Physical Chemistry Chemical Physics

This paper is published as part of a PCCP Themed Issue on:

Stacking Interactions

Guest Editor: Pavel Hobza

Editorial

Stacking interactions Phys. Chem. Chem. Phys., 2008, 10, 2581 DOI: 10.1039/b805489b Perspectives

Nature and physical origin of CH/π interaction: significant difference from conventional hydrogen bonds Seiji Tsuzuki and Asuka Fujii, Phys. Chem. Chem. Phys., 2008, 10, 2584 Nature and magnitude of aromatic stacking of nucleic acid bases Ji í poner, Kevin E. Riley and Pavel Hobza, Phys. Chem. Chem. Phys., 2008, 10, 2595 Papers

Intermolecular π–π interactions in solids Miroslav Rube and Ota Bludský, Phys. Chem. Chem. Phys., 2008, 10, 2611 Induction effects in metal cation–benzene complexes Ignacio Soteras, Modesto Orozco and F. Javier Luque, Phys. Chem. Chem. Phys., 2008, 10, 2616 Crystal packing of TCNQ anion π-radicals governed by intermolecular covalent π–π bonding: DFT calculations and statistical analysis of crystal structures Jingsong Huang, Stephanie Kingsbury and Miklos Kertesz, Phys. Chem. Chem. Phys., 2008, 10, 2625 A post-SCF complete basis set study on the recognition patterns of uracil and cytosine by aromatic and π–aromatic stacking interactions with amino acid residues Piotr Cysewski, Phys. Chem. Chem. Phys., 2008, 10, 2636 Substituent effects in parallel-displaced π–π interactions Stephen A. Arnstein and C. David Sherrill, Phys. Chem. Chem. Phys., 2008, 10, 2646

The excited states of π-stacked 9-methyladenine oligomers: a TD-DFT study in aqueous solution Roberto Improta, Phys. Chem. Chem. Phys., 2008, 10, 2656 The post-SCF quantum chemistry characteristics of the guanine–guanine stacking B-DNA Piotr Cysewski, aneta Czy nikowska, Robert Zale ny and Przemys aw Czele , Phys. Chem. Chem. Phys., 2008, 10, 2665 Thermodynamics of stacking interactions in proteins Simone Marsili, Riccardo Chelli, Vincenzo Schettino and Piero Procacci, Phys. Chem. Chem. Phys., 2008, 10, 2673 Through-space interactions between parallel-offset arenes at the van der Waals distance: 1,8-diarylbiphenylene syntheses, structure and QM computations Franco Cozzi, Rita Annunziata, Maurizio Benaglia, Kim K. Baldridge, Gerardo Aguirre, Jesús Estrada, Yongsak Sritana-Anant and Jay S. Siegel, Phys. Chem. Chem. Phys., 2008, 10, 2686 Ab initio study of substituent effects in the interactions of dimethyl ether with aromatic rings Jay C. Amicangelo, Benjamin W. Gung, Daniel G. Irwin and Natalie C. Romano, Phys. Chem. Chem. Phys., 2008, 10, 2695 A QM/MM study of fluoroaromatic interactions at the binding site of carbonic anhydrase II, using a DFT method corrected for dispersive interactions Claudio A. Morgado, Ian H. Hillier, Neil A. Burton and Joseph J. W. McDouall, Phys. Chem. Chem. Phys., 2008, 10, 2706 Searching of potential energy curves for the benzene dimer using dispersion-corrected density functional theory Prakash Chandra Jha, Zilvinas Rinkevicius, Hans Ågren, Prasenjit Seal and Swapan Chakrabarti, Phys. Chem. Chem. Phys., 2008, 10, 2715

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Structures and interaction energies of stacked graphene–nucleobase complexes Jens Antony and Stefan Grimme, Phys. Chem. Chem. Phys., 2008, 10, 2722 Describing weak interactions of biomolecules with dispersion-corrected density functional theory I-Chun Lin and Ursula Rothlisberger, Phys. Chem. Chem. Phys., 2008, 10, 2730 Physical origins of interactions in dimers of polycyclic aromatic hydrocarbons Rafa Podeszwa and Krzysztof Szalewicz, Phys. Chem. Chem. Phys., 2008, 10, 2735 Benchmark database on isolated small peptides containing an aromatic side chain: comparison between wave function and density functional theory methods and empirical force field Haydee Valdes, Kristýna Pluhá ková, Michal Pitonák, Jan

ezá and Pavel Hobza, Phys. Chem. Chem. Phys., 2008, 10, 2747 Scope and limitations of the SCS-MP2 method for stacking and hydrogen bonding interactions Rafa A. Bachorz, Florian A. Bischoff, Sebastian Höfener, Wim Klopper, Philipp Ottiger, Roman Leist, Jann A. Frey and Samuel Leutwyler, Phys. Chem. Chem. Phys., 2008, 10, 2758 The interaction of carbohydrates and amino acids with aromatic systems studied by density functional and semi-empirical molecular orbital calculations with dispersion corrections Raman Sharma, Jonathan P. McNamara, Rajesh K. Raju, Mark A. Vincent, Ian H. Hillier and Claudio A. Morgado, Phys. Chem. Chem. Phys., 2008, 10, 2767 Probing the effects of heterogeneity on delocalized π···π interaction energies Desiree M. Bates, Julie A. Anderson, Ponmile Oloyede and Gregory S. Tschumper, Phys. Chem. Chem. Phys., 2008, 10, 2775 Competition between stacking and hydrogen bonding: theoretical study of the phenol···Ar cation and neutral complex and comparison to experiment Ji í erný, Xin Tong, Pavel Hobza and Klaus Müller-Dethlefs, Phys. Chem. Chem. Phys., 2008, 10, 2780 Calculating stacking interactions in nucleic acid base-pair steps using spin-component scaling and local second order Møller–Plesset perturbation theory J. Grant Hill and James A. Platts, Phys. Chem. Chem. Phys., 2008, 10, 2785

