FullereneâC60 in Contact with Alkali Metal ... - ACS Publications

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Fullerene−C60 in Contact with Alkali Metal Clusters: Prototype NanoObjects of Enhanced First Hyperpolarizabilities Panaghiotis Karamanis* and Claude Pouchan Groupe de Chimie Théorique et Réactivité, ECP, IPREM CNRS-UMR 5254, Université de Pau et de Pays de l′Adour, Hélioparc Pau Pyrénées 2 avenue du Président Angot, 64053 PAU Cedex 09, France S Supporting Information *

ABSTRACT: The electric first hyperpolarizabilities (β) of a representative set of alkali metal droplets in contact with fullerene (C60) have been explored at the static limit via ab initio and density functional theory methods for the first time. We find that, when alkali metal droplets are adsorbed on the surface of C60, systems of enhanced static dipolar and/or octupolar hyperpolarizabilities are delivered. Both the type and the magnitudes of the first hyperpolarizabilities in such systems are dictated by the way the sodium atoms adsorb on the surface of fullerenes. One large metallic droplet of sodium atoms results to species with large hyperpolarizabilities of dipolar character. Smaller droplets adsorbed on the surface of C60 deliver systems of large octupolar contributions. In both cases two synergic polarization mechanisms have been detected by means of the classical version of configuration interaction singles (CIS) sum-over-states approach and a natural transition orbital analysis. The first comprises charge transport from the fullerene to the adsorbed droplets and resembles the polarization process met in simple diatomic molecules. In this case, C60 unconventionally functions as an electron donor at the excited states. The second, local in character, is related to the easily polarizable excess electrons maintained in the framework of the adsorbed clusters. From a certain point of view, such systems can be considered as hybrids that combine the basic characteristics of a classical donor/acceptor superstructure and systems with easily polarizable excess electrons.

1. INTRODUCTION There are many ways of bearing in mind the 60-atom buckyball (C60)1 whose discovery triggered multiple explosions of growth in a multidisciplinary field that now is known as nanoscience. For instance, in general chemistry, C60 represents the most identifiable member of the first molecular carbon allotrope existing in universe long before it was discovered. In clusterscience, buckyball is considered as a “magic super-atomic cage cluster” of exceptional thermodynamic stability (magic) with electronic structure that resembles a large atom2 (superatomic) and of the outstanding ability of transforming itself into totally different moieties of distinguishable properties when filled (cage) with atoms or small molecules.3 From the perspective of synthetic organic chemistry, C60 is seen as a flexible substrate that can be functionalized4 with different kinds of ligands or doping agents aiming at the improvement or enhancement of its qualities. As a result, in the multidisciplinary realm of nanomaterial science, C60 and its functionalized derivatives have already provided new perspectives in the construction of molecular and supramolecular structures for a vast assortment of advanced applications.5 Out of the various handy features of C60, two have proven quite inspiring in the synthesis of a particular class of materials specially designed to interact with light in an efficient and constructive manner. These are its large electron storage capacity6 and its extended network of π-electrons. As a result, © 2012 American Chemical Society

this extra-stable atomic cluster is currently assessed as the prime building module in the construction of efficient photoactive materials such as photovoltaics,7 while much work has been devoted already to understanding its nonlinear optical (NLO) activity8 and also to the synthesis of new NLO materials. In this last realm, the majority of the reported investigations utilized the knowledge gained from prior studies on a vast variety of organic molecules and mostly the concept of the donor− acceptor systems. Hence, a number of push−pull functionalized fullerenes consisting of carefully chosen electron donors covalently attached to C60 have been designed9,10 and characterized.11 The nonlinear optical responses and the microscopic hyperpolarizabilities of some of those systems have been measured,12 while crucial structure−property correlations have been established.10,11 The outcomes of those nontrivial investigations point out that functionalized fullerenes where C60 acts as an electron acceptor might indeed prove apt for NLO applications. In this work, we explore a rather unconventional class of functionalized fullerenes with respect to their hyperpolarizabilities. Our interest is occupied by fullerenes in contact with nanostructures of completely different electronic properties Received: March 20, 2012 Revised: May 4, 2012 Published: May 14, 2012 11808

dx.doi.org/10.1021/jp3026573 | J. Phys. Chem. C 2012, 116, 11808−11819

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C60.26,15 In striking contrast, when the small Li atoms are replaced by Na, different species appear to become energetically more favorable. This is what has been revealed in gasphase polarizability measurements by Dugourd et al.18 on NanC60 (n = 1−34) and by Rabilloud et al.27 Both studies suggested that, when C60 interacts with high concentration of sodium and potassium, alkali metal clusters begin to segregate on the surface of C60. Recently, Rabilloud23 provided sound theoretical evidence that the formation of small metal droplets on the surface of C60 is energetically more favorable than homogeneous coating, suggesting that two are the most viable types of interaction between C60 and 12 sodium atoms. The first (represented by systems of the (Nan)mC60-type) corresponds to a situation between the complete nucleation of a sodium droplet and homogeneous coating. The second type (represented by NamC60) corresponds to the complete formation of a metallic sodium droplet. From the reported isomers, we picked the three energetically most favorable ones, which for symmetry reasons are expected to possess nonvanishing first hyperpolarizabilities. Two of these structures are of the (Na4)3C60 type (three Na4 clusters adsorbed on C60) and one of the Na12C60 type (see Figure 1). In the latter system, one cluster built from 12 sodium atoms is in fact fixed on the surface of the

