Polyaromatic Systems Combining Increasing Optical Gaps and

Subscriber access provided by BUFFALO STATE

C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Polyaromatic Systems Combining Increasing Optical Gaps and Amplified Nonlinear Optical Properties. A Comprehensive Theoretical Study on BN Doped Nanographene 3

3

Panaghiotis Karamanis, Nickolas D Charistos, Michael P Sigalas, and Michel Rérat J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b05543 • Publication Date (Web): 01 Aug 2019 Downloaded from pubs.acs.org on August 6, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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

The Journal of Physical Chemistry

Polyaromatic Systems Combining Increasing Optical Gaps and Amplified Nonlinear Optical Properties. A Comprehensive Theoretical Study on B3N3 Doped Nanographene Panaghiotis Karamanis,*a Nickolas D. Charistos,b Michael P. Sigalasb and Michel Rérata

a

CNRS/ UNIV Pau & Pays Adour, Institut Des Sciences Analytiques et de Physico-Chimie pour l'environnement

et les Materiaux –, UMR5254, 64000, Pau, France. Hélioparc Pau Pyrénées 2 avenue du Président Angot, 64053 PAU Cedex 09 – France. b

Department of Chemistry, Laboratory of Quantum and Computational Chemistry, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

* [email protected]

1 ACS Paragon Plus Environment

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

Page 2 of 55

Abstract Materials combining amplified nonlinear optical responses and wide optical gaps that ensure high laser-induced damage thresholds and broadband transparency, are highly required for photonic applications. In this article we use well-established quantum chemical methods to demonstrate that a special class of polyaromatic hydrocarbons, in which multiple borazine (B3N3) units substitute aromatic carbon sextets, are suitable for the design and synthesis of systems meeting both above requirements. Computations conducted in wide assortment of purposely designed nanographene model-systems exposed robust doping/property relations which point out that multiple B3N3 doping can be considered as an efficient strategy to enhance the quadratic non-linear optical responses of a given polyaromatic hydrocarbon maintaining at the same time wide optical gaps. A detailed analysis of the underlying charge transfer mechanism revealed that observed features stem from local in character electronic excitations occurring between the incorporated B3N3 units and neighboring aromatic sextets. .


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


1. Introduction The past few years, efficient synthetic strategies have been established for the fabrication of polyaromatic hydrocarbons

(PAHs)

incorporating

stoichiometric

boron

nitride

sections

(BnNn)

in

their

structure.1,2,3,4,5,6,7,8,9,10,11,12,13 Most of the reported attempts, aim to deliver doped PAHs to be used either as stand-alone functional-modules or as precursors of more complex architectures of high technological value, such as two-dimensional graphene-like materials of nonzero bandgaps.14,15 The principal target in this research area is to improve and fine-tune the optoelectronic properties of planar polyaromatic hydrocarbons (e.g. graphenes) using as doping agents foreign units (e. g. borazine) that could homogeneously blend in their framework without causing undesired structural distortions. To this end, Krieg et al.7 reported the synthesis of doped hexabenzocoronene in which the central aromatic sextet is replaced by a borazine ring. Dosso et al2, synthesized a soluble version of the former molecule and confirmed the impact of inorganic benzene on the optical properties of a graphene host.16 In the same context, a convincing bottom-to-up demonstration of how such borazine-doped nanographene monomers can be utilized as building blocks for the construction of graphene-like architectures, has been reported by Sánchez-Sánchez et al.9 The next important step forward has been made by Bonifazi and co-workers who synthesized2,11,17 complex polyphenylene dendritic chains bearing high concentrations of B3N3 units of controlled orientations at preselected positions. Their results not only prove that multiple borazine units can coexist in the same carbon-based scaffold but, as it is argued by Lorenzo-García and Bonifazi,18 might pave the way for the next long-awaited breakthrough in graphene chemistry which is the fabrication of two dimensional multi-B3N3 doped graphenes of tunable bandgaps. Among other technological applications18, the up-to-date research in BN-doped graphenes and/or polyaromatic motifs also suggests that such hybrids might find a prosper ground in the realm of nonlinear optical (NLO) materials. The latter statement is supported by recent experiments conducted by Biswas et al.19 on heterostructures of hexagonal boron nitride-graphene oxide (hBN-GO) and by earlier theoretical predictions20,21,22,23 on hybrid nanographenes which provide solid proofs that hBN-graphene hybrids possess a strong NLO character that could be exploited in advanced NLO applications. Motivated by the aforementioned advances, in this work we shed light on essential features related to the linear and non-linear optical responses of polyaromatic nanographene systems doped with multiple B3N3 units. 3 ACS Paragon Plus Environment


Page 4 of 55

To accomplish this task, we conducted a systematic investigation in a wide assortment of representative B3N3 graphene finite-sections24 doped with multiple B3N3 units. The obtained results exposed that multi-borazinodoping triggers synergic effects of strongly additive character that widen the optical gaps of the resulting system as a linear function of the number of the dopant units. Although one might expect that the respective effect should have a negative impact21 on the second order non-linear optical amplitudes of the resulting systems, our hyperpolarizability computational results predict the opposite. In brief, multi-borazino doping instead of decreasing the NLO capacity of its host by increasing its gap, sparks strong nonresonant second order NLO responses via additive synergic effects. This is a very appealing feature to be considered as an additional guiding principle in the design of graphene-based NLO materials featuring broadband transparency and large laser-induced damage thresholds.25,26,27 The current article is organized as follows. First, we examine the impact of borazine doping on the linear optical properties of several prototype graphene systems of various shapes and sizes and different B3N3 relative orientations. Next, we rationalize the obtained trends in terms of electronic (vertical) excitations and check possible charge transfer interaction between the confined inorganic benzenes. Finally, we investigate the hyperpolarizability evolution in highly doped model-systems in order to obtain a clear picture of essential property/doping relations to be considered in the rational design of polyaromatic systems doped with fully formed units of inorganic benzene.

2. Theory The electronic dipole (hyper)polarizabilities characterize the intrinsic ability of a molecule to adapt its electron density under the influence of an external electric field. In their static forms they are defined by a Taylor series expansion28,29 of the induced molecular dipole moment in the presence of a weak uniform external static electric field, as follows:

α    αβ Fβ  α,β

1 1  αβγ Fβ Fγ    αβγδ Fβ Fγ Fδ  .... (1)  2 β,γ 6 β,γ,δ

In Eq (1), Δμα stands for the induced dipole moment in the presence of the static electric field, (F) ααβ is the static dipole polarizability (or linear polarizability) while βαβγ, γαβγδ are the first and second dipole 4 ACS Paragon Plus Environment

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


hyperpolarizabilities (or second and third nonlinear polarizabilities being proportional to F2 and F3, respectively). Greek subscripts denote tensor components describing the Cartesian direction of the field induced polarization and can be equal to x, y, and z. For instance, αxx represents the linear polarization of the electron density along the molecular Cartesian direction α=x (expressed as the induced dipole moment Δμx) when a field is applied along the same direction. In isolated molecules, the dipole polarizabilities (static or dynamic) are associated to light absorption spectra, RAMAN intensities, HOMO-LUMO gaps (HLGs) and electronic excited states determined by its poles.30 The first order molecular dipole hyperpolarizability (β), on the other hand, is associated with the nonlinear field-induced response of the electron cloud under the influence of an external electric field and it is associated to fundamental processes of nonlinear optics,31 as for instance, the electrooptic Pockels effect or the nonlinear effect of second harmonic generation (SHG). An optional way to define, compute and more importantly, understand the first hyperpolarizabilities of a molecule which are related to the macroscopic quadratic NLO responses, is given by a sum-over-states perturbative approach32 (SOS). Within SOS the perturbed electronic wave-function is approximated in terms of all eigenfunctions of the unperturbed Hamiltonian. In such a manner, any tensorial component of the static electric first hyperpolarizability can be computed as an infinite sum of terms comprising dipole transitions in the nominators and excitation energies in the denominators as follows33:

 (0;0, 0)    6

n0 m0

   nm 00 ) m 0 0n ( nm

( En  E0 )( Em  E0 )

(6)

In Eq. 6 E0 and En,m represent the ground and excited state energies, respectively, moment between the ground (0) and the excited state (n, m) defined as: β µ m nm  n  β

0α,γn ,m is the transition dipole

0α,γn ,m  0 µα,γ n, m

and

stands for the transition dipole moment connecting excited states n and m if n≠m (  nm =0)

and the state-dipole moment if n=m (  nm =1). The inverse proportionality of β on the excitation energies implies that large molecular first hyperpolarizabilities can be observed in molecules featuring low-lying excited states associated with “longdistance” intramolecular charge transfer. In SOS, the later process yields large (  nn , mm  00 ) differences β

β



Page 6 of 55

and/or large transition dipoles between interacting excited states.34,35 This is the case of classic donoracceptor chromophores, intensively studied the past decades.35 In such systems, the rule of thumb suggests that the first hyperpolarizability of a molecule AB should be always larger than the vector sum of the hyperpolarizabilities of its fragments A and B (|βAB|>> |βA+ βB|).

