Size-Dependent Charging Energy Determines the Charge Transport in ZnO Quantum Dot Solids

Clemens G\"ohler; Dorothea Scheunemann; Martijn Kemerink; Morteza Shokrani

REVIEW 4 major objections 4 minor 7 references

Size-Dependent Charging Energy Determines the Charge Transport in ZnO Quantum Dot Solids

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A dot's charging energy, not the hopping model, sets the transport exponent in quantum-dot solids.

desk verdict A clean experimental knob for hopping exponents in QD solids, but the charging-energy attribution is qualitative and underdetermined. read the letter →

arxiv 2412.09275 v1 pith:HEFTOGZ5 submitted 2024-12-12 cond-mat.mes-hall cond-mat.mtrl-sci

Morteza Shokrani , Dorothea Scheunemann , Clemens Göhler , Martijn Kemerink This is my paper · ORCID

classification cond-mat.mes-hallcond-mat.mtrl-sci

keywords quantumdotsolidsZnOchargetransportvariablerangehoppingchargingenergysizedistributionZabrodskiiplotUVillumination

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 claims that the temperature-dependent conductivity exponents observed in quantum-dot solids do not reveal which hopping model applies: values near 0.25 or 0.5, usually read as Mott or Efros-Shklovskii variable-range hopping, can instead be the fingerprint of the size distribution of the dots. The authors measure ZnO quantum-dot films while using ultraviolet illumination to systematically thin the insulating depletion shell at each dot, thereby growing the conducting core and shrinking the inter-dot separation. As the effective dot diameter increases, the measured exponent rises continuously from about 0.25 to 0.62, matching the range predicted for charging-energy disorder in granular systems. They conclude that the dominant energy scale is the dot-size-dependent charging energy, so the exponent becomes a handle on sample microstructure rather than a fixed mechanism label.

What carries the argument

The central object is the size-dependent charging energy $E_c = e^2/(4\pi\varepsilon_0\varepsilon_r D)$, the energy cost of adding one electron to a dot of diameter $D$. In these ZnO films the depletion shell is controlled by surface hydroxyl groups, whose concentration is tuned by UV illumination; from charge conservation $(R^3 - r^3)/(3R^2) = \mu$ (with $R$ the total radius and $r$ the conducting-core radius) the authors convert a measured AFM diameter distribution into a distribution of effective diameters and hence of charging energies. The charging-energy disorder (about 50–80 meV) moves the percolation path toward hops with lower charging energy and grows with increasing hydroxyl uptake, which is what shifts the transport exponent from 0.62 down to 0.25. The Zabrodskii reduced-activation-energy plot supplies the experimental extraction of $\alpha$ that makes this interpretation possible.

What would settle it

A decisive check would be a gating experiment on a single QD film with a fixed size distribution: electrochemically or field-effect gate the carrier density across the same range the UV sweep produces, without changing dot size, and trace the temperature-dependent exponent. If the exponent moves substantially with carrier concentration at constant size distribution, the attribution of $\alpha$ to charging-energy disorder fails; if the exponent stays put while only the conductivity magnitude changes, the paper's interpretation is supported.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that a single physical ingredient, the distribution of Coulomb charging energies caused by the spread of dot diameters, can reproduce the entire observed family of temperature exponents in a semiconductor quantum-dot solid. Fitting the conductivity to $\sigma = \sigma_0 \exp(-(T_0/T)^\alpha)$ yields $\alpha = 0.247$, $0.375$, $0.473$, and $0.624$ for the four hydroxyl concentrations considered, and none of these is compatible with a single Mott ($\alpha = 1/4$) or Efros-Shklovskii ($\alpha = 1/2$) mechanism or with a crossover between them, because each data set is linear over the full temperature range. Instead, the charging energy $E_c = e^2/(4\pi\varepsilon_0\varepsilon_r D)$, evaluated with the measured AFM size distribution and dielectric constant, produces an energetic disorder of 50–80 meV that is comparable to $k_BT$ and grows when the depletion shell makes small dots even smaller. The paper therefore claims that an observed exponent in a QD solid should be interpreted as a property of the size distribution, with the smaller effective dots (higher OH concentration) giving the smaller exponents, in qualitative agreement with the granular-disordered-system models cited in the paper.