than those of C60. Our stimulation has been fuelled from previously reported investigations in two very interesting but independent areas of research activity. The first of those deals with the interaction between C60 and metals, and the second comes from molecular engineering of systems with exceptionally large hyperpolarizabilities. In the first discipline, a significant amount of investigations has been carried out on systems of the type MnC60 (M = metal).13−18 Such studies aimed initially at understanding better the bulk alkali−metal intercalated fullerides owed to some unique properties such as their excellent superconductivity,14 and their potentiality as hydrogen storage materials.15,16 As a result, a variety of alkali− C60 nanoclusters have been produced in the gas-phase, and some of their fundamental properties have been measured.17,18 In the second realm, recent theoretical studies predict that one can increase significantly the hyperpolarizabilities of a given organic system using alkali metals as doping agents.19 Some of such systems are ionic salts, where the anionic site is occupied either by an ejected electron (electrides)20 or by a negatively charged alkali metal (alkalines).21 Perhaps, the most thrilling characteristic of such systems is that impressively large first nonlinear optical responses can be achieved in molecules of small sizes. Unfortunately, only few examples concern systems that might be synthesized in reality. After combining the main breakthroughs of those different research fields concerning mainly the structures and the properties of systems implicating alkali metals, we designed and performed a thorough theoretical study of the first dipole hyperpolarizabilities on a representative set of viable22 (Nan)mC60 (n × m = 12) configurations. Neither the choice of sodium atoms nor their concentration (12) is accidental. It is based on the outcomes of previous experimental and theoretical studies17,18 suggesting that, when 12 sodium atoms are adsorbed on C60, the formation of metal droplets on its surface becomes energetically more favorable than homogeneous coating.23 This is essential for our endeavor since such sort of sodium aggregation on the C60 surface returns systems with no center of symmetry that should be characterized by nonvanishing dipole first hyperpolarizabilities. As it shall be shown, this class of systems not only can deliver dramatically large hyperpolarizabilities, but depending on the type of alkali metal nucleation, one may obtain systems of exceptionally large octupolar24 and/or dipolar hyperpolarizabilities. In addition, it shall be demonstrated that, in such hybrid systems, the function of C60 is reversed in comparison to the conventionally functionalized fullerenes for NLO applications. Thus, instead of acting as an electron acceptor, under the influence of an electric field, C60 works as a donor. This rather unconventional function of the 60-atomic buckyball is connected both to the ionic-salt-like electronic structures of those systems and the excess pseudo-π25 charge delocalized on the carbon skeleton of C60 coming from the alkali metals.

2. COMPUTATIONAL DETAILS 2.1. Cluster Structures. Previous studies on alkali−C60 nanoclusters suggest that, depending on their concentration, the alkali metal atoms either cover homogenously the surface of C60 or form one or more metal islets in contact with the fullerene. The most characteristic example representing the first possibility of interaction is C60Li12. This Li-decorated C60 has been tested as prospective materials for hydrogen storage15 and the most stable configuration is believed to be of icosahedral symmetry with each Li capping the 12 pentagonal sites of

Figure 1. Structures, energetic ordering, standard molecular orientations, and schematic dipole moment representations of (Na3)C60-A, -B, and -C and Na12C60 computed at B3LYP/6-31G(d) level. 11809



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In conditions of Kleinman symmetry,32 1/3∑i≠j(βijj + βjij + βjji) = βijj (βijk = βkij). Hence, for i = x, y, z: βx = βxxx + βxyy + βxzz, βy = βyxx + βyyy + βyzz, and βz = βzxx + βzyy + βzzz. Regardless of the sign of each individual tensorial component βijk, the total first hyperpolarizability is always positive. This quantity is very convenient to use in theoretical studies since it contains no more information than the tensorial components of the first hyperpolarizability βtot (i.e., the dipole moment is not included) but cannot be measured experimentally. Thus, depending on the experimental technique, some additional quantities are routinely considered. For instance, in field induced second harmonic generation experiments (dc-SHG or EFISH), the vector component of the first hyperpolarizability along the direction of the dipole moment is often negotiated. In the static limit, this quantity, usually referred as βvec, is written as

fullerene. The initial structures of these configurations were reoptimized using the same functional as in ref 23 (B3LYP) but this time,28 the all electron 6-31G(d) basis sets have been exploited for all carbon and Na atoms. Interestingly enough, during the optimization process, one additional isomer lower in energy than the three initial ones has been isolated (see Figures 1 and 2). Thus, we included also this structure in our

βvec(0; 0; 0) =

investigation. In a final step, the resulting fullerides were also reoptimized at the B3PW91 and PBE0 levels of theory to insure that both their structural features and their energetic ordering remain unchanged regardless of the functional used. At this point, it must be stressed that there are no unambiguous evidence showing that one of those species represents also the ground state structure. However, the specific configurations, which definitely are expected to lie at the lowest regions of the potential energy surface of these species, cover the most probable options of interaction suggested by the experiment between 12 sodium atoms and the fullerene. These are the intermediate segregation of metallic clusters or the formation of one single droplet. Hence, the four configurations considered in work can serve as an ideal set of viable models for a comprehensive and complete hyperpolarizability predictive investigation. 2.2. Hyperpolarizabilities. We will not expand in detail the theory of molecular electric properties here. More details about those effects and the importance of the hyperpolarizabilities of single molecules can be found in previous articles and textbooks,29,31 while information about the methods we used can be found in ref 30. In this article, we shall only provide the definitions of the necessary quantities to quantify the first order nonlinear electrical response of molecules starting from the simplest to handle, known as the total intrinsic quadratic (first) hyperpolarizability31 or more precisely as total first hyperpolarizability

1 3

∑ (βijj + βjij + βjji) i≠j

(3)

⎛ ⎞1/2 2⎟ ⎜ || β || = ⎜∑ βijk ⎟ ⎝i ,j,k ⎠ = [βxxx 2 + βyyy 2 + βzzz 2 + 3(βxyy 2 + βxzz 2 + βyxx 2 1/2

