A Computational Study of the Interaction and Polarization Effects of

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A Computational Study of the Interaction and Polarization Effects of Complexes Involving Molecular Graphene and C or a Nucleobases 60

Aggelos Avramopoulos, Nikolas Otero, Panaghiotis Karamanis, Claude Pouchan, and Manthos G. Papadopoulos J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b09813 • Publication Date (Web): 21 Dec 2015 Downloaded from http://pubs.acs.org on December 22, 2015

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The Journal of Physical Chemistry

A Computational Study of the Interaction and Polarization Effects of Complexes Involving Molecular Graphene and C60 or a Nucleobases Aggelos Avramopoulos,a* Nikolás Otero,b Panaghiotis Karamanis,b Claude Pouchan,b Manthos G. Papadopoulos a a

Institute of Biology, Pharmaceutical Chemistry and Biotechnology, National

Hellenic Research Foundation, 48 Vas. Constantinou Ave., Athens 11635, Greece. b

Equipe de Chimie Théorique, ECP Institut des Sciences Analytiques et de Physico-

chimie pour l’Environnement et les Matériaux (IPREM) UMR 5254, Hélioparc Pau Pyrénées 2 avenue du Président Angot, 64053 Pau Cedex 09, Pau, France

ABSTRACT A systematic analysis of the molecular structure, energetics, electronic (hyper)polarizabilities and their interaction-induced counterparts of C60 with a series of molecular graphene (MG) models, CmHn, m=24, 84, 114, 222, 366, 546 and n=12, 24, 30, 42, 54, 66, is performed. All the reported data were computed by employing density functional theory and a series of basis sets. The main goal of the study is to investigate how alteration of the size of the MG model affects the strength of the interaction, charge rearrangement, polarization and interaction-induced polarization of the complex, C60-MG. A Hirshfeld-based scheme has been employed in order to provide information on the intrinsic polarizability density representations of the reported complexes. It was found that the interaction energy increases approaching a limit of -26.98 kcal/mol for m=366 & 546; the polarizability and second hyperpolarizability increase with increasing the size of MG. An opposite trend was observed for the dipole moment. Interestingly, the variation of the first hyperpolarizability is relatively small with m. Since polarizability is a key factor for the stability of molecular graphene with nucleobases (NB), a study of the magnitude of the interaction –induced polarizability of C84H24-NB complexes is also reported, aiming to reveal changes of its magnitude with the type of NB. The binding strength of C84H24-NB complexes is also computed and found to be in agreement with available theoretical and experimental data. The interaction involved in C60 B12N12H24 – NB complexes has also been considered, featuring the effect of contamination on the binding strength between MG and NBs.

* Corresponding Author Email: [email protected]

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I.

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Introduction

Carbon nanomaterials, such as fullerenes (0-D), carbon nanotubes (1-D) and graphenes (2-D)1 offer unique properties as potential multifunctional materials with broad applications in nanotechnology science.2-4 Fullerenes, due to their chemical and physical properties, are a highly promising class of materials with potential use in nanophotonics5 and medicine.6 Graphenes is a single-atom thick layer (2D), involving sp2 hybridized bonded carbon atoms. It has a number of exceptional properties (e.g. great mechanical strength, fast electron transport, optical transparency, flexibility, environmental stability).7 Graphene, due to its unique electrical properties, may even replace silicon in electronic applications.8-10 The electronic and magnetic properties of these materials are controlled by their size, shape, carrier types and concentration.11 Tuning the electronic states and controlling the charge carrier mobilities in graphenebased materials, allows the design and fabrication of devices for advanced applications (e.g. electronic devices).12-13

Supramolecular structures have attracted a great interest due to their potential application in organic electronics.14-15 One approach for their fabrication is based on the organic molecular self-assembly dominated by the existence of non-covalent bonds.16-18 Several self-assembled structures have been reported, whereas their cohesion is attributed to van der Waals (vdW) forces and hydrogen bonds.19-21 A series of properties, such as mechanical stability, friction, adhesion, strongly depend on vdW interactions.22 The role of vdW interactions on the stability and the structure of organic compounds on graphite and other surfaces has also been investigated.23

Experimental studies have shown that chemical functionalization of graphene with fullerenes, which are electron-acceptors, is possible.24-25 Additionally, several research teams have studied, experimentally or theoretically, the interaction of fullerenes with graphene substrates. Ulbricht et al. studied experimentally the interaction of C60 with carbon nanotubes (CNTs) and graphite,26 revealing the role of vdW forces in C60-CNT and C60-graphene hybrids. A binding energy of 0.85 eV, was estimated for a single C60 molecule to graphite. A combined theoretical and experimental study by Svec et al., reported the absorption mechanism of ordered C60 2


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layers on graphene.22 It was observed that binding is dominated by vdW interactions. Their computations confirmed that if vdW forces are considered between C60 and single layer graphene, stable absorption geometries and total energies were determined. The previous findings are also consistent with the experimental work of Cho et al.; they studied the behavior of C60 on a graphene layer grown epitaxially on SiC(0001), employing a cryogenic ultrahigh vacuum scanning tunneling microscopy and spectroscopy.27 Berland et al. determined the absorption of benzene and C60 on graphene and boron nitride, employing density functional theory and taking into account vdW correction.28 Their analyses shows that C60 induces a moderate dipole on graphene layer, identifying the effect of vdW forces and shed some light on the nature of physisorption on this type of molecular systems. Another theoretical study by Manna et al., employed a series of DFT computations to study the structures, density of states and electronic properties, of a series of carbon and boron fullerenes interacting with a two-dimensional single-layer graphene (SLG).29 The authors observed that vdW interactions increase with the size of the adsorbed fullerene, whereas the stronger binding of B80-graphene hybrid, is attributed to the larger polarizability of B80, compared with the other carbon fullerenes. The effect of the intermolecular interactions on the linear and non-linear optical (L&NLO) properties of molecules and molecular materials has been studied by several research teams.30 Suponitsky et al. studied the effect of π-π stacking aggregation on the first hyperpolarizbility of a series of paranitroaniline (pNA), 4nitro-4´-aminostilbene stacking aggregates.30 The authors concluded that the effect of intermolecular environment on hyperpolarizability is important and should be taken into account. The effect of the environment on the polarizability, first hyperpolarizability, structure and spectroscopic properties of pNA, caged in various derivatives (e.g. single-walled carbon nanotube, boron nitride nanotube, C92 fullerene) was studied theoretically by Kaczmarek.31 The magnitude of the interaction-induced polarizability and first hyperpolarizability of some hydrogen-bonded π complexes was reported by Gora et al.32 The authors focused their study on the elucidation of the origin of interaction-induced properties, by analyzing the contribution of several energy terms (electrostatic, exchange repulsion and charge delocalization) on the electric properties. 3



