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How orbitals and oxidation states determine apparent topographies in scanning tunneling microscopy: the case of fluorine on silver surfaces

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Pith's one-line read STM depressions over fluorine on silver reveal oxidized silver neighbors

desk verdict Fresh orbital model for F/Ag STM topographies, but the oxidation-state link is a plausible rationalization, not a proven mechanism. read the letter →

arxiv 2411.09392 v1 pith:WF7R3PDA submitted 2024-11-14 cond-mat.mtrl-sci cond-mat.mes-hall

Adrián Gómez Pueyo , Jazmín Aragón Sánchez , Ilya Degtev , Maria Eleonora Temperini , Daniel Jezierski , Conor Hogan , Antonio Caporale , Luciana Di Gaspare
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Luca Persichetti Monica De Seta Wojciech Grochala Paolo Barone Luca Camilli José Lorenzana
This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.mes-hall
keywords scanningtunnelingmicroscopyapparenttopographyfluorineadsorptionsilversurfacesdensityfunctionaltheoryoxidationstateeffectivenuclearchargescreenings-wavetipapproximation
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 combines density functional theory with simulated scanning tunneling microscopy to work out where fluorine atoms sit on silver (100) and (110) surfaces and why those atoms look the way they do. Its central proposal is that an adatom's apparent shape is set by two opposite orbital effects: oxidation of the neighboring silver atoms contracts their $5s$ orbitals, producing the topographic depression seen at positive bias, while the filled $2p$ orbitals of the fluoride ion protrude above that depression at negative bias, producing the sombrero shape. The authors reduce the depression depth to a simple analytic expression proportional to the charge removed from each neighboring silver atom, with matrix elements and coordination numbers cancelling out. If the model is right, STM apparent topographies during halogenation carry local oxidation-state information, not just geometry. The paper also argues that under typical fluorination conditions the observed surface is a kinetic state, since thermodynamics would favor bulk silver fluoride.

What carries the argument

The load-bearing object is a minimal orbital model of the tunneling current built from atom-centered orbitals with hydrogenic radial shapes and screened effective charges. Starting from the s-wave tip approximation, the model keeps only diagonal orbital contributions, so the local DOS at the tip is a sum over shells of the projected DOS times the shell density (Eq. (18)); at tip distances of 5–6 Å the silver $4d$ states, despite their large projected DOS, are too short-ranged to matter, leaving Ag $5s$ and F $2p$ as the active channels. Oxidation of a silver neighbor is represented by a screening-rule increase in its effective nuclear charge, $\Delta Z^{5s}_{\rm eff}=0.35\,\delta/\zeta$, which contracts the $5s$ orbital and lowers the constant-current height; the analytic depression formula (Eq. (25)) cancels matrix elements and coordination factors, leaving a depth that depends only on geometry, effective charge, and cumulative DOS. The protrusion is controlled by the competing F $2p$ and Ag $5s$ densities and cumulative DOS (Eq. (26)), which is why it appears only at negative bias where F $2p$ is occupied.

What would settle it

Measure the apparent depression depth of a fluorine adatom on Ag(100) as a function of tip–sample distance and of an independent local-oxidation probe such as X-ray photoemission core-level shifts, and compare with Eq. (25): the depth should grow linearly with tip height and with the per-atom charge loss. A clear deviation, or a depression that does not scale with per-atom charge loss across different adsorption sites, would falsify the screening-contraction mechanism.