Controlled aggregation of adenine by sugars: physicochemical studies, molecular modelling simulations of sugar–aromatic CH–π stacking interactions, and biological significance Marc Maresca, Adel Derghal, Céline Carravagna, Séverine Dudin and Jacques Fantini, Phys. Chem. Chem. Phys., 2008, 10, 2792 Computational comparison of the stacking interactions between the aromatic amino acids and the natural or (cationic) methylated nucleobases Lesley R. Rutledge, Holly F. Durst and Stacey D. Wetmore, Phys. Chem. Chem. Phys., 2008, 10, 2801 Computational characterization and modeling of buckyball tweezers: density functional study of concave–convex π···π interactions Yan Zhao and Donald G. Truhlar, Phys. Chem. Chem. Phys., 2008, 10, 2813 Non-standard base pairing and stacked structures in methyl xanthine clusters Michael P. Callahan, Zsolt Gengeliczki, Nathan Svadlenak, Haydee Valdes, Pavel Hobza and Mattanjah S. de Vries, Phys. Chem. Chem. Phys., 2008, 10, 2819 N–H···π interactions in pyrroles: systematic trends from the vibrational spectroscopy of clusters Ingo Dauster, Corey A. Rice, Philipp Zielke and Martin A. Suhm, Phys. Chem. Chem. Phys., 2008, 10, 2827 Experimental and theoretical determination of the accurate interaction energies in benzene–halomethane: the unique nature of the activated CH/π interaction of haloalkanes Asuka Fujii, Kenta Shibasaki, Takaki Kazama, Ryousuke Itaya, Naohiko Mikami and Seiji Tsuzuki, Phys. Chem. Chem. Phys., 2008, 10, 2836 IR/UV spectra and quantum chemical calculations of Trp–Ser: Stacking interactions between backbone and indole side-chain Thomas Häber, Kai Seefeld, Gernot Engler, Stefan Grimme and Karl Kleinermanns, Phys. Chem. Chem. Phys., 2008, 10, 2844 Fluorine substitution and nonconventional OH···π intramolecular bond: high-resolution UV spectroscopy and ab initio calculations of 2-(p-fluorophenyl)ethanol Rosen Karaminkov, Sotir Chervenkov and Hans J. Neusser, Phys. Chem. Chem. Phys., 2008, 10, 2852 CH/π interactions in methane clusters with polycyclic aromatic hydrocarbons Seiji Tsuzuki, Kazumasa Honda, Asuka Fujii, Tadafumi Uchimaru and Masuhiro Mikami, Phys. Chem. Chem. Phys., 2008, 10, 2860

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Structures and interaction energies of stacked graphene–nucleobase

complexesw

Jens Antony and Stefan Grimme*

Received 5th December 2007, Accepted 5th February 2008

First published as an Advance Article on the web 5th March 2009

DOI: 10.1039/b718788b

The noncovalent interactions of nucleobases and hydrogen-bonded (Watson–Crick) base-pairs on

graphene are investigated with the DFT-D method, i.e., all-electron density functional theory

(DFT) in generalized gradient approximation (GGA) combined with an empirical correction for

dispersion (van der Waals) interactions. Full geometry optimization is performed for complexes

with graphene sheet models of increasing size (up to C150H30). Large Gaussian basis sets of at

least polarized triple-z quality are employed. The interaction energies are extrapolated to infinite

lateral size of the sheets. Comparisons are made with B2PLYP-D and SCS-MP2 single point

energies for coronene and C54H18 substrates. The contributions to the binding (Pauli exchange

repulsion, electrostatic and induction, dispersion) are analyzed. At a frozen inter-fragment

distance, the interaction energy surface of the rigid C96H24 and base monomers is explored in

three dimensions (two lateral and one rotational). Methodologically and also regarding the results

of an energy decomposition analysis, the complexes behave like other p-stacked systems examined

previously. The sequence obtained for the interaction energy of bases with graphene (G 4 A 4T 4 C 4 U) is the same for all methods and supports recent experimental findings. The absolute

values are rather large (about �20 to �25 kcal mol�1) but in the expected range for p-systems of

that size. The relatively short equilibrium inter-plane distance (about 3 A) is consistent with

atomic force microscopy results of monolayer guanine and adenine on graphite. In

graphene� � �Watson–Crick pair complexes, the bases lie differently from their isolated energy

minima leading to geometrical anti-cooperativity. Together with an electronic contribution of 2

and 6%, this adds up to total binding anti-cooperativities of 7 and 12% for AT and CG,

respectively, on C96H24. Hydrogen bonds themselves are merely affected by binding on graphene.

