# Unravelling the Band Structure and Orbital Character of a $\pi$-Conjugated
2D Graphdiyne-Based Organometallic Network

Paolo D’Agostaa, Simona Achillib,∗, Francesco Tuminoa,c, Alessio Orbelli
Birolid, Giovanni Di Santoe,
Luca Petacciae, Giovanni Onidab, Andrea Li Bassia, Jorge Lobo-Checaf,g,∗,†,
and Carlo S. Casaria,∗,†

(  aDepartment of Energy, Politecnico di Milano, via G. Ponzio 34/3, I-20133
Milano, Italy bDepartment of Physics “Aldo Pontremoli”, Università degli Studi
di Milano, Via G. Celoria 16, I-20133 Milano, Italy cDepartment of Chemistry,
Queen’s University, 90 Bader Lane, K7L3N6 Kingston, ON, Canada dDepartment of
Chemistry, Università di Pavia, Via Taramelli 12, I-27100 Pavia, Italy
eElettra Sincrotrone Trieste, Strada Statale 14 km 163.5, I-34149 Trieste,
Italy fInstituto de Nanociencia y Materiales de Aragón (INMA), CSIC-
Universidad de Zaragoza, E-50009 Zaragoza, Spain gDepartamento de Física de la
Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain
∗Corresponding authors<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>†These authors contributed equally )

Graphdiyne-based carbon systems generate intriguing layered sp$-$sp2
organometallic lattices, characterized by flexible acetylenic groups
connecting planar carbon units through metal centers. At their thinnest limit,
they can result in two-dimensional (2D) organometallic networks exhibiting
unique quantum properties and even confining the surface states of the
substrate, which is of great importance for fundamental studies. In this work,
we present the on-surface synthesis of a highly crystalline 2D organometallic
network grown on Ag(111). The electronic structure of this mixed honeycomb-
kagome arrangement – investigated by angle-resolved photoemission spectroscopy
and scanning tunneling spectroscopy – reveals a strong electronic conjugation
within the network, leading to the formation of two intense electronic band-
manifolds. In comparison to theoretical density functional theory
calculations, we observe that these bands exhibit a well-defined orbital
character that can be associated with distinct regions of the sp$-$sp2
monomers. Moreover, we find that the halogen by-products resulting from the
network formation locally affect the pore-confined states, causing a
significant energy shift. This work contributes to the understanding of the
growth and electronic structure of graphdiyne-like 2D networks, providing
insights into the development of novel carbon materials beyond graphene with
tailored properties.

Keywords:  two-dimensional materials, graphdiyne-based systems, organometallic
networks, electronic structure, orbital character, $\pi$-conjugation, surface-
state confinement

Figure 1: Structural characterization of 2D organometallic network on Ag(111).
(a) Large-scale LT-STM image of the 2D network islands after annealing to
${\sim}$370 K, exhibiting long-range order for hundreds of nm2 (STM set-point:
$-$1 V, 50 pA). Inset: atomic model of the tBEB molecular precursor. (b) High-
resolution LT-STM image of the mixed honeycomb-kagome network showing the
linking Ag adatoms as the brightest spots, the monomers as triangular features
connecting three Ag adatoms, and the Br atoms as blobs within the pores (STM
set-point: 50 mV, 90 pA). The unit cell of the organometallic network (marked
with a blue rhombus) contains two debrominated monomeric units and three Ag
adatoms. Insets: 2D-FFT (top right); averaged line profiles along the two
directions marked by the red and blue arrows (bottom left). (c) Simulated
atomic structure of the organometallic network on Ag(111) in top and side
views. Carbon atoms are shown in gray, hydrogen atoms in white, Ag adatoms in
yellow, and substrate Ag in light-to-dark brown. (d) LEED pattern obtained at
28.6 eV, consisting primarily of a ${(4\sqrt{3}{\times}4\sqrt{3})}$R30∘
supercell over the Ag(111) lattice with a ${2.002\pm 0.10}$ nm lattice
constant. The red circle points to the pattern splitting into triplets (see
text for details). Inset: incommensurate LEED pattern simulated by LEEDpat
using the superlattice matrix $\bigl{(}\begin{smallmatrix}+4.0&-4.0\\\
+3.6&+7.6\end{smallmatrix}\bigr{)}$.

Two-dimensional (2D) organometallic networks and covalent organic frameworks
at their thinnest limit can be classified as quantum materials with relevant
properties, such as the emergence of flat bands,1 topologically protected
states,2 superconductivity,3 or 2D ferromagnetism.4 Such properties emerge in
the presence of extended electronic conjugation of their building blocks.5, 6,
7, 8, 9, 10 Among 2D systems, Graphyne and Graphdiynes stand out as novel 2D
carbon materials beyond graphene, given their combination of sp\- and
sp2-hybridized carbon atoms.11 This leads to the emergence of diverse complex
structures with distinct electronic properties, ranging from metals to tunable
bandgap semiconductors and semi-metals. Their extended $\pi$-electron
conjugation and topology produce multiple Dirac cones and band-manifolds that
are key to their intriguing properties.12, 13

Despite several outstanding theoretical predictions,14, 15 these systems were
initially regarded as elusive and impractical. Such belief was proved wrong as
the synthesis of multilayer graphdiyne was experimentally achieved.16 This
material presented remarkable properties and held promise for many advanced
applications.17, 18, 19, 20 Later on, the synthesis of 2D single-layer
graphdiyne was also realized through on-surface synthesis (OSS).21 The OSS
technique relates to “solvent-free” reactions exploiting the catalytic
activity of a metal surface to promote the formation of new bonds from smaller
precursors.22, 23 In the case of single-layer graphdiyne-like structures, the
molecular precursors contain aromatic sp2 carbon groups with linear acetylenic
units that are usually terminated by a halogen atom. The de-halogenation of
these precursors and the formation of an organometallic network is promoted by
the native atoms from the metal surface.24, 25, 26 Subsequent thermal
treatment can at times induce de-metalation and homocoupling with the
formation of an all-carbon structure.21, 24, 27, 28, 29, 30, 25

