A van der Waals density functional study of adenine on graphene: Single-molecular adsorption and overlayer binding

Article (PDF Available)inJournal of Physics Condensed Matter 23(13):135001 · March 2011with28 Reads
DOI: 10.1088/0953-8984/23/13/135001 · Source: PubMed
Abstract
The adsorption of an adenine molecule on graphene is studied using a first-principles van der Waals functional, vdW-DF (Dion et al 2004 Phys. Rev. Lett. 92 246401). The cohesive energy of an ordered adenine overlayer is also estimated. For the adsorption of a single molecule, we determine the optimal binding configuration and adsorption energy by translating and rotating the molecule. The adsorption energy for a single molecule of adenine is found to be 711 meV, which is close to the calculated adsorption energy of the similarly sized naphthalene. On the basis of the single-molecular binding configuration, we estimate the cohesive energy of a two-dimensional ordered overlayer. We find a significantly stronger binding energy for the ordered overlayer than for single-molecule adsorption.
A van der Waals density functional study of adenine on graphene:
Single molecular adsorption and overlayer binding
Kristian Berland,
1
Svetla D. Chakarova-K¨ack,
2
Valentino R. Cooper,
3, 4
David C. Langreth,
3
and Elsebeth Schr¨oder
1
1
Department of Microtechnology and Nanoscience, MC2, Chalmers University of Technology, SE-41296 oteborg, Sweden
2
Department of Applied Physics, Chalmers University of Technology, SE-41296 oteborg, Sweden
3
Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019, USA
4
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6114, USA
(Dated: September 28, 2010)
The adsorption of an adenine molecule on graphene is studied using a first-principles van der Waals
functional (vdW-DF) [Dion et al., Phys. Rev. Lett. 92, 246401 (2004)]. The cohesive energy of an
ordered adenine overlayer is also estimated. For the adsorption of a single molecule, we determine
the optimal binding configuration and adsorption energy by translating and rotating the molecule.
The adsorption energy for a single molecule of adenine is found to be 711 meV, which is close to the
calculated adsorption energy of the similar-sized naphthalene. Based on the single molecular binding
configuration, we estimate the cohesive energy of a two-dimensional ordered overlayer. We find a
significantly stronger binding energy for the ordered overlayer than for single-molecule adsorption.
I. INTRODUCTION
Physisorption of small biomolecules on inert surfaces
acts as a laboratory of molecular interactions and is an
excellent starting point for addressing molecular recogni-
tion and self-organization processes. By studying these
systems we gain insight into the delicate balance between
intermolecular forces that contribute to supramolecular
binding, for example, the unique identification of anti-
gens and their binding sites in our biochemistry.
It is natural to begin an investigation of molecular in-
teractions and organization by focusing on key building
blocks, like the nucleic acids or the amino acids. Three-
dimensional biopolymer systems, like the DNA double
helix or proteins, permit folding of an extreme complex-
ity that limits direct access to most of the structure, and
direct experimental probing of the atomic-scale organi-
zation is difficult. Theoretical modeling must therefore
map out interactions and organization not only between
primary but also secondary and higher order structure
in the absence of any calibration with experiments. In
contrast, trapping nucleobases on inert surfaces not only
simplifies the possibilities for structural reorganizations
but also makes the molecular interactions accessible to di-
rect characterization through advanced atomic-scale ex-
periments.
Adenine is one of the nucleobases of DNA. The
molecule has been investigated in numerous sophisti-
cated surface experiments that have characterized both
the physisorption and self-organization or overlayer for-
mation on inert substrates, ranging from the insulating
MoS
2
[1] over the semi-metallic graphite [1–5] to sur-
faces of noble metals like Cu and Ag [6, 7]. The ex-
perimental characterization includes thermal desorption
spectroscopy (TDS) [5] for a direct measurement of the
physisorption energy, and scanning tunneling microscopy
[1–4], atomic force microscopy [3], and low-energy elec-
tron diffraction [4] for explicit identification of the ade-
nine assembly into regular overlayers.