I. Introduction

The deoxyribose nucleic acid (DNA) bases adenine (A),

thymine (T), cytosine (C), guanine (G), as well as uracil (U)

due to their Watson–Crick complementarity constitute the

naturally occurring storage of genetic information. It has been

shown that purine and pyrimidine bases can spontaneously

self-assemble at the interface between water and the surfaces of

crystalline inorganic solids,1 supporting the suggestion that

inorganic mineral surfaces might be involved in the origin of

life. The experimental techniques for studying adsorption of

DNA bases on graphite comprise scanning tunneling micro-

scopy (STM),1–6 atomic force microscopy (AFM),4,7 low-

energy electron diffraction (LEED),6 and thermal-desorption

spectroscopy (TDS).6 The combined theoretical, LEED, and

STM study has shown that the observed molecular structure is

commensurate with the graphite substrate, forming a hydro-

gen-bonded network with four bonds per molecule.6 In this

study, the contrast in the STM image was interpreted as being

dominated by geometrical height variations of the tilted

molecules. The evaluation of experimental data is frequently

assisted by molecular mechanics calculations8 and semi-em-

pirical molecular orbital simulations.9

Theoretical understanding of organic molecule binding on

inert surfaces, however, requires a quantum mechanical treat-

ment with an adequate modelling of dispersion forces.10 The

following studies are related to the simulation of molecule–

substrate interactions for the particular case of DNA bases on

graphite. Recently, the adsorption of adenine on graphite has

been modelled by the local density (LDA) and generalized

gradient approximation (GGA) supplemented by the London

dispersion formula for the van der Waals (vdW) interaction in

a plane-wave basis.10,11 In ref. 12, the DFT-LDA approach

has been extended to the nucleobases cytosine, guanine,

thymine, and uracil, with additional calculations utilizing

second-order Møller–Plesset perturbation theory. Also other

adsorbates than DNA bases have been considered. The vdW-

DF theory13 is applied to the adsorption of benzene and

naphthalene on an infinite sheet of graphite, as well as the

binding between two graphite sheets.14 The adsorption of Ar

on graphite has been computed using Kohn–Sham (KS)

density functional theory extended by an empirical nonlocal

Universitat Munster Organisch-Chemisches Institut, Corrensstrasse40, D-48149 Munster, Germany. E-mail: grimmes@uni-muenster.dew Electronic supplementary information (ESI) available: B97-D/TZV(d,p) 3-D potential energy surface of adenine, thymine, cytosine,guanine and uracil on C96H24 (Fig. S1–S5); intermolecular interactionenergies of different size graphene sheet complexes with adenine,thymine, cytosine, guanine and uracil (Fig. S6–S10). See DOI:10.1039/b718788b

2722 | Phys. Chem. Chem. Phys., 2008, 10, 2722–2729 This journal is �c the Owner Societies 2008

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

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and atom-centered potential.15 Water cluster assemblies on a

graphite surface have been treated with the density functional

tight-binding method complemented with an empirical vdW

force correction.16 Finally, also carbon nanotubes as sub-

strates for adenine and thymine and their radicals,17 DNA

bases,18,19 a DNA segment,20,21 and a related molecule (flavin

adenine dinucleotide)22 have been considered theoretically.

Being mainly involved with molecule–substrate interactions

and the accompanying changes of the molecular properties, to

our knowledge none of the theoretical studies has dealt yet

with the influence of organic molecule adsorption on hydrogen

bonding properties of DNA bases at the ab initio level.

In ref. 23 both the interlayer interaction energy and equili-

brium distance of graphene are obtained accurately with the

DFT-D method. From many previous studies it is known that

the accuracy of DFT-D calculated intermolecular interaction

energies is about 10%. The average deviation of DFT-D from

estimated CCSD(T) intermolecular interaction energies for

165 biologically relevant complexes is even smaller.24 Actually,

the DFT-D error is of the same order as that of the reference

data and the DFT-D results have essentially coupled cluster

accuracy for electronically not too complicated systems. Here

we extend this rather accurate approach to the adsorption of

DNA bases and base-pairs on graphene.

As done in ref. 23 the graphene sheet is modelled by

extrapolation using a sequence of polycyclic aromatic hydro-

carbons with increasing size. Thus the infinite conducting

graphene is represented by finite systems whose

HOMO-LUMO gaps, though decreasing, are not zero.

Ref. 23 shows that this extrapolation yields an LDA result

for the interlayer interaction energy of graphite which is in

agreement with periodic computations thus demonstrating the

reliability of the procedure based on non-periodic calculations.

It is a feature of the DFT-D approach used here, that the van

der Waals coefficients are not changed, e.g., with the size of the

aromatic hydrocarbon. As this fact could be a source of error

(see, e.g., ref. 25), the DFT-D intermolecular interaction

energies are supplemented by results from wavefunction

based26 and double-hybrid density functional27,28 methods

which account for the effect of differences in response proper-

ties on induction and dispersion interactions. But again we

refer to ref. 23 where it is shown that the interaction energy of

two graphene sheets obtained by DFT-D supports the most

recent experimental estimate for the exfoliation energy of

graphite.

The adsorption of molecules on metal surfaces can be

naturally treated by DFT in a supercell framework (see, e.g.,

ref. 29). Such plane-wave based calculations to study

the interaction between DNA bases and graphene have

recently been reported10–12 and we compare our results to this

alternative approach below in detail. A further approach to

the intermolecular interaction of large molecules is that

based on a fragmentation scheme (see, e.g., ref. 30). However,

we are not aware of an application to the nucleobase graphene

system yet. Finally, qualitative insight into the lateral interac-

tion energy between pairs of molecules influenced by the

presence of a conducting surface can be obtained by image

theory (see, e.g., ref. 31). As the conductivity of graphite is

highly anisotropic, this approach does not work easily in the

case studied here, and we resort to an all atom treatment in the

following.

We provide fully optimized structures and accurate binding

energies, giving also methodological insight into organic mo-

lecule binding on inert (organic) surfaces. Our particular focus

is on the effect of the graphene substrate on the hydrogen bond

in the Watson–Crick base-pair and the (anti)cooperativity of

base-pair binding. Furthermore we analyze the character of

the intermolecular interactions in comparison to systems with

less polar components (i.e., interacting hydrocarbons).

Comparison to results of previous work illustrates limitations

of LDA in modelling noncovalent interactions for large

systems.