Conversely, enhanced first

hyperpolarizabilities could also be delivered if many of the symmetry-allowed excited states constructively contribute in Eq. 6 regardless of their energetic “distance” of the ground electronic state.

3. Computational details In this work we discuss structure property correlations of the tensorial components of the dipole polarizability and first hyperpolarizability, considering also scalar quantities as the mean (or average) static dipole polarizability (  ), the total first order hyperpolarizability βtot and the squared norm36 of the first hyperpolarizability tensor in terms of Cartesian components referred as the modulus of the -tensor(‖𝛽‖). Definitions of these quantities are given below:

1 3

  ( xx   yy   zz ) (3)

tot    x2   y2   z2 

1/ 2

(4)

Where:  x   xxx   xyy   xzz ,  y   yxx   yyy   yzz and  z   zxx   zyy   zzz 2 ‖𝛽‖ = ∑𝑎.𝛽.𝛾𝛽𝛼,𝛽,𝛾 (5)

The static dipole polarizabilities and first hyperpolarizabilities reported in this work have been computed analytically within the coupled perturbed Hartree-Fock/Kohn-Sham approaches37,38 (CPHF, CPKS) for finite systems. To secure the robustness of the results, we used a variety of methods comprising the Hartree-Fock (HF) approximation and long-range corrected density functional theory (DFT) methods as the Coulombattenuating (CAM-B3LYP)39 and the Head-Gordon-coworkers long range corrected functional (ωB97XD).40 Spectroscopic properties of some of the systems considered have been computed using either the configuration interaction singlets (CIS) method or by applying the TD-CAM-B3LYP time-dependent DFT method. The


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


exited states of interest have been analyzed using charge-transfer indices (CT) including the charge-transfer distance (DCT) proposed by Bahers et al.41 The later quantity provides a measure of the intramolecular distance between the starting and ending points of the transferred charge within a certain quantum transition. In practice, large DCT values imply CT excitations in which the electron density migrates from one part of the molecule to the other. Alternatively, relatively small DCT indices point out local electronic excitations associated with the reorganization of the electron density between neighboring atoms. Finally, intuitive excited state representations have been obtained by means natural transition orbitals42,43 (NTOs) in terms of “excited particle” to “empty hole” of the electronic transition density matrix. All hyperpolarizability and excited state computations have been carried out with GAUSSIAN 0944 suite of programs. The relevant CT indices have been computed with MULTIWFN program.45 We also applied the Heyd-Scuseria-Ernzerhof functional (HSE06),46 and the 6-31G*basis set to performed geometry optimization of infinite periodic ribbons under periodic boundary conditions as implemented in GAUSSIAN 09. Finally, aromaticity pattern determinations have been performed via NICSπzz index computations that correspond to the π-contributions to the out-of-plane component of the induced magnetic field. For this task, the EPR module of ADF47 program have been used by applying the Perdew−Burke−Ernzerhof (PBE) functional and a triple-ζ Slater basis set with one polarization function (TZP) as described in previous works from Charistos and coworkers.48



Page 8 of 55

3. Results and Discussion 3.1 Linear Optical Properties We chose to start our discussion from six doped nanographenes built upon the same all-benzenoid pristine ribbon, namely C114H34 (hereafter C114) (see Figure 1). Clar’s49 aromaticity rules dictate that in this set of molecules, every B3N3 unit should be replacing an aromatic ring of the central phenylene chain of C114. This supposition is further supported by a detailed aromaticity study in all doped systems, relying on NICSπzz (Nucleus Independent Chemical Shift) computations. As seen, in the relative values presented in Figure 1, the replacement of solely one aromatic sextet with a B3N3 unit although renders, as expected23, this ring as nonaromatic, does not change the aromatic character of the rest of phenylene hexagons of C114. The same trend is avrg

observed as the number of incorporated B3N3 units increases. For instance, the average NICSπzz

undergoes a

weak decrease, from -35 ppm in (B3N3)@C114 to -33 ppm and -30 ppm in (B3N3)2@C114 and (B3N3)3@C114, respectively. The obtained changes, not affected by the relative orientation of the B3N3 rings, imply a rather weak counter effect on the magnetic response of neighboring rings. A more detailed discussion about the aromaticity of these species is provided as supporting material. HOMO-LUMO gaps (HLG), excitation energies of the first allowed by symmetry excited state (E01) and mean dipole polarizabilities of (B3N3)n@C114 (n=0, 1, 2, 3) computed at two levels of theory, with basis sets of increasing size, are listed in Table 1. A careful comparison of the computed values reveals that HLGs and E01 energies increase with the number of the fused B3N3 units while the dipole polarizabilities follow the inverse trend. The observed variations are in line with previous experimental and theoretical studies reporting that borazine doped nanographenes, in which one B3N3 core replaces at least one aromatic ring, feature larger HLGs50, smaller dipole polarizabilities23 and thus larger optical gaps10,50 when compared to their parent pristine systems. In addition, the current results point out that either property is practically insensitive to the relative alignment of the incorporated B3N3 units (Table 2). Considering that in isoelectronic molecules of the same size, decreasing dipole polarizabilities are directly associated with absorption bands at higher energies, we simulated, at CIS/6-311G(d) level, the absorption spectra of (B3N3)n=1,2,3@C114 in which the borazino rings are placed in parallel alignment. As it is very well demonstrated in Figure 2, the more borazino units replace aromatic sextets the more “blue-shifted” the spectra become. 8 ACS Paragon Plus Environment

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


In view of the straightforward connection between the optical gaps and/or the molecular dipole polarizability with respect to B3N3 doping, we explored the contribution of an individual borazine unit in the optical gap change of a given ribbon. For this task, we considered a series of ribbons in which one (A and B) and two (AB) borazine rings, respectively, replace symmetry-equivalent aromatic sextets as shown in Figure 3. As a qualitative measure of the optical-gap change in this series of systems we used the percentage change of the dipole

polarizability

(P%)

with

respect

= 100 × [𝛼(𝑝𝑟𝑖𝑠𝑡𝑖𝑛𝑒) ― 𝛼(𝑑𝑜𝑝𝑒𝑑)] 𝛼(𝑝𝑟𝑖𝑠𝑡𝑖𝑛𝑒).

the

pristine

ribbon,

defined

as

𝑃%

From its definition, increasing/decreasing P% should

imply enhanced/reduced optical gaps, and therefore, increasing/decreasing blue/redshifts with respect to the 𝑃%𝐴𝐵

pristine ribbons. Interestingly, the computed ratios 𝑃%𝐴 + 𝑃%𝐵 listed in Table 3 are found close or equal to unity indicating that the optical-gaps in nanographenes, in which B3N3 units replace symmetry-equivalent aromatic sextet, should vary in an additive manner with respect to the number of fused borazine rings. The validity of the latter trend is further confirmed in the systems of different shapes larger sizes, shown in Figure 4. To investigate whether the above effect stems from interactions between the fused B3N3 units we simulated the evolution of P% in two large doped ribbons of different length with respect to the intramolecular distances between two fused B3N3 units, as shown in Figure 5. The respective variations shown in plots (5a) and (5b), reveal that for small phenylene spacers and far from the ribbons’ short edges the obtained P% values are exceptionally stable. Contrariwise, as borazino units approach the two terminal sextets of either ribbon, P% adopts a decreasing pattern and reaches a minimum at the edges. At first glance, this effect could be attributed to a fading interaction between the fused borazine units. However, if we compare the two variations, it is exposed that P% decreases faster in the short ribbon than in the longer one. As a result, after a certain spacer and beyond, the optical gap change becomes independent of the B3N3 concertation which in turn suggests that the optical gaps of these systems should depend more on the distance between the B3N3 units from the terminal side-sextets of the two ribbons than on the size of the phenylene spacer between them. In view of the strong additive effects observed in the linear polarizabilities of multi-borazino-doped graphene flakes, and the minor importance of the intramolecular distance between the fused borazine units, we analyzed the excited states of a prototype model in which two B3N3 units are bridged by one phenylene ring (see Figure