Although OSS is widely used in the synthesis of graphene-based
nanoarchitectures,31 the fabrication of extended graphdiynes is still very
challenging.21, 25 Nevertheless, achieving extended 2D structures with long-
range order is critical to exploring the electronic structure of these layers
beyond the generalized use of local electronic techniques. Indeed, the band
structures of 2D graphdiyne-based organometallic networks are nowadays only
accessible through calculations.24, 13, 32, 33 They show the presence of
electron conjugation throughout the organometallic layer and indicate that the
metal centers induce hybridization and charge transfer to the network. Thus,
it is pressing to experimentally validate these predictions, which are at the
root of the emergence of multiple Dirac-cone band-manifolds that are key to
many quantum properties of interest. Moreover, the doping role of the cleaved
Br atoms existing on the surface as reaction by-products must be revisited,34,
24 as these could extend their influence to the confined surface state (SS)
electrons at the pores35 – i.e. the hexagonal holes contoured by the network
exposing the underlying Ag surface.

In this study, we answer these intriguing fundamental questions. We present
the structural and electronic characterization of an on-surface synthesized 2D
graphdiyne-like organometallic network on Ag(111). The structure is
characterized by scanning tunneling microscopy (STM) and low-energy electron
diffraction (LEED), demonstrating the ability to achieve extended, long-range
ordered structures. This allows us to experimentally explore the occupied
electronic structure by means of angle-resolved photoemission spectroscopy
(ARPES) and compare it to the site-dependent local density of states (LDOS)
obtained from scanning tunneling spectroscopy (STS). Direct comparison with
theoretical ab initio calculations by density functional theory (DFT) allows
us to confirm the presence of extended $\pi$-electron conjugation and also
deduce the dominant orbital character involved in each of these experimental
bands. Finally, we show that the cleaved Br atoms generated during the OSS
process not only electronically dope the 2D network, but also produce a local
energy shift in the pore-confined surface state.

## Results

Network formation and morphology. Our molecular precursor of choice is
1,3,5-tris(bromoethynyl)benzene (tBEB), consisting of a benzene ring
functionalized with three non-adjacent acetylenic groups ending with a bromine
atom (see inset of Fig. 1(a)). This molecule has been used to produce 2D
structures via on-surface synthesis (OSS) on both Au(111) and Ag(111).21, 25,
24, 26 When deposited at room temperature (RT) on Ag(111), the debromination
occurs spontaneously and the Br atoms are replaced by native Ag atoms from the
substrate that bind to the alkynyl groups. The dominant structure formed is a
2D organometallic network coordinated by Ag adatoms, which connect two
adjacent benzene units through their acetylenic groups and form
$-$C$\equiv$C$-$Ag$-$C$\equiv$C$-$ bonds. This well-organized, self-assembled
sp$-$sp2 2D network leads to hexagonal pores enclosing a different number of
detached Br atoms, as shown in the close-up STM image of Fig. 1(b).
Statistically, there is an average of 5.1 Br atoms per unit cell or,
equivalently, per pore (Fig. S1(b)). The missing 0.9 Br atoms from the six
released during the network formation aggregate on the molecule-free areas of
the Ag(111) surface in wiggly 1D arrangements (Fig. S1(d)).

The 2D network structurally forms a mixed honeycomb-kagome network, where the
debrominated tBEB molecules (monomers) occupy the vertices of the pore
contour, while the Ag adatoms (brighter spots in Fig. 1(c)) are in the middle
of its sides. In this configuration, the organometallic bond is considered
practically covalent in strength.36 Indeed, we find this 2D network to be
stable at RT, according to our STM characterization at ${\sim}$300 K (Fig.
S1(e,f)). Annealing to ${\sim}$370 K results in the improved crystallization
of the 2D network in terms of larger domain size and increased coverage (Fig.
1(a) and S1(a)), leading to extended long-range order as extracted from the
well-defined LEED pattern shown in Fig. 1(d). Increasing the post-annealing
temperature to ${\sim}$420 K results in a decrease in overlayer coverage,
which we interpret as desorption of the monomeric units. Differently from the
OSS on Au(111),21, 25 increasing further this temperature (up to 450–470 K)
does not promote the network demetalation and the C–C homocoupling among the
acetylenic units. Instead, at such higher temperatures we observe the
disruption of the network and the formation of non-planar, globular islands
(Fig. S1(h)).

We can extract the average parameters of the 2D network from the 2D fast
Fourier transform (2D-FFT) (inset of Fig. 1(b)), resulting in a mean
periodicity of ${1.953\leavevmode\nobreak\ {\pm}\leavevmode\nobreak\ 0.15}$ nm
and unit vector angles of ${60.5^{\circ}\leavevmode\nobreak\
{\pm}\leavevmode\nobreak\ 1.5\degree}$. These values are in agreement with
previous works.24, 21, 25, 26 However, the flexibility of the alkynyl groups
and the side interaction with a variable number of cleaved bromine atoms
within the pores lead to slight directional distortions that affect the
overall lattice periodicity and introduce some degree of structural
anisotropy. In particular, the line profiles in the inset of Fig. 1(b) reveal
a difference of ${\Delta a=0.12}$ nm. Such deviation is also visible in LEED
patterns (Fig. 1(d)). In a first approximation, the overall LEED arrangement
is hexagonal, exhibiting a ${(4\sqrt{3}{\times}4\sqrt{3})}$R30∘ supercell over
the Ag(111) surface and yielding a lattice constant of 2.002 nm. However, the
LEED pattern shows split higher-order diffraction spots that are more evident
as we move away from the (0,0) spot due to the presence of rotationally non-
equivalent domains. We obtain an excellent match of this distorted hexagonal
superstructure when using nonequivalent unit vectors of 2.010 nm and 1.895 nm
– as extracted from the line profiles of the Fig. 1(b) inset – in the
simulated pattern (LEEDpat software,37 see inset of Fig. 1(d)).