II. Technical details

All structures have been optimized with the dispersion cor-

rected density functional theory (DFT-D) from ref. 32 that has

been described before in ref. 33. In this approach the total

DFT energy EKS-DFT is augmented by an empirical dispersion

correction Edisp,

EDFT-D = EKS-DFT + Edisp.

Edisp is given by

Edisp ¼ �s6XNat�1

i¼1

XNat

j¼iþ1

Cij6

R6ij

fdmpðRijÞ:

Here, Nat is the number of atoms in the system, Cij6 denotes the

dispersion coefficient for atom pair ij, s6 is a global scaling

factor that only depends on the functional used, Rij is an

interatomic distance, and fdmp(Rij) is a damping function to

avoid near-singularities for small R and electron correlation

double-counting effects.32 DFT-D and related methods are

reviewed in ref. 34. Large Gaussian AO basis sets of heavily

polarized triple-35 or quadruple-z quality36 are employed, that

provide DFT results very close to the basis set limit. Inter-

molecular interaction energies are calculated in the super-

molecular approach. The basis set superposition error

(BSSE) has been treated by counterpoise (CP) correction37

when indicated. The intermolecular interaction energy is sub-

jected to an energy decomposition analysis (EDA) as described

originally in ref. 38. The DFT-D results are compared to spin-

component scaled MP2 (SCS-MP2)26 and double-hybrid den-

sity functional (B2PLYP-D)27,28 interaction energies. Both

methods account quantum mechanically for the non-local

character of non-covalent interactions. Density fitting techni-

ques, also called resolution-of-the-identity (RI) approxima-

tion, were used throughout to speed up MP239 and DFT GGA

computations40,41 roughly by a factor of 10–20 at insignificant

extra inaccuracy. All results have been obtained with a slightly

modified version of the Turbomole program package.42 The

Gaussian atomic orbital (AO) basis sets are taken from the

Turbomole library.43 A reduced geometry optimization con-

vergence criterion of 10�7 Eh for the total energy difference

between two consecutive optimization steps is used. For the

quadrature of the exchange–correlation terms, the multiple

grid m4 has been specified. All other computational para-

meters have been chosen as their default values.

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III. Results and discussion

A. Geometries of DNA bases

Starting with the structures of the graphene sheet model

dimers from ref. 23 with 24, 54, 96, and 150 carbon atoms

per monomer, we replaced one of the sheets by a DNA

nucleobase. The resulting complex was then fully optimized

using the DFT-D approach to electronic structure with the

B97-D functional and a triple-zeta valence plus polarization

basis set TZV(d,p). As an example the resulting minimum

energy structures for the C96H24 sheet are shown in Fig. 1. In

the optimized structures, the nucleobase is parallel displaced

with respect to the graphene sheet, so that all carbonyl oxygen

atoms and most of the nitrogen atoms are placed above the

centers of the carbon rings. No significant tilting of the bases is

observed.

The average distance of the heavy atoms of the bases from

the root mean square (RMS) plane through the carbon atoms

of the sheet is given in Table 1. The average distance decreases

with increasing size of the sheet, from about 3.2 A in the

complexes with coronene to about 3.0 A on the C96H24 sheet.

On C150H30, the distance is even smaller, but the rate of

decrease gets slower for larger sheets and the distances con-

verge to a value just below 3.0 A. The inter-ring distance of the

five bases shows only a weak correlation with the magnitude of

the interaction energy (see below).

The structure of the bases is merely affected by the interac-

tion with the graphene sheet. When superimposing their free

structure with the base in the complex, the average distance

between the heavy nucleobase atoms is typically only about

1 pm (Table 1). The main structural relaxation upon binding is

that the acidic protons, attracted by the quadrupole moment

of the carbon rings, are slightly bent towards the surface.

To explore the roughness of the surface potential and

possible other binding modes, we performed for each of the

bases a potential energy scan (PES) in three dimensions. Using

the average distance between the heavy base atoms and the

average plane through the carbon atoms in the sheet of the

fully optimized complex (Table 1), the optimized uncomplexed

structures of the nucleobase and C96H24 are placed parallel to

each other with their respective centers on top. One center is

then displaced in the molecular plane by 2.6 A from �1.3 to

1.3 in steps of 0.2 A for four angular orientations of the (rigid)

monomers differing by 151. The results are shown in the ESI

(Fig. S1 to S5).w The most important result from the PES is,

that no other minima than the ones shown in Fig. 1 are found.

This conclusion is only true if the sheet is sufficiently large, so

that effects from its edge are not important. For the

U� � �coronene and the U� � �C54H18 complexes we found one

additional binding motif different from the one shown in

Fig. 1, which were also different from each other. However,

on the C96H24 sheet neither of them is present.

The roughness of the graphene surface is estimated by the

maximal energy difference obtained. It amounts to 5.2 kcal

mol�1 for the A� � �C96H24, 5.7 kcal mol�1 for the T� � �C96H24,

5.0 kcal mol�1 for the C� � �C96H24, 5.7 kcal mol�1 for the

G� � �C96H24, and 4.3 kcal mol�1 for the U� � �C96H24 complex.

As these values correspond to a fixed intermolecular distance,

the actual barriers between symmetry equivalent local minima

will actually be slightly lower. In any case, this would allow an

almost free lateral motion of isolated bases on the sheet at

elevated temperatures.

In ref. 12 complexes of A, C, G, T and U with graphene

have been investigated using DFT-LDA with a plane-wave

basis. Compared to the inter-plane separation of 3.5 A ob-

tained by LDA, we found smaller values of about 3.0 A.