Here we apply density functional theory calculations
(DFT) with a fully nonlocal density-functional method,
vdW-DF [8, 9], that provides a first-principle account of
dispersive or van der Waals (vdW) forces. The method
permits a parameter-free description of a broad spec-
trum of sparse matter [10]: materials which have regions
with voids in the electron distributions, such as molecu-
lar systems. Unlike the semi-empirical DFT-D methods,
it does not involve an arbitrariness in the construction
of a damping function. The vdW-DF method has previ-
ously been used to describe binding in a large range of
material systems, for example dimers of benzene [9, 11],
nucleobases [12, 13], polymers [14], nanotubes [15], sim-
ple oxides [16], and molecular-crystals [17, 18] systems. It
has furthermore been used to characterize the physisorp-
tion of organic molecules on coinage metals (Au, Ag, Cu)
[19–23], on MoS
2
[24], on Si [25], on alumina [26], and on
graphene [26, 27]. In short, it is a versatile method.
By comparing directly with experimental measure-
ments the vdW-DF method has been documented to
provide good results for benzene and naphthalene on
graphene [27, 28]. This suggests that vdW-DF should
provide a good description also of the adenine physisorp-
tion. The simple form of the non-local correlations in
vdW-DF allows for efficient calculations of the adenine
physisorption and of the mutual adenine interactions
leading to the formation of a two-dimensional overlayer
crystal. These results can be directly compared with
experiments. For an adenine molecule on a graphite
sheet we here find an adsorption energy of 0.711 eV at
an equilibrium separation of 3.5
˚
A, whereas the adenine
molecules adsorb with the energy 1006 meV per molecule
in the overlayer crystal in very good agreement with ex-
periment [5].
In the following, section II describes how we use the
vdW-DF method for the present adsorbate system. In
section III we discuss the framework of the method in
relation to some other methods used for this system, and
in section IV we present and discuss our results for the
arXiv:1009.5793v1 [cond-mat.soft] 29 Sep 2010
2
configuration and binding of the single adenine adsorbate
and an estimate of the binding energy of adenine in the
overlayer. Secction V contains our conclusions.
II. COMPUTATIONAL METHOD
We use the first-principles vdW-DF method within
DFT [8], calculating the vdW-DF energies in a post-GGA
procedure similar to previous studies [11, 16, 21, 26, 27,
29]. We calculate the vdW-DF total energy, E
vdW-DF
,
for a number of positions of the adenine molecule above
a graphite sheet, as described in Section IV. For each po-
sition, a self-consistent GGA (sc-GGA) calculation is car-
ried out, from which the GGA-based total energy E
GGA
tot
and the sc-GGA electron density n are obtained. In a
post-processing phase, we use n to evaluate long-range
correlation contributions that arise from the vdW inter-
actions, E
nl
c
and then in a systematic way combine the sc-
GGA results and the nonlocal results to obtain E
vdW-DF
.
This procedure is described below and is further detailed
in several other publications [11, 27, 29].
For the sc-GGA calculations we utilize the plane-wave
code dacapo [30] with the PBE exchange-correlation
[31]. We use ultrasoft pseudopotentials, a 2 × 2 × 1
sampling of the Brillouin zone in the Monkhorst-Pack
scheme, a wavefunction energy cutoff at 500 eV, and a
fast Fourier transform (FFT) grid with a maximum of
0.15
˚
A between nearest-neighbor gridpoints.
The correlation part of the energy in E
vdW-DF
can be
split into a nearly-local part E
0
c
and a part that includes
the most nonlocal interactions E
nl
c
,
E
c
= E
0
c
+ E
nl
c
. (1)
The nearly-local part is approximated by the correlation
of the local density approximation (LDA) E
LDA
c
, and the
nonlocal correlation functional is given by the integral
E
nl
c
[n] =
1
2
Z
dr dr
0
n(r)φ(r, r
0
)n(r
0
) . (2)
Ref. 8 contains the explicit form of the kernel φ. The
vdW-DF total energy can thus be written as the sum
E
vdW-DF
= E
0
+ E
nl
c
where the E
0
term includes kinetic
and electrostatic terms in addition to GGA exchange and
LDA correlation:
E
0
= E
GGA
tot
E
GGA
c
E
LDA
c
. (3)
This splits off the nonlocal part of the calculation, that
needs a slightly different treatment than the nearly-local
1
term E
0
.
