Spin engineering of triangulenes and application for nano nonlinear optical materials design

Abstract

The recently synthesized triangulenes with non-bonding edge states could have broad potential applications in magnetics, spintronics and electro-optics if they have appropriate electronic structure modulation. In the present work, strategies based on molecular orbital theory through heteroatom doping are proposed to redistribute, reduce or eliminate the spin of triangulenes for novel functional materials design, and the role of B, N, NBN, and BNB in such intended electronic structure manipulation is scrutinized. π-Extended triangulenes with tunable electronic properties could be potential nonlinear optical (NLO) materials with appropriate inhibition of their polyradical nature. The elimination of spin is achieved by B, N, NBN, and BNB doping with the intended geometric arrangement for enhanced polarity. Intended doping of BNB results in an optimal structure with large static first hyperpolarizability (〈β₀〉) as well as strong Hyper–Rayleigh scattering (HRS) β_HRS(−2ω; ω, ω) (ω = 1064.0 nm), TG7-BNB-ba with a large 〈β₀〉 (18.85 × 10⁻³⁰ esu per heavy atom) and β_HRS (1.15 × 10⁻²⁸ esu per heavy atom) much larger than that of a synthesized triangular molecule (1.12 × 10⁻³⁰ esu of 〈β₀〉 per heavy atom and 5.04 × 10⁻³⁰ esu of β_HRS per heavy atom). The strong second order NLO responses in the near-infrared and visible regions, particularly the strong sum frequency generation, make these B or (and) N doped triangulenes promising candidates for the fabrication of novel carbon-based optoelectronic devices and micro-NLO devices.

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Introduction

The demands for nonlinear optical (NLO) materials with high stability and strong NLO responses have become significantly imperative in association with the developments of functional materials. Graphene fragments consisting of sp² carbons, e.g., graphene nanoflakes (GNFs), have been attracting tremendous interest since the fabrication of graphene.¹ The molecular sizes and shapes determine the electronic and magnetic properties of GNFs to a great extent.^2,3 Among the GNFs with various possible shapes and sizes, zigzag-edged triangle-shaped GNFs with n fused hexagons at each side (denoted as [n]triangulenes where n is the number of hexagons at the edge) were predicted to show a radical nature (i.e., with unpaired or non-bonding π-electrons),^4,5 which might allow their potential applications in energy storage devices,⁶ organic spintronics,^7,8 bio-imaging,⁹ and nonlinear optics.^10,11 The successful syntheses of [n]triangulenes (n = 2 to 5)^4,12–14 make it possible to investigate its unique structures and peculiar characters at single molecule level. In [n]triangulenes (defined as TGn), the smallest triangulene, namely phenalenyl¹² (i.e., TG2 in Fig. 1), has 13 carbon atoms and 13 π-electrons. The non-Kekulé structure in [n]triangulenes possesses one or more unpaired π-electrons with net spins according to the Ovchinnikov's rule.¹⁵ Approximately (n − 1) unpaired electrons localize along the zigzag edges rather than at the core of [n]triangulenes.⁵ In other words, the ground state of these [n]triangulenes shows an increasing open-shell nature with the increase of n (Table S1, ESI† and Fig. 1). However, the high chemical reactivity¹⁶ of the outer rims or the closeness of the flat band to the Fermi level² causes the synthesis and isolation of extended triangulenes to be a big challenge,¹⁷ and finding an optimal means to functionalize triangulenes is a key factor for further applications.

Fig. 1 (a) The natural atomic spin distributions and the non-Kekulé structures of [n]triangulenes (TGn; n = 2 to n = 7). I depicts the spin densities of symmetrically unique atoms in different colors, and II indicates the possible sites for spin elimination marked by red dots according to the Clar rule. The red hexagons are Clar aromatic π-sextets. (b) Proposed sites for spin elimination in TG7 through a combination of configurations analyzed by using the Clar rule. (c) Structures, frontier molecular orbitals (L: LUMO; H: HOMO; S: SOMO) and molecular orbital energy (in eV) diagrams of molecule 9H-fluorene-9-ylradical (M) and B (M–B), N (M–N), NBN (M-NBN) or BNB (M-BNB) doped 9H-fluorene-9-ylradical molecules. Atoms in black are carbon, purple are boron, and green are nitrogen. Numbers in blue are spin density and in red are natural atomic charges.

Efforts have been devoted to modulate the electronic state of carbon-based molecules, e.g., through steric hindrance,^18,19 fusion with other aromatic skeletons,²⁰ and introduction of heteroatoms.²¹ Incorporation of heteroatoms [e.g., boron (B), nitrogen (N), oxygen (O), or sulfur (S)] into the π-conjugated carbon skeleton is a promising strategy for such purposes.²² By virtue of the isoelectronic feature of B–N and C=C, the introduction of BN into carbon-based nanomaterials (fullerenes, nanotubes, and graphenes)^23–25 can break the symmetry of systems and polarize charge redistribution (enhance polarity), thereby generating even-order NLO responses. Doping of B or N atoms can also attenuate the net spin of zigzag-edged triangulenes with an edge size n = 6.²⁶ On the other hand, the investigation of the second order NLO properties of octupolar molecules with a threefold symmetry axis has been extensively explored.^27,28 Appropriate doping of B or (and) N in [n]triangulenes provides the possibility to “tune” the electronic structure and related properties for certain applications, e.g., in electro-optics or nonlinear optics.

The present work employs molecular orbital theory (the electronic state – configuration state function – of a system is the linear combination of configurations) to analyse the spin distribution in triangulenes in combination with the Clar's rule, and then functionalize [n]triangulenes (n = 2 to 7) with B(N), i.e. spin engineering, for desired applications. In the present work, applications in the second order nonlinear optics are considered.