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The interaction of DNA nucleobases (NB) with inert surfaces has been studied by many research teams, due to their importance for the understanding of the binding of biological molecules with nanoparticles. A number of theoretical studies has been devoted on the investigation of the binding mechanism and strength leading to the absorption of four DNA nucleobases (guanine (G) adenine (A), thymine (T) and cytosine (C)) on graphene(G).33 A review article by Amirani and Tang reports a series of computational studies on the binding of nucleobases to graphene and carbon nanotube.34 A DFT study on the physisorption of DNA nucleobases on graphene, revealing the importance of the vDW forces on the binding process, was reported by Le et al.35 Czyznikowska and Bartkowiak studied the nature of the interaction in a series of four aromatic amino acid core rings (histidine, phenylalanine, tyrosine, tryptophan) with planar polycyclic hydrocarbons of different sizes, by employing DFT and MP2 theory.36 Tao and Shi studied experimentally the absorption of nucleobases onto graphite surface by using scanning tunneling microscopy and atomic force microscopy. They showed that adenine and guanine form a flat layer on graphite at a distance of approximately 3Å.37 Varghese et al., studied the strength of binding interaction between DNA bases and graphene using isothermal titration calorimetry.38 They found that the binding strength follows the order: G>A>C>T in aqueous solution and G>A>T>C in alkaline solution. This trend is in agreement with several theoretical studies.33, 39-42

Considering the above theoretical and experimental findings, the present work reports several properties (e.g. energies, (hyper)polarizabilities) and interaction induced properties of: (i) C60 interacting with a series of molecular graphene (MG) models and (ii) C84H24 interacting with nucleobases. More specifically: (a) The previous theoretical studies were focused on the determination of the energetics and molecular structure, of several C60-SLG hybrids, where the size of SLG remained unaltered. Therefore, it would be interesting to study changes induced in electronic (e.g. energy of HOMO, LUMO) and polarization properties (e.g. (hyper)polarizabilities) by increasing the size of SLG.

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(b) Since it has been reported that the factor dominating the stability of NB-SLG complex is the molecular polarizability of the NB molecule,40 it would interesting to study the magnitude of the interaction-induced electric properties and how this is modified with the type of NB.

The article is organized as follows: In section II we describe the methods we have used, in section III we report our results and finally in section IV we give our concluding remarks.

II. Methods We shall first provide some definitions on the methodology used for the present study. All the reported data for the molecular structure, energetics, static electronic (hyper)polarizabilities and their interaction-induced counterparts of

C60-MG and

C84H24-NB complexes, have been calculated by employing an integrated computational procedure including, ab initio methods (HF, MP2), Density Functional Theory (CAM-B3LYP, B97D, M062X), perturbation theory (analytic43 and a finite field approach44) and a Hirshfeld based scheme for the representation of the interaction-induced polarizability density. (Hyper)polarizabilities. When a molecule is set in a uniform static electric field F, its energy, E, may be expanded as follows : E= E0 – µiFi – (1/2)αijFiFj –(1/6)βijkFiFjFk – (1/24)γijklFiFjFkFl –...,

(1)

where E0 is the field free energy of the molecule, Fi, Fj, Fk,Fl the electric field components, µi, αij, βijk and γijkl are the tensor components of the dipole moment, linear dipole polarizability, first and second hyperpolarizability, respectively. Summation over repeated indices is implied. Only the electronic part of the (hyper)polarizabilities was considered. The components of the static αij, βijk were computed analytically.43 For the calculation of γijkl, a finite field approach was employed. In order to safeguard the numerical stability of our results for γijkl, computed by the second order derivative of αij with respect to the applied electric field, the Romberg approach was used.45 In all computations field strengths of the magnitude 2mF, where m=0,1,2,3,4 and a base field (F) of 0.0005 a.u. were used. 5



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The average values of the polarizability (α) and second hyperpolarizability (γ) are given by:

α=

and γ =

1 (α + α yy + α zz ) 3 xx

1 (γ + γ yyyy + γ zzzz + 2γ xxyy + 2γ xxzz + 2γ yyzz ) 5 xxxx

(2)

(3)

The studied complexes are rotated so that their dipole moment coincides with the zaxis. The average value of the first hyperpolarizability (β) is given by: β = (3/5) (βzxx + βzyy + βzzz)

(4)

Basis set effect. The complex C60 – C24H12 has been employed in order to study the effect of the basis set on the properties of interest (e.g. EHOMO, polarizabilities). Thus, a series of basis sets has been employed in connection with the CAM-B3LYP functional (Table 1). Comparing the results of 6-31G* and 6-31+G* basis sets, we observe that the added diffuse function leads to an increase of |p|, where p= EHOMO, α, etc, while the value of β decreases. Addition of two diffuse functions (6-311G**/6311++G**), leads to property values, which in several cases (e.g. ΕΗOMO, ∆α), approach a limit. The effect of the diffuse functions has also been checked with respect to the cc-pVDZ/aug-cc-pVDZ basis sets. It is observed that this effect is rather small on some properties (e.g. EHOMO, β; Table 1), while it is significant on some other (e.g. α, βzxx). Αn increase of several properties (e.g. µ, ∆µ, α) is observed by increasing n of cc-pVnZ basis sets, n=D,T. Some of the first hyperpolarizability values do not obey this trend. Comparison of the results produced by 6-31G*, and aug-cc-pVDZ/cc-pVTZ

shows that the former basis set leads to qualitatively

satisfactory property values. The previous data (Table 1) show that the use of 6-31G*, can provide qualitatively correct data for the L&NLO properties and their interaction induced counterparts of the studied C60 – MG complexes. The interaction induced properties (e.g. energy, (hyper)polarizabilities), ∆P, of the C60 – MG and MG-NB complexes, were computed by employing the following equation: ∆P = PAB(G,AB) – PA(G,AB) – PB(G,AB),

(5)