According to previous experience for many vdW complexes,

the typical B97-D error for such distances is 0.05–0.1 A. Note

that also the inter-plane separation between two graphene

sheets is obtained correctly at this B97-D level.23 Such short

inter-plane separations of about 3.0 A seem plausible, as

already the corresponding values for p-stacked base-pairs

reach about 3.2 A.32,33 Strong long-range dispersion interac-

tions with the sheet and the high polarizability of graphene

would easily allow closer contact. The value of 3.0 A is

consistent with the thickness of guanine and adenine mono-

layers on graphite measured by atomic force microscopy.4

The too large LDA distances are attributed to an inaccurate

treatment of dispersion interactions. Furthermore our equili-

brium geometries of Fig. 1 are slightly displaced with respect

to those of Fig. 2 in ref. 12, where the models of the

nucleobases differ from the present work by an attached

methyl group at the position of the 10 carbon of the deoxy-

ribose or ribose of the corresponding nucleoside. Beside this,

the difference between the LDA and B97-D binding geome-

tries can be explained by electrostatics. For the larger LDA

separations, the partial charges are dominating, while at

smaller distances also higher moments play a role.

B. Intermolecular interaction energies

Table 2 shows B97-D intermolecular interaction energies DEwith several basis sets and the results of an energy decomposi-

tion analysis (EDA) with the TZV(d,p) basis for the fully

optimized structures from Table 1. No counterpoise correction

has been applied to the results except for the calculations on

coronene with the quadruple-z basis which are used to esti-

mate the complete basis set (CBS) limit. The DE values

increase with the size of the sheet. For the C96H24 sheet they

range from �16 kcal mol�1 for the complex with uracil to

Fig. 1 B97-D/TZV(d,p) optimized structures of DNA bases adenine,

thymine, cytosine, (top from left to right) guanine, and uracil (bottom

from left to right) on C96H24.

2724 | Phys. Chem. Chem. Phys., 2008, 10, 2722–2729 This journal is �c the Owner Societies 2008

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�24 kcal mol�1 for the complex with guanine, i.e., they are

about �20 kcal mol�1 on average. The sequence of the

intermolecular interaction energies is the same on all sheets

G 4 A \ T \ C 4 U. The exception, that DE for the

T� � �coronene complex is larger than for A� � �coronene, is dueto interactions with the edge of coronene. The calculations on

coronene show that the basis set incompleteness effect for the

TZV(d,p) basis set amounts to 5–7% of DE, similar to what

reported in ref. 23 for graphene sheets or for complexes of

aromatic systems in ref. 32.

The additional gain in energy at the B97-D/TZV(d,p) level

between the C96H24 and C150H30 sheets is only about 0.5 kcal

mol�1 or less (0.2, 0.4, 0.1, 0.5, and 0.3 kcal mol�1 for the

complexes with A, T, C, G, and U, respectively). The limiting

value for an infinitely sized sheet is estimated with a similar

formula as was used in ref. 23 for the case of two sheets in

graphene, namely DE = an/(b + n), where n is the number of

carbon atoms in the graphene sheet model. The results of the

extrapolation differ from the interaction energies with the

C150H30 sheet by about twice the value of the C96H24 to

C150H30 difference, i.e., up to 1 kcal mol�1 (0.3, 0.7, 0.2, 1.0,

and 0.5 kcal mol�1 for A, T, C, G, and U, respectively, see

Table 2). Comparing the values computed with the extrapola-

tion formula and the calculated DE values, larger deviations

for the smaller sheets, as in the case of the graphene sheet

model dimers where the values visibly fall onto the extrapola-

tion curve,23 are observed (Fig. S6 to S10 in the ESI).w In

particular, the interaction energies of the complexes with

coronene are smaller than those estimated with the extrapola-

tion formula. We ascribe this discrepancy to interactions

between the edge of the sheet and the DNA base, which is

more polar than the graphene sheet model used in ref. 23.

Consequently, the two parameters in the extrapolation equa-

tion a and b were determined using only the values with the

two largest sheets, C96H24 and C150H30.

For the optimized structures an energy decomposition

analysis (EDA) at the B97-D/TZV(d,p) level has been per-

formed.34 For recent reports of the decomposition of base pair

interaction energies at the SAPT level, see ref. 44 and 45. The

resulting components of the interaction energies (exchange

repulsion (EXR), electrostatic, induction, and dispersion) are

listed in Table 2 and displayed as bar diagrams together with

the dimer of the corresponding graphene sheet model in Fig. 2.

According to previous experience, the following results remain

qualitatively unchanged with a larger basis set.

There is a strong dispersion contribution to the interaction

energy in all cases. The electrostatic and induction compo-

nents alone do not compensate for the EXR, so that there is no

binding at the dispersion-uncorrected DFT level. As typical

vdW complexes, the dispersion almost compensates for EXR,

and both dispersion and EXR are larger than the electrostatic

component on an absolute scale. For the case of a strongly

polar or electrostatically bound complex in contrast, the

electrostatic or the sum of the electrostatic and induction

components already overcompensate for the EXR. Unlike in

a completely unpolar complex like, e.g., the coronene or

Table 1 Structural data of B97-D/TZV(d,p) optimized graphene–nucleobase complexes (A)

Size of the graphene sheet Geometrical parametersa A T C G U

24 �zn 3.26 3.23 3.19 3.20 3.22�z00n 0.01 0.01 0.01 0.02 0.01

54 �zn 3.11 3.10 3.04 3.05 3.09�z00n 0.01 0.01 0.01 0.02 0.01

96 �zn 3.03 3.01 2.97 3.01 3.00�z00n 0.01 0.02 0.01 0.01 0.01

150 �zn 2.99 2.94 2.89 2.87 2.91�z00n 0.01 0.02 0.01 0.02 0.01

a �zn average distance of the heavy (non-hydrogen) nucleobase atoms from the RMS plane through the graphene carbon atoms. �z00n average distanceof the heavy nucleobase atoms from a superimposed uncomplexed nucleobase.