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Extended reading notes

Core claim

The paper's central claim is that the apparent topography of a fluorine adatom on Ag(100) and Ag(110) is governed by two orbital channels with opposite signs. At positive bias the tunneling current is carried by silver $5s$ states; the fluorine removes roughly $1/\zeta$ of an electron from each of its $\zeta$ nearest silver neighbors, and by the standard screening rule this raises the effective nuclear charge of those silvers, contracts their $5s$ orbitals, and produces a topographic depression whose depth is approximately independent of bias and proportional to the per-atom charge depletion (Eqs. (24)–(25)). At negative bias the filled F $2p$ states contribute strongly, and because the fluorine sits above the surface the $2p$ evanescent density can rise above the depressed silver contour, producing the central protrusion that turns the feature into a sombrero (Eq. (26)). The same model assigns the experimental topographies to specific adsorption sites: the hollow site on Ag(100), and the short bridge, long bridge, and hollow sites on Ag(110), with the rarest observed feature still unresolved. The paper further argues that under realistic fluorination conditions bulk silver fluorides are thermodynamically stable, so the adatom configurations seen in experiments are set by kinetic barriers and sticking rather than by equilibrium.

Load-bearing premise

The argument stands on the assumption that the dominant effect of the fluorine on neighboring silver is the classical screening rule: every fraction of an electron removed shrinks the Ag $5s$ orbital by the textbook 0.35 factor, while wave-function deformation, $4d$ screening, off-diagonal orbital overlap, and tip-induced polarization are all small enough to ignore.

Editorial extensions

If this is right

  • After subtracting the central protrusion, the depth of the STM depression over a fluorine adatom is a direct measure of the oxidation state of the neighboring silver atoms: depth grows with the fraction of an electron removed per neighbor and is essentially independent of bias.
  • The sombrero protrusion appears only at negative bias, where the filled F $2p$ states contribute to the current, and vanishes wherever the Ag $5s$ channel dominates the tunneling.
  • On Ag(100) the stable hollow-site adatom, and on Ag(110) the three near-degenerate short-bridge, long-bridge, and hollow-site adatoms, can be matched to the experimental topographies by combining adsorption energetics, simulated images, and the orbital model.
  • Under the pressures and temperatures of typical fluorination experiments, the clean-to-fluoride equilibrium would favor bulk AgF or AgF$_2$, so the adatom coverages observed in experiments are kinetic states controlled by exposure time and sticking coefficient.
  • The same reasoning implies STM can supply local-valence information on metal surfaces during reactions, not merely geometric corrugation.

Reading between the lines

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

  • Beyond the paper: the same two-channel mechanism should apply to other electronegative adsorbates such as oxygen, sulfur, or chlorine on silver; any adsorbate that oxidizes its nearest metal neighbors should create a positive-bias depression whose depth tracks the per-atom charge loss, which would unify the sombrero shapes reported for S/Ag and O/Ag.
  • Beyond the paper: a direct test would compare STM depression depths with core-level shifts from X-ray photoemission on the same surface; agreement would confirm the oxidation link, while disagreement would point to wave-function deformation or $4d$ screening as the controlling factor.
  • Beyond the paper: because Eq. (25) predicts depression depth grows roughly linearly with tip height, systematic constant-current measurements over a wide tip–sample distance range should expose where the diagonal-orbital approximation breaks down and off-diagonal channels or tip-induced polarization take over.
  • Beyond the paper: the unresolved rarest feature (AT(C)) might be settled by searching off-symmetry adsorption positions or mixed F/H adsorbates; the model's volcano-shaped fingerprint for a vacancy site is a specific prediction that could be tested by deliberately creating single Ag vacancies.
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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

3 major / 5 minor

Summary. This paper combines DFT calculations, Tersoff–Hamann STM simulations, and a simplified hydrogenic orbital model to analyze the early stages of fluorine adsorption on Ag(100) and Ag(110). The authors compute adsorption energies for several high-symmetry sites, construct a thermodynamic coverage phase diagram, and argue that under typical experimental conditions the surface state is controlled by kinetics rather than equilibrium thermodynamics. They then simulate STM apparent topographies, propose assignments of the experimental features to specific adsorption sites, and introduce a model in which the STM depression is attributed to oxidation-induced contraction of Ag 5s orbitals while the protrusion is attributed to filled F 2p orbitals. The central claim is that apparent STM heights can encode the local oxidation state of metal atoms near the adatom.