6


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where P=Etot, charge electron density (ρ) and components of the dipole moment and (hyper)polarizabilities; PAB(G,AB) is the property of the dimer in the optimized geometry (G), computed by employing the basis set (AB) of the whole system; PA/B(G,AB) is the property of the monomer A/B, where its geometry is a subset of G, and the computation has been performed by employing the whole system basis set AB. We have selected a series of methods and basis sets to study their effect on ∆Ε (Table 2). It is observed that ∆Ε, computed by employing the B97D functional46 is in satisfactory agreement with the corresponding value, calculated by the MP2 method. This finding is in agreement with the observation of ref 31, where it was found that the computed MP2 and B97D absorption energies of C48H48 – C6H6, reproduce satisfactorily the experimental interaction energy. In agreement with ref 31, the M062X functional underestimates the interaction energy. The HF and B3LYP methods lead to a positive ∆Ε. The functionals B97D, M062X and the MP2 method are associated with an increase of |∆Ε| by enhancing the size of the basis set. It has been reported that MP2 overestimates the binding energy of systems governed by non-covalent interaction.47-48 It is observed that ∆Ε computed with 6-31G* is in satisfactory agreement with the corresponding values computed by the augmented 631+G*, 6-311G*and 6-311+G* basis sets (Table 2; B97D). Hirshfeld-based intrinsic polarizability density representations. The dipole polarizability can be defined locally through: = − ′ 6 ,,

where ′ stands for the electron density derivative with respect to an external,

uniform and time-independent electric field i in the i direction evaluated in the limit

of zero field strength, and i corresponds to the Cartesian component of . equation 6 allows to represent oriented independent distributions, and these can be employed to study the most polarizable regions in a molecule.49-50 Nonetheless, these plots are directly dependent on the position and origin () one is considering, so they are not comparable among molecules with functional groups in different positions and, especially, with distinct size or volume. 7



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Recently, some of the present authors have proposed a general scheme to visualize polarizability density distributions in order to obtain easy-to-interpret pictorial representations, removing the well-known dependence of the electric-dipole polarizability on size and orientation.51 The idea for obtaining this pictorial representations is to introduce a “weight function” wA), defined by a molecular partitioning scheme (e.g., Quantum Theory of Atoms In Molecules52 (QTAIM) or Hirshfeld-based approaches53 in equation (6). Thereby, the polarizability distributions are easily divided into N atomic contributions allowing us to distinguish which regions belong to each atom. In addition, introducing the corresponding Cartesian i

coordinate of atom A, R , a size independent component, namely the intrinsic A polarizability, can be separated from the global property (equation (7)). Therefore, the final expression of the origin-independent component is expressed as:

=

!

# − $ ′ % 7 −

"

,,

In this work, wA) was obtained through the fractional occupation Hirsfeld-I (FOHI) atomic partitioning scheme, an improved Hirsfeld-I procedure that resolves all known shortcomings of the rest of methods49, 54 minimizing the loss of information in the formation of the molecule by means of an iterative process. Despite the intrinsic polarizability distributions seem to provide qualitatively important graphical information about the reactivity before and after the formation of a dimer, the obtained plots scarcely allow distinguishing which parts of the dimer are mostly affected by the interaction between the monomers. For this reason, and analogously to the molecular energies and the electron density, one can define plots of intrinsic polarizability distributions as an interaction induced property taking into account equation 5 and replacing ′ in equation (7) by:49 ∆ = AB(G,AB) – A(G,AB) – B(G,AB) (8) with the purpose of obtaining more adequate plots for intermolecular studies, considering the response of the polarizability to the interaction between two monomers A and B to form the dimer AB: 8


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∆

=

!

# − $ ∆ % 9 −

"

,,

Hereinafter, we will call the polarizability plots obtained by employing equation (9) as interaction polarizability distributions. We compare our results with experimental or theoretical data, where these are available . However, for further validation, the computational methods we have used, have been employed to calculate a series of properties for C60, which are compared with literature data. The functional B97D provides |H-L| (HOMO-LUMO gap), ionization potential (I.P.) and electron affinity (E.A.) values in satisfactory agreement with the available experimental data. It is observed that the CAM-B3LYP gives reasonable results for the polarizability. There is a discrepancy between our γ and the corresponding experimental value. This is probably due to a number of factors, e.g. the basis set (a more extended basis set would most likely give a better result). However, the size and range of the considered complexes suggests that the selected basis set, 6-31G*, is a good choice for most of the considered properties, in particular for commenting, qualitatively, on the considered trends.

III. Results and Discussion We shall consider the properties of the following interacting systems: (i) nanoparticlenanoparticle (NP-NP) and (ii) nanoparticle-nucleobase (NP-NB).

III.1 NP-NP interactions We shall study the properties of C60-CmHn, m=24, 84, 114, 222, 366, 546 and n=12, 24, 30, 42, 54, 66 (Figure 1). The geometries of C60-CmHn have been optimized by employing the B97D/6-31G* method, which has also been used for the calculation of ∆Ε of the considered complexes (Table 4). This choice is justified by the results of Table 2, where it is demonstrated that B97D gives ∆Ε in satisfactory agreement with those computed by MP2. The dipole moment and the (hyper)polarizabilities have been calculated by using the CAM-B3LYP/6-31G* technique, which is a long range corrected version of B3LYP, employing the Coulomb-attenuating method;55 it has been proven to yield satisfactory values for (hyper)polarizabilities of large and extended systems.56 It has also been shown that DFT methods can be applied for the 9



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analysis of interaction-induced electric properties.57 A study for the adequacy of the employed basis set (6-31G*), used for the computation of the (hyper)polarizabities and their interaction-induced counterparts, has been given in Table 1. Interaction energies, ∆Ε. The interaction energy, |∆Ε|, of C60-CmHn, increases with m, takes a maximum value for m=222 and approaches a limit, -26.98 kcal/mol for m=366 & 546 (Table 4). Charges. Both Mulliken and NBO (Natural Bond Orbital) charges demonstrate a charge transfer from CmHn to C60, as it should be expected, since fullerene is a well known acceptor. It has been found that the charge transfer (∆Q), involved in C60CmHn, is 0.042±0.003e (Mulliken) and 0.0385±0.0035e (NBO). Similar values of ∆Q have been reported in the literature.22, 28-29 EHOMO and ELUMO. Figure 2 shows the dependence of EHOMO and ELUMO of the interacting systems, C60-CmHn, on the number of carbon atoms of the molecular graphene (MG). It is observed that EHOMO and H-L of C60-CmHn and CmHn increase with m, while ELUMO of the above systems presents a maximum (Table 4). EHOMO (Figure 2) and ∆(H-L) approach their limit for m=546. The inequality, ∆(H-L)/|HL|>1.0, implies that the intermolecular interaction has a significant effect on the HOMO-LUMO gap. The variation of EHOMO, ELUMO and H-L vs number of carbon atoms (CMG) of CmHn in the complex (CmHn-C60) is presented in Figure 2. The linear relationship, which connects the total energy (Etot; CmHn-C60) with CMG is shown in Figure 3.