As in recent applications [11, 14, 17, 29] of vdW-DF
we use the revPBE [32] GGA exchange in the post-
processing phase. From the total energy of the sc-GGA
1
Local in correlation.
FIG. 1: (Color online) The molecular configuration of adenine
on graphite as determined in our vdW-DF study. Dark (blue)
circles are N atoms, medium gray (brown) circles are C atoms,
and the small white circles are H atoms. The light-colored
background illustrates the underlying graphite sheet.
calculations we therefore subtract the PBE exchange en-
ergy and instead add the revPBE exchange energy. The
revPBE exchange energy is calculated from the charge
density n that is provided by the sc-GGA calculations.
The revPBE exchange functional is known to be overly
repulsive in the binding region [8]. For a range of systems,
vdW-DF with revPBE exchange provides good values
for the binding energy and quite good, but consistently
overestimated binding separations. The development of
an exchange-functional companion to the non-local cor-
relation of vdW-DF is an active research field showing
promising results [16, 33–35, 37].
The adsorption energy is given by the difference be-
tween E
vdW-DF
for the optimal configuration and for
a reference system corresponding to isolated fragments
(molecules). Since intra-molecular and intra-sheet con-
tributions dominate E
vdW-DF
we must use the same nu-
merical approximations in the two calculations. To con-
veniently cancel parameter-sensitive contributions, the
reference calculation for the sc-GGA part is done in a
manner different from the non-local correlation part. The
difference in total energy E
vdW-DF
of the adsorbate sys-
tem compared to that of separated fragments, the cohe-
sive energy E, is thus the sum of two terms
E = ∆
0
E
0
+
nl
E
nl
c
(4)
where the
0
and
nl
denote the use of two different
sets of reference calculations. At the optimal position of
the adenine on graphite (Fig. 1) the binding energy E
b
is found (with positive sign convention for binding).
A. Reference calculations for the sc-GGA part
For the calculations of the single adenine molecule ad-
sorbed on the graphite sheet the reference sc-GGA cal-
culation uses the same unit cell as the adsorbate system,
but in a configuration where the adenine molecule is lifted
3
9
˚
A away from the graphene sheet:
0
E
0
= E
0
E
0
ref
(5)
where E
0
ref
is the reference calculation. This distance of 9
˚
A is fully sufficient for the GGA calculations which only
include interactions acting at a much smaller distance.
By using the same unit cell for the reference calculation
as for the full calculation, we cancel a small spurious
contribution from the regions of very low electron density
in the sc-GGA calculation [11, 16, 36, 37].
In the calculations for the overlayer of adenine on
graphite the contributions to
0
E
0
are obtained in three
steps, as indicated in Figure 3. In each step, the reference
calculation uses the same unit cell as the full calculation.
First, the adenine overlayer crystal (o), shown in Figure
2 and sketched in Figure 3.a, is lifted off as an intact
sheet (s) from the graphite sheet to a distance 9
˚
A above
the graphite sheet (Fig. 3.b). We denote the energy cost
per molecule of this process by
0
E
0
o-s
. Then the sheet
of the adenine crystal is split into ribbons (r) of width
one adenine molecule (Fig. 3.c), with energy cost
0
E
0
s-r
per molecule, and finally the ribbons are disassembled
into individual molecules (m),
0
E
0
r-m
(Fig. 3.d). In to-
tal, the contribution to the overlayer cohesion energy per
adenine molecule is
0
E
0
= ∆
0
E
0
o-s
+
0
E
0
s-r
+
0
E
0
r-m
. (6)
The quantity
0
E
0
could also have been obtained by
simply taking all five fragments (graphite sheet and four
adenine molecules) far apart within the unit cell, but
this would require an unreasonably large unit cell, both
for the GGA reference calculations and all other GGA
calculations of the molecule overlayer on graphite.