Model and computational details

According to natural atomic spin distribution analyses on the optimized [n]triangulenes structures from density functional theory (DFT)^29,30 based calculations with general gradient approximation of fundamental constant based exchange-correlation functionals PBE³¹ based hybrid method PBE0³² and 6-31G(d,p) basis set,^33,34 all the carbon atoms of CH groups at the three edges of those [n]triangulenes carry net spins (Fig. 1(a)-I) and those spins can be formally represented by non-Kekulé structures (Fig. 1(a)-II) according to the Clar's sextet theory.³⁵ Taking TG7 as an example (Fig. 1(b) and the others are plotted in Fig. S1, ESI†), TG7 can be taken as a linear combination (or superposition) of two non-Kekulé structures (TG7-a and TG7-b). This is similar in the other triangulenes. The C atoms with unpaired electrons in those [n]triangulenes can be replaced with B or N to form a closed-shell electronic state. The non-centrosymmetric nature of second order nonlinear optical materials inspires a doping pattern with a combination of the doping sites in TG7-a and TG7-b resulting in a non-centrosymmetric hetero-triangulenes TG7-ab and TG7-ba (Fig. 2). Besides atoms B and N, NBN and BNB with the merits of polar BN being isoelectronic to CC could also be used to attenuate the edge spin while polarizing the charge distribution of [n]triangulenes. 9H-Fluorene-9-ylradical has an unpaired π-electron at the central C9 (Fig. 1(c)), and the doping of B and N, NBN and BNB at the C9 eliminates the net spin and leads to charge redistribution and the change of the energy gap E_gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Thus, B and N, NBN and BNB are used to attenuate the net spin of those triangulenes and tune their NLO properties. All the designed hetero-TG7 and other hetero-triangulenes are shown in Fig. 2 and Fig. S1 (ESI†).

Fig. 2 The structures of the TG7 series of molecules. The white, deep pink, black, green, red and orange denote the hydrogen, boron, carbon, nitrogen, oxygen and fluorine atoms, respectively. TATB, cmpd-1, cmpd-2 and cmpd-3 are from ref. 27, 56–58, respectively (cmpd refers to compound).

In the present work, all the DFT calculations were carried out by using Gaussian 09.³⁶ On the basis of optimized geometries, the electronic spectra of all systems were predicted with time-dependent CAM-B3LYP³⁷ under the Franck-Condon principle, and the orientation averaged first hyperpolarizability (〈β〉) was calculated by using the LinSOSProNLO program³⁸ based on the sum-over-states (SOS) model^39,40 with improved computational efficiency.⁴¹ The predictions for the charge transfer based excitation by using CAM-B3LYP are in excellent agreement with the highly accurate multireference perturbation calculation with CASPT2³⁷ and charge transfer based excitations are common and also important to the NLO properties of the triangulenes studied in the present work. For π-conjugated systems with charge transfer based electron excitations, “it is mandatory to use range-separated hybrids (e.g., CAM-B3LYP) to reach physically meaningful estimates”⁴² according to the systematic studies on the performance of TDDFT based methods in electronic spectra predictions.^42,43 Other studies found that different DFT methods have different performances on the prediction of electronic spectra of different systems.^44,45

The calculations of the electronic spectra of the TGn (n = 2–6) series of molecules include all possible π-electrons involved in valence excitations, and the TG7 series are predicted with 576 excited states. The convergence of the static first hyperpolarizability (〈β₀〉) with the number of excited states of TG7-BNB-ba indicates that 150 excited states are adequate to predict converged 〈β₀〉 (Fig. S2, ESI†). The SOS model shows consistence in NLO properties (only the electronic contributions) predictions with the other methods or models, e.g., finite field,^46,47 random phase approximation,^48,49 and couple perturbed models.⁵⁰

The orientation averaged first hyperpolarizability is obtained through the rewritten SOS formula⁴⁰ as eqn (1)⁵¹

〈β〉 = (β_x × r_x + β_y × r_y + β_z × r_z)/(r_x² + r_y² + r_z²)^1/2 and β_i = β_iii + [β_ijj + β_jij + β_jji + β_ikk + β_kik + β_kki]/3 (i, j, k∈[x, y, z]) (1)

with the tensor elements given by,where ħ is Planck's constant divided by 2π. ω_i is the frequencies of external fields with . (r_i)_gm = 〈g|r_i|m〉 is the transition moment between the ground state g to the excited state m along the i direction and (r̄_j)_mn = 〈m|r_j|n〉 − 〈g|r_j|g〉δ_mn is the dipole moment fluctuation. Γ_m (Γ_m = 0.01 × ε_m/ε₂) is the damping factor of excited state m. ∑P_ijk stands for a summation over all the terms obtained by permuting pairs of transition moment (or the dipole moment fluctuation) and the external field {e.g., [(r_i)_gm, −ω_σ], [(r̄_j)_mn, ω₁], and [(r_k)_ng, ω₂]}. The transition moments and dipole moment of excited states were calculated with the Multiwfn program.⁵²

To quantify the dipolar (|β_J=1|) and octupolar contributions (|β_J=3|) to the NLO response, the relevant expressions⁵³ [eqn (3) and (4)] can be written as follows:

The Hyper–Rayleigh scattering (HRS)^53,54 technique is a powerful means to explore the second harmonic generation (SHG) and the β_HRS (−2ω; ω, ω) can be expressed as:⁵³

The molecular anisotropy ratio ρ [ρ = |β_J=3|/|β_J=1| runs from 0 (pure dipole) to ∞ (pure octupole)] and is used to evaluate the octupolar (Φ^J=3 = ρ/ρ + 1) and dipolar (Φ^J=1 = 1 − Φ^J=3) contributions to the first hyperpolarizability.

Furthermore, the polarization state of the incident light is determined by two angles (Ψ, δ). When a general elliptically polarized incident light propagates along the X direction, and the intensity of the harmonic light scatters at δ = π/2 along the Y direction, the vertically (V) polarized light along the Z axis can be given by the Bersohn's expression:⁵⁵

Herein, these three HRS invariants 〈β_ZXX²〉, 〈β_ZZZ²〉, and 〈(β_ZXZ + β_ZZX)² − 2β_ZZZβ_ZXX〉 involved in eqn (6) can be written as:

Note that linearly polarized incident lights are described by Ψ = 0 (horizontal, H) or Ψ = π/2 (V). The HRS intensity can exhibit different shapes through varying the polarization angle Ψ of the incident light.

