Bis-TTF-Ge derivatives: promising linear and nonlinear optical properties, a theoretical investigation

Abstract

In this work, based on bis(tetrathiafulvalenyldithio)-germane (bis-TTF-Ge), 37 compounds (denoted T0–T36) are designed by the introduction of donor and acceptor groups at different substituent positions. The ground state electronic structures, reactivity indices, electronic transition, charge transfer properties (charge, distance and dipole moment), hyper-Rayleigh scattering and depolarization ratios (static and dynamic) of these compounds are fully investigated using DFT and TD-DFT calculations. The quantum calculations were performed at the CAM-B3LYP/6-311g(d,p) level and using the sum-over-states (SOS) approach in both static and dynamic cases. The chemical hardness (η) of the two substituted bis-TTF-Ge derivatives at the b position has a smaller value than those with the same substituent at positions d, e, a and c. In both static and dynamic regimes the investigations show that the bis-TTF-Ge derivatives substituted with donor or acceptor groups have larger first hyperpolarizability than T0. Our work predicts that the introduction of the substituent group at the b position can increase the hyperpolarizability values more than those at the other positions, and the NO₂, NO and COCN acceptor groups lead to the largest values. For example, the dynamic β^λ=1064_HRS value of T25 is about 145 times larger than that of T0 and about 11 times that in the static regime. Interestingly, the β^λ=1064_HRS of bis-TTF-Ge substituted with the NO₂ group increases with the number of NO₂ in the TTF fragment. The large nonlinear optical (NLO) origin of bis-TTF-Ge substituted with NO₂, NO and COCN is attributed to charge transfer from the TTF to the acceptor group at the second TTF fragment (overlap S_r index = 0). The studied bis-TTF-Ge substituted with NO₂ compounds exhibits the possibility of being an excellent second-order NLO material.

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Introduction

Nonlinear optics (NLO) is the study of the interaction of high intensity light with matter. In linear optics the relation between polarization (P) and electric field (E) is linear and the frequency is kept. For an intense laser light, this linearity no longer holds and one gets different kinds of frequencies; this frequency transformation has been observed experimentally by Franken,¹ and the intense light induces a change in the refraction index of the material (optical Kerr effect), which leads to a phenomenon called the self-phase modulation.² The induced polarization at the macroscopic level is generally written as³

ΔP = χ⁽¹⁾E + χ⁽²⁾E² + χ⁽³⁾E³ + ⋯

χ⁽¹⁾, χ⁽²⁾ and χ⁽³⁾ are the first, second and third order susceptibility tensors, respectively. χ⁽¹⁾ belongs to the domain of linear optics, whereas χ⁽²⁾ and χ⁽³⁾ quantifies the second and third order NLO effects, respectively.

Since the discovery of lasers by Maiman and Collins in 1960^4,5 great interest has been devoted to the discovery and design of new materials with excellent nonlinear optical properties. This is due to their important applications in different areas such as in photonic devices such as molecular switching, frequency doubling, telecommunications and optical information processing.^6–12

Numerous techniques for developing new high-performance NLO materials have been proposed, including diradical characterization,¹³ synthesis of molecular structures of electron-donor (D)–π–electron-acceptor (A) (D–π–A),¹⁴ reinforcing push–pull effects,^15,16 designing octupolar compounds,^17,18 multidecker sandwich complexes,¹⁹ asymmetric coordination complexes,^20–23 excess electrons,^24–29etc. Among the studied NLO materials the inorganic compounds have attracted exceptional interest because of their physicochemical stability and thermal stability.^30,31 For example, tetrathiafulvalene (TTF) derivatives present excellent second- and third-order nonlinear optical responses, and they are a very active field in contemporary chemistry since shortly after their first synthesis in the early 1970s by Wudl and co-workers.^32,33 These properties are derived from the large π conjugated systems, the strong electron-donor character and the existence of polarizable sulfur atoms, leading to charge density redistribution within the molecule.^34–36

The combination of the TTF group and electron acceptor (A) units that are covalently linked by a π-conjugated bridging group is highly desirable and classified as excellent push–pull organic molecules (D–π–A). So far, TTF–π–A as promising NLO materials have been widely studied by many scientific researchers, because these compounds exhibit intramolecular charge transfer (ICT) and have low energy-gaps.^37–39