B. Reference calculations for the nonlocal part
Our implementation of (2) is sensitive to the choice
of grid on which the charge density is described. To
avoid adverse effects of this sensitivity we use a charge-
density grid with a volume per grid-point smaller than
(0.15
˚
A)
3
in all our dacapo calculations. Further, for
every adsorbed adenine configuration we carry out a sep-
arate reference calculation of the isolated molecule where
the molecule is locally placed in the same position rela-
tive to the charge density grid. A similar reference cal-
culation for the graphite sheet is carried out once, since
this sheet is kept fixed. The contribution of the non-local
correlation to the adsorption energy is thus
nl
E
nl
c
= E
nl
c,system
E
nl
c,adenine
E
nl
c,graphite
, (7)
with obvious definitions of terms.
The extension from a single adsorbant to the full ade-
nine overlayer is straightforward in the nonlocal calcula-
tions. For each data point we perform a total of five refer-
ence calculations, one for each of the adenine molecules
(because each of them has a different position relative
to the grid) and one for the graphite layer; all reference
calculations have the same unit cell size as the main cal-
culation. The energy contribution
nl
E
nl
c
is again per
adenine molecule.
C. Representation of an infinite sheet with an
adsorbed single molecule
The sc-GGA calculations use periodic boundary con-
ditions whereas our implementation of (2) is nonperiod.
Thus in the sc-GGA calculations of E
0
and the charge
density n the graphite sheet is represented by a (periodic)
infinite sheet. The representation of a single molecule on
an infinite sheet requires that no significant inter-sheet or
inter-adsorbate interactions between the supercells exist.
The choice of a unit cell of 18
˚
A in the direction per-
pendicular to the plane secures that within the sc-GGA
calculation the graphite sheet does not interact with the
periodic images of the system in that direction, while a
supercell of 7 × 7 graphite sheet unit cells (containing a
total of 98 graphite sheet carbon atoms) in the plane of
the sheet makes the inter-adsorbate interactions negligi-
ble (less than 0.5 meV) even for the evaluation of the
non-local correlation. With this unit cell, the minimum
distance between any two atoms on two different adenine
molecules is larger than 10
˚
A.
In the evaluation of E
nl
c
from (2) the electron density
from several neighboring supercells within the plane may
be included, in order to capture the full extent of the
adenine-graphite sheet interaction. Based on the decay
of vdW forces at large separations, we can efficiently eval-
uate E
nl
c
by introducing two radius cutoffs |r r
0
| < R
i
.
Around a given point in space, a full grid sampling is used
for the E
nl
c
evaluation in the volume within the smallest
radius, while the volume outside the smallest, but within
the largest radius, is evaluated using a sampling of half
the grid points in all directions. Use of R
1
= 6.0
˚
A
and R
2
= 23.0
˚
A converges the contribution to the bind-
ing energy to sub-meV. Details of the implementation is
given in Ref. [18].
III. OTHER COMPUTATIONAL METHODS
To describe the adsorption of adenine on graphite,
an organic molecule interacting with a chemically in-
ert surface, it is imperative that the vdW forces are
well described. The vdW-DF is a first-principles DFT
method, relieving some of the short-comings of previous
(semi-)local approximations of the exchange correlation
term E
xc
in DFT, such as the GGA approximation. It
combines the excellent description of short-range interac-
tions already present in GGA with good descriptions of
the longer-ranged vdW interactions (including systems
where the binding equilibrium configuration has a range
of distances over which the vdW interaction acts).
4
FIG. 2: (Color online) A two-dimensional adenine crystal on the surface of graphite: The configuration used in our estimate of
the binding energy. There are four molecules in the rectangular unit cell. Same color coding of atoms as used in Fig. 1.
FIG. 3: (Color online) Sketch of the procedure for calculating the contributions to
0
E
0
from the adsorption of the adenine
overlayer. (a): The system of adsorbed adenine molecules (black) in a two-dimensional crystal on the graphite surface (medium
gray/brown). (b): Lifting off the sheet of adenine molecules in order to calculated
0
E
0
o-s
. (c): Creating ribbons of adenine
molecules (each of the four molecules in a unit cell participate in a different ribbon) by moving the molecules apart in one
direction, to calculate
0
E
0
s-r
. (d): Each ribbon is taken apart, yielding the energy
0
E
0
r-m
.
