Theoretical study of the structure of self-assembled monolayers of short alkylthiolates on Au(111) and Ag(111): the role of induced substrate reconstruction and chain-chain interactions.

Abstract

We compare the stability of various structures of high coverage self-assembled monolayers (SAMs) of short alkylthiolates, S(CH(2))(n-1)CH(3) (= C(n)), on Ag(111) and Au(111). We employ: (i) the ab initio thermodynamics approach based on density functional theory (DFT) calculations, to compare the stability of SAMs of C(1) (with coverages Θ = 3/7 and 1/3) on both substrates, and (ii) a set of pairwise interatomic potentials derived from second-order Møller-Plesset (MP2) perturbation theory calculations, to estimate the role of chain-chain (Ch-Ch) interactions in the structure and stability of SAMs of longer chain alkylthiolates. For C(1)/Ag(111) (C(1)/Au(111)) the SAM with Θ = 3/7 is more (less) stable than for Θ = 1/3 in a wide range of temperatures and pressures in line with experiments. In addition, for the molecular densities of SAMs corresponding to Θ = 3/7 and 1/3, the MP2-based Ch-Ch interaction potential also predicts the different chain orientations observed experimentally in SAMs of alkylthiolates on Ag(111) and Au(111). Thus, for short length alkylthiolates, a simple model based on first principles calculations that separately accounts for molecule-surface (M-S) and Ch-Ch interactions succeeds in predicting the main structural differences between the full coverage SAMs usually observed experimentally on Ag(111) and Au(111).

Full text

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This journal is c the Owner Societies 2011Phys. Chem. Chem. Phys., 2011, 13,9353–93629353
Citethis: Phys. Chem. Chem. Phys.,2011,13,9353–9362
Theoretical study of the structure of self-assembled monolayers of short
alkylthiolates on Au(111) and Ag(111): the role of induced substrate
reconstruction and chain–chain interactions
P. N. Abufager,aJ. G. Solano Canchaya,aY. Wang,bM. Alcamı´,bF. Martı´n,bc
L. Alvarez Soria,dM. L. Martiarena,dK. Reutereand H. F. Busnengo*a
Received 10th November 2010, Accepted 8th March 2011
DOI: 10.1039/c0cp02490b
We compare the stability of various structures of high coverage self-assembled monolayers
(SAMs) of short alkylthiolates, S(CH2)n?1CH3(= Cn), on Ag(111) and Au(111). We employ:
(i) the ab initio thermodynamics approach based on density functional theory (DFT) calculations,
to compare the stability of SAMs of C1(with coverages Y = 3/7 and 1/3) on both substrates,
and (ii) a set of pairwise interatomic potentials derived from second-order Møller-Plesset
(MP2) perturbation theory calculations, to estimate the role of chain–chain (Ch–Ch)
interactions in the structure and stability of SAMs of longer chain alkylthiolates. For
C1/Ag(111) (C1/Au(111)) the SAM with Y = 3/7 is more (less) stable than for Y = 1/3
in a wide range of temperatures and pressures in line with experiments. In addition, for the
molecular densities of SAMs corresponding to Y = 3/7 and 1/3, the MP2-based Ch–Ch
interaction potential also predicts the different chain orientations observed experimentally
in SAMs of alkylthiolates on Ag(111) and Au(111). Thus, for short length alkylthiolates,
a simple model based on first principles calculations that separately accounts for
molecule–surface (M–S) and Ch–Ch interactions succeeds in predicting the main
structural differences between the full coverage SAMs usually observed experimentally
on Ag(111) and Au(111).
I.Introduction
Self-assembled monolayers (SAMs) are well ordered organic
layers spontaneously formed upon adsorption, in solution or
in ultra high vacuum, of molecules containing one or more head-
groups that present strong affinity to the substrate.1Their
relativelysimplepreparation,stability,long-rangetwo-dimensional
epitaxy (at the nanometer scale), easy functionalization and
the great variety of molecules (including biomolecules2) that
can be used as building blocks give SAMs a wide range of
potential technological applications. For instance, corrosion
inhibition, lithography, molecular recognition and molecular
electronics (see e.g. refs. 3–8 and references therein).
Metal surfaces and sulfur-containing molecules such as
alkylthiolates [S(CH2)n?1CH3, hereafter referred to as Cn] have
been extensively used during the last 30 years as benchmark
systems for the understanding of the growth kinetics and
structural properties of SAMs. In spite of the large number
of theoretical investigations focused on SAMs of Cnon metal
surfaces, various questions on the origin of their structures
remain open. Concerning Ag(111) and Au(111) (the two most
widely used metal surfaces for preparation of SAMs), it is not
completely clear why substrates with very similar electronic
structures (Ag and Au are iso-electronic) and lattice constants
(aAg= 4.09 A˚and aAu= 4.08 A˚) give rise to very different
SAM structures. For instance, on Ag(111) the saturation
coverage (1 ML), Y, is 3/79and the tilt angle of the chains
with respect to the surface normal, y, is B0–151,10–13whereas
on Au(111) Y = 1/3 and y B30–401.14–16
For Y = 3/7, the molecular density (number of alkylthiolates
per unit area) is very close to that of the orthorhombic phase
of bulk n-alkanes (r B 0.054 mol A˚?2) and the value of the
nearest-neighbor S–S distance, d, is incompatible with adsorp-
tion on all equivalent sites of the ideal (unreconstructed)
aLaboratorio de Colisiones Ato ´micas, Facultad de Ciencias Exactas
Ingenierı´a y Agrimensura, Universidad Nacional de Rosario (UNR)
and Instituto de Fı´sica de Rosario, Consejo Nacional de
Investigaciones Cientı´ficas y Te´cnicas (CONICET),
Av. Pellegrini 250 (2000) Rosario, Argentina.
E-mail: busnengo@ifir-conicet.gov.ar; Fax: +54 341 4802654
bDepartamento de Quı´mica C-13, Universidad Auto ´noma de Madrid,
28049 Madrid, Spain
cInstituto Madrilen ˜o de Estudios Avanzados en Nanociencia
(IMDEA-Nanociencia), Cantoblanco, 28049 Madrid, Spain
dCentro Ato ´mico Bariloche and Instituto Balseiro, Av. Bustillos 9500,
8400 S. C. de Bariloche, Argentina
eDepartment Chemie, Technische Universita¨t Mu ¨nchen,
Lichtenbergstr. 4, D-85747 Garching, Germany
PCCP
Dynamic Article Links
www.rsc.org/pccp
PAPER