On the other hand, the binding of the TTF group with transition metals (TM) through covalent linkages or via electrostatic interactions allows the development of new metal complexes with π-conjugated ligands and can present a respectable class of NLO materials.^36,40–42 For example, in 2015, Liu and coworkers studied static and dynamic HRS hyperpolarizability of a series of extended tetrathiafulvalene (exTTF) and TTF derivatives of metal cations (TM: Ni²⁺, Cu²⁺, Mg²⁺, Zn²⁺ and Cd²⁺) and they found that the TM complexes containing the redox-active TTF unit and the pyridine group exhibit large hyperpolarizability values.⁴³ In addition, the nonlinear optical responses of several square-planar metal TTF complexes^44,45 have been studied theoretically and experimentally and have shown the important role of the ligand in perturbing the electron distribution in these complexes and its effect on both the ground and the excited states and, thus, on the linear and nonlinear optical properties.^46–51 In recent years growing attention has been expressed concerning germanium, and this interest is due to its high carrier mobility, good stability so that Ge is the most logical candidate to substitute carbon; moreover, it has also potential applications in photodetectors and nonlinear optical fields.^52–60

Ueda et al.⁶¹ reported spiro molecules: bis(tetrathiafulvalenyldithio)-germane (here named bis-TTF-Ge T36, see Fig. 1). This asymmetric compound which contains large π systems should be a potential second-order NLO material. In this work, our aim is to study the effects of acceptor/donor substituents (NO, CN, COCN, CHO, NO₂, NH₂ and NMe₂) and the substituent positions (a, b, c, d and e; see Fig. 1) on the reactivity indices, and the linear and nonlinear optical properties of bis-TTF-Ge compounds. Also in this study, we focus to offer new perspectives with respect to the origin of nonlinear optical materials for title compounds. Furthermore, to the best of our knowledge, there are no computational studies that address in detail the effect of the number and the nature of substituent groups in compounds made of two TTF groups linked by spiro germanium on the NLO properties.

Fig. 1 Chemical structures of the studied bis-TTF T0 to T36, where a, b, c, d and e are the substituent position (a: one substituent at R1; b: two substituents at R1 and R2; c: two substituents at R1 and R4; d: three substituents R1, R2 and R3; e: four substituents).

Computational details

The geometries of the bis-TTF-Ge derivatives were fully optimized using Coulomb-attenuating exchange–correlation density functional method CAM-B3LYP⁶² using the 6-311g(d,p)^63,64 basis set. CAM-B3LYP is a long-range corrected functional developed to handle the inaccuracies of the non-Coulomb part of the exchange functional at long distances. Quantum chemical calculations were performed using the Gaussian 09 program with the TIGHT SCF convergence and ultra-fine integration grid.^65–67 No symmetry constraints were applied and the local minima were confirmed on potential energy surface by frequency calculations of the ground state for bis-TTF-Ge compounds at the same level.

Chemical reactivity analysis takes advantage of its ground in DFT through a functional Taylor expansion of energy that introduces several reactivity descriptors from energy derivatives of chemical significance.⁶⁸ According to finite difference approximation and Koopmans’ theorem^69–71 the electronic chemical potential (μ) and global hardness (η) can be evaluated from the frontier orbital energies HOMO and LUMO (ε_H and ε_L, respectively).

Electronic chemical potential (μ) is the tendency of an atom or molecule to attract electrons; it is given by the following equation:

χ is the electronegativity.

The chemical hardness (η) expresses the resistance of a system to change its number of electrons; it is calculated using the relation

η = ε_L − ε_H (2)

It is important to note that the global hardness (η) measures the stability of a system in terms of resistance to electron transfer and the chemical potential (μ) characterizes the escaping tendency of electrons from the equilibrium system.

Global electrophilicity index (ω), introduced by Parr et al.,⁷² is calculated from the hardness and chemical potential:

This index expresses the ability of a molecule to accept electrons from the environment.

Furthermore, to investigate and understand the electronic transition and optical properties, the electron excitation energies, oscillator strengths, for the studied compounds were calculated at the TD-CAM-B3LYP level.