Dipole moments and polarizabilities. The magnitude of the dipole moment (µ) and interaction induced dipole moment, ∆µ, of C60-CmHn decreases with increasing m, while µ of CmHn increases (Table 4). The average interaction induced polarizability, ∆α, is negative and |∆α| increases with m. The in-plane components, αxx αyy, |∆αxx| and |∆αyy|, are larger than the out of plane ones, αzz and ∆αzz. It is observed that ∆αxx < 0.0, ∆αyy < 0.0 and ∆α < 0.0, but ∆αzz > 0.0 (Table 4); ∆αxx approaches its limit quicker than ∆αyy. The ratio |∆α|/α (it is recalled that these quantities are associated with the whole interacting system, C60-CmHn ) considerably smaller than unity for all the studied C60-MG dimers, ranging from 0.02 to 0.06, approaching a limiting value, 10


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which is close to 0.02. The above ratio shows that the effect of the intermolecular interaction on α is small. Figures 4 and 5 show the variation of α (CmHn-C60) vs CMG and Etot, respectively. A second order polynomial has been used to connect these properties (Figures 4 and 5), since it links very well our data. However, it is demonstrated that a linear relationship is a good approximation. A linear relatioship is observed between the pairs α/CMG (Figure 5) and ∆α/∆µ (Figure 6). A visual representation of the interaction polarizabilities in terms of Hirsfeld interaction polarizability distributions is shown in Figure 7. It is observed that the regions in which the electron density becomes more polarizable due to the interaction (red regions), are those between the fullerene and CmHn and on the non-interacting sides of both systems. On the other hand, a large portion of fullerene and CmHn near the edges are covered by negative distributions (blue regions) which imply polarizability decrease. Interestingly, as the graphene flake size increases, the positive/negative regions, localized on the non-interacting side of fullerene, decrease/increase in size indicating that in the case of larger CmHn flakes, fullerene is expected to be less polarizable than in its free form. Hyperpolarizabilities. The variation of βzzz, ∆βzzz and β with m is relatively small; βzzz is much larger than βzxx , βzyy and ∆βzyy (Table 5). A similar observation can be made for the corresponding interaction induced properties ∆βzzz, ∆βzxx and ∆βzyy. The value of ∆βzxx for m=546 is an exception. The ratio of ∆βzzz/βzzz is larger than 1.0, indicating the significant effect of the intermolecular interaction on the first hyperpolarizability; this ratio

modestly changes with m. Αll the second

hyperpolarizability components, for the interacting C60 – MG system, increase with the size of graphene, especially γxxxx , and γyyyy, since the MG molecules lie on the XY-plane. It is observed that ∆γxxxx (MG-A) > (MG-T) > (MG-C) > (MG-U),

12


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where MG = C84H24. The above observation is confirmed by the literature data.40 It has been found that the relative order of ∆E does not depend on the quantum mechanical method.39 The effect of the method, for the optimization of the geometry (M2, Table 6), on ∆E is modest. It is observed that for the MG-NB complexes, the difference |∆E| (B97D//B97D) – |∆E|( B97D//M062X) varies from 0.1 to 0.8 kcal/mol. The B97D//B97D gives larger |∆Ε| compared with those obtained with M062X//M062X, and agrees with the literature data, which were computed with a more accurate method (MP2) and a larger basis set (6-311++G**). A similar behavior has also been observed in the literature.41 Change of NB has a small effect on |H-L| and EHOMO, at a given method. A larger effect, upon changing NB, on ELUMO, may be observed for some methods (e.g. MP2//M062X). b.

(Hyper)polarizabilities of C84H24–NB complexes

The dipole moment, polarizability, first hyperpolarizability and their interactioninduced counterparts, ∆P, of C84H24-NB complexes, are reported in Table 7. The following trend is observed, for both the average and interaction induced polarizability: p(C84H24-G) > p(C84H24-A) > p(C84H24-T) > p(C84H24-C) > p(C84H24-U) where p = α, |∆α|. The same trend has also been found for |∆Ε| of C84H24-NB. This behavior is expected, because the stabilization of the complex, due to van der Waals forces, is proportional to the polarizabilities of the interacting systems and consequently to the total polarizability. The corresponding visual representation of the interaction polarizabilities in terms of Hirsfeld interaction polarizability distributions is provided in Figure 12. It is observed that for the C84H24-NB complexes the effect is somewhat different than the one observed for C60-MG. This is because the NB molecules contain heteroatoms inducing non-uniform interaction with the surface of the C84H24 flake. Nevertheless the general trends are similar. The regions between the interacting systems are characterized by a polarizability increase (red), while the opposite is observed (blue) at the edges of each interacting species, from the side of the interaction. The change of µz, |βzzz|, |∆βzzz| and |β|, for C84H24-NB, follows a different pattern than the corresponding for ∆Ε , α, and ∆α, that is: p(C84H24-C) > p(C84H24-G) > p(C84H24-U) > p(C84H24-T) > p(C84H24-A), 13



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a small difference is observed for µz where µz (C84H24-G) > µz (C84H24-C).

c.