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9354Phys. Chem. Chem. Phys., 2011, 13,9353–9362This journal is c the Owner Societies 2011
Ag(111) surface. This has been interpreted in terms of a weak
energetic corrugation of the Cn/Ag(111) potential energy
surface (PES)17against which the attractive chain–chain van
der Waals interaction prevails. In contrast, Y = 1/3 corres-
ponds to r B 0.046 mol A˚?2and d ?
consistent with adsorption on all equivalent sites of the ideal
Au(111) surface. This has been ascribed to a large energetic
corrugation of the Cn/Au(111) PES, preventing the molecules
to approach to each other to maximize their mutual van
der Waals (vdW) attractive interactions (see e.g. ref. 4 and
references therein). In line with these arguments, density
functional theory (DFT)18,19results pointing to a PES of
C1/Au(111) with a higher energetic corrugation than for
C1/Ag(111) have been reported.20However, in recent years
there is increasing evidence for a strong thiolate-induced
reconstruction of both Ag(111) and Au(111) (see e.g.
ref. 21–33 and references therein). Still most theoretical studies
carried out so far have been restricted to the coverage
observed experimentally for each substrate, i.e. Y = 3/7 for
Ag(111) and Y = 1/3 for Au(111). Though such investigations
do provide extremely valuable information, they do not allow
one to address why the dense SAMs on Ag(111) and Au(111)
present different coverages. This certainly requires to investi-
gate (at least) SAM structures with Y = 1/3 and 3/7 for both
substrates.
In this work we compare the stability of various structures
of SAMs of Cnwith Y = 1/3 and 3/7 on both Au(111) and
Ag(111). In order to separate the contribution of the molecule–
surface (M–S) bond strength and chain–chain (Ch–Ch) inter-
actions we use:
(i) DFT calculations and the ab initio thermodynamics
approach to investigate the stability of various structures of
methylthiolates for which vdW interactions are very small, and
(ii) a recently derived set of pairwise interatomic potentials34
based on second order Møller–Plesset (MP2)35calculations to
account for the effect of Ch–Ch interactions in SAMs of
longer chain alkylthiolates.
In section II we briefly describe the ab initio thermo-
dynamics approach.36In section III we present DFT results
for C1/Ag(111) and C1/Au(111), and in section IV we compute
the optimum orientation of the chains as a function of the
molecular density of the SAM and we discuss the possible
contribution of Ch–Ch interactions to the stability of SAMs of
alkylthiolates as a function of the chain length. Finally, in
section V we summarize the main conclusions of our study.
ffiffiffi
3
p
ðaAu=
ffiffiffi
2
p
Þ, that is
II.
approach
Phase stabilities: the ab initio thermodynamics
In this section we focus on SAMs of methylthiolates but the
generalization of the analysis for longer alkylthiolates is
straightforward. The reactive adsorption of methanethiol on
noble metal (111) surfaces is hindered by large activation energy
barriers.37Then, SAMs of methylthiolates on Au(111) and
Ag(111) are usually prepared by dosing the surface with
dimethyl disulfide molecules, H3CS–SCH3(= (SCH3)2), which
dissociatively adsorb on the surface through the reaction:
(SCH3)2+ 2* - 2SCH3*,(1)
where * represents a generic adsorption site. Therefore, we will
consider a monolayer of SCH3in thermodynamic equilibrium
with a reservoir of (SCH3)2molecules.
At given values of temperature, T, and pressure, p, of
the reservoir the most stable structure will be that with the
lowest Gibbs free energy of adsorption per unit area,
DGad[DmSCH3(T,p)],36
DGad½DmSCH3ðT;pÞ? ’m
A½E ? DmSCH3ðT;pÞ?:
ð2Þ
In eqn (2), A is the area of the unit cell, m is the number of
chemisorbed molecules within the unit cell, E is the binding
energy per methylthiolate and mSCH3(T,p) is the SCH3chemical
potential in the reservoir. The latter expression is approximate
as it equates the difference of the solid Gibbs free energies to
the corresponding difference of their total energies. As such it
neglects small free energy contributions that arise predominantly
from the change of adsorbate vibrational properties (e.g. zero
point energies and vibrational entropy) upon adsorption.36
The term DmSCH3(T,p) that accounts for the energy cost
of removing one methylthiolate from the reservoir at T,p,
can be computed from tabulated enthalpy and entropy values
of (SCH3)2at standard pressure p0= 1 atm (i.e. DH0
S0
ðSCH3Þ2and
ðSCH3Þ2respectively)38using the expression:39
DmSCH3ðT;pÞ ¼1
2DmðSCH3Þ2ðT;p0Þ þ1
2kBTln
p
p0
??
¼1
2
DH0
ðSCH3Þ2? TS0
ðSCH3Þ2
hi
þ1
2kBTln
p
p0
??
;
ð3Þ
with kBbeing the Boltzmann constant.
Let us consider the case of a SAM-induced surface reconstruc-
tion involving X substrate vacancies (v) and Y substrate
ad-atoms (a) per unit cell. In such a case, the remaining energy
term in eqn (2),
E = Eb+ Erec/m,(4)
receives contributions from the average adsorption energy
per thiolate on the clean reconstructed surface, M(111)-Xv,Ya
(M = Au, Ag),
Eb ¼E½mSCH3=Mð111Þ-Xv;Ya? ? E½Mð111Þ-Xv;Ya?
m
?E½ðSCH3Þ2?
2
ð5Þ
and the energy cost per unit cell of producing M(111)-Xv,Ya
from the clean unreconstructed surface (i.e. X = Y = 0),
M(111)-0v,0a,
Erec= E[M(111)-Xv,Ya] ? E[M(111)-0v,0a] + (X ? Y)Ebulk
M .
(6)
Here,
E[M(111)-0v,0a] are the total energies of the structure formed
by m methylthiolates chemisorbed on M(111)-Xv,Ya, of the
corresponding clean reconstructed surface M(111)-Xv,Ya,
and of the clean unreconstructed surface, M(111)-0v,0a, respec-
tively. E[(SCH3)2] is the total energy of gas-phase (SCH3)2
E[mSCH3/M(111)-Xv,Ya],E[M(111)-Xv,Ya],and