The hyper-Rayleigh scattering (HRS) technique involves the detection of the incoherent scattering second harmonic generation at frequency 2ω from a laser with frequency ω incidence. In HRS, we can evaluate the first hyperpolarizability β_HRS and its depolarization ratios DR, through the relation^6,73,74

where 〈β_ZZZ²〉 and 〈β_XZZ²〉 are orientational averages of the β tensor without assuming Kleinman's conditions:

Previous works have pointed out that CAM-B3LYP, adopted in this work, can provide an absorption spectrum close to experimental results and has been proven to be efficient in calculating the static and dynamic NLO responses.^7,75–77 Frequency-dependent hyperpolarizabilities were calculated using an incident wavelength of 1064 nm.

The electron density difference maps (EDDM) corresponding to the crucial excited states can be accurately evaluated as follows:

Δρ(r) = ρ_ex(r) − ρ_GS(r)

where ρ_ex(r) and ρ_GS(r) are defined as the electronic densities associated with the excited and ground states, respectively.

Following the procedure proposed by Bahers et al.⁷⁸ the excited states of interest were examined using charge-transfer indices (CT) including charge-transfer distance (d^CT). The product of these quantities d^CT and q^CT (transferred charge) gives the variation in the dipole moment between the ground and the excited states (Δμ_0→n = d^CT × q^CT).

On the other hand, the overlap distribution between the holes and electrons can be expressed as

To characterize the overlapping extent of holes and electrons, S_r index is defined as
In our work, the crucial excited state wavefunctions have been obtained by natural transition orbitals (NTOs) in terms of “excited particle” to “empty hole” of the electronic transition density matrix. The CT indices have been determined using the MULTIWFN program.⁷⁹

Results and discussion

The optimized geometries of bis-TTF linked by a germane noted Ti (i = 0–36) compounds obtained from DFT quantum chemical calculations is shown in Fig. 2 along with the atom numbering schemes. As can be seen from the figure, the optimized structure of the bis-TTF-Ge is tetrahedral, in which the Ge–S (S is S1, S2, S3 and S4) average length is 2.259 Å and the ∠S3–Ge–S4 and ∠S1–Ge–S2 angles are ∼97° whereas ∠S1–Ge–S3 and ∠S2–Ge–S4 are about 115°. On the other hand, the TTF groups deviate slightly from the perfect planar geometry by 10°, showing a slightly distorted geometry. One of the reasons for this distortion is a steric repulsion between the sulphur atoms and the d orbitals from the germanium atom.

Fig. 2 Optimized molecular geometry of bis-TTF-Ge compounds.

On the other hand we can observe that the TTF fragments in the title compounds are distorted into a boat conformation as shown in Fig. 2 in their ground state and this shape agrees well with the available studies. For instance, Demiralp et al. in their study of organic donors (X) containing the TTF group found that X⁺ always has a planar TTF region but that the neutral is distorted into a boat conformation.⁸⁰ They suggested that the off-planar geometry is caused by ring strain, which is developed when the H atoms of TTF are substituted by bulky ligands.⁴⁸ Furthermore, Linker et al. in their study of ethylenedioxy-TTF (EDO-TTF) indicated that a neutral derivative has a boat-shaped conformation, whereas the positively charged EDO-TTF is planar.⁸¹

Reactivity

The values of the HOMO and LUMO frontier orbital energies (E_HOMO and E_LOMO, respectively), the electronegativity (χ), the chemical hardness (η) and the electrophilicity index (ω), calculated for each bis-TTF-Ge compound, are given in Table 1.

Table 1 Energy HOMO and LUMO (eV), electronegativity (χ, eV), chemical hardness (η, eV) and electrophilicity index (ω, eV) of the Ti (i = 0 to 36) compounds