Figure 2: Electronic characterization of the 2D organometallic network on
Ag(111). (a,b) Occupied electronic structure of the 2D network close to
saturation on Ag(111) after annealing to ${\sim}$370 K. The second derivative
of the ARPES spectral function was recorded along the (a) $\Gamma$K
($k_{y}=0$) and (b) $\Gamma$M ($k_{x}=0$) directions of the network, using a
photon energy of 21 eV and keeping the sample at 120 K. We observe two
dominant band-manifolds with relatively flat appearance related to the 2D
network in the $-$2.25 to $-$3.5 eV region, as well as highly dispersive bands
at large $k_{x}$ and $k_{y}$ values originating from the sp bands of silver
(Fig. S3). (c,d) Blown-up panels at the network’s band-manifolds exhibiting
dispersion. In panels (a–d), the color grayscale is linear (the darker, the
more intense) and the vertical dashed lines indicate high-symmetry points of
the 2D network. Note that the high-symmetry directions of the substrate are
rotated by 30∘. (e) LT-STM image of the STS grid area (STM set-point: $-$100
mV, 50 pA). (f) Averaged LT-STS curves (from 10–15 spectra) taken over several
equivalent points of the 2D network, as indicated by the color-coded dots in
(e). The STS curve of the benzene rings is shown in purple, Ag adatoms in
blue, acetylenic triple bonds in green, and pore centers in yellow. Note that
the central region (from $-$3.0 to $+$1.0 V) has been multiplied by a factor
of 4 for improved visualization. The blue arrows identify peaks within the
ARPES band-manifold range, while "SS" identifies the pore-confined Shockley
peak (STS set-point: $-$500 mV, 14 pA; ${V_{\text{RMS}}=15.5}$ mV and
${f_{\text{osc}}=817.3}$ Hz).

We can obtain further structural information on the hexagonal network by DFT
calculations for the 2D network in the gas phase and on top of a
${(4\sqrt{3}{\times}4\sqrt{3})}$R30∘ supercell of the Ag(111) substrate. In
the gas phase, the calculated free-standing lattice constant of the network is
2.090 nm. In order to match the network with the underlying substrate (whose
theoretical equilibrium lattice constant is ${a_{Ag}=0.295}$ nm), the network
is slightly compressed to a lattice constant of 2.042 nm, in agreement with
our STM results (within the experimental error). In virtue of this, the on-
surface synthesized 2D network experiences a ${\sim}$2.2% stress with respect
to its gas phase equilibrium structure. Additionally, the interaction between
the Ag adatoms and the substrate leads to bent monomers, as the central phenyl
groups protrude from the surface while the linear acetylenic groups point
towards it, as shown in Fig. 1(c). The overall corrugation of the network
amounts to 0.05 nm, being defined as the height difference between the phenyl
rings and the carbon atom in the acetylene moiety adjacent to the Ag adatom.
Experimentally, the apparent corrugation as measured by LT-STM is 0.035 nm
(with a set-point of $-$3.5 V / 800 pA, see Fig. S2(b)).

Figure 3: Comparison of the theoretical and local experimental electronic
properties of the 2D organometallic network on Ag(111). (a,b) Band dispersion
along a high-symmetry path in the network’s Brillouin zone, showing resolved
contributions for pz (blue) and px,y (orange, yellow) states. (b)
Magnification of (a) in the $-$2.2 to $-$3.5 eV range. (c$-$e) Isovalue maps
of the calculated LDOS of the organometallic network on Ag(111) integrated in
an energy window of 0.15 eV and centered at (c) $-$2.50 eV, (d) $-$2.75 eV,
and (e) $-$3.25 eV (Ag substrate not shown). Isosurface level: 0.002 states
eV-1 Å-3. (f$-$h) Simulated $dI/dV$ maps at the same energies of panels (c–e)
and at a constant height of 2 nm from the plane of the benzene rings. (i–k)
Constant-current $dI/dV$ maps acquired at 4.8 K and the same bias as panels
(c–e), with ${V_{\text{RMS}}=10.0}$ mV and ${f_{\text{osc}}=817.3}$ Hz (STS
set-point: (i) $-$2.50 V, 350 pA; (j) $-$2.75 V, 400 pA; (k) $-$3.25 V, 450
pA). The dominant intensity is associated with the phenyl rings at $-$2.50 V
(see the orbital arrangement in the blue triangle of (i)), with the metal
centers at $-$2.75 V, and with the acetylenic units at $-$3.25 V.

Electronic characterization by ARPES. The excellent growth quality of the
network allowed us to determine the occupied electronic structure employing an
averaging technique, such as ARPES (Figs. 2, S3 and S4). Meaningful
measurements at the BaDElPh beamline38 of the Elettra Synchrotron were
obtained after achieving a sample preparation close to a full monolayer
coverage of the mixed honeycomb-kagome network on the Ag(111) surface, which
was followed by thermal annealing to ${\sim}$370 K. From a visual inspection
of Fig. 2, we can easily identify the presence of two shallow-dispersive band-
manifolds in the energy range between $-$2.25 eV and $-$3.5 eV, and highly
dispersive features that reach the Fermi level (EF) at high parallel momenta
(darker grey corresponding to higher photoemission intensity). A comparison
with the pristine substrate (reported on the right side of Fig. S3) evidences
that these highly dispersive features are related to the bulk Ag sp-band.
Notably, we find that the Ag(111) surface state at ${k=0}$, clearly appearing
in the pristine substrate, is not visible anymore, confirming its electronic
depopulation upon network formation.24

