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REVIEW 4 major objections 4 minor 31 references

Fundamental Relation between Conductance of Biomolecules and the Fukui Function

T0 review · 4 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The paper derives that the conductance of a biomolecular junction is fixed by the finite-temperature Fukui function at the contacts, so transport and chemical reactivity are the same local observable.

desk verdict A formally clean derivation that ends up identifying a transport profile with a Fukui function by construction; the load-bearing fast-thermalization assumption is supported only by an average-rate estimate, and the empirical validation does not measure conductance. read the letter →

arxiv 2607.13309 v1 pith:ZKU7DOPQ submitted 2026-07-14 cond-mat.soft cond-mat.mes-hallcond-mat.mtrl-sciphysics.bio-phq-bio.BM

Gabor Vattay This is my paper · ORCID
classification cond-mat.softcond-mat.mes-hallcond-mat.mtrl-sciphysics.bio-phq-bio.BM
keywords FukuifunctionproteinconductanceconceptualdensityfunctionaltheoryopenquantumsystemsAndersonmetal-insulatortransitionmultifractalwavefunctionsallostericregulationlinearresponse
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to prove that for a protein wired between two metallic leads, the electrical conductance is determined entirely by the local chemical reactivity of the protein at the two contact points. Specifically, it derives a formula in which each contact contributes a term proportional to the finite-temperature Fukui function, the standard reactivity descriptor measuring how easily the electron density at a point responds to adding or removing electrons. The derivation runs through density functional theory, an open-system master equation with an electron-phonon bath, and a double perturbation expansion in voltage and molecule-lead coupling. The key step is a projection argument: when internal relaxation is much faster than electron escape, the complicated self-consistent exchange-correlation response drops out, leaving a simple series-resistor formula. If correct, this would mean single-molecule conductance experiments can read out reactive sites and allosteric changes in proteins, linking drug binding to measurable electronic transport.

What carries the argument

The central object is the finite-temperature Fukui function f_T(r) = (1/N)Σ_k |ψ_k(r)|^2 cosh^{-2}((E_k−μ)/2k_BT), the thermally smeared frontier-orbital density that measures local response of electron density to changes in electron number; the paper shows the transport profile Z(r) equals N f_T(r). The argument is carried by the diagonal projection theorem: because the equilibrium Kohn-Sham density matrix is diagonal, the commutator with any self-consistent field change has vanishing diagonal elements, so the exchange-correlation kernel cannot contribute to the slow mode. The slow Liouvillian mode, whose inverse dominates when the relaxation gap |λ_1| ≈ 7.4 meV far exceeds the lead escape

What would settle it

Measure the internal electronic relaxation time of a folded protein directly with time-resolved spectroscopy; if τ_rlx is comparable to the ~22 ps escape time implied by the measured junction conductance, rather than the ~89 fs estimate, the fast-thermalization condition fails and the Fukui-function conductance formula should not hold.

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Extended reading notes

Core claim

The paper's central claim is that for a molecule satisfying the fast-thermalization condition, the two-terminal conductance is G_T = (2e^2/ℏ) Z_L Z_R / (Z_L + Z_R), where Z_{L/R} = Γ_{L/R} S f_T(r_{L/R}) and Γ is the local electron escape rate to the lead, S is the global softness, and f_T is the finite-temperature Fukui function at the contact position. Conductance therefore behaves as two resistors in series, each proportional to the local reactivity at its own contact. The paper further argues that the exchange-correlation self-consistent field response is analytically projected out by the diagonal structure of the slow Liouvillian mode, and that proteins, whose wave functions are extende

Load-bearing premise

The internal electronic relaxation must be much faster than electron escape from the molecule; if real proteins relax slower than about the 22 ps escape time, the exchange-correlation response is not projected out and conductance is not governed by the Fukui function.