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This journal is c the Owner Societies 2011Phys. Chem. Chem. Phys., 2011, 13,9353–9362 9355
and Ebulk
X a Y, we assume that the removed (added) M substrate
atoms attach to (come from) surface kink sites.40In practice,
we have evaluated E[M(111)-Xv,Ya] by fully optimizing
the geometry of the clean surface after removing the
m methylthiolates from the structure mSCH3/M(111)-Xv,Ya.
From eqn (2), it is clear that the relative stability of
structures with the same coverage does not depend on the
specific gas-phase conditions: the most stable is the one with
the lowest adsorption energy per molecule, E. On the other
hand, for T = 0 K, DmSCH3= 0, and the most stable structure
is the one with the lowest total adsorption energy per
unit area,
M
is the total energy per atom of bulk M, i.e. whenever
rE ?m
AE ¼YE
AM
1?1
ð7Þ
where r = m/A, AM
unit cell
(AM
M
the relative stability of adsorption structures with different
coverages is determined by rE instead of simply E. Therefore,
the argument that adsorption at non-equivalent sites implies
that Ch–Ch interactions prevail over the energetic corrugation
of the alkylthiolate/Ag(111) PES is not strictly valid. Even
without any attractive Ch–Ch interaction, a higher coverage
(e.g. Y = 3/7 > 1/3) involving non-equivalent adsorption sites
can entail a smaller (negative) value of rE, and so, a higher
stability.
It is importantto note that, in deriving eqn (6) we have assumed
that the ground state of the clean M(111) (M = Ag,Au) surface is
the ideal M-(1?1) structure, while it is well known that for Au, the
most stable structure corresponds to the so-called herringbone
addedrowreconstruction(22 ?
Au-ð22 ?
only 0:43 eV=½22 ?
B10–20 times smaller than the typical rE values of the SAMs
considered in this work (see Tables 1, 2 and 3 below). Therefore,
the use of eqn (6) for Au is totally justified for our purposes.
1?1is the area of the (1 ? 1) primitive
unreconstructedsurface
=4). Thus, for a given substrate and T B 0 K,
of
p
theM(111)-0v,0a
1?1¼ a2
ffiffiffi
3
ffiffiffi
3
process
ffiffiffi
p
).However,theAu-ð1 ? 1Þ !
isexothermic
2
Þ2? ? 1 meV ˚A?2.41This is
ffiffiffi
3
p
Þ
reconstruction
ffiffiffi
by
3
p
? ðaAu=
p
III.
DFT calculations
SCH3adsorption on Ag(111) and Au(111):
AComputational details
All the DFT results we present below have been obtained by
solving the one-electron Kohn–Sham equation19within the
generalized gradient approximation proposed by Perdew and
Wang42(PW91) to treat electronic exchange and correlation.
We have used a plane wave basis set and the projected
augmented wave (PAW) method43implemented in the Vienna
ab initio simulation package (VASP) (see refs. 44–49 for a
review) with an energy cut-off of 450 eV. Thus, core and
valence electrons are treated within a fully relativistic frame-
work and a scalar relativistic approximation, respectively.48,49
The surfaces were represented by five-layer slabs. In all
calculations we have allowed the relaxation of the substrate
atoms in the three topmost layers, as well as all the atoms of
the adsorbates whereas the substrate atoms in the two bottom
layers were kept fixed in their equilibrium positions in bulk.
All the geometry optimizations were carried out until reaching
forces on every mobile atom smaller than 0.02 eV A˚?1. The
SCH3molecules were adsorbed at one side of the slab and
all the calculations were spin restricted. We have used the
electronic smearing method proposed by Methfessel and
Paxton with N = 1 and s = 0.2 eV50and the DFT total
energies reported were extrapolated to 0 K. The sampling of
the first Brillouin Zone for both substrates, was carried
out according to the Monkhorst and Pack method51with
meshes 13 ? 13 ? 1, 7 ? 13 ? 1, 7 ? 7 ? 1, 7 ? 7 ? 1, and
9 ? 9 ? 1 for the unit cells ð
ð2
For brevity, the latter unit cells will be hereafter referred to as
R3.R3, 2R3.R3, 2R3.2R3, c(4 ? 2) and R7.R7 respectively.
With the settings mentioned above, the resulting binding energies
per methylthiolate reported are converged within B0.01 eV and
Ebulk
Au = ?3.201 eV.
ffiffiffi
3
p
?
ffiffiffi
3
p
ffiffiffi
ÞR30?, ð2
?
ffiffiffi
3
p
?
ffiffiffi
3
p
ÞR30?,
ffiffiffi
3
p
? 2
ffiffiffi
3
p
ÞR30?, c(4 ? 2), and ð
7
p ffiffiffi
7
p
ÞR19:1?respectively.
Ag = ?2.727 eV and Ebulk
BResults
For C1/Au(111) and C1/Ag(111) we have considered various
structures corresponding to the coverages observed experi-
mentally for SAMs of alkylthiolates on both substrates: i.e.
Y = 1/3 and 3/7, respectively. The choice of the unit cells was
motivated by the fact that (see ref. 25 and references therein):
(i) for SAMs on Au(111), a R3.R3 pattern with one molecule
per unit cell is usually observed, as well as a derived super-
structure exhibiting a rectangular ð3 ? 2
as usual, c(4 ? 2)] with four adsorbed molecules per cell, and
(ii) for SAMs on Ag(111), R7.R7 with three molecules
per cell is the structure widely accepted for C1whereas for
longer chain alkylthiolates, though the monolayer might be
incommensurate with the substrate, the structure is thought to
be very close to R7.R7.
In Table 1 we report DFT results for both unreconstructed
Ag(111) and Au(111) surfaces (i.e. with 0 vacancies and 0
ad-atoms) for the unit cells: R3.R3 and R7.R7. On both
substrates, the most stable adsorption site for R3.R3 is near
the mid-point between bridge and hollow (brg-hollow),
whereas the R7.R7 structures involve three non-equivalent
adsorption sites close to: hollow-fcc (fcc), hollow-hcp (hcp)
and the mid-point between top and bridge (top-brg). The
lowest values of rE are found for R3.R3: ?13 meV A˚?2for
Au(111) and ?20 meV A˚?2for Ag(111). This is in line with
the coverage observed experimentally for Au(111) but not
for Ag(111). Though a comparison of structures with different
coverages in terms of rE is only justified for T = 0 K,
and in spite of the very similar values of rE obtained for
Ag-R3.R3-0v,0aandAg-R7.R7-0v,0a(i.e.?20and?18meVA˚?2,
respectively), these results suggest that to explain the preference
ffiffiffi
3
p
Þ unit cell [here called,
Table 1
unreconstructed substrates
Summary of DFT results for C1/Au(111) and C1/Ag(111) for
Unit cell
ffiffiffi
ð
ð
ð
Notation
Y
E/eV
rE/meV A˚?2
ð
3
ffiffiffi
3
ffiffiffi
p
p
p
p
?
?
?
?
ffiffiffi
7
ffiffiffi
7
3
ffiffiffi
3
ffiffiffi
p
p
p
p
ÞR30?
ÞR19:1?
ÞR30?
ÞR19:1?
Au-R3.R3-0v,0a
Au-R7.R7-0v,0a
Ag-R3.R3-0v,0a
Ag-R7.R7-0v,0a
1/3
3/7
1/3
3/7
?0.29
?0.10
?0.44
?0.31
?13
?6
?20
?18
7
ffiffiffi
7