The two-dimensional character of the band-manifold (Fig. 2(c,d)) is deduced by
their invariability after performing a photon energy dependence check (Fig.
S4). Based on previous work,6 these shallow-dispersive bands are assigned to
conjugated kagome multi-bands arising from honeycomb networks. Compared to
free-standing calculations (Fig. S9), in which the band manifold is around the
Fermi level, this kagome multi-band is considerably downshifted (by more than
2 eV) by the Ag(111) substrate. Although umklapps of the sp-bulk bands are
absent, their quality appears to be significantly better than what has been
reported to date,6 to the point that it is visible even in the direct ARPES
signal (Figs. S3 and S4). These intense kagome multi-bands are likely related
to the very strong organometallic bond existing between the molecules and the
Ag adatoms.24 Contrarily, the umklapps absence relates to the observed
distortions of this network compared to other strictly periodic organometallic
systems.6

Assessment of the electronic structure by DFT. To corroborate the existence of
this kagome multi-band we performed DFT calculations of the 2D network on top
of the Ag(111) substrate. The band structure along a high symmetry direction
of the ${(4\sqrt{3}{\times}4\sqrt{3})}$R30∘ supercell is reported in Fig.
3(a). Superimposed to the bands of the whole system, consisting of the 2D
network and the substrate (dotted lines), the p-bands of carbon stand out,
plotted with different colors depending on their orbital symmetry. The
calculation confirms the presence of electronic bands in ${\sim}$1 eV-wide
energy intervals above the top of the Ag d-bands and above the Fermi level.
The overall shift of more than 2 eV observed between the experiment and the
calculated free-standing band structure (Fig. S9) is theoretically reproduced
in the simulation of the Ag(111)-supported organometallic network.

Fig. 3(b), showing an enlargement of the occupied states region, highlights
two groups of energy bands. The first, at larger binding energy, exhibits a
px,y character and can be identified with the band-manifolds centered at
$-3.25$ eV in ARPES. The second, with smaller binding energy, displays a pz
character and corresponds to the flat band-manifolds experimentally centered
around $-2.5$ eV (Fig. 2). This assignment is possible due to the reasonably
good energy correspondence between experimental and calculated bands, and the
slightly different dispersion of the two sets of bands. As in the experiments,
we find that the pz states (top band) are flatter, while the px,y states are
characterized by more dispersive features around the $\Gamma$ point.
Significantly, both the expected Dirac-cone features (typical of kagome
networks, observed in the freestanding band structure in Fig. S9) and the spin
polarization of the states are practically destroyed. This is caused by the
interaction with the substrate, which is more pronounced for pz states than
px,y states due to their different extension in the vertical direction. Note
that the theoretical band structure is folded into the irreducible $\Gamma$K
path of the ${(4\sqrt{3}{\times}4\sqrt{3})}$R30∘ supercell, whereas ARPES data
is displayed along two extended high-symmetry directions ($\Gamma$K and
$\Gamma$M) of the network’s Brillouin zone.

We also performed DFT calculations of the network with Br atoms within the
pores. In these calculations, the halogens are strongly bound to the Ag
surface in positions close to the benzene’s hydrogens between acetylenic
groups, i.e. where they are most frequently observed at the STM (Fig.
S2(e–f)). Br-related bands appear in the energy interval between $-$3 eV and
$-$2 eV, as shown in Fig. S8(c). Despite being energetically very close to the
carbon network’s bands, they have little effect on the latter in terms of
energy shift and dispersion, which is consistent with the hybridization of Br
atoms mainly with the substrate’s Ag atoms. Although bromine atoms have been
reported to induce an upwards rigid shift of about 200 meV (similar to
n-doping effect) in conjugated poly(para-phenylene) systems,39, 34 our
theoretical results do not show evidence of such an effect in the
Ag(111)-supported 2D network, consistently with a negligible value of the
computed charge transfer between Br and C atoms in the present case.

Figure 4: (a) Single-point LT-STS curves acquired at the center of pores
containing a progressively higher number of Br atoms, as indicated by the
color-coded dots in the inset (STS set-point: $-$500 mV, 14 pA;
${V_{\text{RMS}}=15.5}$ mV and ${f_{\text{osc}}=817.3}$ Hz). Inset: reference
LT-STM image (STM set-point: $-$100 mV, 50 pA). (b) Correlation between the
exposed pore area subtracting the Br atoms (labeled as the pores in the inset
of (a)) and the maximum SS peak energy. (c) Simulated PDOS at the center of
the pores (surface Ag atoms) with increasing Br atom occupancy exhibiting the
experimental energy shift. The SS is absent in the dashed curve at the bottom,
which refers to the PDOS on a Ag atom in the middle of the substrate slab.

Electronic characterization by LT-STS. To corroborate and expand the
experimental results on the electronic features obtained by ARPES, we acquired
differential conductivity ($dI/dV$) maps and constant-height (C.H.) images
through LT-STM/STS at 4.8 K. The complete datasets, reported in the S.I.
(Figs. S5 to S7), include sample mapping in the $-$3.50 to 2.00 V range at
both constant current and constant height, as well as a collection of energy
slices of a LT-STS map obtained from a 36${\times}$24-pixel grid. The
corresponding LT-STM image of the $6{\times}4$ nm2 scanned area and selected
point spectra are reported in Fig. 2(e,f). Each curve of the $dI/dV$ spectra
is averaged over 10–15 equivalent points of the network.

Notably, we reproduce the LT-STS data together with the results obtained by
ARPES below the Fermi level (EF). Particularly, we find weak peaks and
shoulders at $-$3.25 V, $-$2.75 and $-$2.50 V, marked as blue arrows in Fig.
2(f). Excluding the peak at $-$2.75 V, which is localized around the Ag
adatoms, the other two peaks would have been overlooked without the ARPES
datasets. The corresponding constant-current $dI/dV$ maps, obtained from the
LDOS at these relevant energies, are shown in Fig. 3(i–k). Evidently,
different orbitals are accessed at each bias, indicating the existence of
distinct electronic states, as will be discussed in the following. Note that
the electronic features visible approximately at $-$2.25 V and $-$1.60 V are
associated with tip states, since their shape and energy remain unvaried at
all sites in the STS grid, but are absent in ARPES. Moving to the empty
electronic region (positive bias) we find energy states as identified in a
previous work;24 in particular, we observe the confined surface state (SS) at
0.60 V, and a state localized around the benzene rings at 1.80 V. A more in-
depth analysis follows in the Discussion section.