+ βyzz 2 + βzxx 2 + βzyy 2) + 6βxyz 2]

(4)

This quantity can be decomposed into two irreducible components as ∥βJ=1∥ = [∥βJ=1∥2 + ∥βJ=3∥2]1/2. The first component (∥βJ=1∥) represents the dipolar contributions and the second (∥βJ=3∥) the octupolar contributions to the first hyperpolarizability of a given system. Both of these components correspond to the moduli of the two irreducible spherical tensors, which are used to decompose the dipolar and octupolar contributions on the β-tensor as β = βJ=1 ⊕ βJ=3. In terms of Cartesian tensorial β-components, the dipolar and octupolar components can be written as follows: || βJ = 1 || =

(1)

⎡ ⎢3 ⎢⎣ 5

where βi = βiii +

|μ|

where μ is the ground-state dipole moment and μi are the respective components of the dipole moment. The vector component of the first hyperpolarizability can be positive or negative; thus, it carries more information about the hyperpolarization process of the system than βtot. For systems with one nonvanishing dipole moment, component βvec should match βtot. Also, in systems where βx ≫ βy, βz, and in systems where the charge transfer upon excitation in one direction is dominant, βvec should be very close to βtot. An alternative quantity, very useful in cases of hyperpolarizability comparisons between molecules of different symmetry and for octupolar24,33,34 systems, is the square root of the squared norm of the β-tensor Cartesian tensorial components, namely, the modulus of the β-tensor, which in conditions of Kleinman symmetry, is written as

Figure 2. Comparison of the structural features of Na4 clusters on (Na4)3C60-A (a) and (Na4)3C60-B (b) nanoclusters at the B3LYP/631G(d) equilibrium geometries.

βtot = (βx 2 + βy 2 + βz 2)1/2

(βx μx + βyμy + βz μz )

(i = x , y , z ) (2)

∑ βiii i

2

6 + 5

3 ∑ βiiiβijj+ 5 i≠i

∑ βijj i≠j

2

6 + 5

∑ i≠j≠k

⎤1/2 βijjβikk ⎥ ⎥⎦ (5)

11810


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∑ βiii

2

i

6 − 5

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∑ βiiiβijj+ 12 5 i≠i

∑ βijj

important structural and electronic features that are relevant to the current investigation. By checking carefully the basic structural features of (Na4)3C60-A, -B, and -C, it is observed that the adsorbed sodium atoms form three tetrahedral-like clusters of Na4. Interestingly, such tetrahedral sodium clusters are not stable as bare species (the ground state of Na4 is a planar rhombus48); however, as seen here, such pyramidal formations can be formed on the suitable surface. For the most stable cluster out of the four, namely, (Na4)3C60-A, each of those well-formed tetrahedrals abut with one of their faces against two hexagonals and one pentagonal sites of C60 (Figure 2a) . This configuration, found during the current investigation, is proven significantly lower in energy (about 0.5−0.62 eV) than the analogue structures considered by Rabilloud (Na4)3C60-(A, B,C) in which each Na4 cluster attaches on the surface of C60 with two Na atoms capping two pentagonal sites and one sodium capping the corresponding hexagonal (Figure 2b). Most likely this new configuration is the fruit of our choice to use an all-electron polarized basis set for both carbon and Na atoms.28 At this point it must be stressed that the interaction between alkali metals and C60 has no large impact on the shape of the latter since in all cases the C60-fragments are found of slightly distorted Ih symmetry (Ih is the ideal symmetry of the free C60). This is supported by computations of the dipole moments and dipole polarizabilities of the C60-fragments at their unrelaxed geometries in the absence of Na atoms. For instance, at Bh&HLYP/6-31G(d) level the C60-fragment of (Na12)C60 is characterized by a weak dipole moment value of 0.11 D. In addition, the mean polarizabilities of the C60-fragments of (Na4)3C60-A, (Na4)3C60-B, and Na12C60 in volume units vary from 69.6 to 69.7 Å3. These values are very close to the mean polarizability of the free C60 (68.96 Å3 at the same level of theory) suggesting that the size of the fullerene cage after the alkali metal adsorption remains practically unaffected. 3.2. Hyperpolarizability Magnitudes. In general, while comparisons between theoretical hyperpolarizability values and experimentally obtained ones are not always obvious,49 the task of defining whether the magnitude of a given electric response property such as the first hyperpolarizability of a specific system is large or not is also far from being trivial. Unavoidably, resolutions and final conclusions have been a matter of subjective character lying more on gained experience into the subject than on absolute values and criteria. For instance, Kanis and Ratner31 attempted to establish some empirical limits concerning the magnitude of this property at a given optical frequency. Through the years, this classification has influenced also studies carried out at static limit; hence, static first hyperpolarizability values ranging from 103 to 2 × 104 a.u. are usually considered as large, values that are found between 2 × 104 and 105 a.u. have been accepted as very large, while when the latter limit is outweighed, the hyperpolarizabilities are loosely characterized as giant. On the basis of the above empirical standards, a first glance at the values of βtot, βvec, and ∥β∥ presented in Table 1 rapidly suggests that highly hyperpolarizable species may be obtained when alkali metal clusters are adsorbed on the surface of fullerene. More specifically, at the Bh&HLYP/6-31+G(d*) level of theory, the values of ∥β∥ range from 78.2 to 117.3 × 103 a.u., βtot of (Na4)3C60-A, -B, and -C vary between 25.8 × 103 and 61 × 103 a.u, while the corresponding quantity for (Na12)C60 of 102.2 × 103 (∼105) a.u. lies dramatically higher.

