Chemical Physics Letters 381 (2003) 315–321
www.elsevier.com/locate/cplett
Density functional calculation of a potential energy surface
for alkane thiols on Au(1 1 1) as function of
alkane chain length
Stefan Franzen
*
Department of Chemistry, North Carolina State University, Box 8204, Raleigh, NC 27695, USA
Received 25 April 2003; in final form 22 August 2003
Published online: 23 October 2003
Abstract
Density functional theory calculations of alkane thiols on Au(1 1 1) have been carried out as a function of the alkane
chain length from 1 to 12 carbons using a slab geometry with periodic boundary conditions. Geometry optimized
structures were obtained and the potential energy was calculated as a function of the binding site and distance from the
surface. While the binding site of minimum energy is only subtly different for different chain lengths there is a pronounced difference in the Au–S bonding and side chain interactions of the methyl group of methane thiol compared to
ethane thiol or any longer alkane thiol self-assembled monolayer. For example, the barrier to lateral motion along the
surface is lowest for motion through fcc sites for methane thiol while the twofold bridge sites present the lowest barrier
to ethane thiol and all longer alkane thiols. The hexagonal close-packed (hcp) and face-centered cubic (fcc) threefold
sites were found to differ in energy by less than 1 kJ/mol and therefore only fcc sites were considered in the study.
According to the calculated potential energy surfaces the top sites have weaker binding than either the bridge or
threefold sites in all cases. The calculations show that ethane thiol is a reasonable model for longer alkane chains.
Ó 2003 Published by Elsevier B.V.
Self-assembled alkane thiol monolayers on gold
are a versatile system for the surface attachment of
molecules for spectroscopic and electrochemical
applications. The structure of self-assembled
monolayers (SAMs) has been studied to determine
the coverage and tilt angle of the alkane chains on
a Au(1 1 1) surface [1–3]. Computational models of
the formation of adlayers on Au(1 1 1) have typi-
*
Fax: +1-919-515-8909.
E-mail address: [email protected] (S. Franzen).
0009-2614/$ - see front matter Ó 2003 Published by Elsevier B.V.
doi:10.1016/j.cplett.2003.08.126
cally used two phases of analysis, parameterization
of a force field using ab initio methods and adlayer
molecular dynamics (MD) simulations using a
classical force field [4]. The first phase has usually
involves density functional (DFT) calculation of
methane thiol (CH3 S) monolayers or gold cluster
models to obtain information on the bonding of
thiols on the surface of Au(1 1 1). DFT studies
have been applied to the mechanism of adlayer
formation as well. The calculated binding energy
of thiols is difficult to compare to experiment [5]
because the mechanism requires an accurate
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S. Franzen / Chemical Physics Letters 381 (2003) 315–321
energy difference between disulfides (CH3 S–SCH3 )
or sulfhydryls (CH3 SH) and surface-bound thiols
bonded to Au atoms in a slab geometry [6–9]. In a
second phase of analysis, the parameters obtained
from DFT calculations have been used in MD
simulations [10–13] to model chain packing configurations and the experimentally observed
c(4 2) superstructure [1–3,10,14–23]. The present
study addresses the chain length dependence of
surface bonding of alkane thiols from methyl to
dodecyl chains on an orthorhombic unit cell consisting of three layers of gold atoms in a slab geometry with periodic boundary conditions (PBC)
as shown in Fig. 1. The structural comparison in
Fig. 1 is based on geometry optimization of the
alkane chains on a Au(1 1 1) surface. Already from
the structural comparison in Fig. 1 it is clear that
the structure of the methyl side chain is quite different from that of ethane thiol. The methyl
groups are tilted much closer to the gold surface
and the C–H bond vector is directed towards the
sulfur of an adjacent methane thiol. In the following, it is shown that ethane thiol has strong
resemblance to longer alkane chains and the
commonly studied methane thiol is anomalous in
this series. Since the majority of experimental data
have been obtained on longer chain alkanes the
results are of practical benefit for the study of selfassembled monolayers [10,14–23].
Fig. 2 shows a Au(1 1 1) surface and binding
energetics of alkane thiol monolayers at full
coverage. Alkane thiol layers are bonded to the
surface by the sulfur atom and are assumed to be
neutral. The procedure used in the study consists
of geometry optimization followed by calculation
of the energy of alkane chains in defined geometries shown in Fig. 2 (fcc, fcb and top) as a
function of distance from the surface. The
p orthop
rhombic unit cell of the Au lattice is 1 3 6
in units of a, the Au–Au internuclear distance
(a
p¼ 2:884
p A). The position of alkane thiols in a
( 3 3)R30° hexagonal lattice corresponds to
two alkane thiols placed in an orthorhombic
p cell of
thiol adsorbate lattice of dimension 3 3 also
indicated in the upper left of Fig. 2 by the heavy
dashed line. The distance dependence
p
pof each pair
of alkane chains on the 3 3 6 unit cell
shown in Fig. 2 was calculated using a fixed slab of
3 layers of Au atoms in three-dimensional PBC.
