SCC-DFTB Insight - ACS Publications - American Chemical Society

Letter pubs.acs.org/JPCL

Origin of the Surface-Induced First Hyperpolarizability in the C60/SiO2 System: SCC-DFTB Insight Sébastien Nénon and Benoît Champagne* Laboratoire de Chimie Théorique, Unité de Chimie Physique Théorique et Structurale, University of Namur, rue de Bruxelles, 61, B-5000 Namur, Belgium S Supporting Information *

ABSTRACT: Using the self-consistent charge density functional tight binding (SCC-DFTB) method, C60 molecules physisorbed on an α-quartz slab are shown to display a first hyperpolarizability, whereas, owing to their symmetry, both the α-quartz slab and C60 molecule have no first hyperpolarizabilities. A larger first hyperpolarizability is achieved when the lowest-lying (five- or six-membered) ring is situated in between two hydroxyl rows, rather than on top, because this situation favors orbital overlaps and charge transfer. Further analysis has demonstrated that (i) the first hyperpolarizability originates from the MO overlap and field-induced charge transfers from the neighboring substrate/adsorbate moieties but not to geometric relaxation of the C60 molecules at the interface and that (ii) larger first hyperpolarizabilities are associated with low surface coverage and with small distances between C60 and the surface. This contribution is a clear illustration of the emergence of second-order nonlinear optical responses (first hyperpolarizability) as a result of breaking the centrosymmetry. SECTION: Molecular Structure, Quantum Chemistry, and General Theory onlinear optics (NLO) is a very challenging field, owing to the numerous applications in high-performance domains, like biomedical imaging,1 chemical sensing,2 communication,3 or optical computing.4 Many devices involved in these applications consist of organic layers grown on a surface, where the first organic layer is chemisorbed or physisorbed depending on its function. Whatever the adsorption mechanism, the interactions at the interface modify the optoelectronic properties. It is therefore critical to understand the physicochemical phenomena at those interfaces in order to control the optoelectronic properties of the devices. In this sense, theoretical calculations are very useful. This Letter deals with the second-order NLO response of C60 on a α-quartz surface. Because C60 is a centrosymmetric molecule, in the electric dipole approximation, it does not display a first hyperpolarizability, β, the molecular property at the origin of the second-order NLO response. On the other hand, endohedral fullerenes have been synthetized with a water molecule inside,5 and the complex displays a large dipole moment, comparable to the one of isolated water, as confirmed also by first-principles calculations.6 The presence of the water dipole in the C60 cavity is supposed to asymmetrize the fullerene electron density, and thus, it induces second-order NLO properties on the C60 moiety as well. A related result is observed for C60 deposited on a surface (even of a centrosymmetric material like silica), where a second-order NLO response can appear. Indeed, Hoshi and co-workers have reported a non-negligible second-order susceptibility (χ(2)) once C60 is adsorbed on silica.7 Later, using semiempirical time-

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© 2013 American Chemical Society

dependent Hartree−Fock (SE-TDHF), Mestechkin8 attributed the appearance of this response to an asymmetrization of the fullerene. However, due to the huge computational cost, in these calculations, the surface has been modeled by point charges, thus eliminating orbital interactions and charge transfer, which are key phenomena at interfaces. Owing to the well-known synthesis and crystal growth of both the substrate and the adsorbate9,10 as well as to the activity of C60 in many devices, such as n-type transistors,11 or solar cells,12,13 there is a need for a more detailed analysis of the first hyperpolarizability of C60 adsorbed on silica. This is carried out here by means of the self-consistent charge density functional tight binding (SCC-DFTB) method.14 This model is based on a tight-binding approximation of the second-order expansion of DFT energy. A detailed explanation of the model can be found in a recent review.15 This semiempirical (SE) model has been previously shown to be efficient for predicting trends of hyperpolarizabilities in conjugated systems as well as molecular switches.16 Moreover, the use of periodic boundary conditions (PBCs) permits consideration of large systems, especially surfaces or slabs interacting with single or layered molecules, at a low computational cost. Within this level, the static first hyperpolarizability was calculated as the third-order electric field derivative of the energy using the finite field procedure17,18 Received: October 28, 2013 Accepted: December 10, 2013 Published: December 10, 2013 149