Results and discussion

Electronic properties tuned by spin engineering

TG7 has a septet ground state (Table S1, ESI†), and the spin density mainly localizes at the zigzag edges (Fig. 1(b)). According to the molecular orbitals of BN doped heptene, the π orbital with a major contribution from the BN pair lies below the other π orbitals (Fig. S3, ESI†), thus the BN pair could be used to modify the π orbitals of graphene-based nano-systems. The intended introduction of BN pairs in the TG7 series redistributes the spin density with BN pairs (Fig. 3(a)). Spin reduction (e.g., from septet to quartet) can be modulated by a combination of B (or N) doping with BN pairs at the zigzag edges (i.e., TG7-BN-c1 and TG7-BN-c-2 in Fig. 3(b) and Table S1, ESI†) while making the spin density localized in the inner carbon atoms. Subtle adjustment of spin distribution can also be achieved by the different doping patterns of NB at the edges of triangulenes (TG7-BN-c1 and TG7-BN-c-2 in Fig. S4, ESI†). A specific arrangement of BNB doping can even create a localized region with a spin of different orientation (the blue region in TG7-BNB-ab in Fig. 3(b)). Such spin engineering of triangulenes renders those nanomaterials with potential applications in other fields, e.g., spintronics⁷ and magnetics.⁵⁹ For applications of triangluenes in the fields requiring a closed-shell electronic state, the spin of triangulenes needs to be eliminated.

Fig. 3 The natural atomic spin distributions (spin up: yellow circle, spin down: blue circle) of the BN-doped TG7-a/b/ab/ba/c series of molecules and TG7-BNB-ab. Atoms in black are carbon, purple are boron, and green are nitrogen.

As depicted in Fig. 2, different doping patterns in TG7 lead to different symmetries. Vibrational frequency calculation confirms that all [7]-triangulenes are minima on the potential energy surface (Table 1 and Table S1, ESI†). For the B, N or NBN series of TG7, the large relative electronic energy differences (ΔE_T–CS) [between triplet (T) and closed-shell singlet (CS), CS is taken as the reference] and the zero spin contamination of singlet indicate that closed-shell singlet is the ground state (Table 1). Remarkably, the polyradical nature in pristine triangulenes (n = 7) can be eliminated in those four series of triangulenes with appropriate doping patterns (i.e., TG7-ba series of molecules).

Table 1 The electronic properties including the energy gap (E_gap, in eV) between the highest occupied molecular orbital (E_H) and the lowest unoccupied molecular orbital (E_L), the lowest vibrational frequency (LVF, in cm⁻¹) and the dipole moment of the ground state (D_g, in Debye), and the static first hyperpolarizability (〈β₀〉, in 10⁻³⁰ esu), the 〈β₀〉 per heavy atom (〈β₀〉/N) of TG7 series of molecules in closed-shell singlet predicted with PBE0/6-31G(d,p) and TD-CAM-B3LYP/6-31++G(d,p)-SOS, respectively. The relative electronic energy differences (ΔE_OS–CS and ΔE_T–CS, in kcal mol⁻¹) between open-shell singlet (OS) or triplet (T) and closed-shell singlet (CS) (CS is taken as reference), and spin contamination of open-shell singlet (〈S²〉) obtained at the UPBE0/6-31G(d,p) level

Compound	ΔEOS–CS	ΔET–CS	〈S^2〉	LVF	D g	E L	E H	E gap	〈β0〉	〈β0〉/N
—: the 〈β0〉s of these molecules were not calculated because of their open-shell electronic ground states.
TG7	−53.55	−55.27	10.34	22.82	0.00	−3.53	−3.96	0.43	—	—
TG7-B-a	0.00	35.71	0.00	3.79	0.17	−3.06	−5.52	2.46	−35.39	−0.45
TG7-B-b	0.00	34.18	0.00	22.40	0.00	−3.08	−5.72	2.64	33.84	0.43
TG7-B-ab	0.00	29.44	0.00	9.62	5.21	−3.10	−5.42	2.32	358.73	4.60
TG7-B-ba	0.00	27.08	0.00	16.61	5.45	−3.25	−5.47	2.22	472.15	6.05
TG7-N-a	0.00	35.71	0.00	22.95	0.00	−1.69	−4.31	2.62	−123.79	−1.59
TG7-N-b	0.00	23.76	0.00	23.76	0.00	−1.51	−4.24	2.73	−0.36	−0.0046
TG7-N-ab	0.00	31.79	0.00	23.63	6.01	−1.79	−4.23	2.44	424.13	5.44
TG7-N-ba	0.00	29.72	0.00	24.13	6.21	−1.74	−4.04	2.30	484.84	6.22
TG7-NBN-a	0.00	5.29	0.00	24.31	0.00	−2.10	−3.69	1.59	−439.17	−5.63
TG7-NBN-b	0.00	−0.58	0.00	25.16	0.00	−2.09	−3.65	1.56	—	—
TG7-NBN-ab	−1.74	1.34	0.12	25.36	1.11	−2.10	−3.71	1.61	—	—
TG7-NBN-ba	0.00	19.70	0.00	25.31	1.31	−2.14	−3.67	1.53	915.73	11.74
TG7-BNB-a	−7.27	−8.80	6.90	4.47	0.00	−3.66	−5.04	1.38	—	—
TG7-BNB-b	−8.18	−4.92	6.23	12.13	0.00	−3.68	−5.11	1.43	—	—
TG7-BNB-ab	−1.23	−8.80	0.48	5.66	0.59	−3.64	−5.04	1.40	—	—
TG7-BNB-ba	0.00	13.27	0.00	7.06	0.82	−3.68	−5.06	1.38	1470.23	18.85
TATB	0.00	56.37	0.00	18.21	0.00	−7.49	−2.56	4.93	−1.35	−0.075
cmpd-1	0.00	55.29	0.00	8.07	0.32	−1.92	−6.27	4.35	6.03	0.13
cmpd-2	0.00	33.43	0.00	33.89	4.21	−6.33	−3.35	2.98	10.20	0.25
cmpd-3	0.00	36.17	0.00	10.23	5.37	−5.96	−2.73	3.23	54.86	1.12

