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Exploring the Linear Optical Properties of Borazine (BN) Doped Graphenes. 0D Flakes vs 2D Sheets 3

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Nicolás Otero Martínez, Panaghiotis Karamanis, Khaled Elsayed El-Kelany, Michel Rérat, Lorenzo Maschio, Bartolomeo Civalleri, and Bernard Kirtman J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10837 • Publication Date (Web): 01 Dec 2016 Downloaded from http://pubs.acs.org on December 7, 2016

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The Journal of Physical Chemistry

Exploring the Linear Optical Properties of Borazine (B3N3) Doped Graphenes. 0D Flakes vs 2D Sheets.

Nicolas Oteroa,b, Panaghiotis Karamanisa*, Khaled el-Kelanya,c, Michel Rerata, Lorenzo Maschiod,e, Bartolomeo Civalleri,d,e and Bernard Kirtmanf.

a

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 – France. b Departamento de Química Física, Universidade de Vigo, 36310, Vigo, Galicia, Spain. c CompChem Lab, Chemistry Department, Faculty of Science, Minia University, Minia 61519 Egypt. d Dipartimento di Chimica, Università di Torino, via Giuria 5, I-10125 Torino, Italy. e NIS (Nanostructured Interfaces and Surfaces) Centre, Università di Torino, via Giuria 5, I-10125 Torino, Italy. f Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States

*Corresponiding author: [email protected]

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Abstract Hybrid graphene/(hexagonal-boron-nitride) systems start to play a pivotal role in the realm of twodimensional materials for atomically thin two-dimensional integrated circuits. As a result, there is significant interest in fabricating BnNn-substituted graphene networks from the bottom-to-up to be used to as precursors in flexible two dimensional one-atom think electronic and optical devices. In this report, we present a piece of theoretical work dealing with the microscopic electronic dipole-dipole polarizabilities (static and dynamic) of borazine (B3N3) doped graphenes in zero- and two-dimensions. Polarizability is a fundamental property that describes the distortion of the electron cloud in the presence of weak static external electric fields and delivers important information about the electronic structure and spectroscopic behavior of molecules. The robust polarizability trends presented and discussed in this work, point out local cyclic electron delocalization (aromaticity in rings) as the leading element that differentiates zero-dimensional B3N3 doped graphene flakes from twodimensional B3N3 doped graphene sheets.


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1. Introduction One of the defining characteristics of pristine graphene,1,2 its gapless semimetal character, is also a major limiting factor for the majority of applications in optoelectronics.3,4 As a result, remarkable efforts in establishing efficient strategies to open its gap and further improve its optoelectronic properties have been documented the recent years.5,6,7One of the proposed angles of attack relies on confining8,

9, 10

in its lattice segments of another two-dimensional material known as “white-

graphene”11 or hexagonal boron-nitride (hereafter hBN). The major challenge in producing functional hBN-graphene lateral hybrid structures (hBNG)

is, to establish effective processes that deliver

systems of stable band gaps for a given application. Upon success, a great assortment of ground breaking hBNG hybrid systems12,13,14 suitable for flexible two dimensional one-atom thick electronic and optical devices are yearned to emerge. One of the promising strategies of synthesizing hBNG hybrids proposed so far relies on atom precise bottom-to-up organic synthesis.15,16,17 The basic aim of such an endeavor is to use well established procedures of organic synthesis (or discover new ones), in building stable nanographenes18 bearing BnNn fragments. Up until now, the first encouraging achievement toward this end has been reported by Krieg et al.

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These authors, after several initial attempts,16 reported the synthesis of a

“borazinephore” nanographene molecule which can be viewed as hexa-peri-benzocoronene19 (HBC) doped with a borazine (B3N3) unit. In a further step, Sánchez-Sánchez et al. 20 fabricated from the bottom-to-up BN-substituted heteroaromatic networks, using surface-assisted polymerization and subsequent cyclodehydrogenation. Such B3N3-doped nanographene monomers could be used as precursors in polymerization or surface assisted growth via chemical vapor deposition21,22,23,24 delivering viable hBNG hybrids. Finally, experiments and simulations on B3N3@HBC deposited on Au(111) single crystal25 provided strong evidences that borazine-doped nanographenes can be successfully used to design graphene-like materials of non-zero tunable band gaps.