Significance. If the central claim holds, the paper would provide a broadly applicable interpretive framework for STM of atomic adsorbates, potentially allowing local valence information to be extracted from topographic images. The DFT calculations are carefully specified and the authors are commendably transparent about discrepancies: depression depth overestimated, width underestimated by about a factor of 0.5, the AT(C) assignment questioned, and the short-bridge sombrero mismatch at -1.5 V. The orbital model is simple, falsifiable, and yields qualitative trends that are consistent with both DFT and experiment. However, the quantitative link between depression depth and oxidation state is not yet established, for the reasons detailed in the major comments.

major comments (3)
  1. [Sec. III D, Eq. (25), and Table II] The numerical estimate in Eq. (25) is obtained with a full-electron oxidation state that is inconsistent with the DFT charge transfer reported in the same paper. The text states that 'we assume that 1/ζ of an electron is transferred to the fluorine' and the numerical check after Eq. (25) uses Zeff = 0.35/ζ, i.e., δ = 1, yielding |Δz| ≈ 15–30 pm. Yet Table II reports δn ≈ 0.16–0.20 e on F, and Sec. III A 1 explicitly uses the smallness of δn to argue that dipole–dipole interactions are weak. Since Eq. (25) is linear in δ, using the tabulated charge transfer would give depression depths of roughly 3–6 pm, an order of magnitude smaller than the DFT and experimental values. The authors must reconcile the effective charge transfer used in the orbital model with the DFT electronic structure, or show through an explicit calculation that the depression depth is insensitive to δ because of a compensating change in the calibrated Zeff.
  2. [Sec. III D, Eqs. (24)–(25)] The derivation does not establish that the depression is specifically caused by Slater-rule contraction of Ag 5s orbitals. The only oxidation-dependent input is the ad hoc ΔZeff = 0.35δ/ζ, and the quantitative comparison is performed only after re-tuning Zeff so that the Ag 5s ionization energy coincides with the silver work function, with the resulting tip position falling in the oscillatory region of the hydrogenic density (text after Eq. (25) and Fig. 10(a)). Under those conditions the asymptotic expression (A4) is not valid, as the authors acknowledge. Other mechanisms, such as the electrostatic potential of the F− ion, tip-induced polarization, or the off-diagonal Wannier products discarded in Eq. (16), would also reduce the Ag 5s density at the tip height. A discriminating test is needed: for example, computing from the DFT Kohn–Sham states the constant-height changes Δρ5s and ΔG5s at the hollow site and comparing their magnitude and radial dependence with the Slater-contracted hydrogenic prediction, rather than only comparing final apparent heights.
  3. [Sec. III D, Fig. 8 and Eq. (24)] The neglect of ΔG5s/G∞5s is asserted but not quantified. The text says that from Fig. 8 the integrated 5s PDOS is 'practically unchanged' and that 'ΔG5s/G∞5s ≪ 1', but Fig. 8 shows PDOS curves for one Ag neighbor and does not display the bias-integrated differences that enter Eq. (24). Because G05s and G∞5s appear in Eq. (24) with the same weight as Δρ5s, a numerical bound on ΔG5s/G∞5s over the full bias range is required before Eq. (24) can be reduced to Eq. (25). If the integrated PDOS change is not small, the depression depth depends on bias and on the cumulative DOS, which would undermine the claimed bias independence of the depression depth (point i after Eq. (25)).
minor comments (5)
  1. [References] Ref. [53] appears to be a mis-citation: the listed paper (Wang et al., Phys. Rev. B 64, 224519 (2001)) is on cuprate superconductors, not on fluorine adsorption on Ag(110). Please cite the correct DFT study with which the 0.5 ML adsorption energies are compared.
  2. [Sec. II B] The phrase 'the energy of a F 2 molecule' should read 'the energy of an F2 molecule'.
  3. [Eq. (26)] The quantity G2p(VB) is used without being defined; please define it as the cumulative F 2p PDOS, analogous to G5s(VB).
  4. [Sec. III D] The sentence 'the 4 s charge transfer is smaller in magnitude' appears to be a typo for '5s charge transfer', since the surrounding discussion concerns the Ag 5s channel and the 4s orbital is not otherwise considered.
  5. [Eq. (13)] The notation is inconsistent: both kbT and kBT appear, as do ¯h and h. Please standardize the symbols for the Boltzmann constant and Planck constant.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the oxidation-to-depression link in the simplified orbital model is a stated assumption tested against independent DFT and experimental comparisons, not a fit to the target topography.

