Investigating Pb Nanostructures with a Density-Functional Tight-
Binding Approach: Slater−Koster Parameters
Andres Unigarro, Florian Günther, and Sibylle Gemming*

Cite This: J. Phys. Chem. C 2025, 129, 5617−5624 Read Online

ACCESS Metrics & More Article Recommendations *sı Supporting Information

ABSTRACT: Intercalation in epigraphene systems is an established
technique widely used to modify the electronic structure of graphene and
to synthesize otherwise unstable two-dimensional layers with exotic electronic
properties. However, capturing the full symmetry of the heterostructure
requires a large number of atoms, rendering traditional electronic-structure
approaches computationally demanding. Density-functional-based tight-
binding (DFTB) offers an efficient alternative, balancing accuracy and
reduced computational cost. For heavy elements such as Pb, however, proper
parameters for these types of calculations are not available in the open
literature. In this work, we developed a Slater−Koster parameter set for the
elements Si, C, and Pb, enabling the investigation of the electronic structure
of various elemental and binary solid-state structures, such as graphene, plumbene, and silicon carbide. Our results obtained with
DFTB for bulk Pb and Pb/SiC structures show good qualitative agreement with pure DFT calculations. Furthermore, the inclusion
of spin−orbit coupling (SOC) significantly modifies their electronic properties, aligning with DFT findings. These results underscore
the capability of the optimized parameters to accurately model complex systems, allowing investigations of larger systems closer to
experimental observations.

■ INTRODUCTION
Density functional theory (DFT)1 within the Kohn−Sham
formulation,2 is a reliable method for investigating the
electronic properties of molecules, clusters and condensed
matter systems. Nowadays, efficient DFT-KS codes, coupled
with high-performance computing systems, have led to the
possibility of studying complex and large systems.3 However,
the complexity and size of the systems required for modern
investigations are growing faster than the nominal compute
power and the algorithmic optimization of DFT codes. For
example, in systems such as epitaxial graphene grown on
SiC(0001), the lattice mismatch between graphene and the
SiC substrate leads to the formation of a nearly commensurate

R(6 3 6 3 ) 30× ° superstructure relative to the SiC(1 × 1)
surface cell, as demonstrated in previous experiments.4,5

Accurately modeling this system while preserving its full
symmetry requires a supercell containing 1310 atoms,6 which
introduces significant computational challenges for realistic
calculations. To study such heterostructures, a common
approach is to simplify the problem by considering an
approximate system that retains the essential features of the
full system. For example, strain or compression is usually
applied to one of the materials to achieve a better match
between the lattice constants, thereby reducing the size of the
system considered. Alternatively, to study those systems
without altering their mechanical properties, approximate
theoretical methods capable of accurately describing specific

properties of interest (e.g., vibrational properties, electronic
transport, etc.) without including all the interactions involved
can be used. In that way, larger systems can be studied while
reducing the computational demands.
One alternative to DFT is provided by classical force field

methods (i.e., empirical potentials) which are several orders of
magnitude faster, allowing the study of the dynamics of
systems composed of up to millions of particles beyond the
nanosecond regime. That method, however, requires the
definition of numerous empirical parameters for a specific
system. The availability of accurate parameters for a number of
chemical elements can be limited, and their transferability
between different bonding types and material systems may be
low, which limits the application of such approaches.
Furthermore, because force field methods ignore the electronic
contributions,7 they yield geometries of van der Waals stacked
2D materials well,8,9 but they can not describe electron
distributions, band structures including spin−orbit coupling
(SOC), transport properties and interlayer bond and
compound formation.

Received: October 29, 2024
Revised: February 14, 2025
Accepted: March 3, 2025
Published: March 11, 2025

Articlepubs.acs.org/JPCC

© 2025 The Authors. Published by
American Chemical Society

5617
https://doi.org/10.1021/acs.jpcc.4c07351
J. Phys. Chem. C 2025, 129, 5617−5624

This article is licensed under CC-BY 4.0

D
ow

nl
oa

de
d 

vi
a 

U
N

IV
 E

ST
A

D
U

A
L

 P
A

U
L

IS
T

A
 o

n 
Se

pt
em

be
r 

17
, 2

02
5 

at
 1

4:
00

:0
5 

(U
T

C
).

Se
e 

ht
tp

s:
//p

ub
s.

ac
s.

or
g/

sh
ar

in
gg

ui
de

lin
es

 f
or

 o
pt

io
ns

 o
n 

ho
w

 to
 le

gi
tim

at
el

y 
sh

ar
e 

pu
bl

is
he

d 
ar

tic
le

s.

https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Andres+Unigarro"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf
https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Florian+Gu%CC%88nther"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf
https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Sibylle+Gemming"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf
https://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.jpcc.4c07351&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?goto=articleMetrics&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?goto=recommendations&?ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?goto=supporting-info&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=tgr1&ref=pdf
https://pubs.acs.org/toc/jpccck/129/11?ref=pdf
https://pubs.acs.org/toc/jpccck/129/11?ref=pdf
https://pubs.acs.org/toc/jpccck/129/11?ref=pdf
https://pubs.acs.org/toc/jpccck/129/11?ref=pdf
pubs.acs.org/JPCC?ref=pdf
https://pubs.acs.org?ref=pdf
https://pubs.acs.org?ref=pdf
https://doi.org/10.1021/acs.jpcc.4c07351?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://pubs.acs.org/JPCC?ref=pdf
https://pubs.acs.org/JPCC?ref=pdf
https://acsopenscience.org/researchers/open-access/
https://creativecommons.org/licenses/by/4.0/
https://creativecommons.org/licenses/by/4.0/
https://creativecommons.org/licenses/by/4.0/


In order to address the scalability problem in solid-state
physics, tight-binding (TB) methods were developed. In the
1980s Seifert and co-workers,10 reported the use of a restricted
atomic orbital (AO) basis set representation for an
approximate treatment of Kohn−Sham DFT. In the sub-
sequent years, these early ideas were further developed
resulting in the so-called density-functional based tight binding
scheme (DFTB).11−14 As reported in the literature,11,15−20 this
method has been successfully applied to studying a variety of
condensed matter systems with a broad range of elements and
its implementation can be orders of magnitude faster than
DFT. The computational efficiency of DFTB relies on the fact
that the involved interactions are reduced to two center term
only, allowing for a precalculation and tabulation of element-
pair interactions employing the Slater-Koster (SK) method.21

The parameters needed for the application of DFTB schemes,
however, are not available for all atoms, e.g., Pb, Bi and Sn
which have been widely used as intercalants in epigraphene
systems.22−26