Page 10 of 55

6) at the CIS/6-311+G(2d) level of theory. To do so, relevant quantities as the dipole moment difference between states, the charge transfer distance DCT and pictorial hole-electron representation of selected excited states corresponding to the first and the most probable quantum transitions, have been computed. Then, we repeated the same analysis in a reference donor/acceptor molecule, namely, para-nitro-aniline (PNA) and we compared the results. The outcomes of this study are schematically summarized in Figure 6. Starting from the computed ground state molecular dipole moment vectors shown in Figure 6 it becomes evident that if the negative pole of PNA lies in the side of the acceptor (-NO2) and the positive in the donor’s side (-NH2), then, in BN-C-BN, the boron-bonded borazine should act as the acceptor and the nitrogen-bonded one as a donor. Therefore, upon electronic excitation a part of the electron density should move toward a direction opposite to its ground state dipole moment. This is exactly what we see in the case of PNA in which the principal charge transfer state is described by one dominant NTO pair, accounting for the 87% of the total excitation. At first glance, a similar charge transfer topology is implied by the obtained hole-electron densities of the first (A) and second excitation (B) of BN-C-BN. However, a careful inspection the hole-electron-pair topologies of transitions A and B of BN-C-BN reveals the absence of obvious transfer of charge from the B- bonded to Nbonded B3N3 unit. Such a polarization mechanism contrasts the one obtained for PNA and delivers dramatically smaller DCT distances and Δμ values suggesting that both A and B excitations should be of strong local character. As a result, the first (A) and the most probable quantum transition (B) of BN-C-BN, respectively, feature Δμ values of 0.10 and 0.3 D, respectively, which fall one order of magnitude shorter than in the case of PNA’s transition A. In the light of the above results we examined the involvement of borazine units in the two most probable transitions of (B3N3)n@C114 ribbons obtained at CIS/6-31G*level. The relevant spectroscopic parameters, matrix elements, charge transfer distances and hole-electron NTO pairs are shown in Table 4. The relatively small Δμ and DCT values obtained for all ribbons points out that, as in BN-C-BN, the respective quantum transitions should be of strong local character. A more intuitive picture is given in Figure 7 where we have plotted the surfaces of the electron density differences (Δρ(r)) between the ground and the excited states considered, together with excited and hole-electron NTO representations for ribbons (B3N3)n@C114 with n=1, 2, 3. The local character of the excited states reflects very well on the high degree of overlap of the ellipsoid 10 ACS Paragon Plus Environment

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


shapes at the center of each system, which represent the centroids of positive to negative electron density difference areas.41 What’s more, the corresponding NTO hole-electron pairs demonstrate that the respective excitations should also involve local reorganization of the electron density in neighboring aromatic sextets with no obvious charge transfer from the one B3N3 unit to the other.

3.2 First Dipole Hyperpolarizabilities. Hyperpolarizability values corresponding to the linear ribbons of Figure 1 computed at the CAM-B3LYP/631G(d), 6-311G(2d) levels are listed in Table 5. A careful study of the computed data exposes two dominant trends. The first concerns the obvious hyperpolarizability increase in ribbons bearing borazino units of parallel alignment. What is interesting in this variation is that the observed property variation is not affected by the energetic differences between the occupied and unoccupied molecular orbitals as one might have been expected judging from Eq 2. For instance, as we go from (B3N3)@C114 to (B3N3)3@C114 we see that βzzz experiences a twofold increase despite a clear increase in the respective HLG and excitation energies of 0.5 eV and 0.3 eV respectively. A similar effect is observed for the systems presented in Figure 8 in which the fused B3N3 units replace aromatic rings belonging to different phenylene chains. The corresponding results summarized in Table 6, verify that that both βtot and ||β|| experience a sharp enhancement with increasing the number of B3N3. The second worthy of analyzing trend comprised in the data listed in Table 5, involves the contradicting correlation between the ground-state polarities of the systems and their first dipole hyperpolarizabilities. Specifically, although β seems to follow the dipole moment increase, which increases with increasing the number of fused B3N3 units of parallel alignment, this is not the case for the last ribbon of the series, namely (B3N3)[email protected] The hyperpolarizability of the latter systems lies about one order higher than in both (B3N3)2@C114BB and (B3N3)2@C114NN, despite its weaker dipole moment. Considering that in (B3N3)3@C114BBNN the two external borazine units are anti-parallel to the central B3N3 unit but parallel to each other, the respective result points at the number of B3N3 units of parallel alignment as the defining feature dominating the first hyperpolarizabilities of these systems. The robustness of this structure-property correlations is nicely demonstrated in a series of doped graphene flakes shown in Figure 9. As starting configuration in this example, we considered the mono-doped flake in which one B3N3 unit replaces the central aromatic sextet of C234. The 11 ACS Paragon Plus Environment


Page 12 of 55

hyperpolarizability of this configuration is represented by the line crossing the perpendicular axis of the corresponding plot. In the first family of doped ribbons (squares) every additional borazino unit replaces, anticlockwise, an aromatic sextet belonging to the axial polyphenylene chains, placed in a parallel alignment with respect to the central B3N3 unit. The same doping strategy has been followed in the creation of the second family of doped systems (circles), this time though, every borazino unit is added in antiparallel alignment with respect to the central B3N3 ring. The hyperpolarizabilities of the two families are compared in the scatter plot at the right. At first glance, it becomes readily apparent that whatever the doping fashion, ||β|| exhibits a sharp increasing pattern despite the significant HLG widening. Therefore, the largest hyperpolarizabilities in each family are scored by the heavily doped systems featuring the largest HLGs. The importance of the B3N3 alignment on the first hyperpolarizability is very well depicted on the hyperpolarizability evolution observed in the second family of doped ribbons. In this group of models, the hyperpolarizabilities of the first members fall considerably below the hyperpolarizability of the mono-doped flake due to cancelation effects between the two antiparallel B3N3 units as we saw in the case of the small linear ribbons examined above. However, after three B3N3 units are fused in this flake the number the peripheral B3N3 units of parallel alignment increases resulting to a strong hyperpolarizability escalation. Let us now turn our attention to the data plotted in Figure 10 where we explore the limits of the hyperpolarizability amplification, through the evolution of the first hyperpolarizability in a large all-benzenoid flake (C366) as a function of the number of fused borazine rings. To facilitate our analysis, we considered systems belonging to the D3h symmetry point group that allows only two nonvanishing β components of equal strengths but opposite signs. Also, for the sake of comparison, we have included the analogue flake of pristine hexagonal boron nitride. A careful look at the obtained results exposes that the first hyperpolarizabilities reach a maximum in hybrid flake 3 in which all B3N3 units are separated by one phenylene ring, the structure of which is dominated by local B3N3-C6-B3N3 configurations. This local structural motif turns out to be of critical importance in the hyperpolarizability evolution of these species since no further increase is observed upon replacement of the bridging aromatic sextets with extra B3N3 units. The latter outcome absolutely complies with the local character of the excited states observed in free B3N3-C6H4-B3N3 discussed in a previous section,


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


pointing out that local interactions between the B3N3 units and the attached aromatic sextets should dominate the non-linear responses of these species. To determine whether the hyperpolarizabilities of multi-borazino-doped systems can be understood as a summation product of the contribution of each B3N3 unit, we revisited the series of ribbons of increasing size shown in Figure 3 in which one (A or B) and two (A and B) B3N3 rings replace aromatic sextets at fixed position with respect to the ribbon edges. The computed property ratios (

‖𝛽‖𝐴𝐵 ‖𝛽‖𝐴 + ‖𝛽‖𝐵

) listed in Table 7 converge

to the unity from below while for all systems |βΑΒ| ≤ |βΑ + βB|. The same trends are obtained by comparing the hyperpolarizabilities of the shortest double-doped ribbons of Figure 5, namely (B3N3)2@C302H74, to the hyperpolarizability sum of its mono-doped counterparts (see values listed in Table 8). Bearing in mind that the hyperpolarizabilities of systems featuring intense charge transfer excited states (as push pull chromophores) should be larger than the hyperpolarizability sum of their constituting fragments, e.g. |β(Η2N-C6H5) + β(C6H5NO2)| < |β(Η2N-C6H5-NO2)|, our results confirm that the hyperpolarizability enhancement we observed in multiborazino doped systems should be predominantly a product of additive effects rising from interactions between each B3N3 unit and the neighboring aromatic sextets. Moreover, a careful comparison of the ratios listed in Tables 7 and 8 exposes that the obtained

‖𝛽‖𝐴𝐵 ‖𝛽‖𝐴 + ‖𝛽‖𝐵

ratios converge to 1 from below, either as the distance

between the B3N3 units increases with increasing the length of the ribbon, or alternatively by pushing the borazine units close to the side-edges of a sufficiently larger ribbon. These trends can be understood as the result of antagonistic effects between additive contributions from each B3N3 unit in the global hyperpolarizability of the system and the anticipated hyperpolarizability decrease due to the doping-induced band-gap widening. The latter effect turns out to be more pronounced either in ribbons of higher C6/B3N3 ratios or if B3N3 units replace internal aromatic sextets. In other words, the smaller the induced bandgap opening is, the more effective the additive effects on their (non)linear optical properties become.