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The HOMO–LUMO energy gap E_gap and frontier molecular orbitals are used to not only characterize reactivity and electronic kinetic stability (feasibility of electron transition from occupied molecular orbitals to virtual molecular orbitals), but also qualitatively predict the optical and electrical properties of a molecule. For medium-sized π-systems, the E_gap values predicted using hybrid density functional methods are in good agreement with the experimental excitation energies.⁶⁰ The E_gap of the triangulenes in the present work increases from 0.43 eV in TG7 to 2.46 eV in TG7-B-a by the introduction of B (Table 1). The unpaired π-electrons at the edges of the pristine triangulenes for example TG7, leads to small E_gap (0.43 eV). The frontier molecular orbitals (including HOMO and LUMO) of these molecules clearly show charge redistribution upon the doping of heteroatoms. The incorporation of those dopants into pristine triangulenes diminishes or even eradicates the nonbonding orbitals formed by the unpaired π-electrons (Fig. S5, ESI†), and results in a low-lying HOMO or an elevating LUMO compared with that of TG7, i.e. a larger HOMO–LUMO energy gap. Compared with the B, N doped TG7 series, the doping of NBN and BNB in triangulenes leads to smaller E_gap, in which the HOMO–LUMO gap of the TG7-ba series is slightly smaller than that of the TG7-ab series (Table 1).

Electronic spectra and the 〈β₀〉 of TG7-ba series of molecules

The doping patterns of B or (and) N in [n]triangulenes have significant effects on the electronic properties of these triangulenes, thereby leading to distinct static first hyperpolarizability (〈β₀〉) (Table 1 and Table S2, ESI†), in which TG7-NBN-a has a relatively large 〈β₀〉 per heavy atom (〈β₀〉/N) (5.63 × 10⁻³⁰ esu). Additionally, the (〈β₀〉/N)s of the TG7-b series of molecules (with BN doped at the positions with the secondary largest spin densities) are weaker than that of the TG7-a series (Table 1). The TG7-ba series with mixed doping sites of TG7-a and TG7-b have large 〈β₀〉. The 〈β₀〉/N of TG7-BNB-ba reaches 18.85 × 10⁻³⁰ esu, which is larger than that of TG7-NBN-ba (11.74 × 10⁻³⁰ esu) and about three times that in TG7-NBN-a (5.63 × 10⁻³⁰ esu) (Table 1).

The evolution of 〈β₀〉 with electron excitations provides information on the correlation between electronic structure and second order NLO properties of a system. The evolution of the 〈β₀〉 with the major electron excitations in the four TG7-ba molecules (i.e., TG7-B-ba, TG7-N-ba, TG7-NBN-ba and TG7-BNB-ba) are investigated in this work to explore the effects of B or (and) N on the electronic properties of these triangulenes.

TG7-B-ba . B-doping has long been adapted as a marvelous strategy for lowering the LUMO energy of graphene or π-conjugated systems,^61–63 and the recently synthesized periphery-tuned boron-containing polybenzenoid PAH⁶³ suggests that the doping at the edge of triangulenes by B is highly feasible. With the substitution of the carbon atoms with unpaired π-electrons in TG7 by electron-deficient boron, i.e., forming TG7-B-ba, the slight raising of the LUMO energy and sharply lowering of the HOMO energy of TG7-B-ba compared with that of TG7 (Table 1) provides a novel approach for frontier molecular orbital energy manipulation for designing organic semiconductors and organic optoelectronics.⁶⁴ The electronic spectra of TG7-B-ba have strong absorption peaks occurring from 200.0 to 600.0 nm in the ultraviolet and visible light region with the strongest peak at 2.69 eV (460.7 nm) (Fig. 4). The lowest dipole-allowed electron excitation occurs at 2.19 eV (566.3 nm) with a dominant contribution (236.31 × 10⁻³⁰ esu out of the total 472.15 × 10⁻³⁰ esu) to the 〈β₀〉 (Table S3, ESI†). Another two major electron excitation peaks at 2.69 eV (460. 7 nm; 60.43 × 10⁻³⁰ esu) and 3.14 eV (395.4 nm; 21.80 × 10⁻³⁰ esu) also have large contributions to the 〈β₀〉. These strong electron excitations at 2.19, 2.69 and 3.14 eV are essentially vertical excitation (electron transition from the occupied MO to the virtual MO of the same region under the Franck–Condon principle), and the molecular orbitals involved in these three electron excitations exhibit strong π-electron conjugation between carbon and boron in TG7-B-ba (Fig. 4 and Fig. S6a, ESI†). To comprehend the process of electronic transition as well as quantify the relative degree of charge transfer based excitation or vertical excitation in these major electron excitations, the hole (where the electrons leave when they get excited) and electron (where the excited electrons go) distributions⁶⁵ (plotted with Multiwfn⁵²) and their corresponding real space representation (electron in yellow and hole in blue) of transition from the ground state (S₀) to the excited state (S_e) for these molecules are plotted in Fig. 4. Hole and electron form an exciton. In TG7-B-ba, the hole distributions essentially delocalize at the carbon skeletons (Fig. 4 and Fig. S7, ESI†), charge transfer based excitation from the carbon skeleton (in the hole distribution) to boron atoms (in the electron distribution) indicates that these boron atoms behave as electron acceptors ascribed to the vacant p orbital (Fig. 4). The effect of boron atom doping on the NLO response of TG7-B-ba can also be verified by saturation of the to-be replaced carbon atoms by hydrogens in TG7-ba (i.e., TG7-H6-ba), and the 〈β₀〉 per heavy atom changes from 6.05 × 10⁻³⁰ esu in TG7-B-ba to 0.93 × 10⁻³⁰ esu in TG7-H6-ba (Fig. S8, ESI†). Besides boron atoms, polyborane clusters can serve as electron acceptors for constructing V-shaped organic–inorganic hybrid NLO materials.⁶⁶

