Proof that<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>ε</mml:mi></mml:math>in density-functional theory

Janak, J. F.

doi:10.1103/physrevb.18.7165

Cited by 1,947 publications

(1,024 citation statements)

References 16 publications

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“…The only exception is for the HOMO level, which is equal to the negative of the ionization potential. [39][40][41] It has been demonstrated experimentally [42][43][44][45][46] that the quasi-particle energy gap, E gap QP , of a molecule, defined as the difference between its ionization potential, I, and electron affinity, A, shrinks with respect to that of the gas phase by adsorbing the molecule on a polarizable substrate. Nevertheless, the electronic structure theories usually used for such calculations can only partly account for this renormalization of the molecular energy levels when the junction is formed.…”

Section: Introductionmentioning

confidence: 99%

Stretching of BDT-gold molecular junctions: thiol or thiolate termination?

et al. 2014

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It is often assumed that the hydrogen atoms in the thiol groups of a benzene-1,4-dithiol dissociate when Au-benzene-1,4-dithiol-Au junctions are formed. We demonstrate, by stability and transport property calculations, that this assumption cannot be made. We show that the dissociative adsorption of methanethiol and benzene-1,4-dithiol molecules on a flat Au(111) surface is energetically unfavorable and that the activation barrier for this reaction is as high as 1 eV. For the molecule in the junction, our results show, for all electrode geometries studied, that the thiol junctions are energetically more stable than their thiolate counterparts. Due to the fact that density functional theory (DFT) within the local density approximation (LDA) underestimates the energy difference between the lowest unoccupied molecular orbital and the highest occupied molecular orbital by several electron-volts, and that it does not capture the renormalization of the energy levels due to the image charge effect, the conductance of the Au-benzene-1,4-dithiol-Au junctions is overestimated. After taking into account corrections due to image charge effects by means of constrained-DFT calculations and electrostatic classical models, we apply a scissor operator to correct the DFT energy level positions, and calculate the transport properties of the thiol and thiolate molecular junctions as a function of the electrode separation. For the thiol junctions, we show that the conductance decreases as the electrode separation increases, whereas the opposite trend is found for the thiolate junctions. Both behaviors have been observed in experiments, therefore pointing to the possible coexistence of both thiol and thiolate junctions. Moreover, the corrected conductance values, for both thiol and thiolate, are up to two orders of magnitude smaller than those calculated with DFT-LDA.This brings the theoretical results in quantitatively good agreement with experimental data.

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Section: Introductionmentioning

confidence: 99%

Stretching of BDT-gold molecular junctions: thiol or thiolate termination?

et al. 2014

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“…Similarly, for a system with N = M + f electrons, ∂ E ∂ N equals the negative of the exact vertical electron affinity of the M-electron system, denoted A M 0 , again independent of f . From Janak's theorem, 17 ∂ E ∂ N equals the energy of the Kohn-Sham orbital whose occupation is varying. It follows that…”

Section: Introductionmentioning

confidence: 99%

Assessment of Tuning Methods for Enforcing Approximate Energy Linearity in Range-Separated Hybrid Functionals

Gledhill

Peach

Tozer

2013

J. Chem. Theory Comput.

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“…Perdew et al 6 showed for an atom of nuclear charge Z that with IP the ionization potential, EA the electron affinity, N a continuous variable representing the total number of electrons, and µ ) ∂E/∂N the first derivative of the total energy (E) with respect to N, the chemical potential. Earlier, Janak proved that 7 where n i is the occupation number of the KS orbital ψ i and i is the corresponding KS orbital energy. On the basis of eqs 1 and 2, Perdew et al obtained 6 in which max represents the maximum occupied KS orbital energy.…”

Section: Introductionmentioning

confidence: 99%

Ionization Potential, Electron Affinity, Electronegativity, Hardness, and Electron Excitation Energy: Molecular Properties from Density Functional Theory Orbital Energies

2003

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Representative atomic and molecular systems, including various inorganic and organic molecules with covalent and ionic bonds, have been studied by using density functional theory. The calculations were done with the commonly used exchange-correlation functional B3LYP followed by a comprehensive analysis of the calculated highest-occupied and lowest-unoccupied Kohn-Sham orbital (HOMO and LUMO) energies. The basis set dependence of the DFT results shows that the economical 6-31+G* basis set is generally sufficient for calculating the HOMO and LUMO energies (if the calculated LUMO energies are negative) for use in correlating with molecular properties. The directly calculated ionization potential (IP), electron affinity (EA), electronegativity ( ), hardness (η), and first electron excitation energy (τ) are all in good agreement with the available experimental data. A generally applicable linear correlation relationship exists between the calculated HOMO energies and the experimental/calculated IPs. We have also found satisfactory linear correlation relationships between the calculated LUMO energies and experimental/calculated EAs (for the bound anionic states), between the calculated average HOMO/LUMO energies and values, between the calculated HOMO-LUMO energy gaps and η values, and between the calculated HOMO-LUMO energy gaps and experimental/ calculated first excitation energies. By using these linear correlation relationships, the calculated HOMO and LUMO energies can be employed to semiquantitatively estimate ionization potential, electron affinity, electronegativity, hardness, and first excitation energy.

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Proof that∂E∂ni=εin density-functional theory

Cited by 1,947 publications

References 16 publications

Stretching of BDT-gold molecular junctions: thiol or thiolate termination?

Stretching of BDT-gold molecular junctions: thiol or thiolate termination?

Assessment of Tuning Methods for Enforcing Approximate Energy Linearity in Range-Separated Hybrid Functionals

Ionization Potential, Electron Affinity, Electronegativity, Hardness, and Electron Excitation Energy: Molecular Properties from Density Functional Theory Orbital Energies

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