Editorial extensions

If this is right

  • In a single-probe geometry with a multi-contact substrate, the measured conductance reduces to G_T ≈ (2e^2/ℏ) Z(r_tip), so a scanning probe maps local Fukui-function values along the protein surface.
  • Allosteric regulation becomes electronically visible: ligand binding that redistributes the Fukui function should suppress or reroute conductive pathways, even at sites far from the binding pocket.
  • Two-terminal protein junctions behave as two resistors in series, meaning contact chemistry at each lead, not the protein length, dominates the resistance once the interior is thermalized.
  • Conducting paths and reactive sites coincide, so the paper predicts that the most chemically active regions of a protein are also its best electron-transport routes.
  • The fast-thermalization requirement ties efficient protein conductance to quantum criticality: only extended multifractal wave functions keep the hierarchy τ_rlx ≪ τ_esc.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable corollary the paper leaves implicit: site-directed mutations that alter local softness at a contact residue should change single-molecule conductance in proportion to the change in f_T, independent of contact chemistry.
  • The projection mechanism is not obviously restricted to proteins; any molecular junction engineered to relax internally faster than it escapes could exhibit the same conductance-reactivity link, which could be tested in disordered organic or polymeric junctions.
  • Because the derivation uses the frozen-orbital approximation for the Fukui function, large nuclear reorganization upon charging would introduce corrections; comparing measured conductance to Fukui functions computed with and without geometry relaxation would bound that error.
  • If the identification holds, conductance imaging could serve as a high-throughput readout for drug screening, since allosteric binding would appear as a reproducible change in the spatial conductance map.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper claims to derive, within open-system time-dependent density functional theory, that the two-terminal conductance of a biomolecular junction satisfying a fast-thermalization condition is determined by the local finite-temperature Fukui function. The derivation starts from a Mermin grand-potential DFT setup, constructs an exchange-symmetric electron-phonon dissipator via Wick's theorem, linearizes the master equation in voltage and lead coupling, and projects the linearized Kohn-Sham Liouvillian onto a slow diagonal mode. The resulting conductance formula, G_T=(2e^2/hbar)Z_L Z_R/(Z_L+Z_R), is then shown to satisfy Z(r)=N f_T(r). The paper also presents a DFTB+ computation of the Fukui function for PTP1B in apo and holo states as 'empirical validation.'

Significance. If the result were established, it would offer an appealing unification of molecular conductance with conceptual DFT, with potential applications in protein bioelectronics and drug design. The manuscript's formal construction of a Pauli-preserving phonon dissipator and the derivation of a conductance expression from a Liouvillian master equation are useful contributions. However, the central identity Z(r)=N f_T(r) is true by definition, and the key projection step rests on a timescale hierarchy that is only estimated, not rigorously established. The PTP1B computation does not validate the transport relation. With these caveats, the significance is moderate: the conductance formula itself is a plausible weak-coupling result, but the paper's headline claim is largely definitional and its physical validation is incomplete.

major comments (4)
  1. [S1, Eqs. (S1)–(S6)] The fast-thermalization condition is not established. The object ⟨|λ1|⟩ computed in Eq. (S1) is an averaged transition rate, not the spectral gap of the linearized superoperator L0. The slowest off-diagonal mode may decay far slower than this average. The inequality Γ_k≈30 μeV ≪ |λ1|≈7.4 meV therefore does not follow from the given calculation. If any off-diagonal coherence decays on a timescale comparable to τ_esc, the Schur-complement correction L_diag,off L_off,off^{-1} L_off,diag is not negligible, and the SCF kernel can re-enter the population sector. Provide either a direct computation of the Liouvillian gap for a representative protein, or a rigorous bound that applies to all off-diagonal modes.
  2. [Eqs. (7), (8), (20)] The relation Z(r)=N f_T(r) is an identity by construction: Eq. (8) defines f_T as N^{-1} times the same sum that Eq. (20) uses to define Z(r). Thus the headline 'fundamental relation' is not a derived prediction but a restatement of definitions. The substantive content lies in the conductance formula (19), which connects measurable conductance to this sum. The manuscript should explicitly acknowledge this circularity and focus the claim on the conductance formula, rather than presenting Z=N f_T as a new relation.
  3. [Empirical Validation, Fig. 1] The PTP1B calculation computes the finite-temperature Fukui function in apo and holo states, showing that ligand binding changes f_T near the WPD loop. This does not validate the conductance–Fukui relation, because no conductance is measured or computed from the DFTB output. To serve as validation, the authors would need to compute Z_L/R from the same wavefunctions and show agreement with experimental conductance values, or at least demonstrate a correlation between predicted conductance changes and measured changes upon ligand binding.
  4. [Eq. (17) and the paragraph after it] The diagonal projection theorem (S29) only proves that diagonal elements of a commutator with a diagonal operator vanish. This does not by itself show that the off-diagonal SCF response 'projects to zero' in the inverse superoperator. That projection requires the slow-mode approximation L^{-1}≈λ0^{-1}V0U0, which is precisely the fast-thermalization assumption that S1 fails to establish. The text should be corrected to state that the SCF terms are controlled by the timescale separation, not by the diagonal projection theorem alone.
minor comments (4)
  1. [Abstract/Introduction] There are formatting errors, e.g., 'conductancethroughfoldedproteins' and 'theprotein length' in the first paragraph. Please run a spell/space check.
  2. [References] Reference [11] is given only as 'see Supplemental Material' with no permanent identifier or URL. For a journal submission, a DOI or supplementary file name should be supplied.
  3. [Fig. 1 caption] The description 'complete suppression of the reactivity pathway' overstates the computed change; the text itself says 'drastically altered and suppressed.' Also, the 'log-linear scale' with '+40 added to the horizontal axis' is unclear—what are the axes and units?
  4. [Eq. (6)/(8)] The factor 4k_B T appears in Eq. (6) but not in the definition of N in Eq. (7). It may be helpful to point out that ∂ρ/∂μ = S f_T, which clarifies the role of the global softness S.