The periodic boundary normal to the surface was
sufficiently far from the terminal methyl group
that interactions of the methyl group with the roof
above it were less than 0.1 kJ/mol. A control calculation with a slab thickness of 6 atoms was also
carried out with nearly identical results for the
geometry of ethane thiol. In all calculations the
alkane chains were in the staggered conformation.
While many studies have found that the lowest
energy structure for CH3 S on Au(1 1 1) has the
thiols in the face-centered cubic (fcc) threefold site,
i.e., bonded to three Au atoms [7,8,10,19], others
have found that methane thiol is most stable in or
Fig. 1. Top down view of a Au(1 1 1) surface and self-assembled monolayers (SAMs) of methane thiol and ethane thiol. (a) Bare
Au(1 1 1). (b) A methane thiol SAM on Au(1 1 1). (c) An ethane thiols SAM on Au(1 1 1).
S. Franzen / Chemical Physics Letters 381 (2003) 315–321
317
Fig. 2. Definition of the three binding sites for alkane thiols on Au(1 1 1) surfaces and calculated energies of alkane thiol binding as a
function of surface site. The orthorhombic unit cells an a Au(1 1 1) surface are shown in the upper left. Potential energy surfaces for
alkane thiol binding to Au(1 1 1) surfaces calculated using the BLYP functional. The calculations were carried out using DMol3
(Accelerys, Inc.) [34] on the IBM RS/6000 SP3 computer at the North Carolina Supercomputer Center. A double-f numerical basis set
was used with effective core potentials for the Au atoms. The distance between the sulfur and the gold plane is given relative to the
optimized geometry for each structure given as the z-coordinates in Table 1. The periodic boundaries were elongated along the z for methane, ethane, hexane, decane and dodecane,
direction to accommodate the longer alkane chains (z ¼ 14, 16, 20, 24 and 26 A
respectively). (a) Methane thiol on Au(1 1 1) full potential energy surface. (b) Dodecane thiol. (c) Energy ordering of the three sites as a
function of alkane chain length. The hourglass symbols on the bottom represent the energy of the molecule–surface interaction energy
for the geometry optimized structure of each respective alkane chain. (d) The barrier height to translocation of the SAM laterally
across the surface in the direction of the fcc, fcb and top sites is shown. The curves were obtained by subtracted the geometry optimized
molecule–surface interaction energy (hourglass in 2c) from the Au–S bond energy of the fcc, fcb and top sites, respectively, in Fig. 2c.
The molecule–surface interaction energy is defined as the energy required to seperate the surface adlayer and the Au(111) surface on a
per molecule basis. It includes both the Au–S bond energy and any interactions of the side chain with the surface.
near to the bridge (fcb) site [12,24–26]. The nature
of distortions that lead to a superlattice could involve either chain packing of the alkane chains or
structure from the gold–sulfur bonds at the surface.
To differentiate between these two possibilities it is
essential to compare computational models of selfassembled monolayers as a function of alkane
chain length [25]. In this letter, DFT calculations
show a difference in surface bonding arises from
stronger interactions with neighboring methane
thiols and the gold surface than the observed for
longer chain thiols. This is evident in ordering of
the fcc and fcb energies in the potential energy
surfaces in Fig. 2. The final positions of the sulfur
318
S. Franzen / Chemical Physics Letters 381 (2003) 315–321
Table 1
Locations of sulfur atoms for two unique thiols in the unit cell following geometry optimization given in units of the gold diameter
)
(a ¼ 2:884 A
Site/chain
S1x
S1y
S1z
S2x
S2y
S2z
Top
fcc
fcb
Methane
Ethane
Hexane
Decane
Dodecane
0.000
0.000
0.721
0.346
0.634
0.577
0.663
0.663
0.000
3.316
3.749
3.720
3.460
3.547
3.431
3.461
–
–
–
2.336
2.278
2.250
2.278
2.278
4.326
4.326
5.047
4.672
4.960
4.931
4.989
4.989
2.509
0.836
1.240
1.240
0.981
1.038
0.952
0.981
–
–
–
2.336
2.278
2.250
2.278
2.278
. The S1z and S2z distances represent the distance between the
All of the positions in the unit cell given in Table 1 are in units of A
sulfur and average plane of the gold atoms along a vector normal to that plane. Fig. 2 refers the Au–S distance as relative distance
where the zero is defined as the equilibrium geometry given in Table 1.