Fig. 4 Evolution of the static first hyperpolarizability (〈β₀〉) with the electron excitations of TG7-B-ba. Hole (blue opaque) and electron (yellow opaque) distributions plotted with an isosurface of 0.0008 a.u., and their corresponding real space representation of electron (transparent yellow) and hole (transparent blue) distributions of the transition from the ground state (S₀) to the excited state (S_e) of TG7-B-ba based on the electronic wavefunction predicted by using CAM-B3LYP/6-31++G(d,p)(plotted with an isosurface value of 0.0004 a.u. for a better view). Hereafter, the red numbers are the distance (D_hole–ele, in Å) between the center of mass of the hole (blue sphere) and the electron (yellow sphere). f is the oscillator strength (in a.u.).

TG7-N-ba . Substitution of the B atoms in TG7-B-ba by N atoms (i.e., resulting in TG7-N-ba) alters the electronic structure of the pristine triangulene as reflected by the charge redistribution in TG7-N-ba (Fig. S5, ESI†). In TG7-N-ba, the lowest dipole-allowed electron excitation has a slight blue-shift (2.19 eV in TG7-B-ba shifts to 2.26 eV in TG7-N-ba) (Fig. 5). The electron excitations below 5.00 eV with major contributions to the 〈β₀〉 of TG7-N-ba (484.84 × 10⁻³⁰ esu) mainly appear in the visible light regions, e.g., at 2.26 eV (549.5 nm; 199.88 × 10⁻³⁰ esu), 2.73 eV (454.4 nm; 41.19 × 10⁻³⁰ esu), 2.88 eV (430.0 nm; 28.18 × 10⁻³⁰ esu), 4.39 eV (282.7 nm; 30.18 × 10⁻³⁰ esu), and 4.57 eV (271.1 nm; 28.30 × 10⁻³⁰ esu) (Fig. 5 and Table S3, ESI†). These five major electron excitations are essentially vertical excitation and minor intramolecular charge transfer based excitations (electron transition from the occupied MO to the virtual MO locating at different regions under the Franck-Condon principle) (Fig. 5 and Fig. S6b, ESI†), and such multiple electron excitations with cumulative contributions to the 〈β₀〉 confer TG7-N-ba with slightly lager 〈β₀〉 per heavy atom (6.22 × 10⁻³⁰ esu) than that of TG7-B-ba (6.05 × 10⁻³⁰ esu) (Table 1). The hole of these electron excitations in TG7-N-ba is mainly located at carbon and nitrogen, while the corresponding electron is located at the carbon skeleton (Fig. 5). The good stability of B- or N-doped molecules also allows further modifications to tune the NLO properties of those triangulenes.

Fig. 5 Evolution of the static first hyperpolarizability (〈β₀〉) with the electron excitations of TG7-N-ba. Hole (blue opaque) and electron (yellow opaque) distributions plotted with an isosurface of 0.0008 a.u., and their corresponding real space representation of electron (transparent yellow) and hole (transparent blue) distributions of the transition from the ground state (S₀) to the excited state (S_e) of TG7-N-ba based on the electronic wavefunction predicted by using CAM-B3LYP/6-31++G(d,p) (plotted with isosurface value of 0.0004 a.u. for better view).

TG7-NBN-ba . When the ortho-positions of B atoms in TG7-B-ba are doped with N atoms, or replacing a C₃ unit at the edges of TG7 with an NBN moiety, i.e., TG7-NBN-ba forms, and the ground state of TG7-NBN-ba is closed-shell singlet (Table 1). There is an absorption peak in the near-infrared region at 0.97 eV (1273.7 nm; 61.41 × 10⁻³⁰ esu) with a large contribution to the 〈β₀〉, and this electron excitation involves the BN of NBN (hole) and the N of NBN (electron) (Fig. 6 and Fig. S9, ESI†). Another five consecutively distributed major electron excitations in TG7-NBN-ba move to the lower energy region with respect to that of TG7-N-ba and TG7-B-ba, and the electron excitations at 1.61 eV (135.91 × 10⁻³⁰ esu), 1.73 eV (67.66 × 10⁻³⁰ esu), 1.83 eV (239.36 × 10⁻³⁰ esu), 2.18 eV (108.98 × 10⁻³⁰ esu), and 2.50 eV (251.02 × 10⁻³⁰ esu) have conspicuous contributions to the 〈β₀〉 of TG7-NBN-ba (Table S3, ESI†). These electron excitations in TG7-NBN-ba involve vertical excitation and partially intramolecular charge transfer based excitation (Fig. 6), and the π-electron conjugation of the NBN or the BN of NBN with the carbon skeleton can be clearly observed in those involving molecular orbitals (Fig. S9, ESI†). TG7-NBN-ba is isoelectronic with TG7-N-ba, and the BN in TG7-N-ba further polarizes the charge distribution as well as lowers the excitation energies, thereby bringing about a larger 〈β₀〉 of TG7-NBN-ba than TG7-N-ba (Table 1). Recently, the syntheses of a series of new three-heteroatom doped carbon-based compounds by the replacement of a C=C–C unit with an X–B–X (X = O or N) unit, for instance OBO-doped nanographenes⁶⁷ and double heliences,^68,69 NBN-incorporated heterohelicenes⁷⁰ and graphene nanoribbons,⁷¹ offer a possibility for the synthesis of novel hetero-triangulene NLO materials.

Fig. 6 Evolution of the static first hyperpolarizability (〈β₀〉) with the electron excitations of TG7-NBN-ba. Hole (blue opaque) and electron (yellow opaque) distributions plotted with an isosurface of 0.0008 a.u., and their corresponding real space representation of electron (transparent yellow) and hole (transparent blue) distributions of the transition from the ground state (S₀) to the excited state (S_e) of TG7-NBN-ba based on the electronic wavefunction predicted by using CAM-B3LYP/6-31++G(d,p) (plotted with an isosurface value of 0.0004 a.u. for a better view).