Interaction between C60 B12N12H24 – NB complexes

In Table 8, several properties, of C60B12N12H24-NB are presented. C60B12N12H24 is derived from C84H24 by replacing C20 with B12N12 (Figure 13).65 For comparison, the corresponding properties of C84H24–ΝΒ are also shown. It is observed that G is more strongly bound in comparison with the other nucleobases. The binding energy, and consequently the strength of the interaction, depends on the contaminant of C84H24. It was found that ∆Ε of C60B12N12H24-G is 1.4 times larger, compared with that of C84H24-G. A similar trend is observed for the rest of C60B12N12H24-NB complexes (Table 8). This implies a slightly stronger adsorption of NBs on C60B12N12H24 compared with C84H24. This finding is in agreement with the study of Lin et al, investigating the adsorption of the five nucleobases on a BN sheet.66 Τhe following trend for |∆E| of C60B12N12H24-NB was observed: (C60B12N12H24-G) > (C60B12N12H24-A) > (C60B12N12H24-C) > (C60B12N12H24-T) > (C60 B12N12H24-U), A slightly different pattern was found for ∆E of C84H24-NB complexes, where ∆E (C84H24-T) > ∆E (C84H24-C). The results of this study show the remarkable change of ∆Ε and |H-L| of C84H24-NB, induced by the presence of the contaminant (B12N12). In C84H24-NB, a charge transfer is observed from C84H24 to NB, except of A, where the reverse trend is observed, although ∆Q is very small, similar to what has been reported in the literature.40,42 In all C60B12N12H24-NB complexes, charge is transferred to C60 from B12N12H24. Thus, contamination of C84H24 with B12N12 leads to a significant increase of charge transferred to the graphene derivative.

IV.

CONCLUSIONS A computational study of the interaction and polarization effects in a series of

complexes involving models of molecular graphene, C60 or and five nucleobases, has been reported. Specifically, the following complexes were considered: a) C60 – CnHm, where CmHn, m=24, 84, 114, 222, 366, 546 and n=12, 24, 30, 42, 54, 66 and b) C84H24-NB, and C60B12N12H24-NB, where NB denotes the five nucleobases thymine 14


Page 15 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(T), cytosine (C), guanine (G), adenine (A) and uracil (U). All the reported data were computed by employing density functional theory. The goal of the present study was to find how the intermolecular interactions affect the electronic and polarization properties of the considered systems. C60-CmHn. We observed that: i) |∆Ε| increases with the size of MG, reaching a maximum for m=366 &546. A limited study of C60- C24H12 demonstrated that the B97D functional provides reasonable values for ∆Ε. ii) EHOMO and H-L of C60-CmHn increase with m, while ELUMO exhibits a maximum. iii) The dipole moment, µ, and ∆µ of C60-MG complexes, decrease with the number of carbon atoms of MG, whereas an opposite trend was found for the polarizability (α), and the second hyperpolarizability (γ). Positive (∆αzz, ∆γzzzz) and negative (∆αxx/yy, ∆γxxxx/yyyy) values were found for their interaction-induced properties. v) A modest variation with the number of CMG, was observed for the first hyperpolarizability of C60-MG complexes. For all the studied complexes the ratio, ∆βzzz/βzzz was found to be always larger than 1.0, demonstrating the significant effect of the intermolecular interaction on the first hyperpolarizability. vi) A charge rearrangement analysis has shown that the negative charge distribution, induced by the interaction, is located closer to MG, while the induced positive charge nearer to or in the C60. vii) An interaction-induced polarizability analysis, based on a Hirsfeld scheme, revealed that an increase of the size of CnHm, leads to a less polarizable C60 in C60-CmHn C84H24-NB. The following trend was found for the interaction energy: (MG-G) > (MG-A) > (MG-T) > (MG-C) > (MG-U), in agreement with previous reported data. A similar behavior was observed for the variation of the polarizability and its interaction-induced

value.

A

different

trend

was

observed

for the

first

hyperpolarizability. We further studied how the presence of B12N12, in C84H24, affects the interaction energy of C60B12N12H24-NB. |∆Ε| follows the trend: (C60B12N12H24-G) > (C60B12N12H24-A) > (C60B12N12H24-C) > (C60B12N12H24-T) > (C60B12N12H24-U), which is slightly different than the corresponding observed for the series C84H24-NB. The binding of C60B12N12H24-G was found to be stronger (1.4 times larger), compared with that of C84H24-G.

15



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Page 16 of 39

The complexes of the present study do not exhibit strong charge transfer effects, known to affect the magnitude of polarization properties. In a forthcoming study we intend to investigate how functional groups anchored on either MG or C60 surface, can affect the binding energy and the polarization properties of the resulting complexes. ACKNOWNLEDGEMENT A.A and M.G.P acknowledge the financial support for this work by the European Commission through project “NanoPUZZLES” (grant agreement no. NMP4-SL2012-309837). This investigation is a part of the PICS project (No 6115). N.O. thanks Xunta de Galicia for a grant under the I2C program and CNRS for twoyear postdoctoral contract. Part of this work was granted access to the HPC resources of [CCRT/CINES/IDRIS] under the allocation 2014-2016 [No. i2014087031 and i2015087031] made by GENCI (Grand Equipement National de Calcul Intensif).

16


Page 17 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


X

Y C24H12 (a)

C84H20 (b) Z

C114H30 (c)

C222H42 (d)

C366H54 (e)

C546H66 (f)

Figure 1. The optimized geometries (B97D/6-31G*) of the considered C60-graphene complexes are presented (a-f).

17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0

100

200

300

400

500

-0.05

Page 18 of 39

600 #CMG

-0.07 -0.09 -0.11 -0.13 -0.15 -0.17 -0.19 -0.21 -0.23 -0.25 E (a.u.)

Figure 2. The HOMO (○), LUMO (∆) and the H-L (□) energies (CAM-B3LYP/631G*) of the interacting systems, versus the number of the carbons atoms (#CMG) of the molecular graphene. The B97D/6-31G* optimized geometry was used.

Figure 3. The variation of the total energy (E(tot)) of C60 –MG complex with the number of the carbon atoms of the molecular graphene (CMG), computed with the CAMB3LYP/6-31G* method at the B97D/6-31G* optimized geometry.

18


Page 19 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. The variation (blue line) of the average polarizability (α) with the total energy (E(tot)) of C60 –MG complex with, computed with the CAMB3LYP/6-31G* method at the B97D/6-31G* optimized geometry. The red line depicts the fitting trend.

Figure 5. The variation of the average polarizability (α; blue line) with the number of the carbon atoms of the molecular graphene (CMG), computed with the CAMB3LYP/6-31G* method at the B97D/6-31G* optimized geometry. The red line shows the fitting trend.

19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-0.5 ∆µ (a.u.)

-0.3

-0.1

0.1

0.3

Page 20 of 39

0.5

0.7

-10 -30

∆α = 168,18 (∆µ) - 125,19 R² = 0,9857

-50 -70 -90 -110 -130 -150 -170 -190 -210 ∆α(a.u.)