Page 14 of 55

3.3 Size Scaling To explore possible effects rising from the ribbon growth, we studied the size scaling of the dipole polarizability and the first hyperpolarizability in a series of consecutive borazino doped ribbons of systematically increasing lengths (see Figure 11). The geometry of each finite ribbon has been extracted by the equilibrium nuclear geometry of the corresponding infinite ribbon optimized under periodic boundary conditions at the HSE06/6-31G*level of theory. From the data plotted in plot 11(a) it becomes evident that the dipole polarizabilities per unit length, in nm, follow an asymptotic51 behavior converging to the polarizability of the corresponding infinite ribbon from below. On the other hand, as seen in plot 11(b), the increasing rate in polarizability due the ribbon growth dies off as the ribbons reach a size of 14 nm. By extrapolating the data points of the finite ribbon fragments obtained at CAM-B3LYP/6-31G*level with an appropriate function of exponential decay51 we found that the asymptotic value for the average dipole polarizability amounts to 700.8 ±1.0 au which is very close to the values obtained for ribbons lengths larger than 8 nm. The corresponding evolution of the first hyperpolarizability in multi-B3N3doped systems of increasing size is presented in Figure 12. The data plotted, expose that βtot per nm converges the hyperpolarizability at the infinite length in a monotonic fashion. The asymptotic values51 at CAMB3LYP/6-31G*levels are found about 18.8×103 ±115 (19.4± 261) au/nm with a saturation length of 5.6 (5.8) nm and an intermediate saturation bandgap of about 4 eV. In addition, to estimate the contribution on the global property at the infinite length of each unit-cell we have considered also the differences Δβtot=(βtot)p+1- (βtot)p, where p is the number of unit cells bearing one B3N3 unit that annihilate the influence of the ribbons’s short side edges52. The CAM-B3LYP/6-31G*asymptotic value in this case, reached a value of 19.8×103 ± 40 au perunit-cell. The above (hyper)polarizability size scaling resemble those obtained53 in several conventional polymer systems terminated with donor and acceptor units54 or built from asymmetric unit cells. However, the hyperpolarizability strengths per-unit-cell in these ribbons prove considerably larger than those reported earlier. For instance by Jacquemin et al. 52 who computed the hyperpolarizabilities of polymethineimine at the polymer limit with various long-range corrected functionals reporting a value of 7.8×103 at the CAM-B3LYP/6-31G* level of theory which is about two times smaller than the values obtained here. Therefore, prolate borazino14 ACS Paragon Plus Environment

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


doped motifs might prove excellent candidates for the achievement of extra-large NLO responses that could be fully tuned by the ribbon length. 55 We chose to close this report with a brief demonstration about the hyperpolarizability evolution in the series of systems of functionalized edges shown in Figure 13. We have designed these trial prototype models to explore the capacity of B3N3-doped nanographenes to enhance their second order NLO responses, if purposeoriented synthetic strategies are to be applied. For this task we considered edge-functionalization with foreign substituents and hydrogen saturation of the edges. Their dominant hyperpolarizability components, are compared in Table 9. Starting from the results obtained for the hexagonal flakes, it is seen that by extending the diagonal phenylene chains of doped flake (a) with NLO-inactive phenylene dimers, a moderate enhancement in NLO responses is achieved without a significant band gap change. On the other hand, a stronger hyperpolarizability increase is observed in the case of flake (c), in which NLO active “BN substituted” phenylene dimers have been used. The respective enhancement cannot be justified by the occurring band gap change and should be attributed to additive contributions of the peripheral units on the already large hyperpolarizabilities of the graphene central system. Of intriguing interest are the also results obtained for the graphene ribbons bearing fully or partially hydrogen saturated edges. In the first case (ribbon e), we see a sixfold increase in the first hyperpolarizability.

In the second (ribbon f), on the other hand, a gigantic

hyperpolarizability enhancement is delivered although the computed HL gaps remain sufficiently wide (>2 eV). For the latter ribbon, wave-function stability tests21 suggest that its singlet-closed-shell ground electronic state should be a subject of wave-function instabilities induced by its narrow bandgap that could result to a ground state of diradical or polyradical character.56,57

This is an interesting finding concerning the effect of edge

hydrogen saturation on the electronic structures of these species that deserves a deeper investigation, however, such a task is beyond the scope of this work. Here, we will only mention that if the ground state of ribbon f is treated as an open-shell-singlet at the unrestricted UCAM-B3LYP/6-31G* level, its hyperpolarizability ||β|| experiences an additional enhancement of 5×105 au. Both of these effects demonstrate the flexibility of borazino doped graphenes to boost their NLO if the suitable edge functionalization strategy is applied.



Page 16 of 55

4. Conclusions In this work we performed a systematic quantum chemical study of charge transfer interactions and the effect of multi-borazino doping in the linear and nonlinear optical properties of medium and large nanographene motifs. The reported results suggest that local in character electronic excitations deliver (non)linear optical properties that increase as a function of the borazino-doping degree, in an additive manner. Accordingly, the concept of polyaromatic motifs doped with multiple "inorganic benzenes” could find a prosper ground in the design and synthesis of carbon based NLO materials that combine two important characteristics: amplified quadratic NLO responses and wide band gaps which are of pivotal importance for the achievement of high laser-induced damage thresholds and broadband transparency.

5. Acknowledgments. Part of this work was granted access to the HPC resources of [CCRT/CINES/IDRIS] under the allocation 2018-2019 [A0040807031] made by GENCI (Grand Equipement National de Calcul Intensif). We also acknowledge the “Direction du Numérique”of the “Université de Pau et des Pays de l’Adour” for the computing facilities provided.

6. Supporting Information Details about the aromaticity of the systems illustrated in Figure 1 and Cartesian Coordinates of selected systems considered in this study.


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


Table 1. Hartree-Fock, CAM-B3LYP HOMO-LUMO gaps (HLG), polarizability tensorial Cartesian components (αxx, αyy, αzz ) mean dipole polarizabilities (𝛼) and excitation energies (E01) corresponding to the first allowed by symmetry excited state of (B3N3)n@C114 series with n=0,1,2,3 (see Figure 1). All properties have been computed on CAM-B3LYP/6-31G* optimized equilibrium nuclear geometries. HLG/eV

E01/eV

𝛼𝑥𝑥

𝛼𝑦𝑦 × 102/au

𝛼𝑧𝑧 × 102/au

𝛼 × 102/au

3.9, 3.8 4.3, 4.3 4.5, 4.5 4.8, 4.8

2.4 2.9 3.0 3.2

290, 377 294, 390 301, 392 301, 400

16.8, 17.4 16.3, 17.0 15.9, 16.6 15.4, 16.0

31.1, 32.4 28.3, 29.6 27.0, 28.3 25.0, 27.1

16.9, 17.9 15.9, 16.8 15.3, 16.2 14.8, 15.7

5.7, 5.6 6.4, 6.3 6.7, 6.6 7.2, 7.1

2.4 3.5 3.6 3.9

289, 383 307, 395 308, 397 314, 403

15.9, 16.6 15.4, 16.1 14.9, 15,6 14.4, 15.0

27.6, 29.0 24.9, 26.2 23.8, 25.0 22.7, 23.7

15.5, 16.5 14.5, 15.3 13.9, 14.9 13.4, 14.3

CAM-B3LYPa 6-31G*,6-311G(2d) n=0 n=1 n=2 n=3 Hartree-Fockb 6-31G*,6-311G(2d) n=0 n=1 n=2 n=3

a

Excitation energies have been computed within time-dependent DFT (TD-DFT). Excitation energies have been computed within the configuration interaction singlets (CIS) approximation. b



Page 18 of 55

Table 2. CAM-B3LYP HOMO-LUMO gaps (HLG), polarizability tensorial Cartesian components (αxx, αyy, αzz ) mean dipole polarizabilities (𝛼) excitation energies (E01) corresponding to the first excited states, of (B3N3)2@C114NN,BB,BN and (B3N3)3@C114NNBB series (see Figure 1). All properties have been computed on CAM-B3LYP/6-31G* optimized equilibrium nuclear geometries. 6-31G*, 6-311G(2d) n=2 n=2 (BB) n=2 (NN) n=3 n=3(NNBB)

a

HLG (eV)

E01 (eV)a

𝛼𝑥𝑥(au)

𝛼𝑦𝑦×102(au)

𝛼𝑧𝑧×102(au)

𝛼×102(au)

4.5, 4.5 4.5, 4.4 4.5, 4.4 4.8, 4.8 4.7, 4.6

3.0, 2.9 2.9, 2.9 2.9, 2.9 3.1, 3.1 3.1, 3.1

301, 392 301, 392 301, 392 308, 400 380, 400

15.9, 16.6 16.0, 16.6 16.0, 16.6 15.4, 16.0 15.9, 16.2

27.0, 28.3 27.0, 28.2 27.1, 28.3 25.9, 27.1 26.3, 27.0

15.3, 16.2 15.3, 16.3 15.3, 16.3 14.8, 15.7 15.3, 15.7

Excitation energies have been computed with time-dependent (TD) CAM-B3LYP method.