TG7-BNB-ba . With the doping of BNB in TG7-ba, the positive triplet–singlet energy difference (13.27 kcal mol⁻¹) and zero spin contamination of open-shell singlet illustrate that TG7-BNB-ba has a stable closed-shell singlet ground state (Table 1). Compared with the electronic spectra of TG7-B-ba (isoelectronic with TG7-BNB-ba), the oscillator strengths of the major electron excitations of TG7-BNB-ba get weaker. The electron excitations with major contributions to the 〈β₀〉 mainly occur in the near-infrared and visible light regions at 0.76 eV (1622.7 nm; 195.65 × 10⁻³⁰ esu), 1.38 eV (895.7 nm; 126.27 × 10⁻³⁰ esu), 1.64 eV (757.7 nm; 112.59 × 10⁻³⁰ esu), 1.66 eV (747.8 nm; 407.69 × 10⁻³⁰ esu), 1.95 eV (635.1 nm; 211.36 × 10⁻³⁰ esu), 1.99 eV (624.4 nm; 78.97 × 10⁻³⁰ esu), and 2.28 eV (544.2 nm; 52.69 × 10⁻³⁰ esu) (Table S3, ESI†), and these strong electron excitations in TG7-BNB-ba are essentially intramolecular charge transfer based excitations mixed with vertical excitations (Fig. 7 and Fig. S10, ESI†). A comparison of the distance between the centers of mass of the hole and electron in TG7-NBN-ba and TG7-BNB-ba indicates that the strong electron excitations in the low energy regions (with major contributions to the 〈β₀〉) make the second order NLO response of TG7-BNB-ba [18.85 × 10⁻³⁰ esu of 〈β₀〉 per heavy atom (〈β₀〉/N)] stronger than that of TG7-NBN-ba (11.74 × 10⁻³⁰ esu of 〈β₀〉/N) and TG7-B-ba (Fig. 6 and 7). The 〈β₀〉/N of TG7-BNB-ba is also much larger than that of TG7-H6-ba terminated with an electron-withdrawing group (NO₂) (4.16 × 10⁻³⁰ esu) (Fig. S8, ESI†). The effect of BNB on the NLO responses can be clearly observed by the hole and electron distributions involved in these strong electron excitations, i.e., the hole mainly distributes at the BN of BNB and the bonded carbon atoms, while the electron of the exciton mainly locates at the N of BNB (Fig. 7). Similar to TG7-NBN-ba, the hole and electron of the exciton of TG7-BNB-ba distribute at the outer rims of the triangulene (Fig. 6 and 7), and this is different from that of TG7-B/N-ba (i.e., the hole and electron essentially delocalize across the molecular skeleton) (Fig. 4 and 5). According to the hole–electron distributions and the molecular orbitals involved in the strong electron excitations with conspicuous contributions to the 〈β₀〉 of TG7-NBN-ba and TG7-BNB-ba, BNB and NBN have a synergetic effect through the combination of BN of NBN or BNB with B (in BNB) or N (in NBN) rather than a single functional moiety in enhancing NLO responses.

Fig. 7 Evolution of the static first hyperpolarizability (〈β₀〉) with the electron excitations of TG7-BNB-ba. Hole (blue opaque) and electron (yellow opaque) distributions plotted with an isosurface of 0.0008 a.u., and their corresponding real space representation of electron (transparent yellow) and hole (transparent blue) distributions of transition from the ground state (S₀) to the excited state (S_e) of TG7-BNB-ba based on the electronic wavefunction predicted by using CAM-B3LYP/6-31++G(d,p) (plotted with an isosurface value of 0.0004 a.u. for a better view).

In summary, B, N, NBN, and BNB act as the spin eliminator and electrostatic potential modulator in tuning electron transitions among frontier molecular orbitals with conspicuous effects on the second order NLO responses. Compared with the doping of B or N, the NBN or BNB doping significantly polarizes charge distribution of the π-electrons of the pristine triangulene, thus inducing strong charge transfer based electron excitations in low energy regions, thereby bringing about large 〈β₀〉/N of TG7-BNB-ba (18.85 × 10⁻³⁰ esu). The NBN or BNB-doping in desired positions provides an opportunity to facilitate tuning triangulenes for their possible applications in triangulene-based nanoelectronic devices.

Hyper–Rayleigh scattering

The Hyper–Rayleigh scattering (HRS) at the external field (0.0 nm or 1064.0 nm) and their corresponding dipolar (β_J=1) and octupolar (β_J=3) contributions to the NLO response of these four molecules are predicted with TD-CAM-B3LYP/6-31++G(d,p)-SOS (Table 2) for future possible measurement. The evolution of the HRS intensity with polarization angle also can reflect the structure-property correlation (Fig. 8), i.e. the HRS intensity ()⁵³ (indication of polarization strength) can be regarded as a function of polarization angle at the designated incident wavelength.