Circularity Check

3 steps flagged · score 7.0 of 10

Headline identity Z = N f_T is true by construction; the conductance formula and the decisive fast-thermalization premise rest on the author's own prior cited results.

  1. self definitional [Eqs. (8) and (20), main text]
    "fT (r) = 1/N Σ k |ψk(r)|2 / cosh2((Ek−µ)/2kBT) (8); ... Defining the spatial conductance function Z(r)≡Σ k |ψk(r)|2 cosh−2((Ek −µ)/2kBT), we obtain: Z(r) =Nf T (r). (20)"

    The Fukui function is fixed in Eq. (8) as N^{-1} times the sum Σ_k |ψ_k|^2 cosh^{-2}((E_k−μ)/2k_BT). The 'derived' Z(r) in Eq. (20) is defined as exactly the same unnormalized sum. Hence Z = N f_T holds for any orbital set, by the definition of Z; it carries no transport content. The advertised result — 'the transport profile is proportional to the finite-temperature Fukui function' — is a relabeling of the local, thermally broadened orbital density. Any transport formula in which conductance is controlled by Σ_k |ψ_k(r_contact)|^2 cosh^{-2} would, after defining Z(r) this way, 'predict' Eq. (20). The claim that conductance is 'governed by' the Fukui function therefore reduces to a choice of notation.

  2. self citation load bearing [Eq. (1); ref. [12]]
    "Under this condition, the finite-temperature conductance obeys a symmetric relation [12]: GT = 2e2/ℏ ZL ZR/(ZL +Z R), (1); [12] E. Papp and G. Vattay, Computation of biological conductance with liouville quantum master equation, Scientific Reports 14, 19571 (2024)."

    The paper's central quantitative formula is introduced by citation to the authors' own prior paper and then recovered by a sketched step ('Substituting this slow-mode approximation into the expression for J L yields the conductance'). No measured protein conductance is compared, so the formula's status in this paper rests on the self-citation plus a one-sentence derivation. The genuinely new element — identifying Z with the Fukui function — is the definitional identity of Eq. (20). The headline claim is thus substantially a restatement of the authors' earlier master-equation result with a new label, not an independently falsifiable prediction.