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


Table 3. Percentage change and percentage change ratios of the dipole polarizabilities in a series of graphene ribbons doped with one (A, B) and two (AB) B3N3 units, respectively (see Figure 5). Equilibrium nuclear geometries and molecular polarizabilities have been obtained at the CAMB3LYP/6-31G and CAM-B3LYP/6-31G* levels, respectively. 𝑃%𝐴𝐵 N Hartree-Fock 1 5 9 13 CAM-B3LYP 1 5 9 13 wB97XD 1 5 9 13

𝑃%𝐴 + 𝑃%𝐵

A

P% B

AB

6.6 4.2 2.9 2.2

6.7 4.3 3.0 2.2

12.0 8.3 5.8 4.4

0.90 0.98 0.98 1.00

5.8 3.8 2.6 2.0

5.7 3.9 2.7 2.0

10.5 7.5 5.3 4.0

0.91 0.97 1.00 1.00

5.5 3.6 2.4 1.8

5.6 3.7 2.5 1.9

10.1 7.1 4.9 3.7

0.91 0.97 1.00 1.00



Page 20 of 55

Table 4. Spectroscopic properties, matrix elements of quantum transitions, charge transfer parameters based on the total densities of the ground and excited states between the ground (S0) and three of selected excited electronic states (Sm) of (B3N3)n@C114 graphene ribbons: (E0m) stands for the excitation energy, f represents the respective oscillator strengths, (⟨0│𝜇𝑧│𝑚⟩) are the transition dipoles along the z axis and Δμ0m represents the dipole moment differences between the ground state and the excited states (m) considered, DCT is the charge transfer distance corresponding to each transition along the z axis (see Figure 1). All properties have been computed using the Configuration Interaction Singles (CIS) method with the 6-31G* basis set. Transitions S0→Sm n=1 S0→Sa S0→Sb S0→Sc n=2 S0→Sa S0→Sb S0→Sc n=3 S0→Sa S0→Sb S0→Sc

⟨0│𝜇𝑧│𝑚⟩

E0m (eV)

f

3.47 4.28 4.64

1.9 3.1 4.6

-4.729 3.067 4.558

-0.131 -0.667 -0.746

0.15 0.89 0.85

3.55 4.04 4.67

1.2 1.8 3.9

-3.776 -4.303 5.871

0.097 -0.219 -0.845

0.12 0.27 0.90

3.88 4.70 5.21

2.8 3.6 1.6

5.403 -5.586 3.548

-0.017 -1.290 0.122

0.02 1.18 0.15

(au)

Δμ0m(au)

DCT (Å)


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


Table 5. HOMO-LUMO gaps (HLG), excitation energies (E01/eV) dipole moments (μz/D), first hyperpolarizability components (βαβγ/au), total first hyperpolarizabilities (βtot/au) and the modulus of the first dipole hyperpolarizability (||β||/au) of (B3N3)n@C114 ribbons. All properties have been computed with the CAM-B3LYP functional applied on CAM-B3LYP/6-31G* optimized geometries. Numbers in parenthesis correspond to values computed with the wB97XD method. E01

βyyz×103

βzzz×103

βtot×103

||β||×103

4.3 4.5 4.8 4.5 4.5 4.7

2.9(3.0) 3.0(3.0) 3.2(3.3) 2.9(3.0) 2.9(3.0) 3.1(3.2)

-1.0 -1.8 -2.4 -0.1 -0.1 0.8

4.1 6.9 8.8 0.3 0.1 -3.8

3.1 5.1 6.4 0.4 0.2 3.0

4.5(5.7) 7.6(8.0) 9.8(10.0) 0.4(0.8) 0.2 (1.0) 4.0(2.9)

4.3 4.5 4.8 4.4 4.4 4.6

2.8 2.9 3.1 2.9 2.9 3.1

-1.0 -1.7 -2.3 -0.1 -0.1 0.7

4.1 6.9 8.7 0.3 0.2 -3.6

3.1 5.2 6.4 0.3 0.3 2.8

4.5(5.4) 7.5(7.7) 9.6(9.6) 0.3(0.8) 0.2(1.0) 3.9(2.8)

μz

HLG

6-31G* n=1 n=2 n=3 n=2(NN) n=2(BB) n=3(NNBB)

1.21(1.20) 1.50(1.50) 1.92(1.90) 0.48 (0.50) 0.62(0.63) -0.08(-0.06)

6-311G(2d) n=1 n=2 n=3 n=2(NN) n=2(BB) n=3(NNBB)

1.22(1.20) 1.52(1.48) 1.92(1.88) 0.50(0.49) 0.61(0.61) -0.08(-0.07)

Table 6. Dipole moment components (μα=y,z/D) with respect to the center of mass of each molecule, HOMO-LUMO gaps (HLG/eV), CPKS first hyperpolarizability components (βαβγ/au), total first dipole hyperpolarizabilities (βtot/au) and modulus of the first dipole hyperpolarizability (||β||/au) of ribbons (B3N3)n@C162 and (B3N3)n@C210 illustrated in Figure 8. All equilibrium nuclear geometries and properties have been computed at the CAM-B3LYP/6-31G* level of theory. (B3N3)n@C162 n=1 n=3 n=5

μa μy -0.04 -0.30 -0.48

(B3N3)n@C210 n=1 n=2 n=3 n=4 n=5

μy , μz -0.46, -0.41 -0.41, -1.04 -0.47, -1.66 -0.36, -2.25 -0.14, -2.37

HLG

βyyy×103

4.7 5.2 5.5

-

4.5 4.5 4.7 4.9 5.2

-0.84 -0.93 -0.99 -0.63 -0.17

βyyz×103

βyzz×103

-2.0 -7.3 -10.0 -1.4 -3.6 -5.7 -8.0 -9.1

βzzz×103

||β||×103

-

0.9 2.0 2.9

5.1 12.9 17.6

-1.0 -0.5 -1.0 -0.4 -0.1

0.2 2.1 4.5 6.8 8.0

2.1 4.7 8.1 11.5 13.2



Page 22 of 55

Table 7. Modulus of the first dipole hyperpolarizability (||β||/au) and the corresponding rations in a series of graphene ribbons of increasing size doped with one (A, B) and two (AB) B3N3 units, respectively (see Figure 3) computed at three levels of theory using the 6-31G* basis set. “N” represents the number of aromatic sextets separating the B3N3 units in the double doped systems. Relaxed equilibrium nuclear geometries have been obtained at the CAM-B3LYP/6-31G level. ‖𝛽‖𝐴𝐵 N A Hartree-Fock 1 5 9 13 CAM-B3LYP 1 5 9 13 wB97XD 1 5 9 13

‖𝛽‖ ×103 au B AB

‖𝛽‖𝐴 + ‖𝛽‖𝐵

4.3 14.0 20.1 22.6

4.6 15.0 21.2 23.8

5.5 24.7 39.6 45.8

0.627 0.849 0.959 0.987

3.2 15.5 25.5 30.4

3.6 17.5 27.9 33.0

4.6 27.5 50.8 62.3

0.681 0.835 0.950 0.983

3.6 13.6 20.2 23.2

4.1 15.3 22.1 25.2

5.1 25.1 40.8 47.8

0.657 0.869 0.964 0.988


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


Table 8. CAM-B3LYP/6-31G* hyperpolarizability components (and the corresponding ratios) of ribbon C302H74 (Figure 5) doped with one (A) and two (AB) B3N3 units of parallel alignment (BN), respectively, as a function of the number of aromatic sextets (N) separating the B3N3 units in the double doped systems. Relaxed equilibrium nuclear geometries have been obtained at the CAM-B3LYP/6-31G level. 𝛽𝐴𝐵 𝑧𝑧𝑧