full rationale

The paper's central interpretive claim is that the apparent STM depression is caused by oxidation-induced contraction of Ag 5s orbitals. In the simplified orbital model, the depression depth Eq. (25) is derived from an assumed Slater-rule change ΔZ_eff = 0.35δ/ζ, stated explicitly in Sec. III D: 'According to Slater rules [61], this should decrease the screening of the core charges by 0.35 per electron. Thus, we increase the positive effective charge of these Ag atoms by 0.35/ζ.' That assumption is an input to the forward model, not a quantity inferred from the STM data and then relabeled as a prediction. The paper compares the model's trends with DFT-computed 5s charge transfers (-0.036, -0.033, -0.045, -0.05 e for the relevant sites) and with DFT/experimental well depths, providing an independent check of the assumed correlation. The Zeff adjustment ('Adjusting Zeff so that the ionization energy coincides with the work function of silver') calibrates the evanescent decay length to a bulk property independent of the target STM topography, so it does not constitute fitting the observable it is used to explain. Limitations explicitly acknowledged in the text, such as the neglect of wave-function deformation by the F− ion and the diagonal approximation in Eq. (16), reduce certainty but do not create a circular reduction. The companion experimental paper Ref. [25] is cited as data source for STM observations, not as an authority or uniqueness theorem; other self-citations are background. No load-bearing argument reduces to a self-citation or to the target result by construction.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central orbital model rests on four load-bearing assumptions: the Tersoff-Hamann current formula, the diagonal Wannier approximation, Slater-type hydrogenic orbitals with literature effective charges, and the Slater-rule oxidation-contraction mechanism. Three hand-set parameters (Z_eff for Ag 5s adjusted to the work function, Z_eff for F 2p set from ionic radius, and a 4.7 Å Gaussian FWHM) are needed to reach quantitative agreement with DFT and experiment. No new physical entities are postulated.

free parameters (3)
  • Z_eff(Ag 5s) = adjusted so that the Ag 5s ionization energy equals the silver work function; final value not stated
    The hydrogenic decay length of Ag 5s is tuned to match DFT depression depths (discussion after Eq. 25); the fit is acknowledged to place the tip in the oscillatory region of the wavefunction.
  • Z_eff(F 2p) = 1.6
    Estimated from the ionic radius of F- (Shannon) via Zeff = a0 n^2 / r_exp; used for protrusion estimates. This is a hand-estimated value, not from a first-principles calculation.
  • Gaussian FWHM = 4.7 Å
    Applied to convolve simulated STM profiles (Fig. 7) to improve agreement with experiment; chosen by hand, not derived from an independent tip characterization.
assumptions (7)
  • domain assumption Tersoff-Hamann approximation with an s-wave spherical tip, constant tip DOS and matrix element
    Used for all STM simulations (Sec. II D); limits quantitative accuracy, as the authors note (depth overestimated, width underestimated).
  • domain assumption Diagonal approximation in Eq. (16): local DOS is a sum of diagonal Wannier orbital densities; off-diagonal terms neglected
    Justified as 'in a first approximation' in Sec. II E; the main quantitative uncertainty of the orbital model.
  • domain assumption Slater-type hydrogenic orbitals with effective charges from Clementi-Raimondi represent the evanescent tunneling tails
    Used throughout Sec. III D; the radial form (Eq. A4) enters Eqs. (24)-(26).
  • ad hoc to paper Slater rules: oxidation by δ/ζ electrons increases the effective nuclear charge of the Ag neighbor by ΔZ_eff = 0.35δ/ζ
    This is the key mechanism linking oxidation state to orbital contraction (Sec. III D, Eq. 25); it is an empirical atomic-physics rule extrapolated to a surface environment.
  • domain assumption Change in integrated 5s PDOS at the nearest-neighbor Ag is negligible compared to the density contraction (ΔG_5s ≈ 0 in Eq. 24)
    Supported by Fig. 8 for the computed voltage range, but it is an input assumption of the analytical formula.
  • domain assumption DFT (PBEsol) and the slab model reliably capture adsorption energetics and charge transfer for this system
    Standard practice; the F2 dissociation energy error (Ed = 1.49 eV theory vs 0.815 eV experiment) is acknowledged, so molecular-gas energetics carry a systematic error.
  • domain assumption Experimental AT population frequencies reflect thermal equilibrium at room temperature (Boltzmann factors)
    Stated as an order-of-magnitude assumption in Sec. III C 2; used to connect observed 60/35/5 ratios to energy differences of at most 60 meV.