1 more flagged steps
  1. self citation load bearing [Main text (fast-thermalization, before Eq. 18) and S1 Eqs. (S1)-(S6)]
    "This rapid spatial equilibration establishes the fast-thermalization condition, where the internal relaxation timescale τrlx is much faster than the electron escape rate... C(ω) follows a universal power-law scaling C(ω) =Aω −1/3 [2] ... Γk ≈30µeV ≪ |λ1| ≈7.4meV (S6)"

    The whole derivation hinges on the hierarchy (S6): only if off-diagonal coherences decay far faster than the lead escape rate does L^{-1}≈λ0^{-1}V0U0 hold and does Eq. (S31) project out the SCF response. This decisive premise is not established in the paper: the spectral gap |λ1| is replaced by an averaged rate ⟨|λ1|⟩ = ∫γ(ω)C(ω)dω (S1), and the input scaling C(ω)=Aω^{-1/3} is cited to the authors' own prior work ([S2] = Papp & Vattay). The quantum-criticality property itself ('wave functions are extended and multifractal due to quantum criticality') is cited to self-authored [9],[10]. Thus the condition that makes the central result possible is asserted by self-citation plus an average-rate estimate, not by a bound on the slowest decay mode.

full rationale

The paper contains genuine derivation content: the Mermin-functional setup, the Wick-derived electron-phonon dissipator, the linearized Kohn-Sham superoperator, and the diagonal projection theorem are all developed in-text (Eqs. 2-17, S7-S31). The conductance formula (1)/(19) is not a pure tautology. However, the paper's headline claim — the identification of the transport profile with the finite-temperature Fukui function — is circular in two ways. First, Eq. (20) is definitional: f_T is defined in Eq. (8) as (1/N)Σ_k|ψ_k|^2 cosh^{-2}((E_k−μ)/2k_BT), and Z(r) is then defined in Eq. (20) as the same unnormalized sum. The 'result' Z(r)=N f_T(r) holds for any wavefunction set and contributes no transport information; the claimed 'fundamental link' reduces to naming the thermal-broadened local orbital density 'the Fukui function.' The physical content of the derivation is that G depends on that combination at the contacts — a standard local-density-of-states result — and the reactivity interpretation is a relabeling. Second, the load-bearing assumptions come from the author's own prior work. The conductance formula is first presented via citation [12] (Papp & Vattay, Sci. Rep. 2024) and then re-derived in one sentence; the fast-thermalization condition that justifies projection of the SCF response (Eq. S31) is verified only by citing the same authors' quantum-criticality results [9],[10] and the ω^{-1/3} wavefunction-correlation scaling [S2]. The S1 estimate computes an average relaxation rate rather than a spectral gap, so the hierarchy Γ_k≈30μeV ≪ |λ1|≈7.4meV (S6) is an estimate, not a proof; if the true gap is smaller, the SCF coupling re-enters and the central formula breaks. This is a validity risk as well as a self-citation chain. The PTP1B 'empirical validation' is not circular — it is a genuine DFTB computation of f_T in apo/holo states — but it does not test the conductance formula, since no conductance is measured or fitted; showing that the Fukui function changes upon binding cannot validate G ∝ f_T. The paper is therefore best characterized as a substantial re-derivation of the authors' earlier master-equation conductance formula, with the novel Fukui-function identification true by construction. Score 7: one central 'prediction' reduces by construction, and the enabling premises are carried by self-citations.

Assumptions & free parameters 5 free parameters · 6 assumptions · 1 invented entities

The central claim rests on an estimated timescale hierarchy (S1), standard OQS-DFT approximations, and a nearly definitional identification of the transport profile with the Fukui function. The free parameters are the constants used to compute the fast-thermalization gap and escape rate; if they are off by an order of magnitude, the projection theorem and the formula break.