Here, we generate Slater-Koster parameters of the main
group-IV elements: Si, C and Pb. These elements are formally
isovalent, but exhibit very different electronic properties: the C
2s and 2p states from the sp2 and sp3 hybrid orbitals present in
graphene and SiC, Si can further include the unoccupied 3d
orbitals into bonding with intercalants, and the heavy element
Pb features relativistic effects, which bind the 6s electrons more
strongly to the atom core and lead to an addition splitting of
the 6p shell. All these effects need to be accounted for when
analyzing the observed multitude of intercalated epitaxial
graphene systems. Since in this work we only focus on the
electronic properties of the structures, our parametrization
does not include interatomic potentials, i.e., the repulsive term,
which would be necessary for the evaluation of geometries,
forces, or phonons. The inclusion of the repulsive energy in the
parametrization will be subject of a forthcoming work.
The work is structured as follows: First, a brief introduction

to the main theoretical concepts utilized in DFTB, along with
the principal equations of the method, is provided. Second, we
discuss the results of a comparative investigation between the
electronic structures obtained using our newly generated set of
parameters and those results derived from DFT calculations,
focusing on various elemental and binary solid-state structures,
in particular graphene and silicon carbide. Given the primary
emphasis of this work on the DFTB parametrization of Pb, we
also examine bulk Pb as well as Pb on SiC interface structures.
In the case of the Pb/SiC system, we restrict our study to the
Pb(1 × 1) phase, for which density functional theory
calculations have suggested its stability,27,28 and which has
been recently reported to form in the early stages of the Pb
intercalation process.29

■ THEORETICAL APPROACH
A detailed derivation of DFTB from density functional theory
(DFT) has been presented in the literature.11,18,30−32 There-
fore, the theoretical fundamentals of DFTB will be only briefly
reviewed in the current work. According to DFT,33,34 the
ground state total energy of a system composed by N nuclei
located at the positions r can be expressed as a unique function
of the electronic density ρ. Within the Kohn−Sham
formulation,2 the atomic orbitals ψi describe a system of
noninteracting electrons that have the same electronic density
ρ(r) as the interacting system. Then, ρ(r) can be expressed as
follows:

r r( ) ( )
i

i

occ
2= | |

(1)

Using the previous definition, the total energy of the system
in the ground state is given as

E E V r

E

r r r

r

( ) ( ) ( ) d

( )

i
iDFT H XC

3

XC

[ ] = [ ] [ ]

+ [ ] (2)

where

E
e

r r
r r

r r2
d d

( ) ( )
H

3 3=
| | (3)

is the Hartree energy and accounts for the classical electrostatic
interaction energy of the electronic density,33,34 EXC is the
exchange-correlation energy33,34 and V E r

XC
( )XC= [ ] . The

orbital energy ϵi is calculated by solving the single-particle
equations:

h t V V Vr r( ( ) ( ) )KS
i i i iext H XC| = + + [ ] + [ ] | = |

(4)

In the previous relation V E r
H

( )H= [ ] and t ̂ is the kinetic
energy of the noninteracting system. Following Foulkes and
Haydock,32 any electronic density ρ can be expressed in terms
of a reference density ρ0 plus some fluctuation δρ, i.e:

r r r( ) ( ) ( )0= + (5)

Expanding EXC[ρ0 + δρ] in a Taylor series up to the second-
order term:

E E

E
d

E
r r rd d

XC 0 XC 0

XC 3
2

XC 3 3

0 0

[ + ] [ ] +

+
(6)

allows to rewrite the total energy as

E E E E, ( )tot BS 0 2nd 0 0
2

rep 0[ ] + [ ] + [ ] (7)

where:

i

k

jjjjjjjjj

y

{

zzzzzzzzz

E V V V

E
E

r r

E E E r E

r r

1
2

1
2

1
d d

d

i
i iBS

2
ext H 0 XC 0

2nd

2
XC 3 3

rep H 0 XC 0 XC 0 0
3

II

0

= + + [ ] + [ ]

= +

= [ ] + [ ] [ ] + (8)

In the DFTB scheme, the effective potential of the Kohn−
Sham formulation is expressed as a superposition of spherical,
atom-centered contributions associated with the atomic
densities ρa, i.e., V V V Veff

KS
0 ext 0 H 0 XC 0[ ] = [ ] + [ ] + [ ]

Va
a a[ ]. This decomposition is possible for Vext and VH

since they depend explicitly on ρa. For VXC, however, this case
represents an approximation due to its nonlinearity. In DFTB
the KS orbitals ψi are expanded in terms of a linear
combination of atomic orbitals (LCAO) ϕν which are
restricted to the valence shell of the atoms, namely,

ci i= .31

The Journal of Physical Chemistry C pubs.acs.org/JPCC Article

https://doi.org/10.1021/acs.jpcc.4c07351
J. Phys. Chem. C 2025, 129, 5617−5624

5618

pubs.acs.org/JPCC?ref=pdf
https://doi.org/10.1021/acs.jpcc.4c07351?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as


When only EBS is considered, the secular equation that has
to be solved is given by

c H S b a a b( ) 0 with and , ,i i
BS =

(9)

with the Hamiltonian matrix elements and the overlap matrix

elements given by H Ha bBS 0= | | and S a b= |
respectively. Neglecting three-center and crystal-field terms
as well as pseudopotential contributions,31 only two center
terms remain in the Hamiltonian HBS. Therefore, in this
representation the Hamiltonian matrix for DFTB is found as

l

m
ooooooo

n
ooooooo

H t V a b

,

, ,

0 ,else

a a b bBS

atom

=

=

+ [ + ]

(10)

where εatom are the orbital energies of the isolated atoms and V
[ρa + ρb] the KS potentials of the superimposed atomic
densities of the neutral atoms. It is worth mentioning that the
superposition of the potentials of isolated atoms, rather than
the superposition of densities, can also be employed to
calculate the matrix elements of this Hamiltonian.35 In order to
account for a possible charge exchange in the system, charge
fluctuations δρa terms must be included, i.e., E2nd has to be
taken into account. Using the Mulliken definition of atomic
point charges36 the Hamiltonian can be expressed as (for more
details see refs 13 and 30):

H H S q q1
2 a b

ab a b
SCC DFTB 0

,

= +
(11)