Table 2 The static β_HRS(0;0,0); the dipolar (|β_J=1|) and octupolar (|β_J=3|) components (in 10⁻³⁰ esu) of β_HRS in the incident wavelength of 1064.0 nm and the corresponding diagonal and off-diagonal tensor (β_iii and β_ijj), octupolar/dipolar contributions ratios (ρ = |β_J=3|/|β_J=1|) of the TG7-ba series of molecules in the closed-shell singlet. The Φ^J=3 = ρ/ρ + 1 (octupolar) and Φ^J=1 = 1 − Φ^J=3 (dipolar) are the proportion of the octupolar and dipolar contributions in the first hyperpolarizability. All triangulenes lie in the XZ plane

Compound	β HRS(0; 0, 0)	β HRS(−2ω; ω, ω)	β ZZZ	β ZXX	|βJ=1|	|βJ=3|	ρ	Φ ^J=1 (%)	Φ ^J=3 (%)
TG7-B-ba	182.72	498.33	386.95	314.01	104.57	1606.85	15.37	6.11	93.89
TG7-N-ba	188.29	959.26	800.68	528.28	1155.35	2558.75	2.21	33.23	66.77
TG7-NBN-ba	360.06	2827.45	2567.80	1183.60	5191.66	4588.16	0.88	53.19	46.81
TG7-BNB-ba	566.16	8931.65	8320.01	3248.34	17898.90	9492.14	0.53	65.36	34.64
TATB	0.82	7.20	5.85	4.20	6.78	20.90	3.08	24.51	75.49
cmpd-1	9.56	33.53	28.57	17.55	46.08	82.76	1.80	35.71	64.29
cmpd-2	10.29	79.25	62.24	49.06	39.76	249.52	6.28	13.74	86.26
cmpd-3	79.30	246.86	210.66	128.68	342.41	605.21	1.77	36.10	63.90

---

Fig. 8 Evolution of the Hyper–Rayleigh scattering (HRS) intensity () under the incident wavelength of 1064.0 nm with the polarization angle from 0° to 180° of four molecules (B: TG7-B-ba, N: TG7-N-ba, NBN: TG7-NBN-ba, and BNB: TG7-BNB-ba).

The predicted β_HRSs (−2ω; ω, ω) (ω = 0.0 nm or 1064.0 nm) follow a similar trend to the 〈β₀〉 of these four molecules (Tables 1 and 2), i.e., in the order of TG7-BNB-ba > TG7-NBN-ba > TG7-N-ba > TG7-B-ba. TG7-B-ba and TG7-N-ba have a large |β_J=3| with the anisotropy ratio ρ > 1, and the proportions of the octupolar contributions (Φ^J=3) in the β_HRS at 1064.0 nm of these two molecules are approximately 93.89% and 66.77% (Table 2) as depicted in Fig. 8. If triamino trinitrobenzene (TATB) is used as a representative reference for second order NLO properties of an octupolar molecule, TG7-B-ba and TG7-N-ba are good octupolar materials (Fig. 2 and Table 2). For the NBN or BNB doped triangulenes, the first hyperpolarizabilities of these molecules are dominated by a dipolar component with dipolar contribution (Φ^J=1) in the first hyperpolarizability of about 50.00–70.00%, and the reinforcement of dipolar character of the second order NLO response is also characterized by the decrease of the anisotropy ratio ρ from 15.37 (indicating a dominant octupolar character) to 0.53 (indicating a dominant dipolar character). Although the octupolar contributions of TG7-NBN/BNB-ba account for a small proportion of the total averaged first hyperpolarizability, the octupolar NLO responses of these triangulenes are significantly enhanced by the incorporation of NBN and BNB with respect to those of TG7-B-ba and TG7-N-ba (Table 2). The |β_J=1| of these four molecules significantly increases from TG7-B-ba to TG7-BNB-ba, and BNB or NBN polarizes charge redistribution (Fig. 3) thus enhancing the dipolar character, further verifying that the variation of dopants leads to a conspicuous change of polarization (Fig. 8). Compared with TG7-B-ba and TG7-N-ba, the strong HRS intensity of TG7-NBN-ba and TG7-BNB-ba is ascribed to the conspicuous contribution of diagonal terms (i.e., β_ZZZ) to the first hyperpolarizability (Fig. S11, ESI† and Table 2) (all triangulenes lie in the XZ plane). In summary, intended modification provides a promising means for stabilizing the radicals and also brings about an excellent NLO response (e.g. 8.93 × 10⁻²⁷ esu of β_HRS at 1064.0 nm in TG7-BNB-ba). The TG7-BNB-ba also has the largest β_J=1 (1.79 × 10⁻²⁶ esu) and β_J=3 (9.49 × 10⁻²⁷ esu) in all studied molecules, much larger than that of other triangular molecules (Fig. 2 and Table 2). This fine control of the ratio of dipolar/octupolar second-order NLO contribution opens interesting perspectives for applications in optoelectronic devices of carbon-based NLO materials.^64,72

Two-dimensional second order NLO spectra

It is impractical, if not impossible, to measure the NLO responses of materials under all possible external fields in an experiment to find all possible applications in NLO. In this case, simulation of NLO responses of materials under all possible external fields is very helpful for this purpose. Two-dimensional (2D) second order NLO spectra^73–75 encompass second order NLO responses of materials to external fields with all possible combinations of the two incident frequencies. The two-dimensional (2D) second order NLO spectra of four representative molecules (i.e., TG7-B-ba, TG7-N-ba, TG7-NBN-ba and TG7-BNB-ba) are investigated under external fields up to 7.00 eV with a scanning step size of 0.05 eV (Fig. 9 and Fig. S12, ESI†).

Fig. 9 The two-dimensional second order nonlinear optical spectra (in 10⁻³⁰ esu) of (a) TG7-B-ba, (b) TG7-N-ba, (c) TG7-NBN-ba, and (d) TG7-BNB-ba scanned up to 7.00 eV with a step size of 0.05 eV.