free parameters (5)
  • Ohmic spectral density coupling η = 1.46
    S1: used in γ(ω)=ηℏω e^{-ω/ω_c}/(e^{ℏω/kT}-1) to obtain λ1≈7.4 meV and τ_rlx≈89 fs. Value is asserted without uncertainty or direct protein-specific measurement.
  • Multifractal correlation prefactor A = 2.15 eV^{1/3}
    S1: C(ω)=A ω^{-1/3}; prefactor from prior work [S2]. It controls the magnitude of the thermalization gap and hence the fast-thermalization condition.
  • Phonon bath cutoff ℏω_c = 0.0185 eV
    S1: cutoff energy entering the Gamma-function integral for λ1. Sourced from a photosynthetic energy transfer paper [S1], with no protein-specific justification.
  • Local lead coupling Γ_local = ≈100 meV
    S1: assumed strong contact chemistry; combined with N≈3,000 gives Γ_k≈30 μeV and τ_esc≈22 ps. The entire timescale hierarchy depends on this assumption.
  • Protein atom count N = ≈3,000
    S1: used to dilute the wavefunction density |ψ(r_contact)|^2≈1/N. Not tied to any specific PTP1B conductance measurement.
assumptions (6)
  • domain assumption Fast-thermalization condition τ_rlx ≪ τ_esc holds for proteins because Kohn-Sham wave functions are extended and multifractal at an Anderson metal-insulator transition.
    Main text and S1: the projection of the xc SCF response (S4 Eq. S31) and the entire Fukui-function conductance formula rely on this hierarchy. No direct measurement of τ_rlx is provided; it is inferred from quantum-criticality claims [9,10] and the S1 estimates.
  • domain assumption Born-Markov approximation for the phonon bath.
    S2: needed to obtain the Redfield-form dissipator in Eq. (S8). Assumes weak electron-phonon coupling and short bath correlation times without system-specific verification for proteins.
  • domain assumption Frozen-orbital approximation: orbital shapes are static under chemical potential variation.
    Main text before Eq. (6): used to define the finite-temperature Fukui function. Neglects orbital relaxation, which is a standard but uncontrolled approximation in CDFT.
  • standard math Wick's theorem for Kohn-Sham fermions.
    S2 Eq. (S9): valid because the KS system is a non-interacting reference; used to factorize four-operator correlations and build the exchange-symmetric dissipator.
  • domain assumption Wide-band limit for leads, symmetric voltage bias, and weak molecule-lead coupling.
    Main text Eqs. (13)-(14) and S3: required for the linear-response current formula and first-order shift of the slow eigenvalue. Breakdown of weak coupling would invalidate the perturbation expansion.
  • standard math Spectral separation justifies L^{-1}≈λ0^{-1} V0 U0.
    S4: a standard spectral projection argument, but its validity inherits the fast-thermalization assumption; no explicit control of the off-diagonal block is given.
invented entities (1)
  • None
    purpose: No new particles, forces, dimensions, or conserved quantities are introduced.
    The paper stays within existing DFT/open-quantum-system machinery; the only novel object is the identification of Z(r) with N f_T(r), which is a mathematical redefinition rather than a new physical entity.

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Cite this review

Pith. "Pith review of Fundamental Relation between Conductance of Biomolecules and the Fukui Function." pith.science (2026). https://pith.science/paper/ZKU7DOPQ

@misc{pith2026260713309,
  author       = {Pith},
  title        = {Pith review of: Fundamental Relation between Conductance of Biomolecules and the Fukui Function},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZKU7DOPQ}},
  note         = {Machine review of arXiv:2607.13309}
}
read the original abstract

The finite-temperature conductance of a molecule coupled to metallic leads is derived entirely within the framework of density functional theory (DFT) and its time-dependent extension for open quantum systems. Starting from the Mermin grand potential, the foundational Kohn-Sham equations, the Fukui function, and the open-system master equation for the single-particle density matrix are systematically formulated. The non-equilibrium electron-phonon dissipator is obtained from the partial trace over the phonon bath. By applying Wick's theorem for non-interacting fermions, a fully exchange-symmetric collision integral is obtained that strictly preserves Pauli exclusion at the operator level. Performing a double perturbation expansion, initially in the applied voltage (linear response), and subsequently in the molecule-lead coupling (weak coupling), it is demonstrated that under the fast-thermalization condition, the complex exchange-correlation self-consistent field response is analytically projected out by the diagonal structure of the slow Liouvillian mode. Consequently, the thermal conductance is governed by the finite-temperature Fukui function, the central reactivity descriptor of conceptual density functional theory. This condition is satisfied in proteins, whose wave functions are extended and multifractal due to quantum criticality at the Anderson metal-insulator transition. This derivation establishes a fundamental link between electronic transport and chemical reactivity, identifying conducting paths with reactive sites. It opens new technological avenues connecting drug design to conductance experiments and also provides a foundation for designing next-generation bioelectronic sensing and computing architectures.

Figures

Figures reproduced from arXiv: 2607.13309 by the authors.