dx.doi.org/10.1021/jz402317x | J. Phys. Chem. Lett. 2014, 5, 149−153

The Journal of Physical Chemistry Letters

Letter

1 2 1 3 αF − βF − ... 2 6 ⎛ ∂ 2E ⎞ ⎛ ∂E ⎞ 1 1 ⎛ ∂ 3E ⎞ 0 = E + ⎜ ⎟ F + ⎜ 2 ⎟ FF + ⎜ 3 ⎟ FFF + ... ⎝ ∂F ⎠ F = 0 2 ⎝ ∂F ⎠ F = 0 6 ⎝ ∂F ⎠ F = 0

E(F ) = E 0 − μF −

Therefore, the system energy was calculated for different amplitudes of the external electric field (Fk = 2k × (4 × 10−4) au, k ∈ [0,1, ..., 4]), and the Romberg procedure18 was used to improve the precision on the third-order derivative. The β values are expressed in atomic units (au) (1 au of β = 3.2063 × 10−53 C3 m3 J−2), within the T convention. All of the electronic structure and energy calculations were performed using the DFTB+ 1.2.2 code,19 with the “PBC 0.3” parameters set20 available online at the www.dftb.org Web site. The functionalized surfaces were constructed from a 4 × 4 (100) α-quartz SiO2 cell21 on which a C60 molecule was deposited. Four different structures were built by varying the position and the orientation of the C60 molecule on the slab. The two possible orientations of the C60 on the surface are named 5c if the bottom ring (parallel to the surface) of the molecule is a pentagon and 6c if it is a hexagon. The second parameter is the position of the molecule on the surface. A “top” position means that the lowest-lying ring is on the top of a dangling hydroxyl group, while a “hollow” position means that the ring is situated between the hydroxyl rows on the silica. Then, the geometries were fully relaxed to equilibrium positions, which kept the character of the initial structures (5c or 6c, top or hollow). In addition to these functionalized surfaces where the C60 molecules interact very weakly between themselves, a complete C60 monolayer deposited on SiO2 was also studied. In that case, the unit cell consisted of a single C60 molecule in 5c-hollow position deposited on a 2 × 2 (100) αquartz SiO2 cell, and the geometry was also optimized. In fact, as mentioned in ref 8, the C60 cell parameters are commensurate with a 2 × 2 SiO2 cell. In practice, because the calculations are performed using PBC, a minimal 100 Å vacuum gap between the functionalized surfaces is created to avoid interactions. The adsorption energies (Table 1) are all negative, though small, demonstrating binding interactions between the surface

Figure 1. Structure of the optimized 5c-hollow system in its Cartesian frame.

is hardly modified (the diameter changes are of the order of 0.05 Å or less), and thus, the arising β is not due to a flattening of the fullerene. Moreover, the β value of the isolated fullerene in its adsorbed geometry is null, further evidencing its centrosymmetry. We observe (Table 1) that the stronger the binding interaction, the larger the charge transfer, and the larger the first hyperpolarizability, though these relationships are qualitative rather than governed by a simple mathematical function. Therefore, the charge transfer participates in the appearance of a first hyperpolarizability. The electron transfer goes from the surface to the C60, and it is small (or very small like in the 6c-top case), evidencing a physisorption mechanism. The charge transfer involves mostly a few atoms, the C atoms of the pentagon or hexagon at the interface and a couple of SiO2 units of the two first layers of the surface (Figure 1S in the Supporting Information). Polarization effects are also visible in the C60 molecule. In addition to the small adsorption energies, physisorption is substantiated by the small modifications of the projected density of states, as well as by the absence of hybridization or of level alignment of the highest occupied levels (around −6 eV) (Figure 2S, Supporting Information) upon adsorption. The energy levels diagram (Figure 2) details the correlation between the geometry and the energy levels shifts. The calculated energy shifts range between 0 and 0.1 eV for a single molecule, in good agreement with the measured 0.2 eV HOMO shift for a 12 nm C60 layer.22 Larger charge transfers lead to larger shifts of the electronic levels and to a band gap decrease. The latter is related to a decrease of the first excitation energy, known to be favorable for enhancing the linear and nonlinear optical responses. However, this effect is small. The MO sketches give qualitative information about the interactions at the interface and therefore about the charge delocalization. For hollow positions, the HOMO is delocalized between the C60 and the first two surface layers, allowing a better charge transfer. At the opposite, the 6c-top structure presents no delocalization, a negligible charge transfer, and a very small β of 15 au. Taking into account the qualitative relationship between the charge transfer and the β amplitudes, the field-induced charge transfer [q(F)] was assessed and expressed in the form of a Taylor expansion, like the energy or the dipole moment.