Table 2 B97-D intermolecular interaction energies (DE, kcal mol�1)with various AO basis sets (counterpoise uncorrected) and theircomponents from an EDA with the TZV(d,p) basis set of B97-D/TZV(d,p) optimized graphene–nucleobase complexes from Table 1

A T C G U

24 CBSa �13.5 �14.7 �13.0 �17.4 �12.6QZVP �13.6 �14.9 �13.1 �17.6 �12.7TZV(2df,2pd) �14.0 �15.1 �13.6 �18.0 �13.0TZV(2d,2p) �14.2 �15.4 �13.7 �18.3 �13.2TZV(d,p) �14.5 �15.6 �14.1 �18.9 �13.5EXR 31.0 33.0 31.5 39.4 27.9ES �14.9 �17.5 �15.9 �22.0 �15.0Ind �5.7 �6.5 �7.2 �8.4 �6.1Disp �24.9 �24.5 �22.5 �27.9 �20.3

54 TZV(2df,2pd) �19.0 �17.7 �17.6 �22.9 �15.2TZV(2d,2p) �19.3 �18.0 �17.8 �23.3 �15.4TZV(d,p) �19.8 �18.4 �18.4 �24.1 �15.8EXR 38.0 36.2 37.0 46.5 30.7ES �18.1 �16.8 �17.4 �22.4 �13.7Ind �8.0 �8.1 �10.0 �12.0 �8.1Disp �31.7 �29.8 �28.0 �36.2 �24.8

96 TZV(2d,2p) �20.2 �19.0 �18.5 �24.2 �16.3TZV(d,p) �20.7 �19.4 �19.2 �25.2 �16.7EXR 38.4 37.4 37.1 47.3 32.0ES �17.0 �15.9 �16.2 �20.4 �11.7Ind �9.4 �9.7 �11.3 �14.5 �10.9Disp �32.8 �31.2 �28.8 �37.8 �26.1

150 TZV(2d,2p) �20.3 �19.3 �18.8 �24.9 �16.5TZV(d,p) �20.9 �19.7 �19.3 �25.7 �17.0EXR 38.1 37.6 37.2 47.6 32.2ES �15.2 �14.5 �15.8 �17.5 �11.0Ind �10.9 �11.4 �11.6 �17.6 �11.7Disp �32.9 �31.6 �29.1 �38.3 �26.4

N TZV(2d,2p) �20.6 �19.9 �19.2 �26.3 �17.0TZV(d,p) �21.2 �20.4 �19.4 �26.8 �17.5

a Complete basis set limit: 1/2(DE(CP) + DE(non-CP)) with QZVP.

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C96H24 dimer, the induction compared to the electrostatic

component is quite large.

The relative size of all components is (almost) the same:

G 4 A 4 T 4 C 4 U as for the total interaction energies.

An exception is the induction component, where adenine

has the smallest, but guanine still has the largest contribution:

G 4 C 4 U 4 T 4 A. On coronene, the electrostatic

contribution is relatively larger than on C96H24. While the

dispersion contribution increases with the size of the sheet, the

electrostatic component is independent of the sheet size.

As a consistency check, we validated the DFT-D results by

comparison with interaction energies based on single point

energy calculations with the spin-component scaled (SCS)

MP2 and double hybrid density functional with empirical

dispersion correction (B2PLYP-D) methods on the B97-D/

TZV(d,p) optimized structures (Table 3 and Fig. 3).

The relative order of the interaction energies is essentially

independent of the quantum chemical method. An exception is

the ordering between A� � �coronene and T� � �coronene DEvalues, which is reversed with SCS-MP2 compared to the

other two approaches. The absolute values differ somehow:

on C54H18 the SCS-MP2 computed energies are lowest, B97-D

results are highest, and the B2PLYD-D values lie in-between,

like those observed in the porphine dimer.46 On coronene

SCS-MP2 computed energies are highest, followed by the B97-

D and B2PLYD-D results. Although the SCS-MP2 method is

essentially correct for the benzene dimer,47 the interaction

between larger stacked aromatic systems seems to be increas-

ingly overestimated. In conclusion, we can state that the

system is well behaved, like similar p-stacked systems.

In ref. 12, in addition to the LDA plane-wave results,

binding energies from MP2 calculations on finite sheets con-

taining 28 carbon atoms in the LDA optimized configuration

with the 6-311++G(d,p) basis set are reported. These treat-

ments result in the same order of binding energies as found

here: G 4 A \ T \ C 4 U. The absolute values differ by 7

(U) to 10 kcal mol�1 (G), with the LDA results at the lower

end. Our results for sheets of comparable size (24 and 54

carbon atoms) are between the LDA and MP2 values. This is

expected as conventional MP2 significantly overestimates

p-stacked complex binding energies,47 while uncorrected

LDA underestimates them.

The extrapolated DE values equal (for adenine) or exceed

(for the remaining bases) the MP2 results of ref. 12. The

adsorption energies for adenine on graphite from ref. 11 are

10.6, 25.1, and 1.6 kcal mol�1 within LDA, GGA+vdW, and

GGA. Our result for the infinite sheet (�20.6 kcal mol�1) is

close to the GGA+vdW result and the experimental value of

23.3 kcal mol�1 from thermal desorption spectroscopy

Fig. 2 B97-D/TZV(d,p) energy decomposition analysis (EDA) for

optimized structures of DNA bases on coronene (top) and C96H24

(bottom). The results of the EDA for coronene and C96H24 dimers (D)

are given as comparison. The components of the C96H24 dimer are

scaled down by the ratio of the EXR contributions on coronene and

C96H24 (55.4/223.5) in order to be visible on the same scale.