N 1 3 5 7 9 11 13

βzzz A 53.7 51.7 48.2 43.8 37.1 34.9 28.7

×103 B 52.3 49.2 45.1 40.7 37.1 34.1 30.7

βyyz×103

/au AB 69.9 70.9 74.3 74.2 71.3 66.9 58.7

A 2.5 2.5 2.3 2.1 1.9 1.6 1.7

B 2.5 2.5 2.4 2.2 1.9 1.7 1.7

/au AB 3.9 4.4 4.5 4.2 3.8 3.2 3.3

𝛽𝐴𝑧𝑧𝑧

+

𝛽𝐵𝑧𝑧𝑧

0.659 0.703 0.796 0.878 0.962 0.969 0.989

𝛽𝐴𝐵 𝑦𝑦𝑧 𝛽𝐴𝑦𝑦𝑧

+

𝛽𝐵𝑦𝑦𝑧

0.763 0.891 0.957 0.981 0.978 0.996 0.999

𝛽𝐴𝐵 𝑡𝑜𝑡 𝛽𝐴𝑡𝑜𝑡

+ 𝛽𝐵𝑡𝑜𝑡

0.654 0.693 0.788 0.872 0.961 0.967 0.988



Page 24 of 55

Table 9. HLGs (eV), CPKS first hyperpolarizability components (βαβγ/au) and the modulus of the first dipole hyperpolarizability (‖𝛽‖/au) of the edge functionalized borazino-doped nanographenes shown in Figure 11. All equilibrium nuclear geometries (of C1 symmetry) and properties have obtained at the CAM-B3LYP and wB97XD methods and the 6-31G* basis set.

βxxx×103

βxyy×103

4.1 4.1 3.7

13.6 -20.0 -46.1

-13.6 20.0 47.1

28 41 96

Ribbon-(d) Ribbon-(e) Ribbon-(f)

4.0 2.9 2.1

3.5 44 272

8.3 49 272

5.0 5.0 4.7

13.2 -19.1 -41.5

-13.1 19.1 42.3

27 39 86

Ribbon-(d) Ribbon-(e) Ribbon-(f)

5.0 3.7 3.1

4.5 45 270

8.8 53 271

HLG CAM-B3LYP Flake-(a) Flake-(b) Flake-(c) wB97XD Flake-(a) Flake-(b) Flake-(c)

||β||×103

HLG

βzzz×103

||β||×103


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


References (1) Stępień, M.; Gońka, E.; Żyła, M.; Sprutta, N. Heterocyclic Nanographenes and Other Polycyclic Heteroaromatic Compounds: Synthetic Routes, Properties, and Applications. Chem. Rev. 2017, 117, 3479–3716. (2) Dosso, J.; Tasseroul, J.; Fasano, F.; Marinelli, D.; Biot, N.; Fermi, A.; Bonifazi, D. Synthesis and Optoelectronic Properties of Hexa- Peri -Hexabenzoborazinocoronene. Ang. Chem. Int. Ed. 2017, 56, 4483–4487. (3) Dosso, J.; Marinelli, D.; Demitri, N.; Bonifazi, D. Structural Properties of Highly Doped Borazino Polyphenylenes Obtained through Condensation Reaction. ACS Omega 2019, 4, 9343–9351. (4) You, J. W.; Bongu, S. R.; Bao, Q.; Panoiu, N. C. Nonlinear Optical Properties and Applications of 2D Materials: Theoretical and Experimental Aspects. Nanophotonics 2018, 8, 63–97. (5) Bonifazi, D.; Fasano, F.; Lorenzo-Garcia, M. M.; Marinelli, D.; Oubaha, H.; Tasseroul, J. Boron–Nitrogen Doped Carbon Scaffolding: Organic Chemistry, Self-Assembly and Materials Applications of Borazine and Its Derivatives. Chem. Commun. 2015, 51, 15222–15236. (6) Campbell, P. G.; Marwitz, A. J. V.; Liu, S.-Y. Recent Advances in Azaborine Chemistry. Ang. Chem. Int. Ed. 2012, 51, 6074–6092. (7) Krieg, M.; Reicherter, F.; Haiss, P.; Ströbele, M.; Eichele, K.; Treanor, M.-J.; Schaub, R.; Bettinger, H. F. Construction of an Internally B3N3-Doped Nanographene Molecule. Angew. Chem. Int. Edit. 2015, 54, 8284–8286. (8)Zhou, H.; Zhou, Z.-J.; Yu, G.-T.; Chen, W.; Huang, X.-R.; Li, Z.-R. Nonlinear Optical Response and Transparency of Hexagonal Boron Nitride Hybrid Graphene Nanoribbons. Chem. Phys. Lett. 2014, 614, 57–61. (9) Sánchez-Sánchez, C.; Brüller, S.; Sachdev, H.; Müllen, K.; Krieg, M.; Bettinger, H. F.; Nicolaï, A.; Meunier, V.; Talirz, L.; Fasel, R.; et al. On-Surface Synthesis of BN-Substituted Heteroaromatic Networks. ACS Nano 2015, 9, 9228– 9235. (10) Kervyn, S.; Kalashnyk, N.; Riello, M.; Moreton, B.; Tasseroul, J.; Wouters, J.; Jones, T. S.; De Vita, A.; Costantini, G.; Bonifazi, D. “Magic” Surface Clustering of Borazines Driven by Repulsive Intermolecular Forces. Ang. Chem. Int. Ed. 2013, 52, 7410–7414. (11) Marinelli, D.; Fasano, F.; Najjari, B.; Demitri, N.; Bonifazi, D. Borazino-Doped Polyphenylenes. J. Am. Chem. Soc. 2017, 139, 5503–5519. (12) Liu, Z.; Zhang, B.; Chen, Y. Recent Progress in Two-Dimensional Nanomaterials for Laser Protection. Chemistry 2019, 1, 17–43. (13) Liu, Z.; Ma, L.; Shi, G.; Zhou, W.; Gong, Y.; Lei, S.; Yang, X.; Zhang, J.; Yu, J.; Hackenberg, K. P.; et al. InPlane Heterostructures of Graphene and Hexagonal Boron Nitride with Controlled Domain Sizes. Nat Nano 2013, 8, 119–124. (14) Müllen, K. Evolution of Graphene Molecules: Structural and Functional Complexity as Driving Forces behind Nanoscience. ACS Nano, 2014, 8, 6531–6541. (15) Bepete, G.; Voiry, D.; Chhowalla, M.; Chiguvare, Z.; Coville, N. J. Incorporation of Small BN Domains in Graphene during CVD Using Methane, Boric Acid and Nitrogen Gas. Nanoscale 2013, 5, 6552–6557. (16) Otero, N.; El-kelany, K. E.; Pouchan, C.; Rérat, M.; Karamanis, P. Establishing the Pivotal Role of Local Aromaticity in the Electronic Properties of Boron-Nitride Graphene Lateral Hybrids. Phys. Chem. Chem. Phys. 2016, 18, 25315–25328. (17) Oubaha, H.; Demitri, N.; Rault-Berthelot, J.; Dubois, P.; Coulembier, O.; Bonifazi, D. Photoactive Boron– Nitrogen–Carbon Hybrids: From Azo-Borazines to Polymeric Materials. J. Org. Chem. 2019, 84, 9101–9116. (18) Lorenzo-García, M. M.; Bonifazi, D. Renaissance of an Old Topic: From Borazines to BN-Doped Nanographenes. CHIMIA Int. J. Chem. 2017, 71, 550–557. (19) Biswas, S.; Tiwary, C. S.; Vinod, S.; Kole, A. K.; Chatterjee, U.; Kumbhakar, P.; Ajayan, P. M. Nonlinear Optical Properties and Temperature Dependent Photoluminescence in HBN-GO Heterostructure 2D Material. J. Phys. Chem. C 2017, 121, 8060–8069. (20) Karamanis, P.; Otero, N.; Pouchan, C. Unleashing the Quadratic Nonlinear Optical Responses of Graphene by Confining White-Graphene (h-BN) Sections in Its Framework. J. Am. Chem. Soc. 2014, 136, 7464–7473. (21) Karamanis, P.; Otero, N.; Pouchan, C. Electric Property Variations in Nanosized Hexagonal Boron Nitride/Graphene Hybrids. J. Phys. Chem. C 2015, 119, 11872–11885. (22) Otero, N.; Pouchan, C.; Karamanis, P. Quadratic Nonlinear Optical (NLO) Properties of Borazino (B3N3)-Doped Nanographenes. J. Mater. Chem. C 2017, 5, 8273–8287. (23) Otero, N.; Karamanis, P.; El-Kelany, K. E.; Rérat, M.; Maschio, L.; Civalleri, B.; Kirtman, B. Exploring the Linear Optical Properties of Borazine (B3N3) Doped Graphenes. 0D Flakes vs 2D Sheets. J. Phys. Chem. C 2017, 121, 709–722. (24) Wu, J.; Pisula, W.; Müllen, K. Graphenes as Potential Material for Electronics. Chem. Rev. 2007, 107, 718–747. (25) Naccarato, F.; Ricci, F.; Suntivich, J.; Hautier, G.; Wirtz, L.; Rignanese, G.-M. Searching for Materials with High Refractive Index and Wide Band Gap: A First-Principles High-Throughput Study. Phys. Rev. Mat. 2019, 3, 44602(112).