The 2D second order NLO spectra landscapes of these four molecules reveal the intensity of NLO responses under external fields (Fig. 9). Overall, the landscape of the 2D second order NLO spectra of TG7-B-ba and TG7-N-ba is similar, and this is a similar case for TG7-BNB-ba and TG7-NBN-ba. For TG7-B-ba, the strong resonant response (different frequency generation – DFG) (1.08 × 10⁻²⁴ esu) occurs at the external fields (3.25 eV, −1.05 eV) and (3.25 eV, −2.20 eV) (Fig. 9(a)), and fine scan with a step size of 0.005 eV finds the strongest NLO resonant (mainly with the electron excitation at 2.19 eV) response (1.78 × 10⁻²⁴ esu) appearing at the external fields of (3.255 eV, −1.065 eV) and (3.255 eV, −2.190 eV) (Fig. S13a, ESI†). Similarly, strong sum frequency generation (SFG) (1.78 × 10⁻²⁴ esu) with ω₁ + ω₂ = 3.255 eV (ω₁, ω₂ ∈ [0.000 eV, 3.255 eV]) is observed at the external field (2.190 eV, 1.065 eV) (Fig. S13b, ESI†). In the 2D second order NLO spectra of TG7-N-ba, there is a strong resonant response (8.46 × 10⁻²⁵ esu) at the external field (2.25 eV, 1.05 eV) (Fig. 9(b)). Fine scanning with a step size of 0.005 eV locates the strongest SFG resonant response (1.28 × 10⁻²⁴ esu) with ω₁ + ω₂ = 3.300 eV at the external field (2.255 eV, 1.045 eV) (Fig. S13c, ESI†), which may be caused by the resonance of external fields with the electron excitations at 2.26 eV and 3.30 eV (Fig. 5 and Table S3, ESI†). Strong DFG (1.28 × 10⁻²⁴ esu) also occurs at the external fields (3.300 eV, −1.045 eV) and (3.300, −2.255 eV) (Fig. S13d, ESI†). Such strong resonant responses of SFGs and DFGs in the visible and near-infrared regions in TG7-B-ba and TG7-N-ba offer promising potential applications in studying the molecular structure and charging at interfaces^76,77 or nonlinear nanophotonic devices.⁷⁸

In TG7-NBN-ba, a strong resonant response (3.20 × 10⁻²⁵ esu) at an external field (2.50 eV, −2.50 eV) is optical rectification (OR), and another strong one at (2.50 eV, 0.00 eV) with a single photon resonance at ω₁ (ω₂) = 2.50 eV is an electro-optical Pockels effect (EOPE) (Fig. 9(c)). Comparatively, another slightly strong NLO response (4.03 × 10⁻²⁵ esu) occurs in the lower energy region (1.83 eV, −1.83 eV) (OR) and (1.83 eV, 0.00 eV) (EOPE) (Fig. S13e, ESI†). For TG7-BNB-ba, a strong resonant response (2.52 × 10⁻²⁵ esu) occurs at the external fields (1.65 eV, 0.00 eV) and (1.65 eV, −1.65 eV) (Fig. 9(d)), and a fine scan with a step size of 0.005 eV locates the strongest response (3.19 × 10⁻²⁵ esu) at external fields (1.66 eV, 0.00 eV) (EOPE) and (1.66 eV, −1.66 eV) (OR) (Fig. S13f, ESI†). Strong resonant response DFG (1.80 × 10⁻²⁵ esu) is observed at a higher external field (1.95 eV, −1.55 eV), and a strong SFG (1.69 × 10⁻²⁵ esu) with ω₁ + ω₂ = 1.95 eV appears at the external field (1.55 eV, 0.40 eV) (Fig. 9(d)). Likewise, strong resonant NLO responses (1.51 × 10⁻²⁵ esu) OR and EOPE (Fig. 9(d)) occur at the external fields (1.95 eV, −1.95 eV) and (1.95, 0.00 eV). These strong ORs and EOPEs in TG7-BNB-ba and TG7-NBN-ba open the possibility for light tuning.

Conclusions

In this work, the spin distribution of triangulenes with a multi-radical character has been analyzed in the frame of molecular orbital theory and the Clar's sextet theory. Strategies for redistribution (by doping of BN pairs), reduction [by doping of B, N, BNB, NBN, and BN chains] and elimination (by doping of B, N, BNB and NBN) of the spin while polarizing the charge distribution of those triangulenes have been proposed. The doping sites are chosen as the combination of electronic configurations with different spin distributions for desired charge distribution. This proposed spin engineering based on molecular orbital theory on triangulenes based nanomaterials would broaden the applications of graphene in molecular magnetics, spintronics, and electro-optics. Such engineering strategies could also be applicable to other similar two-dimensional functional materials designs.

Hole–electron distributions and electronic structure analyses on four TG7-ba molecules find that B essentially functions as an electron-acceptor while N acts as an electron-donor, while NBN and BNB make a concerted effect (combining BN with N or B) to bring about a smaller HOMO–LUMO energy gap and lead to charge redistribution, thus enhancing their second order NLO responses, e.g. the static first hyperpolarizability per heavy atom (〈β₀〉/N) of TG7-BNB-ba reaches 18.85 × 10⁻³⁰ esu in which BNB plays a more delicate role in both polarizing charge distribution and lowering electron excitation energies of the triangulene. The HRS response (β_HRS) of TG7-BNB-ba at 1064.0 nm reaches 8.93 × 10⁻²⁷ esu involving significant dipolar and octupolar NLO responses and is much larger than typical octupolar molecules. The strong second order NLO responses in the visible and near-infrared light regions, e.g., sum frequency generations and difference frequency generations, make these triangulenes potential NLO materials for applications in these regions. Intended heteroatom doping is an important means for improving the NLO response of carbon-based nanomaterials and shedding light on their promising applications, such as organic field-effect transistors,⁷⁹ semiconductors,⁸⁰ electromagnetics,⁸¹ photocatalysts for water splitting⁸² and the next generation of organic spintronic materials.⁷

The recent successful syntheses of BNB- or NBN-doped traiangulenes,^83–85 [7]triangulene quantum rings,⁸⁶ [7]triangulene⁸⁷ and the advance in graphene nanosheets and nanoribbons syntheses⁸⁸ certainly warrant future syntheses and applications of those proposed triangulenes in nano nonlinear optics.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

YCC acknowledges the support from the graduate scientific research and innovation foundation of Chongqing, China (Grant No. CYB21042). This work is supported by the National Natural Science Foundation of China (21673025 and 11974091). The Open Projects of Key Laboratory of Polyoxometalate Science of Ministry of Education (NENU) and the State Key Laboratory of Supramolecular Structure and Materials (JLU) (SKLSSM2021020) are also acknowledged. The constructive comments and suggestions from the anonymous referees are acknowledged.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2cp02915d

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