molecules and Xe- and CO-tip models. Excel-
lent agreement between thewB97X-V inter-
action energies and the experimental data
results is shown in Fig. 4. The calculated en-
ergy minima for all complexes fit the mea-
sured values perfectly within the experimental
error (Fig. 4, inset). The PBE0 functional ( 39 )
with the D3 correction ( 40 ) reproduced the
CCSD(T) results on small-model systems as well
(table S3 and fig. S10). However, its transfer-
ability on the large systems was no longer as
good as the range-separatedwB97X-V func-
tional (fig. S11).
ThewB97X-V functional describes well the
interaction trend for all considered systems
(Fig. 4, inset), with the caveat that it system-
atically slightly overestimates the interaction
energy by ~0.1 kcal/mol. The perfect agree-
ment between theoretical and experimental
values could not be expected because calcu-
lations were limited to free-standing 4FPhM
and 4BrPhM molecules interacting with Xe-
and CO-tip model, and in the experiment,
4FPhM and 4BrPhM molecules were adsorbed
at Ag(111) surface. The results confirmed good
transferability of thewB97X-V functional toward
larger systems. Moreover, the good agreement
between calculated and experimental datasets
obtained for all four complexes also gave
confidence in the multiscale benchmark tech-
nique that uses small-model complexes with
the Xe-tip model. Therefore, this approach
makes it possible to accurately describe sys-
tems whose size does not allow for the direct
application of the accurate coupled-cluster
technique (or a similar technique), or when
other direct experimental measurements are
currently not feasible.Conclusions
We report the possibility of achieving the spa-
tial resolution of anisotropic atomic charge
with the KPFM technique, which not only
provided direct evidence of the existence of
s-holes but is expected to substantially extend
the possibility to characterize charge distribu-
tion in complex molecular systems and on sur-
faces. We anticipate that this technique could
be further extended to provide invaluable
information about the local inhomogeneous
polarizability of individual atoms on surfaces
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ACKNOWLEDGMENTS
We acknowledge fruitful discussions with A. Růžička and
P. Hapala. M.L. acknowledges inspirational advice from his previous
supervisor, J. Kuchár. P.J. and B.d.l.T. dedicate this manuscript
to the memory of J. M. Gómez-Rodríguez.Funding:This work was
supported by the Czech Science Foundation GACR 20-13692X
(A.G., B.M., and P.J.) and 19-27454X (P.H.); Praemium Academie
of the Academy of Science of the Czech Republic (A.G.); Palacký
University Internal Grant Association IGA_PrF_2021_031 (M.L.);
Palacký University Internal Grant Association IGA_PrF_2021_034
(B.M.); and CzechNanoLab Research Infrastructure, supported
by MEYS CR (LM2018110).Author contributions:Conceptualization:
P.J. Methodology: B.M., A.G., B.d.l.T., and P.J. Theoretical
calculations: A.G., M.L., V.Š., P.J., and P.H. Experimental: B.M.
and B.d.l.T. Funding acquisition: P.H. and P.J. Supervision: B.d.l.T.,
P.H., and P.J. Writing, original draft: B.M., A.G., B.d.l.T., P.H., and
P.J.Competing interests:The authors declare that they have
no competing interests.Data and materials availability:All data
needed to evaluate the conclusions in the paper are present in
the paper or the supplementary materials. Data can be found at
Zenodo ( 41 ).SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.abk1479
Materials and Methods
Supplementary Text
Figs. S1 to S20
Tables S1 to S3
References ( 42 – 55 )
24 June 2021; resubmitted 28 July 2021
Accepted 20 September 2021
10.1126/science.abk1479SCIENCEscience.org 12 NOVEMBER 2021¥VOL 374 ISSUE 6569 867
345678-1.0-0.8-0.6-0.4-0.20.0-1.2-1.0-0.8-0.6-0.4-0.20.0z (Å)-1.2 -0.9 -0.6 -0.3 0.0-1.2-0.9-0.6-0.3B97x-v (kcal/mol)Exp. (kcal/mol)F-CO
Br-CO
Br-Xe
F-XeE (kcal/mol) E (kcal/mol)
exp.int. sim.int.SimulatedExperimentalFig. 4.Comparison of experimental and theoretical interaction energies of four complexes. Experimental
(solid curves) and calculated (dots, obtained with DFT/wB97X-V) energy curves versus tip-sample distance
between 4FPhM and 4BrPhM molecules and Xe and CO tips. (Inset) The correlation between experimental
and theoretical values [coefficient of determination (R^2 ) = 0.98] of the energy minima for all complexes.
Bars indicate an estimated experimental error of the energy minima calculated as the difference between a
polynomial fit and the experimental energy (fig. S12).
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