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9356Phys. Chem. Chem. Phys., 2011, 13,9353–9362This journal is c the Owner Societies 2011
of Y = 3/7 over Y = 1/3 found experimentally for Ag(111),
adsorption models involving some surface reconstruction
might be necessary.
Recent experiments strongly suggest that methylthiolate
adsorption induces reconstruction of both Au(111)22–25,28–32
and Ag(111)25,52–54surfaces. In line with these experiments,
DFT calculations for C1/Au(111)21,24,26,28,55and C1/Ag(111)33
have found various structures involving substrate ad-atoms
and vacancies, respectively, which are more stable than the
SAMs on the unreconstructed substrates. Then, we have
explored and compared the stability of various reconstructed
adsorption models involving topmost layer substrate vacancies
and ad-atoms for both C1/Ag(111) and C1/Au(111) and for
Y = 3/7 and 1/3.
For Y = 1/3, we have explored various structures that have
been proposed for C1/Au(111) during the last years. In
particular, we have investigated: (i) the R3.R3 structure with
one vacancy, namely the so-called honeycomb reconstruction
(R3.R3-1v,0a),21(ii) various structures involving C1–M–C1
units formed by two C1groups anchored on top sites and
onemetal (M)ad-atom acting
them24,26,27,56within the 2R3.R3, 2R3.2R3 and c(4 ? 2) unit
cells. For instance, the 2R3.R3 structure (2R3.R3-1v,1a)
involves one C1–M–C1unit and one surface vacancy created
by the M ad-atom that has been lifted from its equilibrium
position to form the C1–M–C1unit. Similarly, the 2R3.2R3
structure (2R3.2R3-2v,2a) involves two C1–M–C1units and
two surface vacancies. Additional test calculations for Au(111)
within a 2R3.2R3 unit cell (carried out with slightly smaller
number of k-points and energy cut-off) involving three vacancies
and two ad-atoms (2R3.2R3-3v,2a) gave rise to less stable
structures and are not presented here. Finally, we have
also considered a c(4 ? 2) model that comprises two
C1–M–C1 moieties in a cis-configuration and no vacancies
(c(4 ? 2)-0v,2a).26We emphasize that (i) we have considered
all the most stable models proposed so far for C1/Au(111)28as
well as some variants of them which have always given rise to
less stable structures and (ii) all the structures mentioned
above were investigated for both Au(111) and Ag(111), except
2R3.2R3-2v,2a which was not considered for Ag(111) because
of the too low energetic stability of Ag-2R3.R3-1v,1a.
For Y = 3/7, we have only considered structures with three
methylthiolates adsorbed within a R7.R7 unit cell. Motivated
by experimental results,52–54we have focused on structures
with a reduced density of topmost layer metal atoms. The
number of possible starting point configurations involving
asa bridgebetween
different number of vacancies to be investigated is huge. Then,
to guide our search of possible stable structures, we have used
the procedure recently proposed by Abufager et al.33We first
considered the unreconstructed surface model (R7.R7-0v,0a)
with three methylthiolates chemisorbed near top, and at
fcc and hcp sites. Starting from this structure we used the
following iterative recipe to guide our search of structural
models involving X = 1, 2, 3 substrate vacancies. For the most
stable structure with X vacancies (R7.R7-Xv,0a) we estimate
the relative bond strengths of the three methylthiolates to the
surface by comparing the total energies Ei(i = 1,2,3) of the
structures obtained by removing the ith methylthiolate from
R7.R7-Xv,0a while keeping frozen the positions of the other
two methylthiolates and the substrate. The most weakly bound
methylthiolate in R7.R7-Xv,0a will be that for which the corres-
ponding Eiis the lowest. Then, we create an extra vacancy by
removing one of the substrate atoms closest to this most weakly
bound methylthiolate with the hope that the new vacancy will
reinforce its bond with the surface. With an x-fold coordination of
the most weakly bound methylthiolate, we then carry out x full
geometry optimizations in which each time, one of the x metal
atoms closest to the most weakly bound methylthiolate is
removed. The structure involving X + 1 vacancies with the lowest
E value obtained this way is denoted as R7.R7-(X + 1)v,0a. This
procedure was applied to both C1/Ag(111) and C1/Au(111).
In addition, we have investigated (on both substrates) various
structures involving four vacancies per unit cell (R7.R7-4v,0a)
previously proposed for C1/Ag(111).53,54,57,58
A summary of the results including only the lowest energy
structures obtained for each unit cell and for given (X,Y)
values for Au(111) and Ag(111) is reported in Tables 2 and 3,
respectively. In addition, the most stable structures obtained
on each substrate for Y = 1/3 and 3/7 are schematically
represented in Fig. 1. Comparing the results for the R3.R3
unit cell (Y = 1/3) on Au(111), the value E for Au-R3.
R3-1v,0a21is much lower than for the unreconstructed model
Au-R3.R3-0v,0a, reported in Table 1 (i.e. ?0.48 vs. ?0.29 eV).
In contrast, for Ag-R3.R3-1v,0a, E is greater than for the
unreconstructed model Ag-R3.R3-0v,0a (i.e. E = ?0.37 vs.
?0.44 eV).
Structures involving the C1–M–C1units on Au(111) (Y = 1/3)
are more stable than the unreconstructed model, in agreement
with previous theoretical results.24,26Moreover, Au-c(4 ? 2)-0v,2a
is slightly more stable than Au-R3.R3-1v,0a, though the
difference between the corresponding E values is very small:
?0.01 eV. This might provide a reasonable explanation for the
Table 2Summary of DFT results for C1/Au(111): reconstructed models
Unit cell
ffiffiffi
ð2
ð2
c(4 ? 2)
ð
ð
ð
ð
NotationVacanciesAd-atomsErec/eV
Y
E/eV
rE/meV A˚?2
ð
3
p
?
ffiffiffi
3
ffiffiffi
p
3
p
ÞR30?
ffiffiffi
3
ffiffiffi
7
ffiffiffi
7
Au-R3.R3-1v,0a
Au-2R3.R3-1v,1a
Au-2R3.2R3-2v,2a
Au-c(4 ? 2)-0v,2a
Au-R7.R7-1v,0a
Au-R7.R7-2v,0a
Au-R7.R7-3v,0a
Au-R7.R7-4v,0a
1
1
2
0
1
2
3
4
0
1
2
2
0
0
0
0
0.62
0.00
0.00
1.34
0.64
1.04
1.13
1.11
1/3
1/3
1/3
1/3
3/7
3/7
3/7
3/7
?0.48
?0.34
?0.35
?0.49
?0.13
?0.24
?0.11
?0.21
?21
?15
?16
?22
?7
?14
?6
?12
3
ffiffiffi
?
?
?
?
p
p
?
? 2
p
p
p
p
3
p
ÞR30?
ffiffiffi
ÞR19:1?
ffiffiffi
7
ffiffiffi
ÞR30?
ffiffiffi
7
ffiffiffi
7
7
ffiffiffi
7
ffiffiffi
p
p
p
p
7
ÞR19:1?
ÞR19:1?
ÞR19:1?