Load-bearing premise

The paper's interpretation rests on the assumption that the only relevant effect of UV illumination is to widen the conducting core by shrinking the depletion shell, while simultaneously changing carrier concentration, mobility, inter-dot coupling, and the density of states either stay constant or do not influence the extracted exponent.

Editorial extensions

If this is right

Exponents close to 1/4 or 1/2 in QD solids should no longer be read as proof of Mott or Efros-Shklovskii hopping; the size distribution must be measured before assigning a mechanism.
UV exposure offers a continuous, reversible tuning knob for the charge-transport exponent in ZnO QD films, replacing synthesis of multiple dot sizes.
The observed correlation, smaller effective dots give smaller exponents, extends to other semiconductor QD solids with low or intermediate dielectric constants where charging energies exceed $k_BT$.
The paper's analysis predicts that monodisperse QD films should show a single, size-independent exponent, so size dispersity becomes a directly testable design parameter.
The percolating current path preferentially uses dots with low charging energies, so transport is dominated by the larger dots in the distribution; the measured activation energies should sit in the lower half of the charging-energy distribution.

Reading between the lines

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

If the charging-energy-disorder picture is right, the measured exponent $\alpha$ is a proxy for the variance (not just the mean) of the dot-size distribution; two films with the same mean diameter but different dispersity should exhibit different exponents, a testable prediction.
The same mechanism could explain the anomalous exponents reported in other disordered granular and nanocrystal systems, suggesting that a common analysis based on the charging-energy distribution may replace case-by-case mechanism assignments.
The UV-dependent shift in exponent might serve as a sensing principle: the transport exponent is a direct readout of surface adsorbate density, which is what the paper's ZnO surface-state mechanism implies.
Because the depletion-shell width itself depends on dot size (smaller dots thin shells relatively more), the effective size distribution is a non-linear transform of the geometric one; this may amplify size-dispersity effects in small-dot samples.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The thing worth knowing about this paper is that it gives you a continuous experimental dial for the hopping exponent in a single ZnO QD film: UV light tunes alpha from 0.25 to 0.62 with no change in synthesis. That is a genuinely useful result. The authors measure temperature-dependent conductivity carefully, use Zabrodskii plots to extract exponents, and show the data are not fit by Mott or ES VRH or by a crossover. They also go out of their way to consider alternative explanations, including temperature-dependent prefactors, and they state plainly at the end that the cited models ignore other disorder sources.

What is not new is the explanatory framework. The idea that a distribution of grain sizes and charging energies produces exponents between 0.25 and 1 goes back to Sheng and Mostefa. The paper applies that framework to ZnO QD solids, which is a reasonable step, but the fit between data and theory is qualitative. They shift the AFM size distribution with one depletion parameter mu=1 nm, compute charging energies, and show activation-energy magnitudes overlap the lower half of those distributions. They never plug the measured size distribution into a Sheng/Mostefa calculation and predict the four observed alphas. So the title's 'determines' is stronger than the evidence.

The bigger soft spot is that UV illumination does more than change the effective dot diameter. The paper itself says it raises carrier concentration and mobility and shrinks the inter-dot hopping distance. Those changes can alter the density of states, localization length, and tunneling. The observed trend in alpha is consistent with the charging-energy story, but it does not uniquely pick it out. A skeptic could explain part of the trend with carrier-density or coupling effects. The authors do not deconvolve these.

The citation pattern is fine, and the self-referential limitation in the Summary is honest. The main thing I would ask for in a revision is a quantitative prediction: compute alpha from the size distribution using the Sheng/Mostefa model, or at least show that the model gives the right ordering and rough values for the four conditions. Independent replication and raw data release would also help.

Bottom line: the experiment is worth refereeing, and the result will be cited. The interpretation needs to be toned down or better supported. Send it out, but expect a major revision.