Page 26 of 55

(26) Mei, D.; Jiang, J.; Liang, F.; Zhang, S.; Wu, Y.; Sun, C.; Xue, D.; Lin, Z. Design and Synthesis of a Nonlinear Optical Material BaAl4S7 with a Wide Band Gap Inspired from SrB4O7. J. Mater. Chem. C 2018, 6, 2684–2689 27 Lin, H.; Chen, H.; Zheng, Y.-J.; Yu, J.-S.; Wu, X.-T.; Wu, L.-M. Coexistence of Strong Second Harmonic Generation Response and Wide Band Gap in AZn4Ga5S12 (A=K, Rb, Cs) with 3D Diamond-like Frameworks. Chemistry – A European Journal 2017, 23, 10407–10412. (28) Buckingham, A. D. Permanent and Induced Molecular Moments and Long-Range Intermolecular Forces. In Advances in Chemical Physics; Hirschfelder, J. O., Ed.; John Wiley & Sons, Inc., 1967; pp 107–142. (29) McLean, A. D.; Yoshimine, M. Theory of Molecular Polarizabilities J. Chem. Phys. 1967, 47, 1927–1935. (30) Albrecht, A. C. On the Theory of Raman Intensities. J. Chem. Phys. 1961, 34, 1476–1484. (31) Boyd, R.W. in Nonlinear Optics 1992 Academic Press, New York. Pyatt, R. D. (32) Orr, B. J.; Ward, J. F. Perturbation Theory of the Non-Linear Optical Polarization of an Isolated System. Molecular Physics 1971, 20, 513–526. (33) Kanis, D. R.; Ratner, M. A.; Marks, T. J. Design and Construction of Molecular Assemblies with Large SecondOrder Optical Nonlinearities. Quantum Chemical Aspects. Chem. Rev. 1994, 94, 195–242. (34) Marder, S. R.; Beratan, D. N.; Cheng, L.-T. Approaches for Optimizing the First Electronic Hyperpolarizability of Conjugated Organic Molecules. Science 1991, 252, 103–106. (35) Lalama, S. J. Origin of the Nonlinear Second-Order Optical Susceptibilities of Organic Systems. Phys. Rev. A 1979, 20, 1179–1194. (36) Zyss, J.; Ledoux, I. Nonlinear Optics in Multipolar Media: Theory and Experiments. Chem. Rev. 1994, 94, 77–105. (37) Dykstra, C. E.; Jasien, P. G. Derivative Hartree—Fock Theory to All Orders. Chem. Phys. Lett. 1984, 109, 388– 393. (38) Hurst, G. J. B.; Dupuis, M.; Clementi, E. Ab initio Analytic Polarizability, First and Second Hyperpolarizabilities of Large Conjugated Organic Molecules: Applications to Polyenes C4H6 to C22H24. J. Chem. Phys. 1988, 89, 385–395. (39) Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid Exchange–Correlation Functional Using the CoulombAttenuating Method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51–57. (40) Chai, J.-D.; Head-Gordon, M. Systematic Optimization of Long-Range Corrected Hybrid Density Functionals. The J. Chem. Phys. 2008, 128, 084106(1-12) (41) Le Bahers, T.; Adamo, C.; Ciofini, I. A Qualitative Index of Spatial Extent in Charge-Transfer Excitations. J. Chem. Theory. Comput. 2011, 7, 2498–2506. (42) Martin, R. L. Natural Transition Orbitals. J. Chem. Phys. 2003, 118, 4775–4777. (43) Karamanis, P.; Pouchan, C. Fullerene–C60 in Contact with Alkali Metal Clusters: Prototype Nano-Objects of Enhanced First Hyperpolarizabilities. J. Phys. Chem. C 2012, 116, 11808–11819. (44) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Revision D.01; Gaussian, Inc., Wallingford CT, 2009. (45) Lu, T.; Chen, F. Multiwfn: A Multifunctional Wavefunction Analyzer. J. Comp. Chem. 33, 580–592. (46) Heyd, J.; Scuseria, G. E. Efficient Hybrid Density Functional Calculations in Solids: Assessment of the Heyd– Scuseria–Ernzerhof Screened Coulomb Hybrid Functional. J. Chem. Phys. 2004, 121, 1187–1192. (47) ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, https://www.scm.com/ (48) Charistos, N. D.; Muñoz-Castro, A.; . Induced Magnetic Field of Fullerenes: Role of σ- and π- Contributions to Spherical Aromatic, Nonaromatic, and Antiaromatic Character in C60q (q = +10, 0, −6, −12), and Related Alkali-Metal Decorated Building Blocks, Li12C60 and Na6C60. J. Phys. Chem. C, 2018, 122, 9688–9698. (49) Clar E.; The Aromatic Sextet, Wiley, London, 1972. (50) Tönshoff, C.; Müller, M.; Kar, T.; Latteyer, F.; Chassé, T.; Eichele, K.; Bettinger, H. F. B3N3 Borazine Substitution in Hexa-Peri-Hexabenzocoronene: Computational Analysis and Scholl Reaction of Hexaphenylborazine. ChemPhysChem 2012, 13, 1173–1181 (51) Karamanis, P.; Pouchan, C.; Weatherford, C. A.; Gutsev, G. L. Evolution of Properties in Prolate (GaAs) n Clusters. J. Phys. Chem. C 2011, 115, 97–107. (52) D. Jacquemin, E. A. Perpète, M. Medved’, G. Scalmani, M. J. Frisch, R. Kobayashi and C. Adamo, The J. Chem. Phys., 2007, 126, 191108(1-9). (53) Medved’, M.; Jacquemin, D. Tuning the NLO Properties of Polymethineimine Chains by Chemical Substitution. Chem. Phys. 2013, 415, 196–206. (54) Morley, J. O. Theoretical Study of the Electronic Structure and Hyperpolarizabilities of Donor-Acceptor Cumulenes and a Comparison with the Corresponding Polyenes and Polyynes. J. Phys. Chem. 1995, 99, 10166–10174. (55) Kirtman, B.; Champagne, B. Nonlinear Optical Properties of Quasilinear Conjugated Oligomers, Polymers and Organic Molecules. Int. Rev. Phys. Chem. 1997, 16, 389–420. (56) Yoneda, K.; Nakano, M.; Kishi, R.; Takahashi, H.; Shimizu, A.; Kubo, T.; Kamada, K.; Ohta, K.; Champagne, B.; Botek, E. Third-Order Nonlinear Optical Properties of Trigonal, Rhombic and Bow-Tie Graphene Nanoflakes with Strong Structural Dependence of Diradical Character. Chem. Phys. Lett. 2009, 480, 278–283.


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


(57) Konishi, A.; Hirao, Y.; Matsumoto, K.; Kurata, H.; Kishi, R.; Shigeta, Y.; Nakano, M.; Tokunaga, K.; Kamada, K.; Kubo, T. Synthesis and Characterization of Quarteranthene: Elucidating the Characteristics of the Edge State of Graphene Nanoribbons at the Molecular Level. J. Am. Chem. Soc. 2013, 135, 1430–1437.

FIGURES



Page 28 of 55

Figure 1. Molecular structures of borazino doped ribbons built upon C114H34 and their aromaticity pattern, represented as NICS maps where each hexagon is colored according to its NICSπzz value at the center of the ring (Table SN1). The maps of C114 reproduce the Clar structure of aromatic sextets. Geometry optimizations at (CAM-)B3LYP/6-31G*level and subsequent vibrational frequency calculations predict that all doped ribbons should feature quasi-planar equilibrium geometries close to the C2v symmetry point group.