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Pith. "Pith review of How orbitals and oxidation states determine apparent topographies in scanning tunneling microscopy: the case of fluorine on silver surfaces." pith.science (2026). https://pith.science/paper/WF7R3PDA

@misc{pith2026241109392,
  author       = {Pith},
  title        = {Pith review of: How orbitals and oxidation states determine apparent topographies in scanning tunneling microscopy: the case of fluorine on silver surfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WF7R3PDA}},
  note         = {Machine review of arXiv:2411.09392}
}
read the original abstract

We use density functional theory calculations to characterize the early stages of fluorination of silver's (100) and (110) surfaces. In the Ag(100) surface, the hollow site is the most favorable for F adatoms. In the Ag(110) surface, three adsorption sites, namely hollow, long bridge, and short bridge, exhibit similar energies. These locations are also more favorable than an F adatom occupying a vacancy site irrespectively of whether the vacancy was present or not in the pristine surface. The computed energy as a function of surface coverage is used to compute the equilibrium thermodynamics phase diagram. We argue that for the typical pressure and temperature of fluorination experiments, the state of the surface is not determined by thermodynamics but by kinetics. Combining these results with scanning tunneling microscopy (STM) topographic simulations, we propose assignments to features observed experimentally. We present a minimal model of the apparent topography of adatoms in different locations in terms of hydrogenic orbitals, explaining the observed trends. The model links the STM apparent topography to structural information and the oxidation states of the Ag atoms near the adatom.

Figures

Figures reproduced from arXiv: 2411.09392 by the authors.

Figure 1
Figure 1. FIG. 1. Geometry of the first two layers of the (a)-(b) Ag(100) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Adsorption energies per atom for atomic fluorine [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Change of surface Gibbs free energy as a func [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Temperature dependence of the chemical potential for [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a)-(f) Simulated STM topographies using DFT and the Tersoff-Hamann approximation for a F adatom in the hollow [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. STM topographies simulated using DFT and the Tersoff-Hamann approximation for the Ag(110) surface for an F [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Height profiles for a bias voltage of 1.0 V and the [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. PDOS of the F adatom located at the hollow site and [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 11
Figure 11. Figure 11: FIG. 11. (a) Constant density plot ( [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Plot of the density of Fig. 9 along the line [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 9
Figure 9. Figure 9: Neglecting possible changes in the PDOS, the [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 6
Figure 6. Figure 6: 1. Analytical estimate of the depression depth It is instructive to compute analytically the factors that determine the depression depth in the present model. Restricting to the contribution of silver atoms, the current is written as, I(r, VB) ≈ 4πe ¯h |M| 2Nt(0)X R GR…
Figure 12
Figure 12. Figure 12: FIG. 12. Height profiles with the F adatom at the short [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]

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