Page 5

This journal is c the Owner Societies 2011Phys. Chem. Chem. Phys., 2011, 13,9353–93629357
fact that both ð
often observed in experiments. However, it is important to
note that only Au-c(4 ? 2)-0v,2a might explain the experi-
mental data pointing to top as the adsorption site for
methylthiolates on Au(111).32,56,59A different scenario is found
for C1/Ag(111), for which the stabilities of Ag-c(4 ? 2)-0v,2a
and Ag-R3.R3-0v,0a are very close to each other (E = ?0.45 vs.
?0.44 eV) and much larger than for Ag-R3.R3-1v,0a
(E = ?0.37 eV).
For Y = 3/7, we obtained that all the structures involving
surface vacancies (on both substrates, i.e. Ag-R7.R7-Xv,0a
and Au-R7.R7-Xv,0a with X = 1, 2, 3, 4) are more stable
than the unreconstructed models. In particular, on Ag(111)
weemphasizethesignificantly
Ag-R7.R7-2v,0a structure compared to the other reconstruc-
tion models with different density of vacancies and even more
so than the unreconstructed surface model (Table 3). Thus,
ffiffiffi
3
p
?
ffiffiffi
3
p
ÞR30?and c(4 ? 2) structures are
largerstability ofthe
our extensive configurational search clearly identifies vacancy-
geometries, in particular the Ag-R7.R7-2v,0a model, with largely
superior stability and thereby fully supports the experimental
understanding of a negligible presence of unreconstructed
domains at the surface.25,33
The Ag-R7.R7-2v,0a structure involves three C1molecules
chemisorbed in similar surroundings next to the sides of an
equilateral triangle formed by three topmost layer Ag atoms, cf.
Fig. 1d. This is reminiscent of the Ag3S3units recently observed
by STM for atomic sulfur on Ag(111).60In Ag-R7.R7-2v,0a
each of these Ag3S3units is surrounded by a regular hexagon of
Ag atoms.33This forces one out of every four Ag atoms in the
topmost layer to occupy hcp sites. The similarity of the two
threefold sites nevertheless ensures only a small overall rumpling
of the S atom layer (DhS= 0.11 A˚) in excellent agreement with
the reported experimental dataDhSr 0.2 A˚.33,54Inaddition, the
average vertical height of the S layer above the ideal nearest
extended bulk (111) plane,?hS= 1.17 A˚, lies perfectly within the
experimental range?hS= (1.23 ? 0.07) A˚.33,53
Interestingly, the values of Erec/m obtained from adsorp-
tion models for substrates with the same (X, Y) values
(e.g. Au-R3.R3-1v,0a and Ag-R3.R3-1v,0a) are very similar.
Thus the differences between the corresponding E values are
mainly due to different adsorption energies per molecule on
the reconstructed substrate, Eb(cf. eqn (4)).
In summary, for both Ag(111) and Au(111), we have found:
(i) for Y = 1/3, c(4 ? 2)-0v,2a is the most stable arrange-
ment, although for Au(111) R3.R3-1v,0a is almost as stable.
(ii) for Y = 3/7, the highest stability corresponds to
structures with a density of topmost layer metal atoms of
5/7 (i.e. R7.R7-2v,0a).
So far, for each substrate we have compared the stability
of adsorption models characterized by the same coverage. In
order to compare the relative stability of SAMs characterized
by Y = 1/3 and 3/7, Fig. 2 shows DG(DmSCH3) only for
the most stable structures obtained for each coverage on
both substrates. The most significant result is that for
Au(111) (Ag(111)), the SAM of methylthiolates with coverage
Y = 1/3 (Y = 3/7) is more stable than for Y = 3/7 (Y = 1/3)
in a wide range of temperatures and pressures in line with
experiments.
It is important to note that in the case of C1/Ag(111)
[in contrast with the case of C1/Au(111)], the SAM coverage
for which the present DFT calculations give the lowest rE value
(i.e. higher stability at low temperatures) is in agreement
with the saturation coverage observed experimentally only if
reconstructed adsorption models are considered.
Table 3Summary of DFT results for C1/Ag(111): reconstructed models
Unit cell
ffiffiffi
ð2
c(4 ? 2)
ð
ð
ð
ð
NotationVacancies Ad-atomsErec/eV
Y
E/eV
rE/meV A˚?2
ð
3
p
?
ffiffiffi
?
?
?
?
ffiffiffi
ffiffiffi
7
ffiffiffi
7
3
p
ÞR30?
ffiffiffi
7
ÞR19:1?
ffiffiffi
7
ffiffiffi
Ag-R3.R3-1v,0a
Ag-2R3.R3-1v,1a
Ag-c(4 ? 2)-0v,2a
Ag-R7.R7-1v,0a
Ag-R7.R7-2v,0a
Ag-R7.R7-3v,0a
Ag-R7.R7-4v,0a
1
1
0
1
2
3
4
0
1
2
0
0
0
0
0.58
0.00
1.23
0.58
1.39
1.11
1.46
1/3
1/3
1/3
3/7
3/7
3/7
3/7
?0.37
?0.25
?0.45
?0.37
?0.51
?0.43
?0.39
?16
?11
?20
?21
?29
?24
?22
3
p
?
3
p
ÞR30?
ffiffiffi
7
ffiffiffi
7
7
ffiffiffi
7
ffiffiffi
p
p
p
p
p
p
p
p
ÞR19:1?
ÞR19:1?
ÞR19:1?
Fig. 1
for C1on Ag(111) and on Au(111) for Y = 1/3 and 3/7 (see text):
(a) Au-c(4 ? 2)-0v,2a; (b) Au-R7.R7-2v,0a; (c) Ag-c(4 ? 2)-0v,2a and
(d) Ag-R7.R7-2v,0a. Red: H atoms, yellow: C atoms, orange: S atoms,
gray: metal atoms. For the R7.R7-2v,0a structures (panels b and d), we
have used dark gray to represent topmost-layer metal atoms and light
gray for lower-layer substrate atoms. For the c(4 ? 2)-0v,2a structures
(panels a and c), the darkest gray is used for ad-atoms, the inter-
mediate gray for atoms in the topmost metal layer and light gray for
the lower-layer substrate atoms. The black lines represent the surface
unit cells.
Schematic representation of the most stable adsorption models