Table 1. Adsorption Energies [Eads = Ecomplex − EC60 − ESiO2] (eV), First Hyperpolarizabilities Per Unit Cell (au), and Charges on C60 (e) for the Five Optimized Systems top

hollow

monolayer

Eads 5c 6c

−0.0079 −0.0029

5c 6c

589 15

5c 6c

−0.002 0.001

−0.0243 −0.0205

−0.0101 −

β 2009 2144 Charge on C60 −0.014 −0.017

349

−0.004

and the adsorbate. The most stable position of the molecule is the hollow one, and the most stable orientation is 5c. In the latter case, the C60 molecule is tilted such that the center of the pentagon is oriented toward the Si bearing a dangling hydroxyl group (Figure 1). The top structures present negligible adsorption energies (smaller than 10−2 eV), especially the 6c geometry. Whatever the adsorption pattern, the C60 geometry 150



Letter

Figure 2. Energy levels diagram and frontier orbitals (isovalue = 0.004 e bohr−3) for the different systems.

q(F ) = q0 + q1F + q2F 2 + ...

which can be viewed as an average or effective distance. This is consistent with the charge-transfer pattern described previously and with its second-order variation with respect to the electric field (Figure S4, Supporting Information). Figure 3 shows the dependence of β as a function of the distance from the C60 equilibrium position (d = deq + δ) for the

This approach presents some similarities with the (hyper)polarizability density analysis developed by Nakano and coworkers23 because the (hyper)polarizability charges (qn) can be obtained by integrating the (hyper)polarizability densities. Then, by multiplying this expression by a distance d, one obtains a field-induced dipole moment and, subsequently, the (hyper)polarizabilities dq(F ) = μ(F ) = (dq0) + (dq1)F + (dq2)F 2 + ... = μ0 + αF +

1 2 βF + ... 2

The charge-transfer amplitudes calculated at the SCC-DFTB level for different F values display a nonlinear evolution as a function of F (Figure 3S, Supporting Information). The qn expansion coefficients were obtained by least-squares fitting. Thus, multiplying q2 by a distance gives a first hyperpolarizability. Alternatively, dividing the SCC-DFTB β values by 2q2 enables estimation of an effective distance, deff. It corresponds to the distance of field-induced charge transfer if a global charge transfer is the sole or dominant origin of β. For 5c orientations, this distance amounts to 4.12 and 4.44 Å (Table 2). If we consider that the charge-accepting moiety of C60 is the bottom pentagon, this distance corresponds to a charge transfer from the top Si layer (Table S1, Supporting Information),

Figure 3. β as a function of the distance with respect to the equilibrium situation (δ, Å).