## Discussion

The 2D organometallic network has a strong semiconductive character. The
calculation for the free-standing network reveals that the unsupported network
would be a half-metal with a calculated energy gap for the majority spin
component of ${\sim}$3 eV (Fig. S9(a)). The frontier orbitals have mixed
px,y–pz character in the occupied region of the energy spectrum, and pz
character in the unoccupied one. A similar energy separation is found as a
pseudo-gap in the empty region of minority spin bands, which are shifted
upward by about 0.5 eV with respect to the majority manifold. When the 2D
network is formed on Ag(111), the spin imbalance is lost as a consequence of
the interaction with the substrate, and the network bands undergo a shift to
lower binding energies. Such shift relates to a net charge transfer of 0.5
eV/unit cell towards the network, resulting from an increase of charge on the
C and H atoms (0.8 eV/unit cell) and a depletion of 0.36 eV/unit cell from the
Ag adatoms. The experimental estimate of a 3.10 eV energy gap can be deduced
from ARPES data, showing no electronic states down to approximately $-$2.25 eV
(Fig. 2(a–d)), and from the onset of the first unoccupied network state,
starting at ${\sim}$0.85 eV according to STS (Fig. 2(f)). Note that we discard
the states related to the confined pore states (peaking at 0.6 eV) as they are
substrate-dependent. Indeed, the $dI/dV$ maps of Fig. S5(g–o) show a reduced
electronic intensity at the network from $-$2.25 eV to 0.6 eV, confirming this
large energy gap. Likewise, DFT calculations for the Ag(111)-supported network
(Fig. 3(a)) show an absence of relevant states on the 2D network between
$-$2.25 and 0.3 eV, corresponding to an energy gap of 2.55 eV. Considering the
expected gap underestimation for DFT calculations,40 this calculated value
agrees with the experiment.

In the following, we focus our attention on the occupied low-energy states at
the energy position of the ARPES bands and compare them with the experimental
STS (Fig. 2(f)) and $dI/dV$ maps (Fig. 3(i–k)). We also compare these
experimental results with the simulated $dI/dV$ maps (f–h) and the calculated
LDOS isosurfaces cut at a specific height (c–e), showing the states’ spatial
symmetry. At $-$2.50 V bias, we detect a weak shoulder on the STS at the
benzene ring position (purple curve in Fig. 2(f)). The dominant contribution
of the $dI/dV$ map at this energy (Fig. 3(i)) corresponds to three circular
features in a triangular arrangement located at the carbon atoms covalently
bound to hydrogens (between the acetylenic groups) in the benzene rings – see
the blue triangle in Fig. 3(i). Note that these features are strongly
modulated in intensity by the presence of neighboring cleaved Br atoms. The
simulated LDOS at this energy (Fig. 3(f)) displays such molecular orbital
(although with differences in the intensity distribution due to the inaccurate
comparison of constant-current conditions with constant-height calculations).
This orbital, according to the isosurfaces in Fig. 3(c), exhibits mainly a pz
character.

Moving down in energy, at $-$2.75 V we observe the main peak at the Ag adatom
position of the STS spectra (blue curve in Fig. 2(f)), which is clearly
localized at the same position in the $dI/dV$ map (Fig. 3(j)). The surrounding
Br atoms do not seem to interfere with this state, which is also evident in
C.H. maps (Fig. S6(d)). The simulated LDOS (Fig. 3(d,g)) localizes the
electronic states at the acetylenic groups and in the proximity of Ag adatoms,
thus revealing that the organometallic linking contributes at this energy to
the overall electronic structure. This is confirmed by the projected density
of states (PDOS), evaluated at the $\Gamma$ point (Fig. S8(a)), i.e. for
slowly decaying states, showing the energy coincidence of states on triple
bonds and Ag adatoms. Here, the orbital character is a mixture of pz and py
states for C, and of s and in-plane d states for Ag. We attribute the enhanced
intensity of the adatom to the strong hybridization with the substrate and to
its expected outer s-character, which would sharply increase the tunneling
probability.

At $-$3.25 eV, the $dI/dV$ map exhibits most of its periodic signal as an
extended halo centered at the Ag adatoms, amplified at the position of the
triple C$\equiv$C bonds (Fig. 3(k)). Indeed, we find a very subtle shoulder at
the acetylenic group (green curve in Fig. 2(f)) of the STS. This feature is
much more evident in the energy slice at $-$3.25 eV extracted from the STS
grid in Fig. S7(b), from which we deduce it is entirely an electronic state of
the 2D network. Note that observing by STS such a subtle peak in the occupied
region, so far away from the zero bias and so close to the substrate’s
d-bands, is an impressive experimental challenge. We find excellent agreement
with the LDOS calculations and isosurfaces (Fig. 3(e,h)), showing that the
charge is located at the triple bonds with a mixture of px and py orbital
character.

This comparison between experiment and theory allows not only to identify the
orbital character of the bands, but also to spatially define the dominant
contribution within the 2D network. In particular, the band-manifold closest
to EF (around $-$2.50 eV) resonates at the central benzene of the monomers
with an out-of-plane (pz) orbital character, whereas the deeper band-manifold
(around $-$3.25 eV) predominantly activates the acetylenic groups coordinated
to the metal centers in a mixture of in-plane (px and py) orbitals.