Here, Δqa is the charge of the atom a described by the
corresponding charge fluctuation δρa and the matrix γab which
accounts for Coulombic and exchange-correlation interactions
of the transferred charge. Since Δq depends on the basis
coefficients, the eigenvalue problem in eq 9, must be solved
self-consistently. The main advantage in relation to full DFT
calculations is that the self-consistency in DFTB must be
achieved for the charges Δqa instead of the charge density ρ.
For the calculation of the total energy of the system and
structural optimizations, repulsive energies (Erep) must be
considered. Although it is possible to access these repulsive
terms directly, in practice they are fitted to full DFT
calculations.11,30,37

As mentioned above, in DFTB only valence electrons are
considered in the LCAO, which are typically bound and
localized around atoms in solids and molecules. Since atomic
orbitals (AO) based on free atoms will be too diffuse for this
purpose,30 the KS equations are usually solved applying an

additional confinement potential( )r
r

n

0
where typically n = 2.38

Therefore, by solving:

Ä

Ç

ÅÅÅÅÅÅÅÅÅÅÅÅ
i
k
jjjjj

y
{
zzzzz

É

Ö

ÑÑÑÑÑÑÑÑÑÑÑÑ
t V

r
r

a
i i

0

2

+ + | = |
(12)

an optimized set of AOs with a faster radial decay is calculated.
These orbitals are commonly defined to represent the so-called
pseudoatom. In practice, different radii r0 are used to
determine the atomic orbitals and the atomic densities. First,
DFT calculations are carried out using a density confinement
radius rd

0 . At a second stage, DFT calculations are performed
again using a wave functions compression radius rw

0 using the
potentials and the density calculated at the first stage. Usually,
the values of rd

0 and rw
0 are empirically determined. In the

DFTB scheme, therefore, two parameters per element have to
be determined at this stage, a confinement radius for the AO
basis, and a confinement radius for the initial density. Once the
AOs and the initial density are defined, the eq 9 can be solved.
Note that as HBS and Sμν depend on two-center integrals only,
they can be calculated and tabulated in advance as a function
of the distance between atomic pairs. The calculated
Hamiltonian matrix as well as the overlap matrix are usually
stored in Slater-Koster tables.21 Therefore, it is not necessary
to recalculate any integral during a DFTB calculation.

■ COMPUTATIONAL DETAILS
The optimization of the initial structures as well as the
reference band structure calculations were performed using
density functional theory (DFT) as implemented in the
ABINIT package.39 As in this work heavy atoms such as Pb
were employed, fully relativistic norm-conserving pseudopo-
tentials with the generalized gradient approximation (GGA) in
the Perdew−Burke−Ernzerhof (PBE)40 formulation were used
to evaluate the exchange-correlation potential. The structural
relaxations were performed using a k-point grid of 8 × 8 × 1
and 8 × 8 × 8 for the bulk structures until residual forces
smaller than 0.0025 eV/Å were achieved. For an accurate
ground state energy a 12 × 12 × 1 grid (12 × 12 × 12 grid for
the bulk structures) was adopted. In all cases, self-consistent
calculations were performed using 2.7 × 10−8 eV as threshold
for the convergence of the total energy and a cutoff energy of
1088 eV for the plane wave basis. The semiempirical density
functional-based tight binding (DFTB) approach was used in
its self-consistent extension31 as implemented in the DFTB+
code.41 The Slater-Koster parametrization was developed using
the skgen routine incorporated in the skprogs package.
In the present work, we focus on the elements C, Si, and Pb

and intercalated epitaxial graphene systems. Therefore, the
confinement radii were chosen to achieve a good qualitative
agreement with DFT regarding the electronic properties for
graphene, bulk Pb, SiC and Pb/SiC structures. In all Pb/SiC
structures, dangling bonds at the lower SiC surface were
passivated with H atoms and a vacuum layer of 15 Å was
considered in order to avoid spurious interactions with
periodic images. To be consistent with the DFT calculations,
the PBE40 functional was employed for the generation of the

Table 1. Confinement Radii are Given in Bohr, whereas Onsite Energies ε are Given in Hartree

element valence shell rd
0 rw

0 εd εp εs
C 2s22p2 9 3 −0.19436081 −0.50490762
Si 3s2 3p2 3d0 7 5.4 5.4 3.3 0.02808580 −0.15061948 −0.39616322
Pb 6s2 6p2 6d0 9 5 0.00529963 −0.14379385 −0.46859817

The Journal of Physical Chemistry C pubs.acs.org/JPCC Article

https://doi.org/10.1021/acs.jpcc.4c07351
J. Phys. Chem. C 2025, 129, 5617−5624

5619

pubs.acs.org/JPCC?ref=pdf
https://doi.org/10.1021/acs.jpcc.4c07351?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as


DFTB parameters. The values used for the calculation of the
SK tables are presented in Table 1 as well as the onsite energies
obtained for each orbital. The onsite energies are found to be
in accordance with values reported in the literature.42 The set
of SK tables generated in this work can be found as Supporting
Information. For the band structure calculation, the maximum
angular momentum was specified as p, d, p, and s for C, Si, Pb
and H atoms, respectively. Note that since repulsive potentials
were not included in our parametrization, the SK tables are not
intended to be used to calculate geometrical properties of the
systems. For this reason, the atomic structures used in the
DFTB calculations were the same as those used to obtain the
DFT results. The inclusion of such potentials is beyond the
scope of this work.

■ RESULTS AND DISCUSSION
We begin our comparative study presenting the band
structures of graphene and bulk 6H-SiC. For this purpose,
we use as a reference the results calculated with DFT and
DFTB, employing the semirelativistic Slater-Koster tables for
material science simulation (matsci-0-3).43 For graphene, the
optimum DFT lattice constant of 2.46 Å was used. From
Figure 1a it is possible to observe a good qualitative agreement
with DFT calculations, especially around the Fermi level. Some
deviations are expected given the minimal basis approximation
in DFTB, and some compression of the bands toward the

Fermi level can be noticed. In the case of SiC (see Figure 1b),
the lattice constants used were a = b = 3.08 Å and c = 15.2 Å.
Overall, a good qualitative agreement between the theoretical
methods can be observed and band gap values of 2, 2.1 and 2.6
eV for DFT, DFTB and DFTB-matsci, respectively, are
obtained. The difference in the band gap value obtained with
the DFTB-matsci parametrization may be related to the fact
that these parameters were calculated using LDA44 functional.
On the other hand, as the DFT calculations as well as the
generation of the DFTB parameters were developed using the
PBE functional, a underestimation of the band gap by about 1
eV it is expected, as this is a well-known feature of this
functional.45

We proceed to evaluate the DFTB parameters generated for
the Pb atom. For this purpose we consider the bulk phase of
Pb which has a face-centered-cubic (fcc) crystal structure and a
lattice constant aPb = 4.95 Å.46 From Figure 2 it is possible to
observe the good qualitative agreement between the band
structures obtained with DFT and DFTB along some of the
high-symmetry points of the first Brillouin zone (BZ). It is
expected that the electronic properties of heavy atoms such as
Pb may be affected by the spin−orbit coupling (SOC).47,48

Therefore, the simulation of the band structure was carried out
without (Figure 2a) and with (Figure 2b) the inclusion of the
spin−orbit interaction. The results obtained in the present
work are in accordance with other theoretical calculations

Figure 1. Band structures obtained with our DFTB parameters (red solid line), matsci-0-3 data set (blue dotted line), and DFT (black dashed line)
for (a) graphene and (b) bulk 6H-SiC.