2

i≠j

⎤ βijk ⎥ ⎥⎦

1/2

+

6 5

∑ i≠j≠k

βijjβikk + 6

∑ i≠j≠k

(6)

In systems with only octupolar contributions ∥βJ=3∥ should be the dominant component, while the opposite should expected in dipolar systems. More information about those nontrivial notations can be found in ref 24. 2.3. Basis Sets, Methods. To prevent possible systematic errors or artifactual results due to basis sets limitations, we performed a detailed basis set effect study on a smaller model structure of the type (Na4)C60 at the HF level of theory. This system has been derived from the most stable (Na4)3C60-type nanocluster of this study by removing two out of the three Na4 adsorbed clusters. The basic structural and electronic features of this simplified local minimum are very close to the rest of the nanoclusters of this study (see Figure 5 and the corresponding discussion in the next section). Our results showed that the 631+G (C:[4s3p]/Na:[5s4p]) basis set substrate polarized with one optimized35 d-Gaussian type function with exponent ηd = 0.4 on the carbon atoms and the standard d-Gaussian type function on Na atom is a very good compromise between efficiency and accuracy. Hereafter, this basis set will be referred as 6-31+G(d*). For the computation of the hyperpolarizabilities, we relied on two carefully assessed density functional methods (DFT). The first is the half and half functional36 Bh&HLYP, as implemented in Gaussian09,37 which has been used throughout out this work. The second functional is CAM-B3LYP, the long-range corrected version of B3LYP, which uses the Coulombattenuating method (CAM).38 It has been shown that these two functionals provide results of better quality than their conventional counterparts for electronic excitation energies,39−41 first42 and second hyperpolarizabilities,43 electric field-induced second harmonic generation,44 and even for the hyperpolarizabilities of hard-to-treat open-shell molecular systems.45 Nonetheless, because of the distinctiveness of the systems we are dealing with, we assessed further their performance on the model (Na)4C60 nanocluster with computations based on the second order Møller−Plesset46 perturbation theory (MP2). Our results clearly showed that these two functionals provide, up to some extent, a correct description of the first hyperpolarizabilities of (Na4C60) as compared to the MP2 level of theory with various basis sets. Detailed information about the basis set effects and the performance of the DFT methods used in this work on (Na)4C60 is provided in the corresponding section of the Supporting Information. Additional work about the performance of DFT methods in the computation of semiconductor− cluster hyperpolarizabilities can be found in ref 47.

3. RESULTS AND DISCUSSION 3.1. Cluster Structures. The four nanoclusters of this study, optimized at the B3LYP/6-31G(d) level, are shown in Figure 1. All equilibrium geometries are local minima of the potential energy surface characterized only by real harmonic vibrational frequencies. Information concerning the bonding and the stability of these systems is given in sufficient detail elsewhere.23 Here, we shall only discuss some of the most 11811



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Table 2. Dipole Moments (μx, μy, μz, μtot), Mean Dipole Polarizabilities (a), ̅ Polarizability Anisotropies (Δα), Tensorial Hyperpolarizability (β) Components (βijk), the Modulus of the β-Tensor (∥β∥), and Its Two Irreducible Components ∥βJ=1∥ and ∥βJ=2∥ of All Nanoclusters of This Studya

Table 1. Hyperpolarizability Values (a.u.) of All Nanoclusters of This Study Computed at the Bh&HLYP and CAM-B3LYP Levels with the Optimized 6-31+G(d*) Basis Seta (Na4)3C60-A Bh&HLYP CAM-B3LYP (Na4)3C60-B Bh&HLYP CAM-B3LYP (Na4)3C60-C Bh&HLYP CAM-B3LYP (Na12)C60 Bh&HLYP CAM-B3LYP

βx

βy

βz

βtot

βvec

∥β∥

−0.01 −0.01

−0.6 −1.3

−41.2 −32.4

41.2 32.4

41.0 32.2

78.2 62.5

0.55 0.40

−0.7 −0.6

−61.0 −47.8

61.0 47.8

61.0 47.8

117.3 93.1

−9.6 −6.6

26.7 20.9

−3.9 −3.4

28.6 22.2

25.8 20.2

101.0 77.3

−102.1 −107.9

0.0 0.0

3.6 3.9

102.2 108.0

102.1 107.9

81.0 86.4

μx μy μz μtot a̅ Δα βxxx βxxy βxyy βyyy βxxz βxyz βyyz βxzz βyzz βzzz ∥β∥ ∥βJ=1∥ ∥β J=3∥

a

All values are divided by a factor of 1000 and correspond to the B3LYP/6-31G(d) geometry.

Owed to the fact that, in all species, μtot is dictated by only one of its three independent tensorial components, βvec values are found very close to the corresponding βtot ones and inevitably follow the same trend. The Bh&HLYP/6-31+G(d*) results that provide a consistent hyperpolarizability picture with respect to the MP2 method (see Supporting Information) are verified also by the CAM-B3LYP approach. In this case, though, for A, B, and C nanoclusters, the latter functional yields smaller values than the ones obtained with Bh&HLYP, while the opposite is observed for Na12C60. Nonetheless, whatever the functional used, the main conclusion is maintained. In such species, large nonlinear electrical responses should be anticipated. Another interesting point that bears mention is the strong correlation between the βtot and βvec and the way the sodium atoms cluster on surface of C60. See, for instance, the values obtained in the case of (Na12)C60. This nanocluster represents the general situation of one large alkali metal droplet adsorbed on the surface of C60. The obtained βtot and βvec values are about 100 × 103 a.u. In striking contrast, both βtot and βvec substantially reduces when, instead of one large droplet, smaller Na clusters are adsorbed on the surface of C60. In Table 2, more information about the hyperpolarizabilities of all configurations computed at the Bh&HLYP level are presented. As seen, for all (Na4)3C60 -A, -B, and -C nanoclusters, large off-diagonal hyperpolarizability values have been obtained. According to eqs 5 and 6, this clearly indicates that, for these particular types of segregation, one should expect strong octupolar contributions. This is true and mirrors very well on the relative magnitudes of ∥βJ=1∥ and ∥βJ=3∥. As seen in all three A, B, and C structures, ∥βJ=3∥ clearly outweighs ∥βJ=1∥. In contrast, for (Na12)C60, only one tensorial component is the dominant one (for the specific orientation βxxx). As a result, for this type of sodium segregation, the relative ordering between ∥βJ=3∥ and ∥βJ=1∥ reverses. 3.3. Comparisons with Similar Systems. To demonstrate in a more convincing manner the indeed highly hyperpolarizable character of those systems, we shall briefly compare their hyperpolarizabilities with those of other similar fullerene-based systems, which have attracted considerable attention due to their large hyperpolarizabilities. In one of the first experimental pioneering-studies on fullerenes, Wang and