5c-hollow case. When the molecule is displaced from the surface (along the z axis), β decreases sharply, which highlights the role of the orbital overlap between the C60 and the surface on the β values. In a last step, the effect of surface coverage on β was investigated and comparisons with the SE results of Mestechkin6 were made (Table 3). It is considered that using

Table 2. SCC-DFTB β (au), C60 Charge (e), q2 (au) Coefficients, and Effective Charge-Transfer Distances Evaluated As deff(q2) = βDFTB/2q2 (Å) SCC-DFTB β qC60 q2 deff(q2)

5c-hollow

5c-top

monolayer

2009 −0.014

589 −0.002

349 −0.004

514 4.12

140 4.44

142 2.60

Table 3. β Values Per Unit Cell (or Per C60) from a 4 × 4 Unit Cell (Single Molecule) to a 2 × 2 Unit Cell (Monolayer), SCC-DFTB versus the SE Results of Reference 8 for the 5c-hollow Configuration

βSE (ref 8) βSCC‑DFTB 151

4 × 4 cell = single

3×3 cell

2 × 2 cell = monolayer

single/monolayer

451 2009

− 1580

58 349

7.78 5.76



Letter

the 4 × 4 SiO2 cell prevents the C60 molecules to interact strongly so that it corresponds to the noninteracting, singlemolecule limit. When the C60 molecules interact, their surfaceinduced first hyperpolarizability decreases. SCC-DFTB calculations predict a decrease by 21 and 83% when going from the noninteraction limit to 3 × 3 and 2 × 2 coverages, respectively. A similar damping effect has been estimated in ref 8, though the β values are substantially smaller, by a factor of at least 4. This difference with respect to DFTB is mostly attributed to the description of the surfaces by point charges, which prevents MO overlaps, rather than to the methods themselves. Two phenomena are raised to explain the decrease of the relative β (β per unit surface) as a function of the surface coverage: (i) when surface coverage increases, the available surface and electron-donor groups per C60 molecule decreases, which is corroborated by the decrease of charge transfer from 1.4 × 10−2 to 0.4 × 10−2 au for the 5c-hollow patterning on 4 × 4 to 2 × 2 surface units, respectively, and (ii) there are mutual screening effects between the adjacent C60 molecules that appear when packing polarizable molecules perpendicularly to the field direction, which was also evidenced for other molecules.24,25 To address the role of coverage symmetry, additional calculations were performed on 8 × 8 (100) SiO2 unit cells on which four C60 molecules have been adsorbed: (i) all four C60 molecules were in the 5c-hollow position and (ii) two C60 molecules were in the 5c-hollow position and the other two were in the 5c-top position. As expected, the first situation is characterized by a β value (7967 au ≈ 4 × 2009 au), which corresponds to 4 times the β value of the 4 × 4 (100) SiO2 unit cell with one C60 molecule. The second situation, which enables to address the role of the coverage symmetry, gives a β value of 5037 au. To a good approximation, this value matches the sum of the β responses of two C60 in the 5c-hollow position and two in the 5c-top position (β = 2 × 2009 + 2 × 589 au = 5196 au; Table 1), demonstrating to a good extent the additivity of the β responses. In summary, the first hyperpolarizability of C60 physisorbed on an α-quartz slab has been calculated at the SCC-DFTB level and rationalized in terms of structural and electronic properties of the interface. Though, owing to their symmetry, both the αquartz slab and C60 have no first hyperpolarizabilities; their interface exhibits a first hyperpolarizability, which originates from MO overlap and field-induced charge transfers from the neighboring substrate/adsorbate moieties. The calculations also show that the largest responses are associated with low surface coverage and for small distances between C60 and the surface. In comparison to surfaces functionalized with push−pull πconjugated systems,13 the C60 layer displays a modest, though not negligible, first hyperpolarizability, but this could be enhanced by appropriate substitutions by donor groups.26 Still, in the case of C60, the interface presents a non-negligible contribution, which should be accounted for when interpreting the second-order NLO response of functionalized surfaces. This contribution is therefore a clear illustration of the emergence of second-order nonlinear optical responses as a result of breaking the centrosymmetry. In order to highlight the impact of the nature of the surface on β, modeling experiments were extended by considering C60 adsorbed on a 3 × 8 (100) TiO2 surface. Like for SiO2, the largest β responses are observed when C60 occupies a hollow configuration on the TiO2 surface, which also corresponds to the largest adsorption energies. β values of 7361 and 8681 au per unit cell characterize the 6c-hollow and CC-hollow

configurations, respectively. The CC-hollow configuration corresponds to the situation where a CC bond sharing a fiveand a six- membered ring lies in a hollow position. This enhancement of β by about a factor of 4 with respect to the SiO2 case is attributed to a smaller gap (1.5 eV).