Figure 2. Band structures of bulk Pb (a) with and (b) without SOC calculated with our DFTB parameters (red solid line) and DFT (black dashed
line).

The Journal of Physical Chemistry C pubs.acs.org/JPCC Article

https://doi.org/10.1021/acs.jpcc.4c07351
J. Phys. Chem. C 2025, 129, 5617−5624

5620

https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_001.zip
https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_001.zip
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig1&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig1&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig1&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig1&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig2&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig2&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig2&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig2&ref=pdf
pubs.acs.org/JPCC?ref=pdf
https://doi.org/10.1021/acs.jpcc.4c07351?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as


reported in the literature.47,49 As depicted in Figure 2, the
bands affected due to the SOC are mainly those which have p-
orbital character (see Figure S1). The inclusion of the SOC,
however, has little impact on the states close to the Fermi level.
The most notable changes due to the SOC are observed along
the symmetry directions Γ − X, Γ − L and K − Γ where the
band splitting at the symmetry points Γ, W, and L obtained
with DFTB (DFT) have the values 1.99 eV (3.33 eV), 1.49 eV
(1.19 eV) and 1.13 eV (1.93 eV) respectively. We also observe
that in the vicinity of the zone boundary point W and close to
the K point in the K − Γ direction, the SOC inclusion leads to
the avoided band-crossings.
In order to complete our study on homoatomic Pb

structures, we perform a DFT study on the structural,
energetic and electronic properties of a 2D Pb layer with a
potentially buckled honeycomb lattice structure (see Figure
3a) usually referred to as plumbene.51,53 Unlike graphene,
which features a planar honeycomb structure due to strong π-
bonding, plumbene has two buckled structures that present
lower energy than the planar configuration. As presented in
Table 2, after DFT relaxations we obtain lattice constants of
5.23, 4.96, and 3.73 Å for the planar, low buckled (LB) and
high buckled (HB) structures respectively, which are
consistent with the values reported in the literature.19,51,52 In
general, out-of-plane buckling may exist depending on the
relative stability of sp2 and sp3 hybridization as well as the
exchange-correlation potential.54 Similar to Si and Ge 2D
structures, in plumbene, there exists a significant interelectron
(lattice) repulsive Coulomb potential.54 To reduce this
repulsion, atoms are shifted relative to each other in the out-

of-plane direction, leading to a weak π − π overlap and a
reduction in the bond length. The pz orbitals, therefore,
overlap more effectively with the s orbitals, which cause a
mixed sp2/sp3 hybridization of electron states. As observed
from previous results, the bonding character approaches sp3 for
heavier atoms,55 making the sp2 hybridization less favorable for
Pb. The buckling has important consequences for the physical
properties of the structure. On the one hand, mixed sp2/sp3
hybridization and the tendency to form sp3 bonds make them
more chemically active.55 On the other hand, the point group
symmetry of the lattices is reduced from D6h to D3d when
transitioning from the planar to the buckled structure, which
modifies the electronic properties of the material.
In Figure 3b−d, the band structures obtained using DFT

and DFTB considering SOC are presented (for the band
structures without SOC see Figure S2). In all three cases, both
methods exhibit good qualitative agreement, especially around
the Fermi energy. The results indicate that while the planar
and HB structures exhibit metallic properties, the LB structure
is a semiconductor with an indirect band gap of 0.5 eV (0.15

Figure 3. (a) Lattice structure of plumbene. Band structures obtained with DFTB (red solid line) and DFT (black dashed line) for (b) planar, (c)
low-buckled, and (d) high-buckled plumbene, including spin−orbit interaction.

Table 2. Energetic and Structural Parameters Obtained after
DFT Relaxationsa

structure |ΔE| (eV) lattice constant (Å) buckling (Å)

planar 1.00 5.3850; 5.23 0.0
low buckled 0.62 4.9251; 4.9350; 4.96 0.9451; 0.98
high buckled 0.00 3.5752; 3.6950; 3.73 2.5550; 2.55

aThe total energy difference ΔE is defined as the energy of a structure
minus the energy of the most stable structure, in this case the HB.

The Journal of Physical Chemistry C pubs.acs.org/JPCC Article

https://doi.org/10.1021/acs.jpcc.4c07351
J. Phys. Chem. C 2025, 129, 5617−5624

5621

https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig3&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig3&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig3&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig3&ref=pdf
pubs.acs.org/JPCC?ref=pdf
https://doi.org/10.1021/acs.jpcc.4c07351?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as


eV) as obtained from DFT (DFTB). This band gap is larger
than those reported in previous theoretical calculations for
other group XIV elements, which are 10−3, 8.23, and 72 meV
for graphene, silicene, germanene, and stanene, respectively.56

In the LB case when no SOC is considered, two bands cross
linearly at the K point, showing Dirac-cone-like features
(Figure S2b). Additionally, the valence band and conduction
band touch at the Γ point. When SOC is included, however,
the degeneracy is lifted and gaps open at both points. Similar
to the results in plotted in Figures 1 and 2, a shift in the lower
energy bands is observed in the DFTB results relative to the
DFT results for all cases.
From the previously discussed results, we observed good

qualitative agreement between DFT and DFTB calculations for
graphene, SiC, and homoatomic Pb structures when
considered individually. Now, in order to evaluate the
performance of the full set of parameters, we focus our
attention on the (1 × 1) phase of Pb on 6H-SiC, i.e., a uniform
Pb layer with SiC-(1 × 1) periodicity. In this triangular lattice,
the distance between Pb atoms is 3.08 Å. For the hexagonal
SiC(0001) structure there exist three high-symmetry absorp-
tion sites on which the Pb atom can be located, namely, T1,