Referee Report

4 major / 4 minor

Summary. The paper reports temperature-dependent conductivity measurements on ZnO quantum dot solids under four different UV illumination conditions, extracts the stretched-exponential temperature exponent 𝛼 from Zabrodskii plots (values 0.624, 0.473, 0.375, 0.247), and interprets the systematic decrease of 𝛼 with increasing hydroxyl concentration as evidence that charge transport is governed by a UV-tunable distribution of QD charging energies, in line with the granular-metal models of Sheng and Mostefa. The authors argue that exponents close to 1/4 and 1/2 need not imply Mott or Efros-Shklovskii VRH when QD size dispersion creates a comparable or larger energetic disorder. The experimental work is careful: hysteresis-free conductivity, stability checks, and a cross-check of 𝛼 via an R-squared method are presented, alongside AFM-derived size distributions and dielectric measurements.

Significance. If the central attribution is correct, the paper provides a clean experimental handle for continuously tuning the hopping exponent in QD solids via UV-controlled depletion, and it makes a strong case that size-dispersion-induced charging-energy disorder, not Mott or ES VRH, dominates transport in weakly coupled QD assemblies. The measurement quality and the use of independent characterization (AFM size distribution, dielectric constant, two exponent-extraction methods) are strengths. However, the paper currently falls short of quantitatively demonstrating that the charging-energy distribution determines the transport: it never inserts the measured size distribution into the Sheng/Mostefa model to predict 𝛼, and it does not rule out concurrent UV-induced changes in carrier density, mobility, or interdot tunneling as the actual drivers of the exponent trend.

major comments (4)

[Results and Discussion, p. 16 and Fig. 3] The central claim that the size-dependent charging energy determines 𝛼 is not quantitatively tested. The paper compares the measured 𝛼 values to the qualitative predictions of Sheng et al. and Mostefa et al. (Refs. 24, 38) but never computes 𝛼 from the measured AFM size distribution using those models. A quantitative test would be to input the size distributions of Fig. 3(a) and 3(c) into the Sheng or Mostefa formalism and show that the resulting exponents match the observed sequence 0.624, 0.473, 0.375, 0.247. Without such a calculation, the statement in the Summary that the exponents are 'attributed to energetic disorder induced by the QD size distribution' remains an interpretation, not a demonstrated mechanism.
[p. 7, paragraph 2 and Fig. 2] The attribution to charging-energy disorder is confounded by simultaneous UV-induced changes in carrier concentration, mobility, and interdot hopping distance. The manuscript itself states that the rise in conductivity 'is attributed to the well-documented reduction of hydroxyls and oxygen species on the surface, leading to a decrease in the depletion layer and an increase in carrier concentration and mobility.' A thicker depletion shell also increases the separation between conductive cores, directly altering the tunneling matrix element. All of these factors can change the effective density of states at the Fermi level and the localization length, both of which influence the value of 𝛼 in a VRH analysis. The paper does not control or model these effects; it assumes that the size-distribution change is the only UV-dependent parameter relevant to 𝛼. This assumption needs explicit justification or a control experiment, e.g., a gate-voltage or carrier-density variation that changes carrier concentration without changing the size distribution.
[Eq. (5) and Fig. 3(c,d)] The quantitative connection between size distribution and charging energy relies on a single arbitrarily chosen value of the depletion parameter, 𝜇 = 1 nm, with no sensitivity analysis or independent determination. Equations (3)-(5) define 𝜇 through the ratio of hydroxyl concentration to electron density, but the chosen value is not derived from any measurement. The shift in the size distribution and the increase in energetic disorder from 50 to 80 meV stated in the text depend directly on this choice. The authors should either determine 𝜇 from a known OH coverage or electron density, or show that the qualitative conclusions are robust over a plausible range of 𝜇, and ideally fit 𝜇 to the measured activation energies in Fig. 4 rather than picking a single value.
[Fig. 4 and discussion of activation energy] The comparison between the measured activation energies and the calculated charging-energy distributions is qualitative. The statement that the activation energies 'correspond to the lower half of the shown distributions' and that 'the percolating path will preferentially use the easier hops' is plausible but is not derived from a percolation calculation. A quantitative percolation treatment, or at least a comparison of the width of the measured activation-energy distribution to the predicted charging-energy width, would substantially strengthen the claim. As written, the agreement in absolute energy scale is suggestive but not conclusive, especially since the activation energy itself is temperature dependent and the calculated distributions are static.