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ASSOCIATED CONTENT

S Supporting Information *

Charge modification upon adsorption in the 5c-hollow system; DOS of the isolated and adsorbed system; electric field effect on the C60 charge; and distances between C60 and the surface atoms; electric field second-order derivatives of the charge in the 5c-hollow system. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.N. acknowledges the F.R.S.-FNRS (Convention N° 2.4520.11) and the Belgium government (IUAP No P7/5) for his postdoctoral grants. This work is supported by funds from the AUL (ARC “Extended π-Conjugated Molecular Tinkertoys for optoelectronics and spintronics”) and by the Belgian Government (IUAP No P7/5 “Functional Supramolecular Systems”). The calculations were performed on the computers of the Consortium des Équipements de Calcul Intensif and mostly those of the Technological Platform of High-Performance Computing, for which we gratefully acknowledge the financial support of the FNRS-FRFC (Conventions No. 2.4.617.07.F and 2.5020.11) and of the University of Namur.

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REFERENCES

(1) Chen, W.-L.; Hu, P.-S.; Ghazaryan, A.; Chen, S.-J.; Tsai, T.-H.; Dong, C.-Y. Quantitative Analysis of Multiphoton Excitation Autofluorescence and Second Harmonic Generation Imaging for Medical Diagnosis. Comput. Med. Imaging Graph. 2012, 36, 519−526. (2) Asselberghs, I.; Flors, C.; Ferrighi, L.; Botek, E.; Champagne, B.; Mizuno, H.; Ando, R.; Miyawaki, A.; Hofkens, J.; Van der Auweraer, M.; et al. Second-Harmonic Generation in GFP-Like Proteins. J. Am. Chem. Soc. 2008, 130, 15713−15719. (3) Lott, J.; Ryan, C.; Valle, B.; Johnson, J. R.; Schiraldi, D. A.; Shan, J.; Singer, K. D.; Weder, C. Two-Photon 3D Optical Data Storage via Aggregate Switching of Excimer-Forming Dyes. Adv. Mater. 2011, 23, 2425−2429. (4) O’Brien, J. L. Optical Quantum Computing. Science 2007, 318, 1567−1570. (5) Kurotobi, K.; Murata, Y. A Single Molecule of Water Encapsulated in Fullerene C60. Science 2011, 333, 613−616. (6) Ensing, B.; Costanzo, F.; Silvestrelli, P. L. On the Polarity of Buckminsterfullerene with a Water Molecule Inside. J. Phys. Chem. A 2012, 116, 12184−12188. (7) Hoshi, H.; Nakamura, N.; Maruyama, Y.; Nakagawa, T.; Suzuki, S.; Shiromaru, H.; Achiba, Y. Optical Second- and Third-Harmonic Generations in C60 Film. Jpn. J. Appl. Phys. 1991, 30, L1397−L1398. (8) Mestechkin, M. M. Theoretical Estimation of Optical Hyperpolarizability Appearance in Fullerene Molecule and Carbon Nanotubes Interacting with Ionic Crystal Surface. Opt. Commun. 2007, 273, 564−574. (9) Mojica, M.; Alonso, J. A.; Méndez, F. Synthesis of Fullerenes. J. Phys. Org. Chem. 2013, 26, 526−539.