H3, and T4 (see Figure 4). As presented in Figure S3 of the
Supporting Information, the energy difference shows that the
most stable structure is obtained when the Pb atom is located
at the T1 site. After optimization, the values of Δz (see Figure
4) obtained for T1, T4, and H3 positions were 2.81, 2.86, and
2.75 Å respectively.
Next, we analyze the band structure of the system with the

lowest energy without and with SOC. The band structures
obtained for the remaining models can be found in the SI. As
shown in Figures 5a,c and S4, the band structures obtained
from DFT and DFTB exhibit good qualitative agreement with
and without SOC. When no SOC is included in the
calculations, as it is evident from Figure 5a, a quasi-linear
dispersion is observed around −1.2 eV below the Fermi level at
K with a small gap of about 0.13 and 0.1 eV for DFT and
DFTB results, respectively. This linear dispersion, mainly
originates from px and py orbitals (see Figure S6). Interestingly,
around the Fermi level a shallower dispersion can be identified,
which as observed from the partial density of states (PDOS)
obtained from DFTB (Figure 5b), arises from contributions of
the p orbitals of both the Pb layer and the substrate, indicating
a significant interaction between them. In order to investigate

Figure 4. Atomic models of (1 × 1)-Pb/SiC(0001) for the three different absorption sites: (a) T1, (b) T4, and (c) H3.

Figure 5. Comparison of the electronic band structure for the Pb/SiC system with Pb at the T1 position, obtained from DFT (black dashed line)
and DFTB (red solid line). Panels (a) and (c) show the results without and with spin−orbit coupling (SOC), respectively. The figure also presents
the density of states (DOS) and projected density of states (PDOS) obtained from DFTB (b) without and (d) with the inclusion of SOC.

The Journal of Physical Chemistry C pubs.acs.org/JPCC Article

https://doi.org/10.1021/acs.jpcc.4c07351
J. Phys. Chem. C 2025, 129, 5617−5624

5622

https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig4&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig4&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig4&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig4&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig5&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig5&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig5&ref=pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?fig=fig5&ref=pdf
pubs.acs.org/JPCC?ref=pdf
https://doi.org/10.1021/acs.jpcc.4c07351?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as


further this interaction, the orbital-projected band structure of
an artificial freestanding Pb(1 × 1) monolayer is calculated
(Figure S5), from which a parabolic dispersion with pz
character it is observed around Γ. Upon interfacing with the
SiC substrate (see Figure S6), the pz orbitals hybridize with
substrate dangling bonds, leading to the shallower dispersion
observed near the Fermi level. When the SOC is included in
the calculations, as displayed in Figure 5c, the bands at the K
point split, causing the linear dispersion to disappear.
Furthermore, the bands close to the Fermi level show a
Rashba-like splitting around K and the flatter dispersion near
the Fermi level in the direction K − M can still be observed.
Close to the M symmetry point in the Γ − M direction, the
band splitting of the band below the Fermi level takes the
values of 0.42 and 0.5 eV for the band structures obtained with
DFT and DFTB respectively. Also, from the PDOS (Figure
5b,d) and the orbital-projected band structure (see Figure S6)
it is evident that in the range of 0 and 1.4 eV only p-type
orbitals of Pb contribute to the electronic states in both with
and without SOC cases.

■ CONCLUSIONS
A comparative study between DFT and DFTB using the new
set of Slater-Koster parameters has been presented. It was
found that our parameter set provides a good qualitative
description for systems composed of C, Si, and Pb atoms. In
the case of bulk Pb, significant impacts of spin−orbit coupling
(SOC) were observed, particularly affecting the p-type bands
around the Γ, L, andM symmetry points. Investigation into the
three configurations of plumbene revealed that due to a
substantial lattice Coulomb repulsive potential, the hexagonal
Pb structure prefers to form buckled structures. Among these,
the high buckled structure exhibited the lowest energy.
Furthermore, while the planar and high buckled structures
are metallic, the low buckled structure exhibits a band gap of
0.5 and 0.15 eV in DFT and DFTB, respectively. In order to
evaluate the performance of the complete set of parameters, we
examined a SiC(0001)-(1 × 1)-Pb system, where Pb can
occupy three absorption positions: T1, T4, and H3. It was
found that the most stable structure occurs when the Pb atom
is positioned at T1. In the absence of SOC, a quasi-linear
dispersion was observed around −1.2 eV below the Fermi level
at the K point, with a small gap of approximately 0.13 and 0.1
eV in DFT and DFTB, respectively. Upon adding SOC, the
bands split and the linear dispersion disappeared. Therefore,
the spin−orbit interaction plays an important role in the
system and strongly affects its electronic structure. Overall, our
parameter set for DFTB calculations enables an accurate
qualitative description of these systems. As DFTB is a
computationally efficient method, this opens the possibility
to investigate bigger systems closer to the structures observed
experimentally.

■ ASSOCIATED CONTENT

*sı Supporting Information
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351.

Slater−Koster tables used in this manuscript (ZIP)

Supplementary results (PDF)

■ AUTHOR INFORMATION
Corresponding Author

Sibylle Gemming − Technische Universität Chemnitz, Institut
für Physik, 09107 Chemnitz, Germany; orcid.org/0000-
0003-0455-1945; Email: sibylle.gemming@physik.tu-
chemnitz.de

Authors
Andres Unigarro − Technische Universität Chemnitz, Institut
für Physik, 09107 Chemnitz, Germany; orcid.org/0009-
0002-3283-5283

Florian Günther − Departamento de Física, Universidade
Estadual Paulista, Instituto de Geocien̂cias e Cien̂cias Exatas,
Rio Claro 13506-900, Brazil; orcid.org/0000-0001-
5002-4172

Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.jpcc.4c07351

Notes
The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS
The authors acknowledge funding from the Deutsche
Forschungsgemeinschaft via FOR 5242, project T1
(449119662), and Fundação de Amparo a ̀ Pesquisa do Estado
de São Paulo via 2024/07315-1.