The vdW force originates primarily from the most
loosely bound electrons, which for molecular monomers
are in states modified by chemical bonding. It is not di-
rected through nuclear centers, as assumed by some semi-
empirical methods. In the vdW-DF method the vdW in-
teraction is correctly described as an effect originating in
the tails of the electron distribution, and it is well suited
to include effects of image planes [17].
In recent years the system of adenine on graphite has
also been studied by other methods. The authors of Refs.
38 and 39 use semi-empirical methods which add an em-
pirical term for the dispersion to the results of standard
GGA-based DFT calculations. Methods similar to that
have been widely used [40–49], apparently first in 1952
[40].
The empirical term for the dispersion in those methods
incorrectly assumes that the vdW interaction arises in
the atomic centers. Similarly, the often assumed notion
that such forces have strengths given by their asymptotic
free-atom forms is also undocumented.
The earlier users of such methods recognize their ad
hoc or semi-empirical nature. For example, in describing
5
TABLE I: Single adenine molecule adsorption, the values of
the energy terms and distance d at the optimal vdW-DF bind-
ing position, the binding energy E
b
, and the minima of the
revPBE and PBE GGA calculations.
Term d (
˚
A) E (meV)
0
E
0
420
nl
E
nl
c
1131
E = ∆
0
E
0
+
nl
E
nl
c
3.5 711
E
b
(single molecule) = 711 meV
0
E
GGA
tot
with revPBE GGA 5.0 11
0
E
GGA
tot
with PBE GGA 4.0 45
the cutoff leading to the notion of damping functions,
Brooks [40] writes, “This procedure cannot be rigorously
justified, although it is certainly more reasonable than
the use of [the vdW potential] where it is divergent.” Re-
cent damping functions [41–49] take varying forms, but
most require a semi-empirical parameter for each atom-
atom pair.
Ref. 50 is another recent study addressing the adsorp-
tion of nucleobases on graphite. They use Hartree-Fock
(HF) calculations coupled with Møller-Plesset perturba-
tion theory (MP2), in addition to LDA-based
2
DFT. The
approach of HF with MP2 is obviously accurate if the (in
principle infinite) graphite sheet is represented by a suf-
ficiently large flake of graphite, but the approach is then
also very expensive. Thus, to keep the computational ex-
pense down often rather small graphite flakes are used.
The graphite flakes, terminated by hydrogen atoms, are
polycyclic aromatic hydrocarbon (PAH) molecules. In
the following section we discuss the effect of mimicing
the graphite substrate by PAH molecules of insufficient
extension.
Results of the above studies are mentioned in and com-
pared to our vdW-DF results in section IV.
IV. RESULTS AND DISCUSSIONS
The optimal molecular configuration of adenine adsor-
bate is determined by first placing the molecule relative
to the graphite sheet in a configuration that resembles
AB stacking of graphite. Next, we calculate the optimal
2
LDA-based DFT cannot be used as a substitute for the inclusion
of vdW interactions. As pointed out by Harris already in 1985
[51] “LDA predicts attraction between all systems at large sep-
aration mainly because it assigns an unphysically long range to
exchange interactions and not because, in any sense, it simulates
van der Waals interactions.” This issue is summarized and dis-
cussed also in Ref. 33. In some flat systems the numerical results
predicted by LDA happen to end up in the range of the physical
results for these unphysical reasons, whereas in other geometries
the LDA gives results that are not in accordance with experiment
nor with more accurate methods [14, 52, 53].
FIG. 4: (Color online) Top panel: Cohesive energy of adenine
above a graphite surface at distance d. The insert shows the
energy variation for small in-plane rotations of the molecule
around the center of the six-fold ring close to its optimal ad-
sorption structure. The point 0
corresponds to the config-
uration used for the cohesive energy curve. Bottom panel:
Illustration of the wavefunctions of the three lowest vibra-
tional states (arbitrary units on vertical axis for the wave-
functions) in the cohesive energy potential (black line). The
wavefunctions are offset from the potential well bottom by
their vibrational energies.
distance to the graphite layer. Then we rotate and trans-
late the molecule in the plane until optimal in-plane posi-
tions are found, within the accuracy of the method. We
here only consider positions with the adenine molecule
parallel to the graphite plane.