Page 6

9358Phys. Chem. Chem. Phys., 2011, 13,9353–9362 This journal is c the Owner Societies 2011
At a pressure of p = 10?11atm, typical for ultra-high
vacuum (UHV) experiments, the value of the chemical potential,
above which a SAM on Au(111) with Y = 1/3 is more stable
than the clean Au(111) surface, is DmSCH3(T,p) = ?0.49 eV.
This value corresponds to a critical temperature of Tc= 206 K
(see Fig. 2a). Thus, for the C1/Au(111) system, the SAM with
coverage Y = 1/3 is thermodynamically the most stable state
for temperatures lower than 206 K. In the case of Ag(111), the
SAM with Y = 3/7 is more stable than the clean surface for
temperatures below Tc= 214 K, cf. Fig. 2b.61These critical
temperatures are somewhat below the known desorption
temperatures above B400 K of short chain alkylthiolate
SAMs in UHV on both substrates (see e.g. refs. 62 and 63).
A possible reason that could well account for such a B200 K
difference is that the present thermodynamic theory neglects
a possible activation energy barrier for (SCH3)2dissociation
(of B0.27 eV for (SCH3)2/Au(111)64). On the other hand, it
could also indicate the existence of not yet considered
reconstruction models with even higher stability or reflect
the uncertainty of the employed semi-local DFT functional.
In conclusion,
(i) for C1/Au(111), the c(4 ? 2)-0v,2a26and R3.R3-1v,0a21
models are possible good candidates for explaining the experi-
mental saturation coverage Y = 1/3,
(ii) for C1/Ag(111), the R7.R7-2v,0a model33involving a
reduced (5/7) density of topmost layer Ag atoms accounts for
the preference of Y = 3/7 found in experiments.
IV.
orientations
Chain–chain interactions and optimum
AComputational details
In the previous section we have restricted the analysis to SAMs
of the shortest alkylthiolate (n = 1) for which the intermolecular
vdW attraction is the lowest. Therefore, the resulting relative
Fig. 2
and (b) Ag. In the upper x-axis the dependence on the gas-phase chemical potential has been cast into a temperature scale at constant pressure
p = 10?11atm.
Gibbs free energy of adsorption per unit area DG(DmSCH3), for the most stable structures obtained for Y = 1/3 and 3/7 on (a) Au
Fig. 3
structure including nearest neighbor S–S distances. (c) Same as (b) but for the Ag-R7.R7-2v,0a structure.
(a) Schematic representation of C10and definition of the angles: y, f and c. (b) Schematic representation of the S layer in the Au-c(4 ? 2)-0v,2a