atoms are compared to the top, fcc and fcb sites in
Table 1. The sulfur atom positions shown in Fig. 2
and reported numerically in Table 1. The position
of each of the sites is given below in units of the
):
Au–Au distance
(a ¼ 2:884p
A
p
fcc: [0, 2 3/3] and [3/2,
3/6],
p
top: [0, 0] and
[3/2,
3/2],
p
p
fcb: [3/4, 3 3/4] and [9/4, 3/4].
The difference in energy between hcp and fcc
were <1 kJ/mol and therefore only the fcc values
are reported. The potential energy surfaces for thiol
binding were then calculated as a function of distance from the surface for each of the three positions using both GGA [27] and BLYP [28,29]
functionals. The objective of the study is the comparison of the potential energy surfaces and structures of different chain lengths. Up to the present
there has been limited study of chain lengths up to 4
carbons [24,25]. The computed potential energy
surfaces shown in Fig. 2 represent the first systematic study of chain length on self-assembled alkane
thiol monolayers at full coverage.
Figs. 2a and b show two of the potential energy
curves for the BLYP calculation. The energies of
the GGA calculation are 30% larger than those
of the BLYP calculation, but otherwise the same
trends are observed (see Supporting Information).
While the energies are larger than the experimental
values they are similar in magnitude to those estimated in previous DFT calculations. There is
little change in the calculated binding energy for
alkane thiols with increasing chain length. This is
reasonable since the calculation is performed as a
function of the distance the entire self-assembled
monolayer with respect to the Au(1 1 1) surface.
Table 1 shows that the optimum geometry is between the fcc and fcb sites and the position of
methane thiol is distinctly different from all of the
longer chain alkane thiols studied.
The geometry-optimized structures show a significant difference between methane thiol and the
longer chain thiols both in side chain orientation
and in the potential energy of interaction with the
surface. The calculated conformation for methane
thiol is in reasonable agreement with previous
DFT studies. The angle for methane thiol has been
found to be 63° with respect to the azimuth in
the geometry-optimized structure [30] compared to
the value of 66° given in Table 2. The larger tilt
angle is consistent with shorter Au–C distances
due to stronger van der WaalÕs interactions between Au and CH3 as well as stronger H-bonding
of methyl with adjacent S atoms. The steric interference of longer alkane chains prevents these interactions. The conformational effect of chain
packing and carbon–sulfur repulsive interactions
drive the shift in binding from the fcc threefold site
for methane to the fcb bridging site for the longer
chain alkanes. Table 2 shows that the azimuthal
tilt angle drops sharply from 66° for methane
thiol to 42° for the ethane thiol. The angle drops
further to 37° for hexane and longer alkane side
chains in closer agreement with the experimental
result of 30° for long alkane chains on Au(1 1 1)
[31,32]. The energetic differences observed in Fig. 2
arise from steric interaction of the tilted methyl
S. Franzen / Chemical Physics Letters 381 (2003) 315–321
319
Table 2
Alkane chain tilt angle and interaction distances for calculations of SAMs of various length
Chain
Angle
(°)
C–H. . .S
)
(A
Au–S
)
(A
Methane
Ethane
Hexane
Decane
Dodecane
65.8
42.1
38.8
38.3
37.4
2.55,
3.62,
3.54,
3.53,
3.19,
2.68,
2.61,
2.62,
2.58,
2.59,
2.84
3.21
3.24
3.17
3.54
2.85,
2.82,
2.74,
2.82,
2.81,
Au–C
)
(A
3.67
3.56
3.52
3.29
3.24
3.25
3.79
3.65
3.51
3.53
The Au–C distance refers to the closest distance between the first methylene (methyl) carbon and the Au surface. The C–H. . .S
distances refer to the hydrogen bonding interactions of the first methylene (methyl) group with adjacent sulfur atoms. The angle was
calculated using a dot product vector from the surface-attached sulfur atom to the carbon atom in the terminal methyl group of each
respective chain and the surface normal.
group. Methane thiol has much stronger interactions through C–H. . .S hydrogen as shown by the
bond lengths in Table 2. Table 2 also shows that
the Au–C distance is shorter in CH3 S SAMs than
for the longer chain alkane thiols. Because of the
larger tilt angle for methane thiol the average
larger for methane
gold–thiol distance is 0.06 A
thiol than for the remaining thiols (see Table 1).