(Na4)3C60-A

(Na4)3C60-B

(Na4)3C60-C

(Na12)C60

−0.002 0.469 −4.284 4.310 1515.7 511.4 −0.1 32.9 0.1 −34.1 18.7 0.0 13.9 0.0 1.8 8.7 78.2 31.9 71.4

0.016 −0.029 −4.611 4.612 1620.0 362.7 −50.0 9.6 49.5 −8.9 23.7 0.0 23.5 −0.1 0.0 13.8 117.3 47.3 107.3

−0.164 1.148 −0.265 1.190 1637.3 601.3 −1.8 41.4 11.9 −66.5 −1.2 3.9 6.0 −0.5 −1.6 −0.9 101.0 22.2 100.8

−9.037 0.000 0.195 9.039 1669.3 1150.1 72.0 15.8 −1.2 −0.9 14.3 −1.5 81.0 79.1 17.1

a

The presented values, given in atomic units (a.u.), correspond to the standard orientation of the nanoclusters (see Figure 1) and have been computed at the Bh&HLYP/6-31+G(d*) level of theory. All hyperpolarizability values are divided by a factor of 1000 and correspond to the B3LYP/6-31G(d) optimized geometry.

Cheng50 measured the nonresonant first hyperpolarizability of a charge transfer complex between N,N-diethylaniline and C60. Their measurements yielded a value of about 8 × 103 a.u. Also, in one of the early theoretical studies on push−pull fullerenes of the type NH2−C60−NO2 by Fanti et al.,51 the largest reported βtot value (computed at the semiempirical CNDO/S level) was of about 50 × 103 a.u. In another more recent experimental attempt, Yamamoto and co-workers52−54 synthesized several fullerene hybrid molecules, combined with ferrocene and carborane and measured their first hyperpolarizabilities. For the first class of systems, the largest measured value of first HRS hyperpolarizability at 1.06 nm was about 65 × 103 a.u., while the corresponding theoretical value was found near 37 × 103 a.u. For the second class of hybrid systems, the measured hyperpolarizabilities varied between 40 to 137 × 103 a.u. What is interesting in those compounds is the fact that both C60 and carborane are electron attractor units. More recently, Loboda et al. reported β̅ = 3/5βvec values of a collection of purely organic60 fullerene dyads. The largest static value of βvec reported in this study amounts to 13.8 × 103 a.u. Finally, in a recent study, Ma et al.55 studied the first hyperpolarizability of endohedral fullerene dimers of the type Na@(C60)2@F. The largest reported βtot value computed at the CAM-B3LYP level computations was of 42 × 103 a.u. Of particular interest should also prove some comparisons between the magnitudes of the modulus ∥β∥ obtained here and the off-resonant optical nonlinearities of previously studied octupolar systems. For instance, Brunel et al.56−58 studied the octupolar hyperpolarizabilities of some propeller (or boomerang) shaped conjugated organic molecules, specially designed 11812



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to deliver giant octupolar hyperpolarizabilities. In those studies, the modulus ∥β∥ was found near the limit of 100 × 103 a.u., a value that is in the range of our outcomes. Finally, it is worthy of stressing that the obtained βtot values are comparable to other systems that have attracted considerable attention owning to their large hyperpolarizabilities. For instance, recently Xu et al.59 studied the hyperpolarizabilities of some Li-doped fluorocarbon chains and cyclacene.60 The largest βtot value that can be found in both of those studies amounts to 128 × 103 a.u.,59,61 and it is owed to the electride character of the Lidoped fluorocarbon chains. The above brief comparisons of course do not cover the large amount of work done in the area. Also, most of the previously reported hyperpolarizabilities are either experimental outcomes obtained at certain frequencies or theoretical predictions processed with different methods than those used here. Nonetheless, the hyperpolarizability magnitudes obtained here are of the same magnitude or significantly larger. Hence, it can be safely claimed that, when alkali droplets are adsorbed on a substrate such as C60, the resulting mixed nanoclusters should definitely possess static first hyperpolarizabilities of large magnitudes. 3.4. Polarization Mechanism from Chemical Intuition. We choose to elucidate the polarization mechanism of these species starting from some enlightening natural population analysis (NPA) results of all four structures obtained at the B3LYP level with the 6-31G(d) basis set. As seen in Figure 3 for the (Na4)3C60-type structures, the net NPA charges of sodium atoms in contact with the surface of C60 are clearly positive with orbital occupancies corresponding to 10.5 electrons. On the contrary, the charges of the apical Na