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This journal is c the Owner Societies 2011Phys. Chem. Chem. Phys., 2011, 13,9353–93629359
stabilities of the considered structures with Y = 3/7 and 1/3
on Ag(111) and Au(111) are mainly determined by the
(Y-dependent) M–S interaction only. To estimate to what
extent these relative stabilities change for SAMs of longer
chain alkylthiolates (Fig. 3a), it is imperative to evaluate the
additional contribution of Ch–Ch interactions. A simple but
reasonable way to accomplish this is to compute the optimum
structure and the corresponding cohesive energy, ECh–Ch,
of a periodic arrangement of alkylthiolates with S atoms
forming an infinite 2D-hexagonal grid, in order to mimic a
SAM. This is justified because for both Ag-R7.R7-2v,0a and
Au-c(4 ? 2)-0v,2a (the structures with the lowest rE values
found in the previous section), the S atoms form an almost
regular and flat hexagonal grid characterized by average
nearest neighbor (NN) S–S distances?dAg= 4.53 A˚
?dAu= 5.11 A˚, respectively (see Fig. 3b and c).
For a periodic arrangement of Cnmolecules with m chains
per unit cell, the Ch–Ch interaction energy per molecule is
given by (using periodic boundary conditions)
and
VCh?Ch¼
1
2m
X
m
k¼1
X
k0ak
Vkk0;
ð8Þ
with Vkk0 the interaction potential between the chains k and k0.
In eqn (8), the sumP
cell and their periodic images) whose interaction with the
chain k is not negligible, and the factor 1/2 is included to
avoid double counting.
The Vkk0 potential can be approximately evaluated by
considering a sum of exp-6 pairwise interatomic potentials
recently obtained by fitting a set of MP2 interaction energies
for dimers of alkanethiols in gas phase.34Then, Vkk0 can be
written
"
kruns over all the molecules within the
k0akruns over the chains (within the unit
unit cell, the sumP
Vkk0 ¼1
2
X
N
i;j
Aijexpð?BijrijÞ ?Cij
r6
ij
#
;
ð9Þ
where the index i (j) runs over the atoms of the chain k(k0), rijis
the distance between atoms i and j, and the factor 1/2 avoids
double-counting. The parameters Aij, Bijand Cijused in the
present work are listed in Table 4.34Given that in SAMs, the
S–S interaction is largely mediated by the substrate, this
interaction is not taken into account in eqn (9).
We have considered rigid Cnchains in their ground (all-trans)
state. The internal molecular degrees of freedom of Cnwere
obtained from full geometry optimizations of the corresponding
isolated alkanethiol molecules [HS(CH2)n?1CH3] through
DFT-PW91 calculations. Considering (for simplicity) only
one Cnmolecule per unit cell (m = 1), for a given value of
the NN S–S distance, d, VCh–Chonly depends on the three
angles that define the orientation of the chain: y, f, c
(see Fig. 3a). Then, we have determined the optimum molecular
orientation (yop, fop, cop) for which VCh–Chis the lowest,
within a dense 3D (y, f, c)-grid (spacings = 0.11) for various
values of d (4.2 A˚r d r 5.4 A˚). Thus, we define the binding
energy per molecule for a structure of Cnmolecules (due to
Ch–Ch interactions only) as ECh–Ch(n) = VCh–Ch(n; yop,
fop, cop). Accordingly, the energetically most favorable
molecular density is that for which rECh?Ch¼ 2ECh?Ch=ð
is the lowest. Such a comparison of the stability of structures
in terms of rE, as well as the use of rigid chains in their ground
state (all-trans) conformer (see e.g. ref. 65), is strictly valid for
T B 0 K. A detailed study of temperature effects for more
than a single chain per unit cell and considering the internal
degrees of freedom of the chains (e.g. using molecular
dynamics, MD) is beyond the scope of this paper. However,
it is important to mention that previous MD simulations have
shown that different conformers of Cn chains in a SAM
(e.g. involving trans-to-gauche transformations) only play
some role above T B 300 K.66
ffiffiffi
3
p
d2Þ
BResults
In Fig. 4 we plot the optimum angles yop, fopand copas a
function of d for C3, C6and C10. The three d-dependences
present a sharp transition from almost perfectly upright chains
to tilted chains which takes place at dcB 4.82 A˚for C6and
C10and at dcB 4.92 A˚for C3, with the transition less abrupt
in the latter case. For C6and C10(and also for intermediate
and longer chains not shown), yopB 1–21 for d o dc, whereas
for d > dc, yopB 29.01 + 25.91 A˚?1? (d ? dc) (Fig. 4a). At
d B dc, the angles fopand copvary from 0 to B201 and from
0 to B40–501, respectively. For d > dc, Ch–Ch interactions
favor a tilt angle y that increases when d increases and a tilt
direction of the chains B81 away from the next nearest
neighbor (NNN) molecule in the SAM.
In Fig. 4, the vertical dashed lines indicate the values of
?dAg= 4.53 A˚and?dAu= 5.11 A˚that correspond to the most
stable structures obtained in DFT calculations for C1on Ag(111)
and Au(111) (i.e. Ag-R7.R7-2v0a and Au-c(4 ? 2)-0v2a),
respectively. For relatively short alkylthiolates for which the
most favorable d value is determined by the M–S bond, the
fact that?dAgo dco?dAuexplains why the experimental tilt
angle of SAMs on Au(111)14–16are much larger than on
Ag(111).10–13Moreover, for d =?dAuand d =?dAg, we have
respectively obtained yopB 371 and yopB 21, in reasonably
good agreement with the typical experimental values for both
substrates10–16(Fig. 5). In addition, the optimum tilt direction
B81 away from the direction corresponding to NNN chains
obtained for d =?dAu(Fig. 4b), is also in good agreement with
one of the models proposed from experimental data for SAMs
of alkylthiolates on Au(111) (see section 3.1.1.1 of ref. 4 and
references therein).
Various relationships between yopand the molecular packing
density for SAMs of alkylthiolates have been proposed making
Table 4Optimum set of parameters used to describe the Ch–Ch interactions between Cnmolecules taken from ref. 34
Parameteri = H; j = Hi = H; j = Si = H; j = Ci = S; j = Ci = C; j = C
Aij/eV
Bij/A˚?1
Cij/eV A˚6
80.619
3.685
0.965
386.878
3.313
13.874
358.443
4.137
4.589
1720.116
3.009
65.961
1593.693
3.109
21.819