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Within the above subject, two recent theoretical studies26,

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on hBNG nanographene hybrids

bearing stoichiometric BnNn patches with n≥3 revealed that the incorporation of hBN segments in 0D graphene flakes triggers dramatic changes on the nonlinear optical electronic properties of the host systems. More specifically, Karamanis et al.26 reported that specific hBNG nanographenes may exhibit exceptionally high non-linear-optical activities dictated by the size or shape of the hBN segment confined in their framework. In a subsequent article27, the same authors showed that these effects largely depend on the electron delocalization in rings of the nanographene host. This last outcome was the subject of a third article by Otero et al.

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in which a strong connection between the

multidimensional property of aromaticity29,30,31,32 and the energetic difference between the highest occupied (HOMO) and lowest unoccupied LUMO orbitals of zero dimensional (0D) finite flakes, was reported. The key finding of that study was that partially substituted aromatic rings formed locally at the hBNG interfaces are linked to irregular band gap variations either in stoichiometric 0D (BN)n/graphene hybrids or in hBNG 2 dimensional (2D) sheets. The term "partially substituted benzenoid rings” refers to heterocycles formed locally at the (graphene)/(white-graphene) heterojunction by replacing of at least one carbon-carbon bond belonging to an aromatic sextet of the pristine graphene flake. Finally, in a recent study it was shown by Maschio et al.33 that BN substitutions in graphene have very distinct and unique features in the Raman spectra. In particular the spectrum relative to B3N3 substitution (named “Island 1” in that work) appears to be very sensitive to defect concentration. Relying on the knowledge gained from the above theoretical studies and motivated by the recent advances in atom precise organic synthesis of “borazinephore” nanographenes, in this work we discuss structure property correlations concerning the linear optical properties of graphene species bearing isolated B3N3 units. State of the art density functional methods are used to treat both finite systems and periodic architectures. More specifically, we report, explain and compare variations and trends of the electric dipole-dipole polarizability (static and dynamic) in zero- and two dimensional


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systems. One of the main purposes of this work is to bring to light fundamental similarities and differences between 0D and 2D borazine doped graphene architectures with respect to their linear optical properties as these are described the universal property of polarizability. 2. Background - Computational Details. The electronic (electric) dipole polarizability34,35,36 is associated with the distortion of the electron cloud of an atom, molecule37, atomic cluster38,39 or any material system that arises as the linear response to a weak homogeneous external electric field ( ). This property may, thus, be expressed40

as the linear term in an expansion of the dipole moment induced by the field, i.e. ind=α + ... . Since µind and F are vector quantities α is a second-rank Cartesian tensor: =

(1)

Each of the above tensorial elements (ααβ, (α, β)=x, y, z) represent the molecular polarization along the Cartesian direction of the incident field (the column index indicates the direction of the field and the row index gives the direction of the induced dipole moment). The number of nonvanishing independent polarizability components, ααβ, describing the polarization of a given particle depends on its symmetry. For instance, Oh point group symmetry allows only one independent static component. In this case, α in =α is a scalar quantity. On the other hand, the number of tensorial elements grows to six: αxx, αyy, αzz, αxy=αxy, αxz=αzy, αzy=αyz in the absence of symmetry (c.c. C1 symmetry point group if Kleinman41 symmetry is assumed). In this work we shall focus on trends and variation of individual electronic ααβ tensorial components as well as on the mean (or average) polarizability defined as:

= +

+ (2)