atoms are negligible resulting in a total natural population of about 11.0 electrons as in the free atomic sodium. Accordingly, the sum of the net NPA charge of C60 in all (Na4)3C60-type clusters is about −4.8e, suggesting that about 5 electrons in total migrate from all Na4 clusters to the C60 cage. The analogue picture is also observed in the case of Na12C60. Once again the net NPA charge of the apical sodium is negligible with a natural population of 11.0 electrons. Also, the net NPA charges of all sodium atoms of the pentagonal layer fixed on the fullerene are clearly positive with a natural population close to 10.5 electrons. In the second pentagonal layer, all Na atoms possess yet again positive net NPA charges, but this time, they are less positive with natural populations of about 10.8 electrons. What is more, as seen in Figure 3, the charge of the central sodium atom, encapsulated in the Na11-cage, is strongly negative with a natural population that amounts to 12.4e.62 As a result, the total charge of the sodium droplet is +2.5e, which shows that, in this particular case of complete segregation, the occurring charge transfer is significantly weaker than in the case of (Na4)3C60-type structures. In terms of the perturbation-theoretical description of the first hyperpolarizability,29 the above analyzed charge partition suggests that, during a field induced electronic excitation, electronic charge from C60 is expected to migrate to the peripheral sodium clusters. Such a process complies well with the large spatial asymmetry between the occupied and unoccupied molecular orbitals (MOs) of Na4C60-type clusters shown in Figure 4. More specifically, 5 out of 8 highest occupied MOs (HOMOs) localize on the carbon framework of C60. However, all 6 lowest unoccupied MOs (LUMOs) of (Na4)C60-A, which represents also the other two Na4C60-type clusters, localize on the sodium clusters. Provided that these virtual orbitals participate on the formation of possible chargetransfer excited states, then they are supposed to act as electron hosts. Of particular interest are also the diffuse nonbonding molecular orbitals HOMO − 3, −4, and −5 of s-type, which in accord with their NPA electronic configuration,63 localize in the area of the apical sodium atoms. As it has been shown in a considerable number of theoretical studies,19 such type of molecular orbitals, frequently met in systems with excess electrons such as electrides, are related to large first hyperpolarizabilities. A similar picture is observed for (Na12)C60; however, in this case, 3 out of 6 virtual molecular orbitals localize on C60. This could be taken as a hint for the opposite charge transfer process. Nevertheless, this most likely is not the case since, if indeed the mechanism that is responsible for the large hyperpolarizabilities values involved charge transfer from Na12 to C60 then for the specific molecular orientation (with μx < 0), the sign of βxxx should be negative. Once again, for this nanocluster, particularly interesting occupied molecular orbitals are revealed in the space of the sodium cluster. The shapes of these orbitals are more of p-character, and they are related with the negative charge found on the central sodium atom. This last characteristic is met in similar systems known as alkalides, which as electrides have been recognized as systems of large first hyperpolarizabilities. 3.5. Sum-Over-States Analysis. To verify whether the above intuitive polarization mechanism indeed governs the hyperpolarizabilities of these systems, we conducted first a test by approximating at the CIS/6-31G(d) level the exited state properties of the model structure shown in Figure 5. As in Na12C60, the hyperpolarizability of Na4C60 is dominated by only

Figure 3. Atomic charges on sodium clusters adsorbed on the surface of C60 from a natural population analysis of the B3LYP/6-31G(d) density at the B3LYP/6-31G(d) equilibrium geometry. For the sake of clarity, no carbon atoms are shown. 11813



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Figure 4. Frontier molecular orbitals of (Na4)3C60 (left) and Na12C60 (right).

31G(d) outcomes for the first 50 lowest excited states with a classical truncated version of the well-known sum-over-state (SOS)66 approach. According to the SOS method at the static limit of the dominant hyperpolarizability component of Na4C60, hereafter βL, should be proportional to the following two term infinite sum: ⎡ βL ∝ ⎢∑ (μ0n Δμn0 μn0 )(E0n)−2 ⎢⎣ n ⎤

+

∑ ∑ (μ0n μnm μm0 )(E0nE0m)−1⎥ n

m≠n

⎥⎦

(7)

In the above compact formula, μ0n and μm0 stand for the transition electric dipole moments from the ground state (0) to the excited states (n) and (m), μnm for the transition moments from the state n to the state m, Δμn0 for the dipole moment difference between the ground state (0) and the excited state (n), and E0n and Em0 represent the energies for the transitions 0→n and 0→m. The first and second terms of eq 7 are often referred to as the dipole and the octupolar terms, respectively. In Figure 6, we analyzed both the dipole and octupolar terms of eq 7 by plotting the contributing quantities μ0nΔμn0μn0(E0n)−2 and ∑m≠nμ0nμnmμm0(E0nE0m)−1 together with the evolution of their sums, normalized with respect to their convergent values and dipβL and octβL. As seen, both terms rapidly saturate within the first 12 excited states as has been observed in other cases of prototypical organic push−pull organic molecules.67 For the dipolar term, the crucial transitions involve the fourth, fifth, eighth, and 11th excited states. Conversely, the octupolar term is dominated by two

Figure 5. Optimized structure of Na4(C60) together with NPA charges and the atomic electronic configuration on sodium atoms (blue spheres) computed at the B3LYP/6-31G(d) level (left). The frontier HF molecular orbitals of Na4(C60) (right).

one tensorial component, which not only lies along the direction of the dipole moment but also points at the same direction as in Na12C60.64 Also, as shown in Figure 3, the frontier molecular orbitals of (Na4)C60 are of the same type with those of (Na12)C60 and (Na4)3C60-A localizing either on C60 or on the sodium cluster. Finally, (Na4)C60 can be loosely considered as the parent dipole65 of (Na4)3C60-type clusters; thus, their polarization mechanism can be straightforwardly linked. To identify what transitions contribute the most on the hyperpolarizabilities of Na4C60, we processed the CIS/611814