The geometry-optimized position of methane
thiol given in Table 2 is intermediate between the
fcc threefold and fcb bridge sites. The locations
given in Table 1 can be compared with ppairs of
coordinates that correspond to the (3 3)R30°
lattice of alkane thiols in a self-assembled monolayer. Although the location of methane thiol is
only slightly different than the location of the
longer alkane thiols the potential energy surface is
quite different as shown in Fig. 2. The calculated
binding energies in Fig. 2c can be used to calculate
the barrier height for lateral translocation of the
layer of alkane chains on the surface. Fig. 2d was
obtained by subtracting the geometry-optimized
Au–S bond energy (hourglass in Fig. 2c) from the
Au–S bond energies of the fcc, fcb and top sites. It
is evident that the DFT method predicts that
methane thiol is significantly different from the
longer chain alkane thiols in its interaction with
the surface.
The Au–S bonding interaction involves both rand p-bonding interactions. Based on extended
H€
uckel theory (EHT) calculations the sulfur 3s
and 3p orbital energy orderings have been found
to be top > fcb > fcc and fcc > fcb > top, respectively [33]. Moreover, the energy difference for
3p in methane thiol is larger for r-bonding, an
effect that favors binding to the top site [33]. Although DFT predicts stable binding for methane
thiol in the fcc site rather than the top site, the
DFT results agree with the bonding picture that
emerges from EHT calculations. This can be seen
in the Mulliken bond orders in Fig. 3, which shows
that methane thiol has a greater r-bonding contribution and a smaller p-bonding contribution
than the longer chain alkane thiols. The steric
hindrance of the longer chains and decreasing tilt
angle both cause the replacement of the r-bonding
with a p-bonding interaction in the fcc and fcb
sites. Overall the Mulliken bond order increases
for the longer chain alkane thiols consistent with
the shorter bond length for ethane thiol and longer
chains compared to methanol. The shorter Au–S
bond length for the longer chains is also consistent
with the larger Mulliken charge of )0.21 on
sulfur for the longer alkane thiols compared to
)0.20 for the sulfur of methane thiol (see Supporting Information for complete listing of Mulliken charges). This is interpreted as arising from
stronger bonding interaction with gold, however,
the matter is complicated by fact that the methyl
group also interacts with the gold surface for
methane thiol. The surface gold Mulliken charge is
larger for methane thiol (Au ¼ +0.53) than for the
longer alkane thiols (e.g., Au ¼ +0.45 for ethane
thiol). The interaction of the methyl group with
surface gold atoms may also be the explanation for
the fact the apparent contradiction between the
bond strength and bond length of methane thiol.
The interaction energy for methane thiol with the
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S. Franzen / Chemical Physics Letters 381 (2003) 315–321
neighboring sulfur. These factors result in the
smaller azimuthal angle for longer alkane chains in
agreement with experiment. We suggest that MD
forcefield parameters would benefit from an ethane thiol model that is a compromise of small size
and correct geometry for future studies of reconstruction of the gold surface layer and other systematic studies of the bonding and mechanism of
adlayer formation on Au(1 1 1).
Acknowledgements
SF gratefully acknowledges support from the
North Carolina Supercomputer Center through a
Faculty Research Account and NSF grant MCB9874895. Supporting Information Available
Comparison of the GGA and BLYP functionals is
presented. Mulliken charges for alkane chains are
listed.
Fig. 3. Mulliken bond orders calculated for the bonding of a
single sulfur atom with the layer of gold atoms. (a) The total
Mulliken bond order is shown as a function of the chain length
of the alkane chain on the surface. (b) A breakdown of the
Mulliken bond order is shown for the s, pr and p orbitals of a
single sulfur atom on a gold slab.
surface is 4 kJ/mol greater than the average of
the alkane thiol series shown in Fig. 2c while the
Mulliken bond order is smaller and Au–S bond
length is greater for methane thiol than for the
other thiols. All of these observations are consistent with a unique interaction of the methyl group
of methane thiol with the surface.
The major conclusion of this DFT study is that
methane thiol differs from the remainder of the
alkane thiol series. Three interactions can account
for the difference of methane thiol: (1) Change in
sp-hybridization from sp2 in methane thiol to spx
where 1 < x < 2 for longer alkanes and sp for
ammonia and pyridine (see Supporting Information). (2) C–H. . .S hydrogen bonding. (3) The interaction of the methane group with an adjacent
gold atom. For ethane and any higher alkane
chain the C–H. . .S hydrogen bonding and interaction with surface gold are both weaker due to
the steric repulsion between the alkane chain and
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