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The above quantity is accessible from theory with high accuracy.42 Experimentally, it can be only estimated in an indirect manner because upon application of an electric field, apart from the electronic distribution, other fundamental features of the molecule, as for instance their nuclear geometry of equilibrium, are perturbed. More information about and its experimental determination can be found in Ref [43]. If the electric field (from, say, a laser source) oscillates at the frequency ω, then the induced dipole moment will oscillate at the same frequency and, of course, the electronic polarizability denoted α(ω,ω) will depend upon ω. Dynamic polarizability α(-ω,ω) is a complex quantity44 and reflects field induced perturbations to both vibrational and electronic motions of a given molecule. The real electronic part of α(-ω, ω) in solids, liquids and gasses is macroscopically related to the dielectric constant and to light propagation determined by the refractive index. Through its imaginary part, α(ω, ω) is associated to the absorption coefficient that determines the absorption of a particular lightwavelength. In isolated free molecules, dynamic molecular polarizabilities are in strong connection with light absorption spectra, RAMAN intensities, and electronic excited states determined by its poles.45 Here, we shall limit our investigation on frequency effects on the electronic part of the polarizabilities of 0D nanographenes and 2D borazine doped graphene lattices. Both static and dynamic polarizabilities of 0D finite systems and 2D periodic lattices have been computed analytically by means of perturbation theory and more specifically within the coupled perturbed Hartree-Fock46 and Kohn-Sham approaches (CPHF, CPKS) for finite47 and periodic48 systems. Computations on 2D periodic BN/graphene systems have been performed with a development version of the periodic ab initio CRYSTAL14 code.49 For static and dynamic polarizability computations on 0D molecular graphenes we relied on the GAUSSIAN 0950 suite of programs and home-made FORTRAN codes51 for post-Hartree-Fock treatments. As in previews studies,52,53,54,55,56 we have employed the fractional occupation Hirsfeld-Iterative (FOHI) scheme57,58 for an analysis of the static CPHF/KS polarizabilities. FOHI partitioning allow us 6 ACS Paragon Plus Environment

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to gain chemical insight, based on the quantum theory of atoms in molecules (QTAIM)59, by partitioning the total value of the polarizability component into atomic contributions as follows: = − ∑$ % −

" !

+

"# !

'() *( = & + & (3)

'() *( where, is the weight function, & the intrinsic polarizability and & the so called is the

charge transfer (or delocalization) component. The weight function allows to identify the atom, n, in .

the molecule located at the position

As in the ordinary Hirsfeld iterative scheme (H-I)60 , is

computed iteratively to eliminate ambiguities in the selection if the promolecular density. The intrinsic polarizability, depends on the relative reference of the molecular space with respect to the position of each selected atom n providing the “pure” contribution of a given atom in a molecule, or cluster, on its global polarizability which depends on its nature (e.g. size, electronegativity). On the other hand, the charge transfer term, which relies on the nuclei reference (

)

and on the size of the

molecule, reflects the charge redistribution among the atoms of a molecules under the influence an external electric. It depends on the first-order perturbed populations of the atom and on their position *( '() in the molecule for a given origin. Both & and are expressed on the basis of the electron

density derivative (! ) with respect to an external, uniform static electric field in the limit of

zero field strength and multiplied by the Cartesian component a of . Based on Eq. (2, 3), the

expression of the mean molecular intrinsic polarizability is written as follows:

'() = − ∑$(-./ ∑'% , ,0 − %

' ' # !

(4)

The distinct feature of FOHI partitioning, as compared to other discrete schemes (e.g., QTAIM and Voronoi), is that divides the molecular space into continuous and overlapping atomic distributions. This element, is conceptually crucial for properties such as the dipole electronic polarizability which decay in different manner than the electron density. A demonstration of differences between nonoverlapping and overlapping approaches is shown in the following scheme that illustrates positive mean intrinsic polarizability (+MIP) density contour plots on the molecular plane of HBC computed with both FOHI and QTAIM approaches. Despite the obvious differences in the +MIP densities 7 ACS Paragon Plus Environment


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between the two approaches due to the different definition of atoms, both methods provide an accurate description of the aromaticity pattern of HBC as compared to Clar’s theory of aromatic sextets.61,27 FOHI partitioning of the electron density, obtained from GAUSSIAN 09, using the atomic densities has been carried out with the BRABO package62 and the STOCK program.63

Scheme 1. In-plane representations of the analytical all-heavy-atom positive mean intrinsic polarizability (+MIP) distributions obtained by means of the use QTAIM and FOHI partitioning schemes for hexabenzo-coronene. The molecular geometry, electron density and dipole polarizability have been obtained at B3LYP/6-31G(d).