Figure 1
Figure 1. FIG. 1. Empirical validation of the conductance-reactivity [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic representation of sequential transport. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

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Works this paper leans on

31 extracted references · 2 canonical work pages

  1. [1]

    J. A. Fereiro, X. Yu, I. Pecht, M. Sheves, J. C. Cuevas, and D. Cahen, Tunneling explains efficient electron trans- port via protein junctions, Proceedings of the National Academy of Sciences115, E4577 (2018)

    2018

  2. [2]

    Zhang, W

    B. Zhang, W. Song, P. Pang, H. Lai, Q. Chen, P. Zhang, and S. Lindsay, Role of contacts in long-range protein con- 5 ductance, Proceedings of the National Academy of Sci- ences116, 5886 (2019)

    2019

  3. [3]

    M. P. Ruiz, A. C. Aragonès, N. Camarero, J. Vilhena, M. Ortega, L. A. Zotti, R. Pérez, J. C. Cuevas, P. Goros- tiza, and I. Díez-Pérez, Bioengineering a single-protein junction, Journal of the American Chemical Society139, 15337 (2017)

    2017

  4. [4]

    Amdursky, D

    N. Amdursky, D. Marchak, L. Sepunaru, I. Pecht, M. Sheves, and D. Cahen, Electronic transport via pro- teins, Advanced Materials26, 7142 (2014)

    2014

  5. [5]

    Nawade, K

    A. Nawade, K. B. Busi, K. Ramya, G. K. Dalapati, S. Mukhopadhyay, and S. Chakrabortty, Improved charge transport across bovine serum albumin–au nanoclusters’ hybrid molecular junction, ACS omega7, 20906 (2022)

    2022

  6. [6]

    K. Garg, M. Ghosh, T. Eliash, J. H. van Wonderen, J. N. Butt, L. Shi, X. Jiang, F. Zdenek, J. Blum- berger, I. Pecht,et al., Direct evidence for heme-assisted solid-state electronic conduction in multi-heme c-type cy- tochromes, Chemical science9, 7304 (2018)

    2018

  7. [7]

    C. D. Bostick, S. Mukhopadhyay, I. Pecht, M. Sheves, D. Cahen, and D. Lederman, Protein bioelectronics: A re- view of what we do and do not know, Reports on Progress in Physics81, 026601 (2018)

    2018

  8. [8]

    Jiang, B.-F

    T. Jiang, B.-F. Zeng, B. Zhang, and L. Tang, Single- molecular protein-based bioelectronics via electronic transport: fundamentals, devices and applications, Chem- ical Society Reviews52, 5968 (2023)

    2023

Show all 31 references
  1. [9]

    Vattay, D

    G. Vattay, D. Salahub, I. Csabai, A. Nassimi, and S. A. Kauffman, Quantum criticality at the origin of life, J. Phys.: Conf. Ser.626, 012023 (2015)

    2015

  2. [10]

    Papp and G

    E. Papp and G. Vattay, Holographic nature of critical quantum states of proteins, Computational and Structural Biotechnology Journal30, 59 (2025)

    2025

  3. [11]

    (2026), see Supplemental Material

    2026

  4. [12]

    Papp and G

    E. Papp and G. Vattay, Computation of biological con- ductance with liouville quantum master equation, Scien- tific Reports14, 19571 (2024)

    2024

  5. [13]

    R. G. Parr and W. Yang, Density functional approach to the frontier-electron theory of chemical reactivity, Journal of the American Chemical Society106, 4049 (1984)

    1984

  6. [14]

    Yang and R

    W. Yang and R. G. Parr, Hardness, softness, and the fukui function in the electronic theory of metals and catal- ysis., Proceedings of the National Academy of Sciences82, 6723 (1985)

    1985

  7. [15]

    R. G. Parr, Density functional theory of atoms and molecules, inHorizons of Quantum Chemistry: Proceed- ings of the Third International Congress of Quantum Chemistry Held at Kyoto, Japan, October 29-November 3, 1979(Springer, 1979) pp. 5–15

    1979

  8. [16]