Figure 6. The variation average interaction induced polarizability (∆α) with the interaction induced dipole moment (∆μ) computed with the CAMB3LYP/6-31G* method at the B97D/6-31G* optimized geometry. The red line depicts the fitting trend.

Figure 7. Hirsfeld interaction polarizability distributions computed at CAMB3LYP/6-31G(d) level (isovalue=0.001 au). Positive and negative regions are shown with red and blue, respectively. 20


Page 21 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

(c)

(d)

Figure 8. Interaction Induced Density, ∆ρ, computed for the C60 - MG dimers, where MG: C24H12 (a), C84H24(b), C222H42 (c), C366-H54(d). Method: CAMB3LYP/6-31G*. Red and blue regions depict negative and positive charge, respectively.

21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(a)

Page 22 of 39

(b)

(c)

(d)

Figure 9. Top view of the Interaction Induced Density, ∆ρ, computed for the C60 A dimers, where A: C24H12 (a), C84H24(b), C222H42 (c), C366-H54(d). Method: CAMB3LYP/6-31G*. Red and blue regions depict negative and positive charge, respectively.

22


Page 23 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 10. The structures of the five nucleobases used for this study. O, C, N and H atoms are shown in red, gray, blue and white, respectively.

Adenine

Cytosin

Guanine

Thymine

Uracile

Figure 11. The model systems involving C84H24 and nucleobases. Geometries were computed with the M062X/6-31G* method. O, C, N and H atoms are shown in red, gray, blue and white, respectively.

23



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Page 24 of 39

Figure 12. Hirsfeld interaction polarizability distributions computed at CAMB3LYP/6-31G(d) level (isovalue=0.001 au). Positive and negative regions are shown with red and blue, respectively.

24


Page 25 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 13. The structure of C84B12N12H24. B, C, N and H atoms are shown in, pink , gray, blue and white, respectively.

25



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Page 26 of 39

Table 1. Basis set study of the EHOMO, ELUMO, EHOMO-ELUMO gap (H-L), the dipole moment, polarazibility and first hyperpolarizability, of C24H12 -C60. The reported values (a.u.) were computed at the B97D/6-31G* geometry with the CAM-B3LYP method. Basis Set

6-31G*

6-31+G*

6-311G**

6-311++G**

cc-pVDZ

aug-cc-pVDZ cc-pVTZ

B.Fa

1284

1620

1584

1932

1236

2040

2688

EHOMO ELUMO EHOMO-ELUMO µb ∆µc αxx x 10-3 αyy x 10-3 αzz x 10-3 α x 10-3 ∆α x 10-3 d βzzz ∆βzzz e βzxx βzyy β

-0.245 -0.078 -0.167 0.765 0.496 0.728 0.731 0.629 0.696 -0.036 2293 2770 17 5.4 1418

-0.255 -0.095 -0.160 0.828 0.632 0.815 0.817 0.778 0.803 -0.033 2206 2205 2.1 -11 1318

-0.255 -0.095 -0.160 0.759 0.521 0.764 0.766 0.694 0.741 -0.035 2414 2860 -20 -36 1414

-0.257 -0.098 -0.159 0.839 0.604 0.819 0.821 0.783 0.808 -0.033 2210 2204 26 15 1350

-0.252 -0.089 -0.163 0.752 0.529 0.751 0.754 0.664 0.723 -0.037 2393 2860 -4.9 -20.3 1421

-0.256 -0.096 -0.160 0.805 0.631 0.827 0.829 0.794 0.816 -0.034 2181 2175 26 15 1333

-0.255 -0.094 -0.161 0.774 0.590 0.793 0.796 0.747 0.779 -0.034 2126 2498 -0.2 -14 1267

a

Number of basis functions.; b The dipole moment is oriented along z-axis [µ =µz]; c ∆µ = µz (AB) - (µ(A) + µ (B)), where µ(A)and µ (B) denote the magnitude of the dipole moment of A and B, respectively.; d Induced average polarizability computed by using equation 5; e ∆βzzz is given by equation 5.

26


Page 27 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. The interaction energy, ∆Εa, of C60 – C24H12, computed by employing various methods and basis sets. All computations were done at the B97D/6-31G*optimized geometry. The values are in a.u.

∆Ε Method

HF

B97D

M062X

B3LYP

MP2

0.025 (15.69)b 0.024 (15.06)b 0.023 (14.43)b

-0.024 (-15.06)b -0.027 (-16.94)b -0.028 (-17.57)b -0.027 (-16.94)b

-0.011 (-6.90)b -0.017 (-10.67)b -0.018 (-11.29)b

0.002 (1.25)b

-0.032 (-20.08)b -0.044 (-27.61)b -0.043 (-26.98)b

Basis set 6-31G* 6-31+G* 6-311G* 6-311+G* a

∆Ε is given by equation 5.; b kcal/mol

27



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Page 28 of 39

Table 3 Comparison of theoretical with experimental property values for the HOMO-LUMO gap, |H-L|/eV, the ionization potential (I.P./eV), electron affinity (E.A./eV), the average polarizability, α /Å3 of second hyperporarizability γ (a.u.) of C60. All the reported values were computed with 6-31G* basis set. The geometry was optimized and the properties were computed with the corresponding functionals C60 |H-L|

I.P.

E.A.

γx10-3

α

B3LYP

2.75

B97D

1.66

7.21

2.07

71.60

wB97XD

6.04

8.29

1.96

67.2

M062X

4.54

7.83

2.47

67.25

CAMB3LYP

4.79

Exp. values

1.85±0.0467,a 2.8668,b

69.36

69.5 7.5870,c 7.59

2.6572,e

76.5

56.1 873,f

0.0271,d

93

1474,n

3.769 Theor. Values

82.275,g

109.178,j

75.176,h

113.778,k

92.4277,i

137.979,l 87.480,m

a

Band gap resulted from a critical evaluation of conductivity data; b Photoemission, inverse photoemission and xray absorption measurement on C60 (111) films grown epitaxially on VSe2 layer; c Single-photon ionization with synchrotron radiation measurment on C60 molecular beam; d Single-photon excitation with synchrotron radiation on C60 molecular beam; e Photoelectron spectra on C60-;f beam deflection technique;g Method: CCSD/ZPol; h Linear response function, basis set:6-31++G; I Method: CC2/aug-cc-pVDZ; j Method: SCF-RPA/6-31++G;k Method:MCSCF/6-31++G; l Method:LDA, Basis set:C [6s4p2d1f], H[ 4s2p1d];m Method: LDA; n χ3 (third-order susceptibility) measurement at 0.019 – 0.043 a.u. frequency range.