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Figure 6. Analysis of the dipole (a) and octupolar (b) terms of eq 7 in terms of the contributing quantities μ0nΔμn0μn0(E0n)−2 (blue columns) and ∑m≠nμ0nμnmμm0(E0nE0m)−1 (red columns) together with the evolution of their sums computed at the CIS/6-31G(d) level (blue line for the octupolar; red line for the dipole term). All quantities were normalized with respect to their convergent values dipβL and octβL. Also, for each crucial transition shown in both subfigures a and b, the corresponding values of the transition electric dipole moments (μ0n, μm0 and μmn), the dipole moment difference between the ground state (0) and the excited state (n) (Δμn0), and the energies needed for each transition (E0n, Em0) are given. All matrix elements correspond to the y Cartesian direction shown in panel a.

character and involves excitations from HOMO to LUMO and LUMO + 3 localized on the adsorbed cluster. The spatial partition of the specific transition complies very well with the strong charge separations in the direction of the dipole moment as suggested by the obtained Δμ40 value of −5.46 a.u. (see Figure 6). The same overall picture holds for both the fifth and 10th excited states where yet again the dominant NTO pairs associate to fullerene-to-cluster charge transfer transitions. As a result, large spatial charge separations are obtained in concurrence with the obtained Δμ50 and Δμ80 values of −5.01 and −7.38 a.u., respectively. Once again, the HOMO orbitals retain their leading role in the composition of the excited states. However, in contrast to the first crucial transition for both the fifth and 10th excited states a second NTO pair is found to contribute to their overall representation. The contributions of the additional NTO pairs represent about the 7% of the fifth excited state and 9% of the 10th and reveal interesting charge transfer transitions localized only the adsorbed cluster. Apparently, these transitions are related to the particular electronic structure of the apical Na atom since, in the description of the corresponding empty holes, the nonbonding orbital HOMO − 1 localized on the adsorbed sodium cluster is clearly implicated. Such local charge transfer transitions, confined on the sodium cluster, become more pronounced in the eighth and 11th excited states. These states are characterized by small Δμn0 values but strong transition dipole moments, and apart from their contribution to the dipolar term, they are also implicated in the octupolar term of eq 7. As seen in Figure 7, for both of these states, two NTO pairs instead of one are needed in order for a description larger than 90% of the actual excited states to be reached. Interestingly, both of those NTO pairs describe competitive charge transfer transitions to opposite edges of Na 4 C 60 for both states. See, for instance, the NTO

intense transitions involving the eighth and the 11th excited states. The contributing states lie in a range from 1.7 to 2.9 eV higher than the ground state comprising large Δμn0 values or sizable transition electric dipole moments μ0n, μ0m, and μnm. For instance, the fourth and fifth excited states, lying at 1.71 and 2.35 eV, respectively, are characterized by large and negative Δμn0 of −5.46 and −7.38 a.u. but weak μ0n magnitudes of −0.92 and 0.87 a.u., respectively. In contrast, both the eighth and 11th states become important due to the square of their μ0n values of 3.41 and −2.32 a.u., respectively. In all cases, the direction of the occurring charge transfer process can be easily understood from the sign of the Δμn0, which is negative, matching the sign of the obtained analytical value of βL64 corresponding to the orientation of Figure 3. This observation confirms that the main polarization mechanism should definitely involve charge transfer from the fullerene to the alkali metals, exposing the function of C60 as an electron donor. 3.6. Natural Transition Orbital Analysis. To gain more insight about the nature of the crucial SOS excited states and the first hyperpolarizabilities of Na4C60, we carried out an analysis based on the natural transition orbital (NTO) treatment demonstrated by Martin.68 This approach uses the orbital transformation proposed by Amos and Hall69 and allows a convenient excited particle to empty hole orbital representation of the electronic transition density matrix. In Figure 7, we show the natural transition orbital pairs (NTO pairs) for each of the five dominant SOS transitions70 as computed from the density matrix at the CIS/6-31G(d) level together with the CIS description of each excitation and the associated eigenvalues λi,68 which mirror the importance of a particular particle−hole representation to the overall transition. As seen, the fourth excited state can be described by one NTO pair accounting for the 99% of the overall excitation (λi = 0.998). This state is fullerene-to-cluster charge transfer in 11815



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analysis of the CI density of Na4C60 can help us to understand the way the electrons of (Na4)3C60-A, -B, and -C and Na12C60 respond under the influence of a static electric field. First, the intuitive hypothesis about the charge transfer mechanism on the nanoclusters of this study based on the NPA analysis is fully confirmed. As in Na4C60 in the case of Na12C60, the charge is expected to transfer in one direction from C60 to Na12 explaining the large dipolar contributions to the first hyperpolarizability of this type of segregation. The above-described fullerene-to-cluster charge transfer is met in classical donor− acceptor molecules and, in fact, mimics the one we come across in simple diatomic ionic molecules. See, for instance, Figure 8

Figure 8. Two of the dominant natural transition orbital pairs corresponding to the 3rd and 7th excited states of NaI computed from the CIS/6-311G(d) density matrix. Descriptions: 3rd excited state, λi =0.98, 0.64(H − 2 → L) + 0.20(H − 2 → L + 3) + 0.10(H − 2 → L + 3); 7th excited state, λi =0.96, −0.33(H − 1 → L + 1) + 0.33(H − 1 → L + 2) + 0.34(H → L + 1) + 0.33(H → L + 2). H stands for HOMO and L for LUMO.

