽  
Ionisation Potential ◽  
Electron Number ◽  
Conceptual Density Functional Theory ◽  
Functional Theory ◽  
Atomic Systems ◽  
Additional Information ◽  
Turning Radius

The classical turning radius Rt of an atom can be defined as the radius where the KS potential is equal to the negative ionisation potential of the atom, i.e. where v_s(R_t)=\epsilon_h. It was recently shown [P.N.A.S. 115, E11578 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work we show that extension of the concept to non-integer electron number yields additional information about atomic systems, and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells, and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g. going from Na to Na^{2+}). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H_2^+. Results are consistent when properties are calculated exactly, or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.

scholarly journals What Do We Learn from the Classical Turning Surface of the Kohn-Sham Potential as Electron Number Is Varied Continuously?

2019 ◽  
Author(s):  
Tim Gould ◽  
Benjamin Libereles ◽  
John P. Perdew
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Principal Quantum Number ◽  
Ionisation Potential ◽  
Electron Number ◽  
Conceptual Density Functional Theory ◽  
Functional Theory ◽  
Atomic Systems ◽  
Additional Information ◽  
Turning Radius

The classical turning radius Rt of an atom can be defined as the radius where the KS potential is equal to the negative ionisation potential of the atom, i.e. where v_s(R_t)=\epsilon_h. It was recently shown [P.N.A.S. 115, E11578 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work we show that extension of the concept to non-integer electron number yields additional information about atomic systems, and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells, and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g. going from Na to Na^{2+}). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H_2^+. Results are consistent when properties are calculated exactly, or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.

scholarly journals What Do We Learn from the Classical Turning Surface of the Kohn-Sham Potential as Electron Number Is Varied Continuously?

2019 ◽  
Author(s):  
Tim Gould ◽  
Benjamin Libereles ◽  
John P. Perdew
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Principal Quantum Number ◽  
Ionisation Potential ◽  
Electron Number ◽  
Conceptual Density Functional Theory ◽  
Functional Theory ◽  
Atomic Systems ◽  
Additional Information ◽  
Turning Radius

The classical turning radius Rt of an atom can be defined as the radius where the KS potential is equal to the negative ionisation potential of the atom, i.e. where v_s(R_t)=\epsilon_h. It was recently shown [P.N.A.S. 115, E11578 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work we show that extension of the concept to non-integer electron number yields additional information about atomic systems, and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells, and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g. going from Na to Na^{2+}). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H_2^+. Results are consistent when properties are calculated exactly, or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.

scholarly journals Discontinuous Behavior of the Pauli Potential in Density Functional Theory as a Function of the Electron Number

2019 ◽  
Author(s):  
Eli Kraisler ◽  
Axel Schild
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Electron Systems ◽  
Electron Number ◽  
Functional Theory ◽  
Fractional Number ◽  
Finite Systems ◽  
Pauli Potential ◽  
Spin Polarized ◽  
Orbital Free

<div>The Pauli potential is an essential quantity in orbital-free density-functional theory (DFT) and in the exact electron factorization (EEF) method for many-electron systems. Knowledge of the Pauli potential allows the description of a system relying on the density alone, without the need to calculate the orbitals.</div><div>In this work we explore the behavior of the exact Pauli potential in finite systems as a function of the number of electrons, employing the ensemble approach in DFT. Assuming the system is in contact with an electron reservoir, we allow the number of electrons to vary continuously and to obtain fractional as well as integer values. We derive an expression for the Pauli potential for a spin-polarized system with a fractional number of electrons and find that when the electron number surpasses an integer, the Pauli potential jumps by a spatially uniform constant, similarly to the Kohn-Sham potential. The magnitude of the jump equals the Kohn-Sham gap. We illustrate our analytical findings by calculating the exact and approximate Pauli potentials for Li and Na atoms with fractional numbers of electrons.</div>

Aromaticity and conceptual density functional theory

2011 ◽  
pp. 45-98 ◽  
Author(s):  
Pratim Kumar Chattaraj ◽  
Ranjita Das ◽  
Soma Duley ◽  
Santanab Giri
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Conceptual Density Functional Theory ◽  
Functional Theory
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