28


Page 29 of 39


Table 4. A series of properties for C60 - MGa . All reported values are in a.u.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

System

C60C24H12

C60C84H24

C60 C114H30

C60C222H42

C60C366H54

C60C546H66

-0.024 (-15.06)d -0.245 (-0.256)g

-0.032 (-20.08)d -0.210

-0.041 (-25.72)d -0.207

-0.044 (-27.61)d -0.192

-0.043 (-26.98)d -0.184

-0.043 (-26.98)d -0.178

-0.264e/-0.242f

-0.264e/-0.208f

-0.264e/-0.205f

-0.078 (-0.01)g

-0.074

-0.073

Property ∆Ea,b EHOMO

ELUMO

e

-0.088 /-0.017

f

e

-0.176 /-0.225 ∆(H-L)b

f

0.234

Eexca

0.15

c

e

0.252 /0.017 ∆µc

e

0.465 /0.355 ∆αxx x 10-3 b

-0.092

αyy x 10-3

0.731 e

0.465 /0.358 ∆αyy x 10-3 b αzz x 10

-3

f

-0.186

0.629 (0.644) e

0.476 /0.078 ∆αzz x 10-3 b -3

0.075 e

0.469 /0.263 ∆α x 10-3

b

-0.036

f

0.795 e

0.477 /0.226

e

0.469 /1.188 -0.095

0.465 /2.380

e

0.477 /0.358

0.469 /1.690 -0.108

e

0.465 /5.628

e

0.477 /0.729

0.469 /3.990 -0.137

0.176

e

0.288 /0.203

0.107 f

0.284e/0.260f -0.437 18.002

e

0.465 /10.801

f

0.466e/17.823f -0.287 18.906

e

0.465 /11.028

f

0.465e/18.800f

-0.263

-0.359

1.761 f

e

0.476 /1.223

3.228 f

0.476e/2.712f

0.062

4.322 e

0.176e/-0.08f

11.230 f

0.077 f

-0.176 /-0.093

f

-0.279

1.283 f

2.062 e

0.465 /5.615

-0.080

e

10.988 f

-0.250

0.087 f

e

f

-0.271

5.843 f

0.890 f

1.561 f

e

-0.196

0.092

0.696

α x 10

g

0.282 /0.143

-0.088e/-0.098f

0.220 f

-0.238

2.676 f

-0.088 /-0.090

f

0.175

5.842 f

-0.215

1.950 0.465 /1.674

0.466 /2.345

-0.176 /-0.113

e

-0.098

e

-0.094

e

-0.039

2.621

-0.191 e

f

0.110 e

-0.088 /-0.078

-0.264e/-0.178f

-0.090 f

0.386

0.291 /0.126

f

e

0.176

e

1.938 0.465 /1.664

-0.092

f

0.527 f

e

f

-0.176 /-0.145

0.10

0.277 /0.09

f

-0.113

e

0.11

0.219

0.728 (0.738)

αxx x 10

f

0.187

e

g

-0.088 /-0.06

0.192

0.586

0.496 -3

-0.176 /-0.152

f

-0.079

e

-0.134

e

g

0.765 (0.813)

µ

-0.088 /-0.056

f

-0.136

-0.167

H-L

e

-0.264e/-0.191f -0.264e/-0.183f

0.040

7.993 f

e

0.469 /7.684

13.378 f

0.469e/13.111f

-0.160

-0.202

a For the definition of the symbols see text and footnotes of Tables 1-3. ∆E has been computed and the geometry has optimized by the B97D/6-31G* method, all the properties have been calculated by employing the CAM-B3LYP/6-31G* method. Eexc, denotes the energy of first allowed electronic transition. b∆P (BSSE corrected value) is given by equation 5, P: denotes the property of interest. c The dipole moment is oriented along z-axis [µ =µz]. The definition for ∆µ is given in the footnote c of table 1. d kcal/mol; e Property of the C60 monomer computed by employing the dimer basis set ; f Property of the CnHm monomer computed by employing the dimer basis set. g Value computed with the MP2/6-31G* method.

29


The Journal of Physical Chemistry A series of properties for C60 - MGa . All reported values are in a.u.

Table 5.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 39

System

C60C24H12

C60C84H24

C60 C114H30

C60C222H42

C60C366H54

C60C546H66

2454

2089

2389

1868

Property 2293 (2550)c

βzzz

d

-586 /109 ∆βzzzb

e

d

-626 /77

2770 d

d

112

e

d

-73 /22 ∆βzyyb

1418 -3

417.9 (440) d

c

e

∆γzzzz x 10 γxxxx x 10

-3

∆γxxxx x 10-3 γyyyy x 10

56.7 (78) b

-3

-3

-3

-3

γxxyy x 10 γxxzz x 10 γyyzz x 10 γ x 10-3

d

-85 /-277

e

-85 /-224

e

-640 /136

-595d/-44e

2893

2507

d

734 d

-108 /702

e

-31

404 e

d

563

d

-221 e

1172

-453 e

-103d/-329e

d

739 e

-92 /342

-81 /-784

-88d/435e

194

88

154

412

392

1423

1435

1500

1499

2004

565

820

4700

35500

170000

471000f

35400

171000

492000g

487.8

1880

622 e

d

58.3 /4.600

4200

-544.5

-1055.6

1910

4400

24.3d/2420e

e

559.1

-41.5

-42.1

e

370

24.5d/2400e

57.2

2638

-45

24.1d/74.1e

23.9d/75.4e ∆γyyyy x 10-3 b

-88 /293

427.65 c

-637 /88

e

8

d

57.9 /2.250

358.491

d

160 e

d

56.1 /3.309 -3 b

e

2987

-82 /-0.02

56

β

-625 /92

176

5.4 d

γzzzz x 10

-88 /92

68

βzyy

d

180 e

-74 /23 ∆βzxxb

e

2629

17

βzxx

2080

25.6d/5230e

24.3d/5390e

-534.3

-1014.3

18.6

620

1425

11800

58000

15.5

45.9

52.9

850

2820

14.6

57.2

108

396

2409

114.4

762.8

1600.3

12431.4

59455

a

For the definition of the symbols see text and footnotes of Tables 1-3. The dipole moment is oriented along z-axis [µ =µz] ; b ∆P (BSSE corrected value) is given by equation 5, P: denotes the property of interest. c Value computed with the MP2/6-31G* method. d Property of the C60 monomer computed by employing the dimer basis set. e Property of the CnHm monomer computed by employing the dimer basis set . f Estimated value computed by γ = 4.5(CMG)2.93, where CMG denoted the number of the carbon atoms of the molecular graphene; g Estimated value computed by γ = 4.7(CMG) 2.93 , where CMG denoted the number of the carbon atoms of the molecular graphene.