Coming to the unoccupied states, we find electronic contributions related to
the 2D network for voltages in the 1.60 to 2.00 V range (Fig. 2(f)). At these
energies, the intensity is mostly localized around the benzene rings (Fig.
S5(s–u)), similarly to what was observed at $-$2.50 V (Fig. 3(i)).
Nevertheless, a progressive change in the orbital character of these states is
observed as the energy increases. The $dI/dV$ signal changes from
homogeneously triangular at the carbon atoms linked to the hydrogens, to a
smeared, almost circular shape. In contrast, the intensity of the Ag adatoms
gradually decreases, as also confirmed by C.H. imaging (Fig. S6(j,k)). Indeed,
at 2.00 V the dominant intensity is fully located on the benzene rings, with a
pz orbital character as demonstrated by the isosurfaces shown in Fig. S10.

Finally, the prominent feature of the confined Shockley state peaking at 0.60
V (yellow curve in Fig. 2(f)) deserves further attention. The main energy
shift is dependent on the pore size, shape, and barrier potential landscape
created by the 2D network.41, 35 In this system, the network is able to
completely deplete the Ag SS, as the ARPES cannot detect it below EF. On top
of this, the Br atoms could also influence this shift, as previously
reported.24 Indeed, we find that the number and position of bromine atoms are
key to understanding the observed SS shift. Increasing the number of Br atoms
moves the peak energy from 0.51 to 0.69 V (Fig. 4(a)), but we could find
shifts as far as 0.85 V. Such energy differences are visible as intensity
modulations in the $dI/dV$ maps and energy slices of the STS grid of Figs.
S5(n–p) and S7(g–i). Notably, we observe an inverse correlation between the SS
energy and the pore area, which strictly depends on the Br atom pore occupancy
(Fig. 4(b)). In this analysis, the pore area is measured as the region of
exposed silver inside each pore after subtracting the Br atom space. Such SS
shift due to the presence of Br atoms is also reproducible by DFT. The
projected density of states (PDOS) for Ag of Fig. 4(c) confirms the shift in
the SS position, but it is however similar for both the four Br and six Br
situations. This is likely because the simulation does not take into account
the distortion of the network caused by the randomly placed bromine atoms,
which can significantly influence the real pore area.

## Conclusions

In summary, we show that we can synthesize a high-quality 2D organometallic
network by evaporating tBEB molecules on Ag(111). By means of ARPES and
STM/STS, we experimentally determine the electronic gap of this organometallic
network, amounting to 3.10 eV. The observation of two evident band-manifolds
manifests a high degree of electronic conjugation throughout the 2D network.
DFT calculations shed light on these electronic features, confirming a non-
negligible charge transfer from the substrate to the network. Notably, we
identify the orbital character of each band-manifold and correlate it with
their main spatial distribution, either out-of-plane at the benzenes or in-
plane at the acetylenic groups. Finally, we elucidate the role of the residual
Br atoms located within the pores and find that we can correlate the energy
shift of the confined Shockley state with the available pore area (subtracting
the space occupied by the halogens). These results further evidence that
strong organometallic conjugation of these 2D networks is possible even on top
of metallic surfaces. Moreover, they uncover the effect of the halogen
byproduct of OSS reactions on the confined states of the underlying substrate.
As materials based on sp-carbon show peculiar fundamental properties including
topological states,42, 43 our findings might be of great interest to future
studies and could be key to the implementation of these networks in high-end
applications.

## Methods

Experiment. All experiments were performed in situ under ultra-high vacuum
(UHV) conditions, with a base pressure in the $10^{-12}$ to $10^{-10}$ mbar
range. Single-crystal Ag(111) (MaTeck) was employed for the on-surface
synthesis (OSS) process unless otherwise specified. Low-temperature scanning
tunneling microscopy and spectroscopy (LT-STM/STS) investigations were
conducted with a Scienta Omicron microscope, cooled down to 4.8 K by liquid
helium. LT-STS spectra and maps were obtained through a lock-in amplifier with
an oscillation frequency of ${f_{\text{osc}}=817.3}$ Hz and a modulation
amplitude of ${V_{\text{RMS}}=10{-}15.5}$ mV (root-mean-square), as indicated
in figure captions. The lock-in output was compared to the numerical
derivative of the $I(V)$ signal in order to express it in pA/V. Room
temperature (RT) STM experiments were carried out with a variable-temperature
microscope (VT-STM by Scienta Omicron), using homemade electrochemically
etched tungsten tips and mica-supported polycrystalline Ag(111) substrates.
Low-energy electron diffraction (LEED) and angle-resolved photoelectron
spectroscopy (ARPES) measurements were carried out at 120 K at the BaDElPh
beamline38 of the Elettra Synchrotron in Trieste using an Omicron SpectaLEED
and a SPECS Phoibos 150 hemispherical analyzer, respectively. In the ARPES
experiments, the photon energy of the synchrotron radiation was varied in the
21–31 eV range; the total energy of the photoemitted electrons was set to 20
meV, while its angular resolution was below $0.3\degree$. STM data were
analyzed using the image processing Gwyddion 2.63 software.44 The LEED pattern
was simulated using the LEEDpat 4.3 software.37

The surfaces were prepared through several cleaning cycles of Ar+ sputtering
and annealing to 620$-$720 K until STM or LEED inspection revealed negligible
traces of contaminants. The molecular precursor, i.e.
1,3,5-tri(bromoethynyl)benzene (tBEB), was synthesized as previously reported
in the literature.45, 46 The precursor in powder form was loaded in a quartz
crucible and inserted in an organic molecular evaporator (OME, provided by Dr.
Eberl MBE-Komponenten). As the vacuum sublimation temperature is around RT,
the crucible was kept at 303 K through a PID feedback control loop employing
resistive heating and a water cooling system. After placing the substrate at
RT in front of the OME opening, at a distance of about 10 to 20 cm, the OME
shutter was kept open for several minutes (1 to 5 min, depending on setup),
reaching a maximum chamber pressure of 8 $\times\leavevmode\nobreak\ 10^{-8}$
mbar. The samples were subsequently annealed for 10–15 min to ${\sim}$370 K.