■ REFERENCES
(1) Hohenberg, P.; Kohn, W. Density functional theory (DFT).
Phys. Rev. 1964, 136, B864.
(2) Kohn, W.; Sham, L. J. Self-consistent equations including
exchange and correlation effects. Physical review 1965, 140, A1133.
(3) Pakdel, S.; Rasmussen, A.; Taghizadeh, A.; Kruse, M.; Olsen, T.;
Thygesen, K. S. High-throughput computational stacking reveals
emergent properties in natural van der Waals bilayers. Nat. Commun.
2024, 15, 932.
(4) Ohta, T.; Bostwick, A.; Seyller, T.; Horn, K.; Rotenberg, E.
Controlling the Electronic Structure of Bilayer Graphene. Science
2006, 313, 951−954.
(5) Forbeaux, I.; Themlin, J.-M.; Debever, J.-M. Heteroepitaxial
graphite on 6H−SiC(0001): Interface formation through conduction-
band electronic structure. Phys. Rev. B 1998, 58, 16396−16406.
(6) Cavallucci, T.; Tozzini, V. Multistable Rippling of Graphene on
SiC: A Density Functional Theory Study. J. Phys. Chem. C 2016, 120,
7670−7677.
(7) Leach, A. R. Molecular modelling: principles and applications;
Pearson Education, 2001.
(8) Naik, M. H.; Maity, I.; Maiti, P. K.; Jain, M. Kolmogorov−Crespi
Potential For Multilayer Transition-Metal Dichalcogenides: Captur-
ing Structural Transformations in Moire ́ Superlattices. J. Phys. Chem.
C 2019, 123, 9770−9778.
(9) Liang, Q.; Jiang, W.; Liu, Y.; Ouyang, W. Anisotropic Interlayer
Force Field for Two-Dimensional Hydrogenated Carbon Materials
and Their Heterostructures. J. Phys. Chem. C 2023, 127, 18641−
18651.
(10) Seifert, G.; Eschrig, H.; Bieger, W. An approximation variant of
LCAO-X-ALPHA methods. Z. Phys. Chem. Leipzig 1986, 267, 529−
539.
(11) Porezag, D.; Frauenheim, T.; Köhler, T.; Seifert, G.; Kaschner,
R. Construction of tight-binding-like potentials on the basis of
density-functional theory: Application to carbon. Phys. Rev. B 1995,
51, 12947.
(12) Seifert, G.; Porezag, D.; Frauenheim, T. Calculations of
molecules, clusters, and solids with a simplified LCAO-DFT-LDA
scheme. International journal of quantum chemistry 1996, 58, 185−192.

The Journal of Physical Chemistry C pubs.acs.org/JPCC Article

https://doi.org/10.1021/acs.jpcc.4c07351
J. Phys. Chem. C 2025, 129, 5617−5624

5623

https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?goto=supporting-info
https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_001.zip
https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c07351/suppl_file/jp4c07351_si_002.pdf
https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Sibylle+Gemming"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf
https://orcid.org/0000-0003-0455-1945
https://orcid.org/0000-0003-0455-1945
mailto:sibylle.gemming@physik.tu-chemnitz.de
mailto:sibylle.gemming@physik.tu-chemnitz.de
https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Andres+Unigarro"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf
https://orcid.org/0009-0002-3283-5283
https://orcid.org/0009-0002-3283-5283
https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Florian+Gu%CC%88nther"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf
https://orcid.org/0000-0001-5002-4172
https://orcid.org/0000-0001-5002-4172
https://pubs.acs.org/doi/10.1021/acs.jpcc.4c07351?ref=pdf
https://doi.org/10.1103/PhysRev.136.B864
https://doi.org/10.1103/PhysRev.140.A1133
https://doi.org/10.1103/PhysRev.140.A1133
https://doi.org/10.1038/s41467-024-45003-w
https://doi.org/10.1038/s41467-024-45003-w
https://doi.org/10.1126/science.1130681
https://doi.org/10.1103/PhysRevB.58.16396
https://doi.org/10.1103/PhysRevB.58.16396
https://doi.org/10.1103/PhysRevB.58.16396
https://doi.org/10.1021/acs.jpcc.6b01356?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/acs.jpcc.6b01356?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/acs.jpcc.8b10392?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/acs.jpcc.8b10392?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/acs.jpcc.8b10392?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/acs.jpcc.3c03275?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/acs.jpcc.3c03275?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/acs.jpcc.3c03275?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1103/PhysRevB.51.12947
https://doi.org/10.1103/PhysRevB.51.12947
https://doi.org/10.1002/(SICI)1097-461X(1996)58:2<185::AID-QUA7>3.0.CO;2-U
https://doi.org/10.1002/(SICI)1097-461X(1996)58:2<185::AID-QUA7>3.0.CO;2-U
https://doi.org/10.1002/(SICI)1097-461X(1996)58:2<185::AID-QUA7>3.0.CO;2-U
pubs.acs.org/JPCC?ref=pdf
https://doi.org/10.1021/acs.jpcc.4c07351?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as