30


Page 31 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 6. BSSE corrected interaction energy (∆E, kcal/mol), EHOMO (eV), ELUMO (eV) energies and the HOMO-LUMO gap (|H-L|, eV) of C84H24-NB. The properties have been computed by employing the method M1 and the gas phase optimized geometry, calculated by using the method M2 with the 6-31G* basis set. M1//M2a,b

B97D// B97Db

M062X// M062Xb

MP2// M062Xb

B97D// M062Xb

-20.7 1.67 -4.37 -2.60

-12.5 3.92 -5.77 -1.85

-16.3 5.36 -5.74 -0.38

-19.9 1.72 -4.30 -2.58

-24.7c -25.2d -17.47e

-17.6 1.69 -4.35 -2.66

-11.4 3.97 -5.79 -1.82

-14.7 5.44 -5.71 -0.27

-17.7 1.90 -4.35 -2.45

-21.7c -20.7d -14.95e

-15.7 1.69 -4.35 -2.66

-11.0 3.97 -5.97 -1.82

-12.2 5.44 -5.71 -0.27

-16.0 2.54 -4.35 -1.81

-19.1c -19.4d -14.29e

-10.8 3.94 -5.76 -1.82

-11.6 5.47 -5.74 -0.27

-15.8 1.88 -4.33 -2.45

-18.4c -19.2d -13.3e

-8.1 3.97 -5.77 -1.80

-9.7 5.31 -5.74 -0.43

-12.6 1.77 -4.33 -2.56

-17.1c -16.7d -11.92e

Complex C84H24-G ∆E |H-L| EHOMO ELUMO C84H24-A ∆E |H-L| EHOMO ELUMO C84H24-T ∆E |H-L| EHOMO ELUMO C84H24-C ∆E |H-L| EHOMO ELUMO C84H24-U ∆E |H-L| EHOMO ELUMO

-15.6 1.69 -4.35 -2.66 -13.2 1.69 -4.33 -2.64

a M1//M2 refers to the energy value calculated with the M1 method at molecular geometry computed with M2 method; bBasis set: 6-31G*; cBinding energies: Method:MP2//LDA Basis set: 6-311++G** 40. d System:C96H24-NB, Method:B97D//B97D. Basis set: TZP(d,p) 39; e Method: BSSE corrected B3LYP-D/631G*//ONIOM (M06-2X/6-31G*:AM1). 42

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Table 7 . The dipole moment, (hyper)polarizabilities and the interaction induced properties (∆P, P=µ,α,β) of the complexes, C84H24-NB, NB:G,A,T,C,U. The CAMB3LYP/6-31G* method was used at the gas phase optimized geometry (M062X/631G*). All values are in a.u. Complex Property

C84H24-G

C84H24-A

µa ∆µz αxx x 10-3 ∆αxx αyy x 10-3 ∆αyy αzz x 10-3 ∆αzz (α x 10-3) ∆α βzzz x 10-3 ∆βzzz x 10-3 βzxx x 10-3 ∆βzxx x 10-3 βzyy x 10-3 ∆βzyy x 10-3 β x 10-3

1.528 -0.978 0.394 -0.79 1.652 -73.27 1.519 -52.49 1.188 -42 -1.726 -1.647 -0.152 -0.169 -0.572 -0.620 -1.470

0.722 -0.245 0.651 -15.2 1.645 -59.58 1.260 -45.54 1.185 -40 -0.411 -0.375 -0.121 -0.142 -0.235 -0.177 -0.460

a

C84H24-T

0.973 -0.671 0.268 6.08 1.644 -61.23 1.631 -46.80 1.181 -34 -1.105 -1.149 0.0009 -0.007 -0.462 -0.389 -0.939

C84H24-C

1.504 -1.002 0.297 3.52 1.641 -51.22 1.596 -46.02 1.178 -31 -1.961 -1.770 -0.0584 -0.037 -0.642 -0.704 -1.597

C84H24-U

1.009 -0.713 0.252 4.01 1.636 -50.32 1.632 -42.04 1.173 -29 -1.215 -1.237 -0.0204 -0.012 -0.436 -0.375 -1.003

The dipole moment is oriented along z-axis.

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Table 8. BSSE corrected interaction energy (∆E, kcal/mol), the HOMO-LUMO gap (|H-L|, eV), EHOMO (eV), ELUMO (eV) and the charge Q of C84H24-NBa, C60B12N12H24-NBa complexes, using the gas phase optimized geometry with B97D/6-31G* method. Complex NBa

C84H24-NB

C60 B12N12H24-NB

G ∆E |H-L| EHOMO ELUMO QMGb

-20.7 1.67 -4.37 -2.60 0.005

-28.8 1.90 -4.32 -2.42 -0.072

A ∆E |H-L| EHOMO ELUMO QMGb

-17.6 1.69 -4.35 -2.66 -0.001

-24.5 2.01 -4.38 -2.37 -0.041

C ∆E |H-L| EHOMO ELUMO QMGb

-15.6 1.69 -4.35 -2.66 0.009

-20.7 1.90 -4.30 -2.40 -0.049

T |H-L| EHOMO ELUMO QMGb

U ∆E |H-L| EHOMO ELUMO QMGb

-15.7 1.69 -4.35 -2.66 0.014

-20.1 2.01 -4.38 -2.37 -0.013

-13.2 1.69 -4.33 -2.64 0.014

-17.6 1.98 -4.35 -2.37 -0.030

a

NB: nucleobase; bMulliken charge of graphene (MG).

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A Computational Study of the Interaction and Polarization Effects of

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