Table 3 SCS-MP2 and B2PLYP-D DE valuesa (kcal mol�1) of B97-D/TZV(d,p) optimized graphene–nucleobase complexes from Table 1

A T C G U

24 SCS-MP2 �15.1 �14.9 �13.4 �18.0 �13.0B2-PLYP-D �14.6 �15.7 �14.0 �18.7 �13.5

54 SCS-MP2 �20.8 �18.4 �18.2 �24.1 �16.1B2-PLYP-D �19.7 �18.5 �18.2 �23.9 �15.9

a TZV(2df,2pd) basis set with counterpoise correction 1/2(DE(CP) +DE(non-CP)).

Fig. 3 SCS-MP2, B2PLYP-D, and B97-D/TZV(2df,2pd) intermole-

cular interaction energies for B97-D/TZV(d,p) optimized structures of

DNA bases on coronene (left) and on C54H18 (right).

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(TDS)48, while—as found in ref. 49 for graphite—the LDA

underestimates the binding energy of extended weakly bonded

systems. Finally, we mention that the order of the intermole-

cular interaction energies is consistent with the adsorption

behavior of nucleic acid bases dissolved in water on the surface

of crystalline graphite.50

C. DNA base-pairs

Using the same approach as for the DNA bases, we optimized

complexes of the Watson–Crick base-pairs A-T, C-G, and

A-U with graphene sheet models of different size fully at the

B97-D/TZV(d,p) level (Fig. 4). As for the individual bases the

equilibrium distance of the base-pairs decreases with increas-

ing sheet size, e.g. from 3.3 A for C-G on coronene to 3.0 A on

C150H30 (see Table 4). The equilibrium distance of the base-

pair is larger than the distances of the separate bases, by about

5 pm on C96H24 and C150H30 (compare Table 4 to Table 1).

The geometry of the base-pair is hardly affected by the

adsorption on graphene, the average deviation of the heavy

atoms from the geometry of the uncomplexed base-pair ex-

ceeds 5 pm only in three out of 11 cases (7, 8, and 7 pm for

A-T, C-G, and A-U on C54H18, respectively). Being confined

in the hydrogen bonded geometry of the base-pair, the in-

dividual bases cannot assume the same optimal position on

graphene in the base-pair as separately.

Table 5 lists for each complex the fragmentation energy

DE = E � EA � EB � EC, the nonadditivity DE � DEAB �DEAC � DEBC, the interaction energy between the base-pair

and the sheet E � EAB � EC, and the hydrogen bond energy of

the base-pair on the sheet DE � DEAC � DEBC, when AB

denotes the base pair and C stands for the sheet. All fragment

energies Ei are determined in the geometry of the complex.

The nonadditivity is positive in all instances, i.e., pairwise

interactions are weakened in the trimer. For the case of the

C96H24 sheet, it amounts to 0.7 and 2.1 kcal mol�1 for the AT

and CG pairs, respectively, at the B97-D/TZV(d,p) level. This

is 1 and 3%, respectively, of the fragmentation energies for

A-T and C-G on C96H24 (�55.1 and �71.6 kcal mol�1).

Comparing the hydrogen bond energy of the base-pair on

the sheet to the uncomplexed base-pair with the bases in the

geometry of the complex results in the same absolute value for

the nonadditivity. Relating it to the hydrogen bond energies of

�17.0 and �30.4 kcal mol�1 this now corresponds to relative

nonadditivities of 4 and 7% for the A-T and C-G pair on

C96H24, respectively. The same holds for the interaction

energies between the base-pair and the sheet, which is

weakened by 2 and 6% compared to the sum of the interaction

energies between the individual bases and C96H24 in the

geometry of the complex, respectively.

However, comparing the interaction energies between the

base-pair and C96H24 to the sum of the interaction energies for

the fully optimized complexes of �40.1 kcal mol�1 (adenine

plus thymine) and �44.4 kcal mol�1 (cytosine plus guanine)

(Table 2), base-pair binding is weakened by 7 and 12%. In the

Watson–Crick pair the individual bases cannot fit as optimally

to the graphene sheet as they do independently. The nonaddi-

tivity is enhanced for the smaller sheets by additional interac-

tion of the base-pair with the edge of the finite sheet, e.g., a

weakening of 6.5 kcal mol�1 for A-U on C54H18 in comparison

to 10.6 kcal mol�1 for A-U on coronene is obtained. In

Fig. 4 B97-D/TZV(d,p) optimized structures of Watson–Crick base-

pairs A-T (left), C-G (right), and A-U (bottom) on C96H24.

Table 4 Structural data of B97-D/TZV(d,p) optimized graphene–nu-cleobase-pair complexes (A)

Size of thegraphene sheet

Geometricalparametersa A-T C-G A-U

24 �zn 3.27 3.28 3.28�z00n 0.04 0.05 0.02

54 �zn 3.21 3.16 3.19�z00n 0.07 0.08 0.07

96 �zn 3.07 3.04 3.07�z00n 0.04 0.05 0.04

150 �zn 2.96 2.99�z00n 0.04 0.03

a See Table 1.