Page 8

9360Phys. Chem. Chem. Phys., 2011, 13,9353–9362This journal is c the Owner Societies 2011
use of the experimental interchain distance for bulk n-alkanes.
For instance, Heinz et al.67computed yopusing the expression
yop¼ cos?1Ac
As
??
¼ cos?1 2 ? 17:5 ˚A2
ffiffiffi
3
p
? d2
!
;
ð10Þ
and obtained a good general agreement with experimental
data for a wide range of SAM coverages. In eqn (10), Acis
the average cross-sectional area of an alkyl chain (AcB 17.5 A˚2
at 90 K68,69), and As is the surface area per chain
(i.e. As¼
Fig. 4(a) we compare our results of yopwith the values predicted
by eqn (10) (dashed line). It is interesting to note that, for
d > dc, our results are properly explained by a simple model as
that given by eqn (10). In contrast, for d o dc, our calculated
yop values are significantly smaller than those predicted by
eqn (10). Furthermore, the model does not predict the sudden
increase of yoparound d = dc. This discrepancy is likely due to
the neglect of the actual atomic structure of the alkyl chain in
the model.
In Fig. 6a, we plot the value of rECh– Chas a function of
d for C3, C6and C10. The lowest value of rECh–Chis obtained
for d B 4.4 A˚. This value of d is close to that of the NN
distance corresponding to a molecular packing in C1/Ag(111)
with Y = 3/7 (?dAgB 4.53 A˚). Therefore, for Ag(111), both the
M–S and the Ch–Ch interactions favor a coverage Y = 3/7
over Y = 1/3. This is consistent with the experimental coverage
(Y = 3/7) of SAMs of alkylthiolates on Ag(111) irrespective
of the chain length. In contrast, the optimum value of d
(i.e. B4.4 A˚) differs significantly from that of the NN distance
in C1/Au(111) with Y = 1/3 (?dAgB 5.11 A˚). The latter
molecular packing is favored by the M–S interaction, but
it is clear that the Ch–Ch interactions rather point towards
Y = 3/7. Indeed, as the chain length increases, the effect of the
Ch–Ch interactions becomes progressively more important
and, therefore, for a long enough alkyl chain, it must become
the dominant effect. As the difference between the DFT
rE values of Ag-R7.R7-2v,0a and Au-c(4 ? 2)-0v,2a is only
8 meV A˚?2(cf. Table 2), according to Fig. 6b this must occur
for n larger than B9.70In other words, on Au(111), SAMs
with Y = 1/3 should only be more stable than for Y = 3/7 for
alkylthiolates with less than B9 C atoms. However, Y = 1/3
is the experimental saturation coverage for SAMs of alkyl-
thiolates with even more than 20 C atoms.16This disagreement
suggests that the y-dependence of the M–S bond strength,
effects due to the non-rigid character of the chains (e.g. gauche
defects) and/or entropic contributions not considered in the
present simplified analysis should be taken into account to
explain the structure of SAMs of long chain alkylthiolates on
Au(111). Still, in view of the simplicity of the present descrip-
tion (that separately accounts for the role of M–S and Ch–Ch
interactions and combine them in a simple additive model), it
is actually remarkable that our calculations do allow us to
predict the main distinct signatures of SAMs of short chain
alkylthiolates on Ag(111) and Au(111).
ffiffiffi
3
p
d2=2) which depends on the surface coverage. In
V. Conclusions
We have used density functional theory (DFT) calculations
and a set of pairwise interatomic potentials derived from
second-order Møller–Plesset (MP2) perturbation theory calcula-
tions to investigate the structure and stability of various
possible structures of SAMs of short chain alkylthiolates
(S(CH2)n?1CH3= Cn) on Ag(111) and Au(111). Our results
unambiguously show that, for both C1/Ag(111) and C1/Au(111),
Fig. 4
C10as a function of d. The vertical dashed lines denoted by Ag(111)
and Au(111) indicate the values of d =?dAg= 4.53 A˚and d =?dAu=
5.11 A˚respectively (see text). In panel (a), the dashed line represents
the yopvalues predicted by eqn (10).67
Optimum angles yop(a), fop(b) and cop(c) for C3, C6and
Fig. 5
(black squares) and Ag(111) (red circles). Open symbols: theory (the
lines are a guide to the eye), solid symbols: experiments taken from
refs. 11, 12, 16.
Optimum tilt angle yopof SAMs of alkylthiolates on Au(111)

Page 9

This journal is c the Owner Societies 2011Phys. Chem. Chem. Phys., 2011, 13,9353–9362 9361
adsorption
important stabilization of the SAMs. For C1/Au(111), both
reconstructed and unreconstructed adsorption models predict
that SAMs with Y = 1/3 are more stable than those with
Y = 3/7 in agreement with experiments. In contrast, for
C1/Ag(111), the experimentally observed value, Y = 3/7,
can only be explained by invoking SAM-induced substrate
reconstruction. By using the most stable molecular packing
densities predicted by DFT calculations for C1on both sub-
strates, the addition of chain–chain (Ch–Ch) interactions
allows us to account for the very different tilt angles observed
on Au(111) and Ag(111). Thus, a model that combines Ch–Ch
and molecule–surface (M–S) interactions obtained from gas-
phase and C1–substrate calculations, respectively, succeeds
in predicting the main and somewhat surprising structural
differences of SAMs of alkylthiolates on Ag(111) and Au(111).
It is important to emphasize that, in contrast with existing
simple models, our method is based on first principles and,
therefore, does not make use of any experimental information
or fitting parameters. Finally, in view of the crucial role played
by the substrate reconstruction induced by the adsorbed
molecules in explaining the stability of the SAM of alkylthiolates,
it would not be surprising that similar reconstructions might play
a key role in explaining the stability of SAMs of more complex
molecules, e.g., biomolecules. Thus, further theoretical efforts for
such systems should check this possibility.
inducedsubstratereconstruction entailsan
Acknowledgements
This work has been supported by ANPCyT-Argentine (projects
NoPICT 2005-33595 and PICT 2008-1260), the Agencia
Espan ˜ ola de Cooperacio ´ n Internacional (AECI), projects
No. A/3067/05 and No. A/4722/06, the Centro de Estudios
para Ame ´ rica Latina - Banco de Santander of the Universidad
Auto ´ noma de Madrid (CEAL-BSCH-UAM), the MICINN
projects FIS2010-15127, ACI2008-0777 and CONSOLIDER-
INGENIO 2010C-07-25200 on Molecular Nanoscience, and
the Comunidad de Madrid through the program NANOBIO-
MAGNET S2009/MAT1726, and the Deutsche Forschungs-
gemeinschaft, DFG. We also thank Mare Nostrum BSC and
CCC-UAM for computer time and Prof. R. Salvarezza for his
useful comments about this work.
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Fig. 6
d =?dAg= 4.53 A˚and d =?dAu= 5.11 A˚, respectively (see text). (b) Ch–Ch contribution to the adsorption energy per unit of surface area as a
function of the number of C atoms in the alkyl chain.
(a) ECh–Chas a function of d for C3, C6and C10. The vertical dashed lines denoted by Ag(111) and Au(111) indicate the values of

Page 10

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DFT34.