Theory. Theoretical calculations were performed by density functional theory
(DFT) within the generalized gradient approximation (GGA) in the PBE form;47
van der Waals interactions between the organic overlayer and the substrate
were included via a DFT-D2 Grimme potential.48 We used the approach
implemented in the SIESTA code49 that relies on norm-conserving
pseudopotentials and an atomic-orbitals basis set. We adopted a double-zeta
basis set with polarization orbitals and a mesh-cutoff of 400 Ry for the
kinetic energy value that sets the real-space grid. The pseudopotential for Ag
includes only s and p states in valence in order to achieve a better agreement
with the experiments for the energy position of the d band.

The simulated STM images are obtained with the Tersoff-Hamann approach.50 The
organometallic network matches a ${(4\sqrt{3}{\times}4\sqrt{3})}$R30∘
supercell of the underlying Ag(111) surface, as can be deduced from the STM
images and the calculation of the free-standing network, which exhibits an
equilibrium lattice constant equal to 2.090 nm; this leads to a 2.2%
compression when placed on Ag(111) (theoretical equilibrium lattice constant
${a_{Ag}=0.295}$ nm). We relaxed the organometallic layer and the first
substrate layer until the forces reached the tolerance value of 0.04 eV
$\AA^{-1}$. We used a $3{\times}3$ sampling of the Brillouin zone. Along the
$z$ direction, the slab includes three layers of the Ag substrate, the
molecular overlayer, and ${\sim}85\leavevmode\nobreak\ \AA$ of vacuum. Upon
relaxation, the slab thickness is increased to 9 layers of Ag for a better
description of the electronic states.

Author contributions
A.O.B. synthesized the molecular precursor. P.D., F.T., and J.L.-C. conducted
the STM and LEED experiments, and P.D. analyzed the data. P.D., F.T., G.D.S.,
L.P., A.L.B., J.L.-C., and C.S.C. conducted the ARPES experiments, and J.L.-C.
analyzed the data. S.A. conceived the theoretical modeling, performed the DFT
calculations, and analyzed the data. G.O. contributed to the analysis of the
theoretical results. P.D., S.A., J.L.-C., and C.S.C. wrote the manuscript.
C.S.C. conceived the project. All authors contributed to the revision and
final discussion of the manuscript.

Data Availability
The data that support the findings of this study are available from the
corresponding authors upon reasonable request.

## Associated Content

Supporting Information: additional LT- and RT-STM data (Fig. S1-S2), including
complete datasets of $dI/dV$ maps (Fig. S5), constant height imaging (Fig.
S6), and STS grids (Fig. S7); additional ARPES data showing the 2D network’s
signal contrasted with the Ag(111) substrate (Fig. S3), and at different
photon energies (Fig. S4); additional DFT calculations simulating the atomic
structure including cleaved Br atoms (Fig. S2), the 2D network’s density of
states, band dispersion (Fig. S8), spin band structure (Fig. S9), and $dI/dV$
maps (Fig. S10).

## Acknowledgements

The authors acknowledge Elettra Sincrotrone Trieste for providing access to
its synchrotron radiation facilities and for financial support under the SUI
internal project. P.D., F.T., A.L.B. and C.S.C. acknowledge funding by the
European Research Council (ERC) under the European Union’s Horizon 2020
Research and Innovation Programme ERC-Consolidator Grant (ERC CoG 2016 EspLORE
Grant Agreement No. 724610, website: https://www.esplore.polimi.it). P.D.,
A.L.B. and C.S.C. also acknowledge the project funded under the National
Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.3 –
Call for tender No. 1561 of 11.10.2022 of Ministero dell’Università e della
Ricerca (MUR); funded by the European Union – NextGenerationEU. Award Number:
Project code PE0000021, Concession Decree No. 1561 of 11.10.2022 adopted by
Ministero dell’Università e della Ricerca (MUR), CUP D43C22003090001, Project
title “Network 4 Energy Sustainable Transition – NEST”. S.A. and G.O.
acknowledge CINECA for the use of supercomputing facilities under the IscraC
program (project DECANET – ID: HP10CN6MUU). S.A. and G.O. also thank the
support of the project “TIME2QUEST” (Progetto di Iniziativa Specifica INFN).
A.O.B. acknowledges support from the Ministero dell’Università e della Ricerca
(MUR) and the University of Pavia through the program “Dipartimenti di
Eccellenza 2023–2027”. J.L.-C. acknowledges the use of Servicio General de
Apoyo a la Investigación-SAI and the Laboratorio de Microscopías Avanzadas of
the Universidad de Zaragoza. J.L.-C. also acknowledges financial support from
Grant References No. PID2019-107338RB-C64 and PID2022-138750NB-C21 funded by
MCIN/AEI/10.13039/501100011033, by “ERDF A way of making Europe” and “European
Union NextGenerationEU/PRTR”. J.L.-C. also thanks the Aragonese Projects
RASMIA E12_20R co-funded by Fondo Social Europeo.

Competing interests
The authors declare no competing financial interests.