Figure 7. Dominant natural transition orbital pairs for each of the five crucial excitations computed from the CIS/6-31G(d) density matrix, along with their description and their relative weights λi. H stands for HOMO and L for LUMO.

where the transition orbital pairs for the analogue dominant excitations in the case of the diatomic salt NaI71 is shown. The similarity of these transition pairs and those corresponding to the fourth, fifth, and 10th excited states of Na4C60 is more than obvious with iodine representing C60 and Na playing the role of Na4. In the second family of nanoclusters, the process is identical. However, in these cases, given that three small clusters are adsorbed on the surface of C60, the charge is expected to split in three different directions instead of one. Such a process justifies the large βijj off-diagonal tensorial components pointing out that this type of cluster resembles the prototype octupolar systems that have been studied intensively in the past.24 Similarly to these systems, here, a central unit (C60) acts as an electron donor and a number of peripheral subunits (Na4 clusters) as electron acceptors causing some kind of chargedevolution during the polarization process. Finally, for all clusters, including the model structure, the above mechanism is accompanied by a second process, which implicates charge transfer excited states confined on the sodium clusters. These states contribute on the final value of their first hyperpolarizabilities in a constructive manner. Thus, a second synergic effect linked to the formation of excess electrons on

representation of the heavily mixed eighth excited state. The 71% of the respective transition is described by an NTO pair representing a repartition of the charge in the naked side of the nanocluster, while a nonnegligible 25% of this state associates with an NTO pair involving charge transfer confined only on the Na4 cluster. The same picture is observed in the case of the 11th excited state. The only difference between these states lies in the relative contribution of each NTO pair, which in the latter case is the reverse. The combined NTO pair representation complies very well with the small Δμ80 and Δμ110 values of −0.66 and −1.22 a.u., respectively, since there is a mutual cancelation of the charge separation. However, the negative signs of both Δμ80 and Δμ110 clearly suggest that the transitions localized on the cluster are of more decisive importance and, in fact, define the sign of the contributions of those states on the overall hyperpolarizability SOS value. What’s more, the λi weights of each pair qualitatively match the relative ordering of Δμ80 and Δμ110 with the latter being larger in absolute value, seemingly, due to the increased contribution of the NTO pair that confines on the Na4 cluster. 3.7. Resolution of the Polarization Mechanism. Let us now see how the above results on the natural transition orbital 11816



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efficient nonlinear optical activity. Lastly, some recent results on similar silicon-based clusters72 suggest that, in addition to large first hyperpolarizabilities, one should expect from such systems large nonlinear second-order electrical responses. Therefore, it would be of particular interest to investigate this perspective on metal-coated fullerenes as well.

some of the atoms of the adsorbed sodium clusters complements the push−pull polarization process. Apparently, this last effect depends on the size of the Na cluster adsorbed on the surface of C60. The larger the alkali metal cluster, the greater the chances for such type of negative ions to be formed in its framework.

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4. CONCLUSIONS AND PERSPECTIVES In an attempt to explore for the first time the nonlinear electrical response properties of fullerenes in contact with alkali metal clusters, we performed a thorough computational study of the first microscopic hyperpolarizabilities of two of the most plausible types of interaction between C60 and 12 sodium atoms. Our results clearly suggest that, when alkali metal droplets are adsorbed on the surface of C60, systems of exceptionally large static hyperpolarizabilities may be obtained. In addition, it is found that both the type and the magnitudes of the first hyperpolarizabilities of such systems are dominated by the way the sodium atoms adsorb on the surface of fullerenes. Accordingly, when a large metallic droplet of sodium atoms is adsorbed on C60 as one piece, systems of large dipolar hyperpolarizabilities should be expected. However, when smaller clusters of sodium dispense on different adsorption sites, systems of large octupolar hyperpolarizabilities emerge. Thus, by controlling the alkali metal adsorption in such systems, one might be able to tune as well their hyperpolarizabilities. Owed to the particular electronic structure of these alkali− fullerene dyads, their first order nonlinear polarizabilities are found to be in close connection with the electron-donating character of fullerene in the excited states and some particular features of the adsorbed alkali metal clusters. In this context, two synergic polarization mechanisms have been identified. The first consists of a classical donor−acceptor process with the fullerene acting as donor and sodium droplets as acceptors. Hence, the frequently met function of C60 in the majority of previously studied fullerene-based NLO systems as an electron acceptor in the excited states does not hold here. What is more, such a polarization mechanism resembles the one observed in simple diatomics. Thus, given that there is no conjugation path connecting the donor and acceptor moieties as in conventional conjugated organic push−pull systems, one can picture those nanoclusters as giant oligoatomic molecules. The second mechanism indentified by analyzing the NTO results is related to the electron density localized on the framework of the adsorbed clusters. As it seems, easily polarized diffuse electrons, resembling those we meet in electrides and alkalides, contribute in the formation of charge transfer excited states local character. It is hoped that the reported results shall find a prosper ground in the context of designing mixed fullerene−metal based systems that exploit large nonlinear optical microscopic responses. Thus, starting form this work, future endeavors may focus on the incorporation of alkali metal clusters or other types of substrates such as other clusters or different kinds of fullerenes (nanotubes, nanocones, larger buckyballs, heterofullerenes, and properly functionalized fullerenes), that can facilitate the absorption of metal clusters, or even fullerenes filled with atoms or small molecules and clusters. Such attempts should not only be directed to large nonlinear electrical responses but also be able to deliver stable species that can be synthesized and studied further having an ultimate aim to expose their true nonlinear-optical efficiency. Hence, new ideas may emerge in the design of realistic hybrid metal−fullerenes of

ASSOCIATED CONTENT

S Supporting Information *

A brief discussion and detailed data concerning the basis set and electron correlation effects on the first hyperpolarizabilities of the model structure (Na4C60). 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 We thank F. Rabilloud for providing the initial Cartesian coordinates of the systems studied in this work. Also, P.K. thanks M. Rerrat and B. Champagne for the constructive discussions concerning the SOS method that has been applied in this work. Finally, we acknowledge CINES for the generous computational support.

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REFERENCES

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