    Geerlings, F

    P. Geerlings, F. De Proft, and W. Langenaeker, Concep- tualdensityfunctionaltheory,Chemicalreviews103,1793 (2003)

    2003

  9. [17]

    G. Roos, P. Geerlings, and J. Messens, Enzymatic catal- ysis: the emerging role of conceptual density functional theory, The Journal of Physical Chemistry B113, 13465 (2009)

    2009

  10. [18]

    Geerlings, E

    P. Geerlings, E. Chamorro, P. K. Chattaraj, F. De Proft, J. L. Gázquez, S. Liu, C. Morell, A. Toro-Labbé, A. Vela, and P. Ayers, Conceptual density functional theory: sta- tus, prospects, issues, Theoretical Chemistry Accounts 139, 36 (2020)

    2020

  11. [19]

    Cárdenas, N

    C. Cárdenas, N. Rabi, P. W. Ayers, C. Morell, P. Jaramillo, and P. Fuentealba, Chemical reactivity de- scriptors for ambiphilic reagents: dual descriptor, local hypersoftness, and electrostatic potential, The Journal of Physical Chemistry A113, 8660 (2009)

    2009

  12. [20]

    Cárdenas, P

    C. Cárdenas, P. Ayers, F. De Proft, D. J. Tozer, and P. Geerlings, Should negative electron affinities be used for evaluating the chemical hardness?, Physical Chemistry Chemical Physics13, 2285 (2011)

    2011

  13. [21]

    Franco-Pérez, J

    M. Franco-Pérez, J. L. Gázquez, P. W. Ayers, and A. Vela, Revisiting the definition of the electronic chem- ical potential, chemical hardness, and softness at finite temperatures, The Journal of Chemical Physics143, https://doi.org/10.1063/1.4932539 (2015)

    2015 doi

  14. [22]

    Franco-Pérez, P

    M. Franco-Pérez, P. W. Ayers, J. L. Gázquez, and A. Vela, Local and linear chemical reactivity re- sponse functions at finite temperature in density func- tional theory, The Journal of Chemical Physics143, 10.1063/1.4938422 (2015)

    2015 doi

  15. [23]

    Hohenberg and W

    P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Physical review136, B864 (1964)

    1964

  16. [24]

    N. D. Mermin, Thermal properties of the inhomogeneous electron gas, Physical Review137, A1441 (1965)

    1965

  17. [25]

    Runge, Density-functional theory for time-dependent systems, Physical review letters52, 997 (1984)

    E. Runge, Density-functional theory for time-dependent systems, Physical review letters52, 997 (1984)

    1984

  18. [26]

    Yuen-Zhou, D

    J. Yuen-Zhou, D. G. Tempel, C. A. Rodríguez-Rosario, and A. Aspuru-Guzik, Time-dependent density functional theory for open quantum systems with unitary propaga- tion, Physical review letters104, 043001 (2010)

    2010

  19. [27]

    D. G. Tempel, J. Yuen-Zhou, and A. Aspuru-Guzik, Open quantum systems: density matrix formalism and applications, inFundamentals of Time-Dependent Density Functional Theory(Springer, 2012) pp. 211–229

    2012

  20. [28]

    Breuer and F

    H.-P. Breuer and F. Petruccione,The theory of open quantum systems(OUP Oxford, 2002)

    2002

  21. [29]

    Blum,Density matrix theory and applications, Vol

    K. Blum,Density matrix theory and applications, Vol. 64 (Springer Science & Business Media, 2012)

    2012

  22. [30]

    Wiesmann, K

    C. Wiesmann, K. J. Barr, J. Kung, J. Zhu, D. A. Erlan- son, W. Shen, B. J. Fahr, M. Zhong, L. Taylor, M. Randal, et al., Allosteric inhibition of protein tyrosine phosphatase 1b, Nature structural & molecular biology11, 730 (2004)

    2004

  23. [31]

    Vattay, S

    G. Vattay, S. Kauffman, and S. Niiranen, Quantum bi- ology on the edge of quantum chaos, PloS one9, e89017 (2014). S1 Supplementary Material: Fundamental relation between conductance of biomolecules and the Fukui function Gábor Vattay Institute for Physics and Astronomy, Eötvö...

    2014

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.