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Figure S1. Selection of LT and RT-STM images of 2D organometallic network on
Ag(111), highlighting typical defects encountered alongside the mixed
honeycomb-kagome 2D network. (a) Large-scale LT-STM image overview of the 2D
network after annealing to ${\sim}$370 K, showing the coexistence of the
porous and compact phase (STM set-point: 1.0 V, 50 pA). (b) Zoom-in at the
green square of (a) showing a typical line defect at a grain boundary of
coalescing 2D network islands consisting of aligned octagonal and pentagonal
pores (STM set-point: $-$50 mV, 90 pA). (c) Zoom-in at the blue square of (a)
displaying the residual compact phase (STM set-point: 70 mV, 100 pA). (d)
Zoom-in at the yellow square of (a) showing the atomic arrangement of the
cleaved Br atoms on the Ag(111) surface (STM set-point: $-$1.0 V, 50 pA). (e)
Large-scale RT-STM overview image after molecular deposition and annealing on
the Ag surface (STM set-point: 700 mV, 400 pA). (f) RT-STM image showing that
the 2D network is stable at this temperature (STM set-point: $-$400 mV, 400
pA). (g) RT-STM image showing the emergence of two different defects with
respect to the LT case: a single monomeric vacancy that does not disrupt the
surrounding network, and a multiple monomeric vacancy aggregating into a
larger network hole that distorts the adjacent pores into rectangles,
pentagons, heptagons, or octagons to accommodate the deformation (STM set-
point: 600 mV, 400 pA). (h) RT-STM image of the degraded network after
annealing to ${\sim}$470 K (STM set-point: 700 mV, 400 pA). Figure S2. (a)
High-resolution LT-STM image (STM set-point: $-$3.5 V, 800 pA). (b) Average
line profile measured along the direction indicated by the white arrow in (a).
(c,d) Simulated STM images in the presence of four (c) and six (d) Br atoms in
the network, obtained by integrating occupied states in an energy window 0.5
eV wide, at a distance of $2\leavevmode\nobreak\ \AA$ from the surface. (e,f)
Simulated atomic structure of the Ag(111)-supported 2D organometallic network
in top and side view with four (e) and six (f) Br atoms in each pore. Carbon
atoms are in gray, Br atoms in red, Ag adatoms in yellow, and substrate Ag
atoms in orange. Figure S3. Electronic band structure comparison of the 2D
organometallic network versus the Ag(111) substrate along the two high-
symmetry directions. The direct photoemission signal, measured with a photon
energy of 21 eV, is shown in panels (a), (c), (e), and (g), while the
corresponding second derivative in the side panels (b), (d), (f), and (h). The
highly dispersive sp bands of the substrate at large $k_{x}$ and $k_{y}$
values are visible in all panels, whereas the relatively flat band-manifolds
at the lowest energy region are only visible in the network’s signal (left
columns). Contrarily, the Shockley state is only visible at $\Gamma$ for the
pristine substrate, as it is depleted in the 2D network. The color grayscale
is linear (the darker, the more intense) and the vertical dashed lines
indicate the high-symmetry points (rotated by 30∘ with respect to one
another). Figure S4. Electronic band structure evolution of the 2D
organometallic network as a function of photon energy along the two high-
symmetry directions, specifically at 21 eV (a–d), 26 eV (e–h), and 31 eV
(i–l). The direct photoemission signal is shown in panels (a), (c), (e), (g),
(i), and (k), while the corresponding second derivative in the side panels
(b), (d), (f), (h), (j), and (l). The substrate’s sp bands change their
dispersion with the photon energy, whereas the band-manifolds of the network
do not, corroborating their 2D origin. The color grayscale is linear (the
darker, the more intense) and the vertical dashed lines indicate the high-
symmetry points (rotated by 30∘ with respect to one another). Figure S5. (a)
Reference LT-STM image (STM set-point: $-$2.0 V, 300 pA). (b$-$u) LT dI/dV
maps taken at different set-point biases with ${V_{\text{RMS}}=10.0}$ mV and
${f_{\text{osc}}=817.3}$ Hz. STS set-points: (b) $-$3.50 V, 450 pA; (c)
$-$3.25 V, 450 pA; (d) $-$3.00 V, 400 pA; (e) $-$2.75 V, 400 pA; (f) $-$2.50
V, 350 pA; (g) $-$2.25 V, 350 pA; (h) $-$2.00 V, 300 pA; (i) $-$1.75 V, 300
pA; (j) $-$1.50 V, 250 pA; (k) $-$1.25 V, 250 pA; (l) $-$1.00 V, 200 pA; (m)
$-$0.75 V, 200 pA; (n) $+$0.40 V, 100 pA; (o) $+$0.60 V, 100 pA; (p) $+$0.85
V, 120 pA; (q) $+$1.00 V, 120 pA; (r) $+$1.35 V, 150 pA; (s) $+$1.60 V, 150
pA; (t) $+$1.80 V, 200 pA; (u) $+$2.00 V, 200 pA. Figure S6. (a) Reference
(constant-current) LT-STM image (STM set-point: $-$100 mV, 50 pA). (b$-$k)
Constant-height LT-STM images taken at different set-point biases. STM set-
points: (b) $-$3.50 V; (c) $-$3.25 V; (d) $-$2.75 V; (e) $-$2.50 V; (f)
$-$2.00 V; (g) $-$1.25 V; (h) $+$0.85 V; (i) $+$1.35 V; (j) $+$1.60 V; (k)
$+$2.00 V. Figure S7. LT-STS maps of a 36$\times$24 pixel grid collected with
${V_{\text{RMS}}=10.0}$ mV and ${f_{\text{osc}}=817.3}$ Hz. A STS curve is
associated with each pixel, and each map is an energy slice at a specific bias
voltage. (a) Reference LT-STM image (STM set-point: $-$500 mV, 14 pA). STS
set-points: (b) $-$3.50 V; (c) $-$2.75 V; (d) $-$2.50 V; (e) $-$1.75 V; (f)
$-$1.25 V; (g) $+$0.40 V; (h) $+$0.60 V; (i) $+$0.85 V; (j) $+$1.35 V; (k)
$+$1.60 V; (l) $+$2.00 V. Figure S8. Theoretical electronic properties of the
2D organometallic network on Ag(111). (a) Density of states at the $\Gamma$
point projected on different groups of atoms. Band dispersion along the high-
symmetry path of 2D network without (b) and with (c) Br adatoms in the pores.
Carbon bands are reported in blue (pz), and orange/yellow (px,y). Red bands
correspond to states mainly localized on Br atoms. Figure S9. Majority (a) and
minority (b) spin band structure of the free-standing 2D organometallic
network along high-symmetry paths of the Brillouin zone. (c) Band structure of
the Ag(111)-supported 2D network for comparison. Cyan and yellow/orange lines
correspond to different p bands, respectively pz and px,y. Figure S10. LDOS
(a) and simulated $dI/dV$ map (b) of the Ag(111)-supported 2D network at
$+$2.0 eV from the Fermi level.