minor comments (4)

[Eq. (2)] In the sentence preceding Eq. (2), 'vacuum primitivity' should read 'vacuum permittivity.'
[Fig. 3 and Fig. 4 captions] The gray solid lines in Fig. 3 are described as log-normal fits to the diameter and charging-energy distributions, but the fitting parameters (mean and standard deviation) are not reported; including them would make the increase in energetic disorder from 50 to 80 meV reproducible.
[p. 10, R-squared method] The text says 'the R-square method proves quite reliable' but the description in the SI (Fig. S5) refers to fitting ln(𝜎) with fixed 𝛼 and plotting R² versus 𝛼; a brief sentence in the main text explaining the procedure would improve readability.
[p. 13, Fig. 3(d)] The sentence 'The energetic disorder extracted from the fitted log-normal distribution of the charging energy (solid gray line) shows an increase from 50 to 80 meV' should specify whether this is the standard deviation or the full width at half maximum, as the two are not interchangeable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the charging-energy interpretation is benchmarked against external theories and independent measurements, with no fitted-parameter-as-prediction reduction.

full rationale

The derivation chain is self-contained and externally anchored. The temperature exponents are extracted from Zabrodskii plots (Fig. 2b), giving 0.624, 0.473, 0.375, and 0.247, and the charging-energy distributions are computed from an independent AFM diameter histogram (Fig. 3a) via Eq. (2) with a measured dielectric constant, together with Eq. (5) using a stated depletion parameter mu = 1 nm. The activation energies in Fig. 4 are obtained by numerical differentiation of the measured conductivity and are compared, not fitted, to the charging-energy distributions. The interpretation via the Sheng and Mostefa granular-metal models is qualitative; the paper does not claim to insert the measured distribution into those models and predict the measured exponents, so there is no fitted-input-called-prediction or self-definitional reduction. The only self-citation is Ref. 27, which supports the peripheral statement that ZnO surface states respond to ambient gases; that statement is not load-bearing for the central claim. The paper's own caveat that Sheng and Mostefa ignore other sources of energetic disorder, and the fact that UV also changes carrier density and mobility, are limitations on uniqueness or robustness, not circularity. Therefore no significant circularity is present.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the standard classical capacitance formula for charging energy, the representativeness of the AFM size distribution, and the assumption that UV acts only through the depletion shell. One free parameter, mu = 1 nm, is chosen to construct the effective-core distribution, and the absence of a quantitative percolation model leaves the interpretation qualitative.

free parameters (1)

mu (depletion parameter) = 1 nm (chosen, not fitted)
Eq. 5 defines mu = n_OH/n_e = (R^3 - r^3)/(3R^2). The paper uses mu = 1 nm to shift the AFM diameter distribution to an effective-core distribution (Fig. 3c,d). The charging-energy disorder increases from 50 to 80 meV for this choice; the qualitative conclusion is not shown to be sensitive to mu.

assumptions (5)

domain assumption The charging energy of a QD is Ec = e^2/(4*pi*epsilon_0*epsilon_r*D) (Eq. 2) with the film's measured dielectric constant.
Used to convert the AFM size distribution into a charging energy distribution (Fig. 3b,d). More elaborate expressions are mentioned but not used.
domain assumption The diameter measured by AFM on a diluted, drop-cast sample represents the size distribution in the conducting film, with a ligand contribution below about 1 nm.
The size distribution is the sole input for the charging-energy disorder; the paper notes possible skewing toward larger diameters due to agglomeration and ligands.
domain assumption UV illumination only changes the depletion-shell width, with the un-depleted core being the conductive and screening volume; other transport parameters are assumed unchanged or negligible.
The paper attributes the systematic alpha variation to effective diameter alone, while also stating that carrier concentration and mobility increase with UV exposure.
domain assumption The percolating current path preferentially uses hops with lower charging energies, so measured activation energies correspond to the lower part of the charging-energy distribution.
Used to reconcile the lower activation energies in Fig. 4 with the distributions in Fig. 3; no percolation calculation is performed.
standard math Spherical QDs and uniform electron density n_e allow Eq. 4 from charge conservation.
Geometry assumption for the depletion-shell relation; known limitations for nonspherical or aggregated dots.