A. Single molecule adsorption
Using the updated in-plane configuration, shown in
Fig. 1, we determine the cohesive energy curve E(d) as
a function of the distance to the surface in the direction
perpendicular to the surface, d (Fig. 4). We find that the
molecule binds at d = 3.5
˚
A above the graphite layer,
with a binding energy E
b
= 711 meV. The exchange part
6
of revPBE is overly repulsive [8] at this distance and thus
we expect our value for the binding energy to be some-
what too small. For naphthalene, an aromatic molecule
with approximately the same number of electrons as ade-
nine, Ref. 27 reports a binding energy of 763 meV, using
the same vdW-DF method and choice of exchange func-
tional as used here. In contrast, as shown in Table I
for adenine and in Ref. 27 for naphthalene, pure GGA
functionals such as revPBE or PBE bind at unphysically
large binding distances (4–5
˚
A) at unphysically low bind-
ing energies (< 50 meV).
For the single adenine molecule, rotation around the
hexagon shows little variation in energy (insert of Fig. 4).
Roughly 90% of this small variation originates from the
E
0
part of the total energy. This confirms that the di-
rectional dependence of the vdW interaction is small.
The vertical vibrational states of the adenine molecule
adsorbed on the graphite sheet may be estimated by solv-
ing the one-dimensional Schr¨odinger equation for the co-
hesive energy potential shown in Fig. 4. We find that the
ground state energy when including zero-point vibrations
is 707.6 meV (up from the result 711 meV without
zero-point vibrations) and the first and second excited
states are found at 700.7 meV and 693.9 meV. This
spectrum of lowest lying states closely resembles that of
a harmonic oscillator at frequency around 6.8 6.9 meV.
The wavefunctions of the three lowest vibrational
states are illustrated in the bottom panel of Fig. 4, off-
set with their vibrational energies. The spatial extension
of these lowest vibrational state wavefunctions is about
0.3
˚
A. In combination with the small energy changes for
lateral motion (illustrated also by the effect of rotational
displacement of adenine, shown in the insert of Fig. 4) we
conclude that the precise position of the adenine molecule
on the surface of graphite has very little bearing on the
binding energy.
In this work and most of the work cited here only the
interaction from one graphite layer is included. If the
molecules adsorb at a (multilayer) graphite surface the
layers below the top graphite layer also contribute to the
interaction, but has previously been shown to be at a
very low level (3%, as discussed in Ref. 27). We therefore
ignore multilayer effects here.
Other groups have studied the adsorption of single
molecule on graphite using other theory methods. Using
DFT-D methods, Ortmann et al. [38] found a binding
energy of 1.01 eV, and a separation of 3.4
˚
A while more
recently Antony et al. [39] found binding at 0.91 eV and
3.0
˚
A, both results are for single molecules adsorbed on
a sheet of graphite. Unlike the above-mentioned and the
present study, the MP2 calculations of Gowtham et al.
[50] use an adenine molecule with a methyl group at-
tached. They find a binding energy 0.94 eV and separa-
tion 3.5
˚
A.
100%
50%
0%
5 10 15
R
cut
[Å]
100%
99%
98%
97%
14 12 10 8 6
R
cut
[Å]
nl
E
c
nl
(R
cut
) /
nl
E
c
nl
(R
i
→ ∞)
nl
E
c
nl
(R
cut
) /
nl
E
c
nl
(R
i
→ ∞)
FIG. 5: Convergence of
nl
E
nl
c
with graphite sheet cutoff
radius R
cut
, relative to a calculation with converged values of
the cutoff radii, R
1
and R
2
. The use of converged values of R
1
and R
2
is symbolically denoted R
i
”. The calculations
are carried out for a single adenine molecule on a sheet of
graphite at the optimal position (d = 3.5
˚
A).
B. Graphite size convergence test study
We use calculations of the long-range correlation con-
tribution,
nl
E
nl
c
, to estimate the effect of using small
PAH molecules as substitutes for the graphite sheet in
the MP2 calculations of Ref. 50 and other similar stud-
ies. We perform a number of crude but generous test
calculations. The tests are available directly from the
vdW-DF method simply by restricting the cutoff radii
R
1
and R
2
in the
nl
E
nl
c
calculations by the value R
cut
.