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


Figure 2. CIS/6-31G* spectra of doped graphene ribbons with an increasing number of B3N3 units placed in parallel alignment.



Page 30 of 55

Figure 3. Graphene ribbons of increasing size doped with two (AB) and one (A, B) B3N3 units. All ribbon geometries have been optimized at CAM-B3LYP/6-31G level.


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


Figure 4. Dipole polarizability percentage change ratios in multi-doped graphene flakes computed at CAM-B3LYP/6-31G* level of theory. Flake geometries have been optimized at CAM-B3LYP/6-31G level.



Page 32 of 55

Figure 5. Evolution of the percentage change on the dipole polarizability with respect the pristine ribbon. Where 𝑃% = 100 × [𝛼(𝑝𝑟𝑖𝑠𝑡𝑖𝑛𝑒) ― 𝛼(𝑑𝑜𝑝𝑒𝑑)] 𝛼(𝑝𝑟𝑖𝑠𝑡𝑖𝑛𝑒).


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


Figure 6. CIS/6-311+G(2d) spectra, dipole moments, ΝΤΟ hole-electron representations and excited state data of a benzene ring functionalized with two B3N3H5 units in ortho and meta position in comparison to para-nitro-aniline (PNA). To draw the molecular dipole moments, physics’ convention of electric dipoles according to which the dipole moment vector points from (-) → (+), was adopted. Δμ stands for the dipole moment differences between the ground state and the excited states considered, μ is the ground state dipole moments computed at the (HF, MP2)/6-311+G(2d) level and DCT is the computed charge transfer for each transition based on electron density differences between the respective excited states and the ground state of each system computed at the CIS/6-311+G(2d) level. The global minimum of B3N3-C6H5-B3N3 features a non-planar twisted geometry, however, we conducted this analysis in its planar configurations characterized by two strong imaginary frequencies the normal modes of which induce out of plane distortions, in order to compare the obtained results with those referring to doped ribbons.



Page 34 of 55

Figure 7. Δρ(r) isosurfaces (left) and hole-electron representations (right) of the most intense transition of (B3N3)n@C114 ribbons (n=1, 2, 3). The ellipsoid shapes at the center of each system represent the centroids of charge and imply that the transfer of charge should occur from the positive to the negative side.


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


Figure 8. Molecular structures of B3N3 doped nanographenes built upon two different types of ribbons, one of linear shape and zigzag edges and one of armchair edges and zigzag shape. Numbers attributed to each B3N3 correspond to the respective doping order followed in each case. The geometries of the linear (zigzag) ribbons have been optimized at CAM-B3LYP/6-31G* (6-31G) levels of theory.



Page 36 of 55

Figure 9. Evolution of the modulus of the first dipole hyperpolarizability as a function of the B3N3 doping in a large hexagonal graphene flake computed at the CAM-B3LYP/6-31G* level of theory. The computed gap of (B3N3)@C234 at the same level of theory is 3.27 eV. All geometries have been optimized at the B3LYP/6-31G level.


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


Figure 10. Hyperpolarizability evolution as a function of the borazino doping in a large hexagonal graphene flake (C366) computed at four levels of theory.



Page 38 of 55

Figure 11. Size scaling of the mean dipole polarizability in borazino doped ribbons. The geometry of the infinite ribbon has been optimized with the Heyd-Scuseria-Ernzerhof functional (HSE06) and the 6-31G* basis set (k point (-π, π)-mesh: 78×78×0 yielding 40 k-points in the irreducible part of the Brillouin zone. In plot (a) the relaxed ribbon geometries have been obtained at the CAM-B3LYP/6-31G level.


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


Figure 12. First hyperpolarizability evolution as a function of the ribbon length (ribbon structures are explained in Figure 11).



Page 40 of 55

Figure 13. Molecular structures of a series of B3N3 doped nanographenes of different edge structures optimized with the CAM-B3LYP/6-31G method.


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


TOC



Figure 1. Molecular structures of borazino doped ribbons built upon C114H34 and their aromaticity pattern, represented as NICS maps where each hexagon is colored according to its NICSπzz value at the center of the ring (Table SN1). The maps of C114 reproduce the Clar structure of aromatic sextets. Geometry optimizations at (CAM-)B3LYP/6-31G*level and subsequent vibrational frequency calculations predict that all doped ribbons should feature quasi-planar equilibrium geometries close to the C2v symmetry point group.

ACS Paragon Plus Environment

Page 42 of 55

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


Figure 2. CIS/6-31G* spectra of doped graphene ribbons with an increasing number of B3N3 units placed in parallel alignment. 80x112mm (300 x 300 DPI)



Graphene ribbons of increasing size doped with two (AB) and one (A, B) B3N3 units. All ribbon geometries have been optimized at CAM-B3LYP/6-31G level. 80x33mm (300 x 300 DPI)


Page 44 of 55

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


Figure 4. Dipole polarizability percentage change ratios in multi-doped graphene flakes computed at CAMB3LYP/6-31G* level of theory. Flake geometries have been optimized at CAM-B3LYP/6-31G level. 80x120mm (300 x 300 DPI)



Evolution of the percentage change on the dipole polarizability with respect the pristine ribbon. Where P^%=(100×[α (pristine)-α (doped)])⁄(α (pristine).) 74x152mm (300 x 300 DPI)


Page 46 of 55

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


Figure 6. CIS/6-311+G(2d) spectra, dipole moments, ΝΤΟ hole-electron representations and excited state data of a benzene ring functionalized with two B3N3H5 units in ortho and meta position in comparison to para-nitro-aniline (PNA). To draw the molecular dipole moments, physics’ convention of electric dipoles according to which the dipole moment vector points from (-) → (+), was adopted. Δμ stands for the dipole moment differences between the ground state and the excited states considered, μ is the ground state dipole moments computed at the (HF, MP2)/6-311+G(2d) level and DCT is the computed charge transfer for each transition based on electron density differences between the respective excited states and the ground state of each system computed at the CIS/6-311+G(2d) level. The global minimum of B3N3-C6H5-B3N3 features a non-planar twisted geometry, however, we conducted this analysis in its planar configurations characterized by two strong imaginary frequencies the normal modes of which induce out of plane distortions, in order to compare the obtained results with those referring to doped ribbons. 165x90mm (300 x 300 DPI)



Figure 7. Δρ(r) isosurfaces (left) and hole-electron representations (right) of the most intense transition of (B3N3¬)n@C114 ribbons (n=1, 2, 3). The ellipsoid shapes at the center of each system represent the centroids of charge and imply that the transfer of charge should occur from the positive to the negative side. 79x101mm (300 x 300 DPI)


Page 48 of 55

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


Figure 8. Molecular structures of B3N3 doped nanographenes built upon two different types of ribbons, one of linear shape and zigzag edges and one of armchair edges and zigzag shape. Numbers attributed to each B3N3 correspond to the respective doping order followed in each case. The geometries of the linear (zigzag) ribbons have been optimized at CAM-B3LYP/6-31G* (6-31G) levels of theory. 80x79mm (300 x 300 DPI)



Figure 9. Evolution of the modulus of the first dipole hyperpolarizability as a function of the B3N3 doping in a large hexagonal graphene flake computed at the CAM-B3LYP/6-31G* level of theory. The computed gap of (B3N3)@C234 at the same level of theory is 3.27 eV. All geometries have been optimized at the B3LYP/631G level. 144x85mm (300 x 300 DPI)


Page 50 of 55

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


Figure 10. Hyperpolarizability evolution as a function of the borazino doping in a large hexagonal graphene flake (C366) computed at four levels of theory. 80x65mm (300 x 300 DPI)



Figure 11. Size scaling of the mean dipole polarizability in borazino doped ribbons. The geometry of the infinite ribbon has been optimized with the Heyd-Scuseria-Ernzerhof functional (HSE06) and the 6-31G* basis set (k point (-π, π)-mesh: 78×78×0 yielding 40 k-points in the irreducible part of the Brillouin zone. In plot (a) the relaxed ribbon geometries have been obtained at the CAM-B3LYP/6-31G level. 112x44mm (300 x 300 DPI)


Page 52 of 55

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


Figure 12. First hyperpolarizability evolution as a function of the ribbon length (ribbon structures are explained in Figure 11). 80x58mm (300 x 300 DPI)



Figure 13. Molecular structures of a series of B3N3 doped nanographenes of different edge structures optimized with the CAM-B3LYP/6-31G method. 80x58mm (300 x 300 DPI)


Page 54 of 55

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


TOC 82x44mm (300 x 300 DPI)


Polyaromatic Systems Combining Increasing Optical Gaps and

Recommend Documents