A variety of DFT functionals, including long-range corrected and hybrid versions, were used to compute the polarizability, and also the electronic band gap, in order to establish the robustness of our conclusions. The basis set is specified along with the method in each case. In few instances we have also performed finite field51 computations by means of Møller-Plesset (MP) many body perturbation theory (MP2) and the semi-empirical double hybrid functional including corrections from perturbation theory based in the Görling–Levy perturbation theory widely known as B2PLYP.64 We will not describe one by one all DFT-functionals we applied in this work. In most of the instances we shall be using their standard abbreviations (e.g. B3LYP, M06L etc). We will only mention that the majority of the reported polarizability computations of the finite systems have been obtained with the long range corrected version of B3LYP using the Coulomb-attenuating method (CAM-B3LYP) and


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the long-range separated functional developed by Hirao and co-workers, namely LC-BLYP,65 recently implemented in the development version of CRYSTAL 14 for static and dynamic CPHF and CPKS computations which are not implimented in the availbale version of the Periodic Boundary Conditions code of G09. In the latter functional we fixed the corresponding range separating parameter66 (µ or ω), which defines the division ratio of the two-electron operator to 0.33 and 0.47 (default).

3. Results-Discussion 3.1 0D Graphene Flakes We begin our discussion with static dipole polarizability comparisons among four reference molecular systems namely, HBC (C42H18), coronene (C24H12) and their B3N3 doped counterparts: B3N3@HBC and B3N3@COR (see Figure 1). All molecules belong to Dnh symmetry point group with n=6 for HBC and COR and n=3 for B3N3@HBC and B3N3@COR. Note, that the latter two molecules adopt the symmetry of the B3N3 unit replacing their middle carbon rings. For both D6h and D3h the polarizability tensor has two independent components, one perpendicular (α┴) and one parallel (α||) to the molecular plane. If the molecules are placed on the xy plane, with z being the symmetry axis, then, αxx=αyy≡α|| and αzz≡α┴. The electronic polarizability values of the above molecular graphene models, computed at various levels of theory with the triple-ζ 6-311G(2d,2p) basis set for equilibrium nuclear geometries determined at the B3LYP/6-311G(2d) level, are presented in Table 1. As expected, the molecular polarizability of HBC is larger than COR due to its larger size. For instance, the predicted mean molecular polarizabilities of HBC range from 490.8 au (HF) to 541.2 au (M06L) while those of COR from 269.1 au (HF) to 288.6 au (M06L). The same holds for B3N3@HBC and B3N3@COR. In this case the corresponding values vary between 452.7 au (HF) to 509.9 (M06L) and from 294.7 au (HF) to 316.2 au (MP2), respectively. 9 ACS Paragon Plus Environment


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The basic trends found here, with respect to the relative polarizability orderings as a function of the functional, are in qualitative agreement with recent studies on the performance of various DFT functionals on the computation of (hyper)polarizabilities (see for instance Refs [67], [68], [69], [70] and references therein). For instance, the long range corrected, CAM-B3LYP, ωB97X-D and the range separated functional LC-BLYP return values between HF and MP2 for all four systems. On the other hand, hybrid B3LYP functional overshoots the mean polarizabilities of HBC, COR and B3N3@HBCwith respect to MP2 approximation but not the one of B3N3@COR. Finally, the pure functional of Truhlar and Zhao, M06L,71 is the one that brings the largest polarizabilities for all four systems. Despite the evident differences in polarizability magnitudes, originating from the various approximations used, all applied methods describe in a uniform manner two opposite effects. On one hand, a decrease in the mean dipole polarizability follows the transition from HBC to B3N3@HBC. On the other hand, the substitution of the central ring of COR with B3N3 leads to a clear mean polarizability increase. Taking the pristine systems as a reference the percentage change observed in the mean polarizabilities varies from -5.5% (M06HF) to -7.8% (HF) for pristine-doped HBC and from 12.1% (MP2) to 7.4% (M06L) for pristine-doped COR. In either case the tensorial elements responsible for the observed evolution are those describing the polarization along the respective molecular planes. Hence, all levels of theory indicate that HBC(αǁ)> B3N3@HBC(αǁ) and COR(αǁ)

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