Figure 5 illustrates the convergence of
nl
E
nl
c
with
R
cut
. The value of R
cut
sets the amount of interactions
with the graphite sheet included. For R
cut
9
˚
A Fig. 5
shows that about 1% of the interaction is discarded. In
the production runs we find that at more than 6
˚
A dis-
tance between interacting points only every second grid
point in each direction needs to be included, which is re-
flected in our choice of R
1
= 6
˚
A (and R
2
= 23
˚
A). For
our convergence tests we further do not include any pairs
of points in space r and r
0
that have |r r
0
| > R
cut
. The
value Rcut = 9
˚
A corresponds approximately to the use
of a 96 C atom PAH molecule as a representant for the
graphite sheet, for which we therefore predict that 1%
of the interaction (compared to graphite) is lost.
For smaller R
cut
the convergence is much worse, as il-
lustrated in the insert of Figure 5. If we include only a
radius of 4
˚
A, corresponding approximately to the inclu-
sion of 24–30 C atoms of the graphite sheet in the ∆
nl
E
nl
c
calculation (2) we loose 21% of the interaction contribu-
tion. We therefore estimate that the use of a 28 C atom
PAH molecule in Ref. 50 misses an important part of the
long-range interaction compared to the use of graphite or
a larger size of PAH molecule.
Our convergence tests are not fully equivalent to using
PAH molecules to model the graphite layer, such as done
in the MP2 calculations. This is because for this E
nl
c
cal-
7
culation any point on the adenine molecule is paired with
all grid points at a distance less than R
cut
, even those out-
side the volume covered by a PAH model substitute. At
a specified cutoff radius R
cut
this test is therefore more
generous than a similar calculation using a PAH molecule
having roughly the radius R
cut
.
Another test of the effect of using small PAH molecules
instead of graphite as a substrate is reported in Ref. 39,
using actual PAH molecules but an empirical dispersion
term (via DFT-D). There, similar results were found: re-
ducing the size of the PAH molecule from 150 C atoms
to 24 C atoms caused a loss of 24% of the dispersion
interaction (from 32.9 kcal/mol to 24.9 kcal/mol for
adenine). The use of a 150 C atom PAH molecule roughly
corresponds to the value 11
˚
A of our cutoff radius R
cut
,
where we find minimal ( 0.4%) loss of interaction com-
pared to a converged size (Fig. 5).
C. Adenine overlayer
Some molecular adsorbates, such as adenine molecules
[3, 4], can spontaneously form an ordered lattice on a
graphite surface. Here we present an estimate of the for-
mation energy of the two-dimensional adenine crystal.
This calculation illustrates the potential of the vdW-DF
method to discern the different phases of adsorbate crys-
tals and can therefore lend credibility to interpretations
of scanning-tunneling microscopy images.
Figure 2 shows the molecular position on the surface of
graphite for the two-dimensional adsorbate crystal. The
crystal symmetry is chosen to be the same as that de-
termined with the force-field calculations in Ref. 4, but
with the molecules each in a configuration relative to the
graphite layer identical to our single adsorbate result.
TABLE II: Various contributions to the adenine overlayer
binding energy E
b
, per adenine molecule. Values at the opti-
mal graphite-overlayer separation d = 3.5
˚
A.
Term Energy (meV)
nl
E
nl
c
1780
0
E
0
o-s
482
0
E
0
s-r
199
0
E
0
r-m
93
0
E
0
= ∆
0
E
0
o-s
+
0
E
0
s-r
+
0
E
0
r-m
774
E = ∆
0
E
0
+
nl
E
nl
c
1006
E
b
(overlayer) = 1006 meV
E
b
(overlayer) - E
b
(single molecule) 295
E
b
(free-floating crystal) 239
In the process of calculating the cohesive energy E (the
difference between the adenine overlayer on the graphite
sheet and the adenine molecules all lifted off individually)
a number of partial energy terms are calculated, corre-
sponding to the terms illustrated in Fig. 3. These partial
energy terms are provided in Table II.