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Cite this review

Pith. "Pith review of Size-Dependent Charging Energy Determines the Charge Transport in ZnO Quantum Dot Solids." pith.science (2026). https://pith.science/paper/HEFTOGZ5

@misc{pith2026241209275,
  author       = {Pith},
  title        = {Pith review of: Size-Dependent Charging Energy Determines the Charge Transport in ZnO Quantum Dot Solids},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HEFTOGZ5}},
  note         = {Machine review of arXiv:2412.09275}
}

read the original abstract

Building up a solid-state material from quantum dots (QD), which are often referred to as artificial atoms, offers the potential to create new materials with unprecedented macroscopic properties. The investigation of the electronic properties of such QD assemblies has attracted attention due to the increasing applications of QD solids in both electronics and optoelectronics. In the past, charge transport in QD assemblies has been explained by a variety of mutually exclusive theories, with the Mott and Efros-Shklovskii variable range hopping models being most common. However, these theories fall short in explaining the anomalous exponents of the temperature-dependent conductivity observed in various QD materials. Here, we measure the temperature-dependent conductivity of semiconducting ZnO QDs under different UV illumination intensity. Regulating the UV intensity allows us to systematically change the effective diameter of the ZnO QDs without having to rely on cumbersome size control by synthesis. Instead, the UV level controls the width of the QD depletion shell and therefore the size distribution in the overall material. We observe exponents that systematically increase from {\alpha}=0.25 to {\alpha}=0.62 with increasing illumination intensity, which we interpret in terms of a charge transport being limited by the (size-dependent) charging energy of the QDs.

Figures

Figures reproduced from arXiv: 2412.09275 by the authors.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

[1]

(1) Ashoori, R. C. Electrons in Artificial Atoms. Nature 1996, 379 (6564), 413 –419. https://doi.org/10.1038/379413a0. (2) Huang, C.-Y.; Li, H.; Wu, Y.; Lin, C. -H.; Guan, X.; Hu, L. ; Kim, J.; Zhu, X.; Zeng, H.; Wu, T. Inorganic Halide Perovskite Quantum Dots: A Versatile Nanomaterial Platform for Electronic Applications. Nano-Micro Lett. 2022, 15 (1),

work page doi:10.1038/379413a0 1996
[3]

See also Fig

we are likely in an intermediate regime where quantum confinement effects are finite but unlikely t o dominate over charging effects that amount to a few times 𝑘𝐵𝑇 at room temperature. See also Fig. 4 and its corresponding discussion in the main text. 36 Supplementary references (1) Bera, D.; Qian, L.; Tseng, T. -K.; Holloway, P. H. Quantum Dots and Their...

work page doi:10.3390/ma3042260 2010
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M.; Marín, G

(34) Rodríguez, M.; Quiroga, C.; Bonalde, I.; Medina, E.; Wasim, S. M.; Marín, G. Preexponential Factor in Variable-Range Hopping Conduction in CuInTe2. Solid State Commun. 2005, 136 (4), 228–233. https://doi.org/10.1016/j.ssc.2005.07.018. (35) Kang, M. S.; Sahu, A.; Norris, D. J.; Frisbie, C. D. Size - and Temperature -Dependent Charge Transport in PbSe ...

work page doi:10.1016/j.ssc.2005.07.018 2005
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(9) Baek, I

https://doi.org/10.1039/c3tb21151g. (9) Baek, I. C.; Seok, S. I.; Pramanik, N. C.; Jana, S.; Lim, M. A.; Ahn, B. Y.; Lee, C. J.; Jeong, Y. J. Ligand -Dependent Particle Size Control of PbSe Quantum Dots. J. Colloid Interface Sci. 2007, 310 (1), 163–166. https://doi.org/10.1016/j.jcis.2007.01.017. (10) Burda, C.; Chen, X.; Narayanan, R.; El -Sayed, M. A. C...