(13) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.;
Frauenheim, T.; Suhai, S.; Seifert, G. Self-consistent-charge density-
functional tight-binding method for simulations of complex materials
properties. Phys. Rev. B 1998, 58, 7260.
(14) Seifert, G. Tight-binding density functional theory: an
approximate Kohn- Sham DFT scheme. J. Phys. Chem. A 2007, 111,
5609−5613.
(15) Fowler, P.; Heine, T.; Manolopoulos, D.; Mitchell, D.; Orlandi,
G.; Schmidt, R.; Seifert, G.; Zerbetto, F. Energetics of fullerenes with
four-membered rings. J. Phys. Chem. 1996, 100, 6984−6991.
(16) Ivanovskaya, V. V.; Ranjan, N.; Heine, T.; Merino, G.; Seifert,
G. Molecular dynamics study of the mechanical and electronic
properties of carbon nanotubes. Small 2005, 1, 399−402.
(17) Frauenheim, T.; Weich, F.; Köhler, T.; Uhlmann, S.; Porezag,
D.; Seifert, G. Density-functional-based construction of transferable
nonorthogonal tight-binding potentials for Si and SiH. Phys. Rev. B
1995, 52, 11492.
(18) Frauenheim, T.; Seifert, G.; Elstner, M.; Niehaus, T.; Köhler,
C.; Amkreutz, M.; Sternberg, M.; Hajnal, Z.; Di Carlo, A.; Suhai, S.
Atomistic simulations of complex materials: ground-state and excited-
state properties. J. Phys.: Condens. Matter 2002, 14, 3015.
(19) Liu, H.; Elstner, M.; Kaxiras, E.; Frauenheim, T.; Hermans, J.;
Yang, W. Quantum mechanics simulation of protein dynamics on long
timescale. Proteins: Struct., Funct., Bioinf. 2001, 44, 484−489.
(20) Nair, M. N.; Palacio, I.; Celis, A.; Zobelli, A.; Gloter, A.;
Kubsky, S.; Turmaud, J.-P.; Conrad, M.; Berger, C.; de Heer, W.; et al.
Band gap opening induced by the structural periodicity in epitaxial
graphene buffer layer. Nano Lett. 2017, 17, 2681−2689.
(21) Slater, J. C.; Koster, G. F. Simplified LCAO method for the
periodic potential problem. Physical review 1954, 94, 1498.
(22) Yang, D.; Xia, Q.; Gao, H.; Dong, S.; Zhao, G.; Zeng, Y.; Ma,
F.; Hu, T. Fabrication and mechanism of Pb-intercalated graphene on
SiC. Appl. Surf. Sci. 2021, 569, No. 151012.
(23) Schädlich, P.; Ghosal, C.; Stettner, M.; Matta, B.; Wolff, S.;
Schölzel, F.; Richter, P.; Hutter, M.; Haags, A.; Wenzel, S.; et al.
Domain Boundary Formation Within an Intercalated Pb Monolayer
Featuring Charge-Neutral Epitaxial Graphene. Adv. Mater. Interfaces
2023, 10, No. 2300471.
(24) Matta, B.; Rosenzweig, P.; Bolkenbaas, O.; Küster, K.; Starke,
U. Momentum microscopy of Pb-intercalated graphene on SiC:
Charge neutrality and electronic structure of interfacial Pb. Physical
Review Research 2022, 4, No. 023250.
(25) Hsu, C.-H.; Ozolins, V.; Chuang, F.-C. First-principles study of
Bi and Sb intercalated graphene on SiC(0001) substrate. Surf. Sci.
2013, 616, 149−154.
(26) Mamiyev, Z.; Tegenkamp, C. Sn intercalation into the BL/
SiC(0001) interface: A detailed SPA-LEED investigation. Surfaces and
Interfaces 2022, 34, No. 102304.
(27) Yang, K.; Wang, Y.; Liu, C.-X. Momentum-Space Spin
Antivortex and Spin Transport in Monolayer Pb. Phys. Rev. Lett.
2022, 128, No. 166601.
(28) Visikovskiy, A.; Hayashi, S.; Kajiwara, T.; Komori, F.; Yaji, K.;
Tanaka, S. Computational study of heavy group IV elements (Ge, Sn,
Pb) triangular lattice atomic layers on SiC(0001) surface. arXiv 2018.
(29) Schölzel, F.; Richter, P.; Unigarro, A. D. P.; Wolff, S.; Schwarz,
H.; Schütze, A.; Rösch, N.; Gemming, S.; Seyller, T.; Schädlich, P.
Large-Area Lead Monolayers under Cover: Intercalation, Doping, and
Phase Transformation. Small Struct. 2025, 6, No. 2400338.
(30) Koskinen, P.; Mäkinen, V. Density-functional tight-binding for
beginners. Comput. Mater. Sci. 2009, 47, 237−253.
(31) Elstner, M.; Seifert, G. Density functional tight binding.
Philosophical Transactions of the Royal Society A: Mathematical, Physical
and Engineering Sciences 2014, 372, 20120483.
(32) Foulkes, W. M. C.; Haydock, R. Tight-binding models and
density-functional theory. Phys. Rev. B 1989, 39, 12520.
(33) Parr, R. G. Density functional theory. Annu. Rev. Phys. Chem.
1983, 34, 631−656.
(34) Fiolhais, C.; Nogueira, F.; Marques, M. A. A primer in density
functional theory; Springer Science & Business Media, 2003; Vol. 620.

(35) Oliveira, A. F.; Seifert, G.; Heine, T.; Duarte, H. A. Density-
functional based tight-binding: an approximate DFT method. J. Braz.
Chem. Soc. 2009, 20, 1193−1205.
(36) Mulliken, R. S. Electronic population analysis on LCAO−MO
molecular wave functions. I. The Journal of chemical physics 1955, 23,
1833−1840.
(37) Panosetti, C.; Anniés, S. B.; Grosu, C.; Seidlmayer, S.; Scheurer,
C. DFTB modeling of lithium-intercalated graphite with machine-
learned repulsive potential. J. Phys. Chem. A 2021, 125, 691−699.
(38) Eschrig, H. Optimized LCAO Method and the Electronic Structure
of Extended Systems; De Gruyter: Berlin, Boston, 1988.
(39) Gonze, X.; Amadon, B.; Anglade, P.-M.; Beuken, J.-M.; Bottin,
F.; Boulanger, P.; Bruneval, F.; Caliste, D.; Caracas, R.; Côté, M.;
et al. ABINIT: First-principles approach to material and nanosystem
properties. Comput. Phys. Commun. 2009, 180, 2582−2615.
(40) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient
approximation made simple. Physical review letters 1996, 77, 3865.
(41) Aradi, B.; Hourahine, B.; Frauenheim, T. DFTB+, a sparse
matrix-based implementation of the DFTB method. J. Phys. Chem. A
2007, 111, 5678−5684.
(42) Wahiduzzaman, M.; Oliveira, A. F.; Philipsen, P.; Zhechkov, L.;
Van Lenthe, E.; Witek, H. A.; Heine, T. DFTB parameters for the
periodic table: Part 1, electronic structure. J. Chem. Theory Comput.
2013, 9, 4006−4017.
(43) Frenzel, J.; Oliveira, A.; Jardillier, N.; Heine, T.; Seifert, G.
Semi-relativistic, self-consistent charge Slater-Koster tables for
density-functional based tight-binding (DFTB) for materials science
simulations. Zeolites 2004, 2, 7.
(44) Perdew, J. P.; Wang, Y. Accurate and simple analytic
representation of the electron-gas correlation energy. Phys. Rev. B
1992, 45, 13244−13249.
(45) Wang, X.; Zhao, J.; Xu, Z.; Djurabekova, F.; Rommel, M.; Song,
Y.; Fang, F. Density functional theory calculation of the properties of
carbon vacancy defects in silicon carbide. Nanotechnology and Precision
Engineering (NPE) 2020, 3, 211−217.
(46) Zubizarreta, X.; Silkin, V. M.; Chulkov, E. V. First-principles
quasiparticle damping rates in bulk lead. Phys. Rev. B 2011, 84,
No. 115144.
(47) Heid, R.; Bohnen, K.-P.; Sklyadneva, I. Y.; Chulkov, E. Effect of
spin-orbit coupling on the electron-phonon interaction of the
superconductors Pb and Tl. Phys. Rev. B 2010, 81, No. 174527.
(48) Sklyadneva, I. Y.; Heid, R.; Echenique, P. M.; Bohnen, K.-B.;
Chulkov, E. V. Electron-phonon interaction in bulk Pb: Beyond the
Fermi surface. Phys. Rev. B 2012, 85, No. 155115.
(49) Zubizarreta, X.; Silkin, V. M.; Chulkov, E. V. Ab initio study of
low-energy collective electronic excitations in bulk Pb. Phys. Rev. B
2013, 87, No. 115112.
(50) Lu, Y.; Zhou, D.; Wang, T.; Yang, S. A.; Jiang, J. Topological
properties of atomic lead film with honeycomb structure. Sci. Rep.
2016, 6, 21723.
(51) Farzaneh, S.; Rakheja, S. Spin splitting and spin Hall
conductivity in buckled monolayers of group 14: First-principles
calculations. Phys. Rev. B 2021, 104, No. 115205.
(52) Rivero, P.; Yan, J.-A.; Garcia-Suarez, V. M.; Ferrer, J.; Barraza-
Lopez, S. Stability and properties of high-buckled two-dimensional tin
and lead. Phys. Rev. B 2014, 90, No. 241408.
(53) Yuhara, J.; He, B.; Matsunami, N.; Nakatake, M.; Le Lay, G.
Graphene’s latest cousin: Plumbene epitaxial growth on a “nano
WaterCube”. Adv. Mater. 2019, 31, No. 1901017.
(54) Takeda, K.; Shiraishi, K. Theoretical possibility of stage
corrugation in Si and Ge analogs of graphite. Phys. Rev. B 1994, 50,
14916.
(55) Krawiec, M. Functionalization of group-14 two-dimensional
materials. J. Phys.: Condens. Matter 2018, 30, 233003.
(56) Yu, X.-L.; Huang, L.; Wu, J. From a normal insulator to a
topological insulator in plumbene. Phys. Rev. B 2017, 95, No. 125113.