Table 5 B97-D DE values (kcal mol�1) with various AO basis setswithout counterpoise correction of B97-D/TZV(d,p) optimized gra-phene–nucleobase-pair complexes from Table 4: fragmentation/non-additivity/base-pair binding/hydrogen bond (see text for definition).The B97-D/TZV(d,p) DE value of the free base-pair is given inparentheses at the top of each column

AT (�17.7) CG (�32.3) AU (�17.9)

24 TZV(2df,2pd) �34.7/0.5 �49.9/2.2 �34.3/0.6�17.5/�16.7 �18.1/�29.6 �16.8/�16.9

TZV(2d,2p) �35.1/0.5 �50.3/2.2 �34.6/0.6�17.7/�16.8 �18.3/�29.8 �17.0/�17.0

TZV(d,p) �35.7/0.5 �51.0/2.1 �35.3/0.5�18.0/�17.2 �18.6/�30.3 �17.4/�17.4

54 TZV(2d,2p) �47.3/0.5 �64.2/2.1 �46.2/0.7�29.9/�16.9 �32.0/�30.1 �28.5/�17.0

TZV(d,p) �48.4/0.5 �65.5/2.2 �47.2/0.7�30.6/�17.3 �32.9/�30.4 �29.2/�17.3

96 TZV(2d,2p) �53.9/0.6 �70.0/2.0 �51.6/0.7�36.5/�16.7 �37.9/�30.1 �34.0/�16.9

TZV(d,p) �55.1/0.7 �71.6/2.1 �52.9/0.7�37.4/�17.0 �39.0/�30.4 �35.0/�17.2

150 TZV(2d,2p) �70.9/2.0 �52.5/0.7�38.7/�30.1 �34.9/�16.8

TZV(d,p) �72.6/2.1 �53.8/0.7�39.9/�30.5 �35.9/�17.2

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contrast, the hydrogen bond energy of the bases in the

geometry of the complex is essentially equal to the DE value

for the uncomplexed base-pair.

The connection between the nonadditivity and the relaxa-

tion of the separate bases on the surface is illustrated in Fig. 5,

where values based on frozen (el) and relaxed fragments (tot)

are displayed together with the relaxation energies of the first

and second base on the surface (1c and 2c, respectively) and

the base-pair hydrogen bonding (hb). The relaxation energy of

the hydrogen bond is small (o1 kcal mol�1) compared to the

values for the bases on C96H24. The relaxation energies of the

monomers (not shown in Fig. 5) are typical for strong hydro-

gen bridges as concerns the nucleobases and for noncovalent

adsorption as concerns C96H24.

IV. Conclusions

This study presents detailed results for the noncovalent bind-

ing of nucleobases and hydrogen-bonded (Watson–Crick)

base-pairs on graphene using state-of-the-art quantum chemi-

cal methods that include important dispersion interactions.

The applied DFT-D/GGA, B2PLYP-D and SCS-MP2 meth-

ods typically provide interaction energies for p-stacked com-

plexes with an error smaller than 5–10% of DE. Opposed to

previous theoretical treatments for the same or similar sys-

tems, our study thus allows rather definite conclusions regard-

ing basic energetic aspects of these systems. Similar accuracy

considerations hold for the fully optimized geometries which

should be within 0.05–0.1 A of experimental observables for

the intermolecular distances. From the methodological point

of view it seems also important to perform convergence tests

with respect to the size of the graphene model. According to

our detailed studies, nucleobase adsorption requires sheets

with at least about 50 carbon atoms, while the prerequisite

for the investigation of base-pairs is about 100 carbon atoms

in the sheet model.

According to an analysis of the intermolecular interactions,

the complexes behave similar to other p-stacked systems. The

dispersion contribution to binding is so significant, that all

complexes would be unbound with conventional (uncorrected)

GGAs or hybrid-GGAs. Comparison with DFT results from

the literature shows, that also the LDA functional severely

underbinds these systems, i.e., the typical overbinding error of

the Slater exchange is only short-ranged and cannot fully

simulate long-range dispersion effects. The polar character of

the bases is evident from an increased contribution of the

induction component to the binding compared to a non-polar

hydrocarbon reference system.

The total p-stacking interaction energies of the bases alone

are very large (about �20 to �25 kcal mol�1) and not very

dependent on the choice of the quantum chemical method,

as long as dispersion interactions are taken properly

into account. They are on the same order of magnitude as

Watson–Crick hydrogen bond energies. This together with

small energy barriers with respect to lateral movement

(o5 kcal mol�1) is expected to provide distinct chemical and

physical properties of these complexes. Furthermore

our computed inter-plane distances are very short (about

3 � 0.1 A), which seems to be beneficial for electronic devices

that require coupling of organic molecules with the surface.

The sequence obtained for the interaction energy of bases with

graphene (G 4 A 4 T 4 C 4 U) is the same for all methods

and supports recent experimental findings.

The base-pair hydrogen bonds are merely affected by the

binding on graphene. In graphene� � �Watson–Crick pair com-

plexes the bases lie differently from their isolated energy

minima, leading to geometrical anti-cooperativity, i.e., pair-

wise interactions are weakened in the three-component system.

As expected for a vdW complex, the electronic contribution to

the anti-cooperativity is small (2 and 6% of DE for A-T and

C-G, respectively). These findings are consistent with stacking

and hydrogen bond potentials of about the same depth, but

very different force constants, i.e., rather floppy and stiff,

respectively. In conclusion, the above study in particular

provides detailed structural insight of polar organic molecules

binding on graphite-like surfaces which is difficult to obtain

otherwise. The future for such investigations even for larger

systems seems to be bright.

Acknowledgements

Financial support by the german research foundation (SFB

424 ‘‘Molecular Orientation and its Function in Chemical

Systems’’) is gratefully acknowledged.

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