We determine the binding energy of the adenine over-
layer to be 1006 meV per molecule, which is larger than
that of an isolated adenine molecule. The energetic gain
of the system when single, adsorbed molecules are moved
together to form an overlayer crystal (the overlayer for-
mation energy), is found to be 295 meV per molecule
in our not-fully optimized overlayer crystal structure.
This result shows that a two-dimensional ordered crystal
structure is energetically much more preferred than iso-
lated molecules on the surface, in agreement with exper-
imental findings showing spontaneous formation of the
adenine crystal overlayers [3, 4]. Using TDS the binding
energy of adenine clusters on graphite has been measured
to be 23.2 kcal/mol (1006 meV per molecule) [5], in very
good agreement with our results for the crystal overlayer.
The value of the overlayer formation energy may be
compared to the energy gained by creating a free-floating
two-dimensional adenine crystal (with the same structure
as the overlayer) from isolated molecules, E
b
(free-floating
crystal) = 239 meV/molecule. The gain of assembling
the crystal on the graphite surface (295 meV/molecule)
instead of away from the graphite (239 meV/molecule)
is a mere 56 meV/molecule, not insignificant but clearly
smaller than the effect of the mutual binding of the ade-
nine molecules. Of course, if the free-floating adenine
molecules were allowed to assemble in the most optimal
structure, the molecules would stack and the gain in bind-
ing energy would increase to about 300 meV/molecule,
depending on the details [12].
V. CONCLUSIONS
We use the first-principles vdW-DF method to study
the adsorption of adenine on graphite. We find that the
adenine molecule is physisorped at a distance 3.5
˚
A above
the graphite surface. We also find that the physisorption
well is shallow and therefore small changes in position
(all directions and rotations) lead to only small changes
in adsorption energy; the molecule is mobile.
Our calculations show an adsorption energy of 711
meV per molecule for adenine molecules far apart on the
surface, whereas molecules forming a two-dimensional
overlayer cluster gain significantly more: 1006 meV per
molecule, both situations compared to molecules floating
off as a dilute gas.
The small barriers for changing the position, men-
tioned above, along with this 295 meV/molecule gain per
molecule for moving molecules closer together, is consis-
tent with the tendency of adenine on graphite to assemble
into clusters of two-dimensional overlayers. We find that
although it is more favorable for the adenine molecules
to form the overlayer crystal at the graphite surface, the
largest part of the energy gain, about 239 meV/molecule,
is also obtained in the (unphysical) situation of the ade-
nine molecules being moved together into the same posi-
tions but without having a graphite surface nearby. The
role of the graphite surface in forming clusters therefore
8
seems to be mainly to attract the molecules and orient
them (flat on the surface) before assembly into cluster,
rather than contributing any major part to the cluster
formation energy.
In a crude estimate of the effect of using small PAH
molecules to model the graphite surface we found that an
important part of the long-ranged correlation effects are
lost in such models. If a PAH molecule is used to model
graphite, it must be significantly larger than the adsorbed
molecule: in the case of adenine we estimate that a 96 C
atom PAH molecule is the smallest acceptable, and for
full convergence an even larger PAH molecule should be
used. For comparison, a 96 C atom PAH molecule has
the approximate radius 9
˚
A and the adenine radius is
approximately 2.5
˚
A.
In summary, we find adsorption energies of adenine
on graphite using vdW-DF. The energies are calculated
both for single adenine molecules on a graphite sheet
and a two-dimensional crystal overlayer of adenine on
a graphite sheet. The adsorption energy is highest per
molecule for the overlayer compared to single molecular
adsorption, in agreement with the tendency to cluster
formation seen in experiment.
Acknowledgments
We thank P. Hyldgaard and B.I. Lundqvist for useful
discussions. Partial support from the Swedish Research
Council (VR) to ES and SC is gratefully acknowledged.
We also acknowledge the allocation of computer time at
UNICC/C3SE (Chalmers) and SNIC (Swedish National
Infrastructure for Computing) and funding from SNIC
for KB’s participation in the national graduate school
NGSSC. Work at Rutgers supported by NSF Grant
DMR-0801343.
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