The Journal of Physical Chemistry C pubs.acs.org/JPCC Article

https://doi.org/10.1021/acs.jpcc.4c07351
J. Phys. Chem. C 2025, 129, 5617−5624

5624

https://doi.org/10.1103/PhysRevB.58.7260
https://doi.org/10.1103/PhysRevB.58.7260
https://doi.org/10.1103/PhysRevB.58.7260
https://doi.org/10.1021/jp069056r?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/jp069056r?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/jp9532226?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/jp9532226?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1002/smll.200400110
https://doi.org/10.1002/smll.200400110
https://doi.org/10.1103/PhysRevB.52.11492
https://doi.org/10.1103/PhysRevB.52.11492
https://doi.org/10.1088/0953-8984/14/11/313
https://doi.org/10.1088/0953-8984/14/11/313
https://doi.org/10.1002/prot.1114
https://doi.org/10.1002/prot.1114
https://doi.org/10.1103/PhysRev.94.1498
https://doi.org/10.1103/PhysRev.94.1498
https://doi.org/10.1016/j.apsusc.2021.151012
https://doi.org/10.1016/j.apsusc.2021.151012
https://doi.org/10.1002/admi.202300471
https://doi.org/10.1002/admi.202300471
https://doi.org/10.1103/PhysRevResearch.4.023250
https://doi.org/10.1103/PhysRevResearch.4.023250
https://doi.org/10.1016/j.susc.2013.06.002
https://doi.org/10.1016/j.susc.2013.06.002
https://doi.org/10.1016/j.surfin.2022.102304
https://doi.org/10.1016/j.surfin.2022.102304
https://doi.org/10.1103/PhysRevLett.128.166601
https://doi.org/10.1103/PhysRevLett.128.166601
https://doi.org/10.48550/arXiv.1809.00829
https://doi.org/10.48550/arXiv.1809.00829
https://doi.org/10.1002/sstr.202400338
https://doi.org/10.1002/sstr.202400338
https://doi.org/10.1016/j.commatsci.2009.07.013
https://doi.org/10.1016/j.commatsci.2009.07.013
https://doi.org/10.1098/rsta.2012.0483
https://doi.org/10.1103/PhysRevB.39.12520
https://doi.org/10.1103/PhysRevB.39.12520
https://doi.org/10.1146/annurev.pc.34.100183.003215
https://doi.org/10.1590/S0103-50532009000700002
https://doi.org/10.1590/S0103-50532009000700002
https://doi.org/10.1063/1.1740588
https://doi.org/10.1063/1.1740588
https://doi.org/10.1021/acs.jpca.0c09388?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/acs.jpca.0c09388?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1016/j.cpc.2009.07.007
https://doi.org/10.1016/j.cpc.2009.07.007
https://doi.org/10.1103/PhysRevLett.77.3865
https://doi.org/10.1103/PhysRevLett.77.3865
https://doi.org/10.1021/jp070186p?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/jp070186p?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/ct4004959?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1021/ct4004959?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as
https://doi.org/10.1103/PhysRevB.45.13244
https://doi.org/10.1103/PhysRevB.45.13244
https://doi.org/10.1016/j.npe.2020.11.002
https://doi.org/10.1016/j.npe.2020.11.002
https://doi.org/10.1103/PhysRevB.84.115144
https://doi.org/10.1103/PhysRevB.84.115144
https://doi.org/10.1103/PhysRevB.81.174527
https://doi.org/10.1103/PhysRevB.81.174527
https://doi.org/10.1103/PhysRevB.81.174527
https://doi.org/10.1103/PhysRevB.85.155115
https://doi.org/10.1103/PhysRevB.85.155115
https://doi.org/10.1103/PhysRevB.87.115112
https://doi.org/10.1103/PhysRevB.87.115112
https://doi.org/10.1038/srep21723
https://doi.org/10.1038/srep21723
https://doi.org/10.1103/PhysRevB.104.115205
https://doi.org/10.1103/PhysRevB.104.115205
https://doi.org/10.1103/PhysRevB.104.115205
https://doi.org/10.1103/PhysRevB.90.241408
https://doi.org/10.1103/PhysRevB.90.241408
https://doi.org/10.1002/adma.201901017
https://doi.org/10.1002/adma.201901017
https://doi.org/10.1103/PhysRevB.50.14916
https://doi.org/10.1103/PhysRevB.50.14916
https://doi.org/10.1088/1361-648X/aac149
https://doi.org/10.1088/1361-648X/aac149
https://doi.org/10.1103/PhysRevB.95.125113
https://doi.org/10.1103/PhysRevB.95.125113
pubs.acs.org/JPCC?ref=pdf
https://doi.org/10.1021/acs.jpcc.4c07351?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as