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

(1) Ashoori, R. C. Electrons in Artificial Atoms. Nature 1996, 379 (6564), 413 –419. https://doi.org/10.1038/379413a0. (2) Huang, C.-Y.; Li, H.; Wu, Y.; Lin, C. -H.; Guan, X.; Hu, L. ; Kim, J.; Zhu, X.; Zeng, H.; Wu, T. Inorganic Halide Perovskite Quantum Dots: A Versatile Nanomaterial Platform for Electronic Applications. Nano-Micro Lett. 2022, 15 (1),

work page doi:10.1038/379413a0 1996

[2] [3]

See also Fig

we are likely in an intermediate regime where quantum confinement effects are finite but unlikely t o dominate over charging effects that amount to a few times 𝑘𝐵𝑇 at room temperature. See also Fig. 4 and its corresponding discussion in the main text. 36 Supplementary references (1) Bera, D.; Qian, L.; Tseng, T. -K.; Holloway, P. H. Quantum Dots and Their...

work page doi:10.3390/ma3042260 2010

[3] [16]

(3) Fan, J.; Han, C.; Yang, G.; Song, B.; Xu, R.; Xiang, C.; Zhang, T.; Qian, L

https://doi.org/10.1007/s40820-022- 00983-6. (3) Fan, J.; Han, C.; Yang, G.; Song, B.; Xu, R.; Xiang, C.; Zhang, T.; Qian, L. Recent Progress of Quantum Dots Light‐Emitting Diodes: Materials, Device Structures, and Display Applications. Adv. Mater. 2024, 2312948. https://doi.org/10.1002/adma.202312948. (4) Zou, T.; Choi, T.; Liu, A.; Zhu, H.; Noh, Y. -Y. ...

work page arXiv

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(30) Ghosh, M.; Ningthoujam, R

https://doi.org/10.1186/1556-276X-6-404. (30) Ghosh, M.; Ningthoujam, R. S.; Vatsa, R. K.; Das, D.; Nataraju, V.; Gadkari, S. C.; Gupta, S. K.; Bahadur, D. Role of Ambient Air on Photoluminescence and Electrical Conductivity of Assembly of ZnO Nanoparticles. J. Appl. Phys. 2011, 110 (5), 054309. https://doi.org/10.1063/1.3632059. (31) Tudose, I. V.; Horvá...

work page doi:10.1186/1556-276x-6-404

[5] [1984]

M.; Marín, G

(34) Rodríguez, M.; Quiroga, C.; Bonalde, I.; Medina, E.; Wasim, S. M.; Marín, G. Preexponential Factor in Variable-Range Hopping Conduction in CuInTe2. Solid State Commun. 2005, 136 (4), 228–233. https://doi.org/10.1016/j.ssc.2005.07.018. (35) Kang, M. S.; Sahu, A.; Norris, D. J.; Frisbie, C. D. Size - and Temperature -Dependent Charge Transport in PbSe ...

work page doi:10.1016/j.ssc.2005.07.018 2005

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(9) Baek, I

https://doi.org/10.1039/c3tb21151g. (9) Baek, I. C.; Seok, S. I.; Pramanik, N. C.; Jana, S.; Lim, M. A.; Ahn, B. Y.; Lee, C. J.; Jeong, Y. J. Ligand -Dependent Particle Size Control of PbSe Quantum Dots. J. Colloid Interface Sci. 2007, 310 (1), 163–166. https://doi.org/10.1016/j.jcis.2007.01.017. (10) Burda, C.; Chen, X.; Narayanan, R.; El -Sayed, M. A. C...

work page doi:10.1039/c3tb21151g

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21 (15) Lan, X.; Chen, M.; Hudson, M

https://doi.org/10.1039/c0jm01221a. 21 (15) Lan, X.; Chen, M.; Hudson, M. H.; Kamysbayev, V.; Wang, Y.; Guyot -Sionnest, P.; Talapin, D. V. Quantum Dot Solids Showing State -Resolved Band-like Transport. Nat. Mater. 2020, 19 (3), 323–329. https://doi.org/10.1038/s41563-019-0582-2. (16) van Staveren, M. P. J.; Brom, H. B.; de Jongh, L. J. Metal -Cluster Co...

work page doi:10.1039/c0jm01221a 2020