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Letter

(10) George, S. M.; Ott, A. W.; Klaus, J. W. Surface Chemistry for Atomic Layer Growth. J. Phys. Chem. 1996, 100, 13121−13131. (11) Haddon, R. C.; Perel, A. S.; Morris, R. C.; Palstra, T. T. M.; Hebard, A. F.; Fleming, R. M. C60 Thin Film Transistors. Appl. Phys. Lett. 1995, 67, 121. (12) Brabec, C. J.; Sariciftci, N. S.; Hummelen, J. C. Plastic Solar Cells. Adv. Funct. Mater. 2001, 11, 15−26. (13) Idé, J.; Mothy, S.; Savoyant, A.; Fritsch, A.; Aurel, P.; Méreau, R.; Ducasse, L.; Cornil, J.; Beljonne, D.; Castet, F. Interfacial Dipole and Band Bending in Model Pentacene/C60 Heterojunctions. Int. J. Quantum Chem. 2013, 113, 580−584. (14) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Self-Consistent-Charge DensityFunctional Tight-Binding Method for Simulations of Complex Materials Properties. Phys. Rev. B 1998, 58, 7260−7268. (15) Cui, Q.; Elstner, M. “Multi-Scale” QM/MM Methods with SelfConsistent-Charge Density-Functional-Tight-Binding (SCC-DFTB). In Multi-scale Quantum Models for Biocatalysis; York, D. M., Lee, T.-S., Eds.; Springer: New York, 2009; pp 173−196. (16) Nénon, S.; Champagne, B. SCC-DFTB Calculation of the Static First Hyperpolarizability: From Gas Phase Molecules to Functionalized Surfaces. J. Chem. Phys. 2013, 138, 204107. (17) Cohen, H. D.; Roothaan, C. C. J. Electric Dipole Polarizability of Atoms by the HartreeFock Method. I. Theory for Closed-Shell Systems. J. Chem. Phys. 1965, 43, S34. (18) Mohammed, A. A. K.; Limacher, P. A.; Champagne, B. Finding Optimal Finite Field Strengths Allowing for a Maximum of Precision in the Calculation of Polarizabilities and Hyperpolarizabilities. J. Comput. Chem. 2013, 34, 1497−1507. (19) Aradi, B.; Hourahine, B.; Frauenheim, T. DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method. J. Phys. Chem. A 2007, 111, 5678−5684. (20) Köhler, C.; Hajnal, Z.; Deák, P.; Frauenheim, T.; Suhai, S. Theoretical Investigation of Carbon Defects and Diffusion in αQuartz. Phys. Rev. B 2001, 64, 085333. (21) Ogata, K.; Takéuchi, Y.; Kudoh, Y. Structure of α-Quartz as a Function of Temperature and Pressure. Z. Krist. 1987, 179, 403−413. (22) Cho, S. W.; Yi, Y.; Chung, K. B.; Kang, S. J.; Cho, M.-H. The Interfacial Electronic Structure of Fullerene/Ultrathin Dielectrics of SiO2 and SiON. Chem. Phys. Lett. 2010, 499, 136−140. (23) Nakano, M.; Shigemoto, I.; Yamada, S.; Yamaguchi, K. SizeConsistent Approach and Density Analysis of Hyperpolarizability: Second Hyperpolarizabilities of Polymeric Systems with and Without Defects. J. Chem. Phys. 1995, 103, 4175. (24) Kirtman, B.; Dykstra, C. E.; Champagne, B. Major Intermolecular Effects on Nonlinear Electrical Response in a Hexatriene Model of Solid State Polyacetylene. Chem. Phys. Lett. 1999, 305, 132−138. (25) Suponitsky, K. Y.; Masunov, A. E. Supramolecular Step in Design of Nonlinear Optical Materials: Effect of Π···π Stacking Aggregation on Hyperpolarizability. J. Chem. Phys. 2013, 139, 094310. (26) Loboda, O.; Zaleśny, R.; Avramopoulos, A.; Luis, J.-M.; Kirtman, B.; Tagmatarchis, N.; Reis, H.; Papadopoulos, M. G. Linear and Nonlinear Optical Properties of [60]Fullerene Derivatives. J. Phys. Chem. A 2009, 113, 1159−1170.

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