	Ti	E HOMO	E LUMO	η	χ	ω
	T0	−5.311	−2.577	2.733	3.944	2.845
a	T1	−5.329	−3.495	1.834	4.412	5.307
b	T2	−5.341	−3.776	1.564	4.558	6.644
c	T3	−5.361	−3.505	1.855	4.433	5.296
d	T4	−5.374	−3.790	1.583	4.582	6.631
e	T5	−5.430	−3.798	1.631	4.614	6.523
a	T6	−5.388	−2.708	2.680	4.048	3.057
b	T7	−5.429	−2.786	2.642	4.107	3.192
c	T8	−5.670	−2.838	2.832	4.254	3.195
d	T9	−5.710	−2.914	2.795	4.312	3.326
e	T10	−5.860	−2.985	2.874	4.423	3.402
a	T11	−5.377	−2.957	2.419	4.167	3.589
b	T12	−5.429	−3.374	2.054	4.401	4.715
c	T13	−5.600	−3.000	2.600	4.300	3.555
d	T14	−5.701	−3.416	2.284	4.559	4.548
e	T15	−5.855	−3.437	2.418	4.646	4.463
a	T16	−5.361	−2.657	2.703	4.009	2.973
b	T17	−5.400	−2.728	2.672	4.064	3.091
c	T18	−5.527	−2.738	2.788	4.132	3.062
d	T19	−5.528	−2.746	2.782	4.137	3.076
e	T20	−5.710	−2.878	2.831	4.294	3.256
a	T21	−5.382	−3.009	2.373	4.195	3.708
b	T22	−5.412	−3.790	1.622	4.601	6.523
c	T23	−5.624	−3.054	2.570	4.339	3.663
d	T24	−5.653	−3.834	1.819	4.744	6.184
e	T25	−5.838	−3.798	2.039	4.818	5.691
a	T26	−5.247	−2.576	2.671	3.912	2.864
b	T27	−5.019	−2.450	2.569	3.734	2.714
c	T28	−5.199	−2.502	2.697	3.851	2.749
d	T29	−4.996	−2.413	2.583	3.704	2.656
e	T30	−4.971	−2.363	2.607	3.667	2.578
a	T31	−5.203	−2.536	2.667	3.870	2.807
b	T32	−5.031	−2.451	2.579	3.741	2.713
c	T33	−5.179	−2.495	2.684	3.837	2.743
d	T34	−4.989	−2.409	2.580	3.699	2.651
e	T35	−4.964	−2.323	2.641	3.644	2.513
e	T36	−5.291	−2.715	4.003	2.575	3.111

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The electronegativities (χ = −μ) of the T1 to T25 bis-TTF-Ge which are substituted with the acceptor group increases with the number of acceptor groups in the title compounds. These results indicate that the trend of the electrons to leave the equilibrium systems increases from the four-acceptor substituted (e) to one-substituted (a) bis-TTF-Ge. The reverse trend is observed for the bis-TTF-Ge with the electron donor R (NH₂ and NMe₂), so it can be concluded that the bis-TTF-Ge with four electron donors (e) have the largest tendency to donate electrons than d, b, c and a, respectively.

On the other hand, we observe that the substituent position and the number of the substitution play an important role in the stability of studied bis-TTF-Ge. In each group with the same substituent, the substituent position b has a smaller hardness than the d, e, a and c substituent positions. The CHO and CN substituents in bis-TTF-Ge compounds show a decrease according to the following order: a, d, c and e. The ordering of the chemical hardness at the a position is T1 (NO) < T21 (NO₂) < T11 (COCN) < T31 (NMe2) < T26 (NH2) < T6 (CN) < T16 (COH). The smallest η values are obtained for acceptor substituents and similar trends for the substituent positions b, c, d and e. Therefore, the hardness of bis-TTF-Ge can be effectively reduced when substituent positions are substituted with acceptor groups. According to the theoretical scale of electrophilicity proposed by Domingo et al.⁸² of global electrophilicity power (ω) the title compounds can be assigned to a strong electrophile class (2.51 to 6.70 eV).

Electronic transitions

The TD-DFT calculation results of absorption spectra parameters such as excitation energy (ΔE), absorption wavelength (λ) and corresponding oscillator strength (f), charge transfer parameters (q^CT, d^CT, and Δμ_0→i) and S_r index are calculated at the CAM-B3LYP/6-311g(d,p) level and summarized in Table S1 (ESI†).

The simulated spectra and the electron density difference maps (EDDMs) are provided in Fig. 3 and Fig. S1, S2 (ESI†), respectively. In general, the absorption spectra of the title compounds are characterized by a strong band (B3) at 267 nm, two weak bands (B1 and B2) and two moderate absorption shoulders (S1 and S2).

Fig. 3 Calculated UV-vis absorption spectra of bis-TTF-Ge T1–T5 compounds (B: bands; S: shoulders).

The bis-TTF-Ge with NO electron acceptor substituents have five absorption bands, and their absorption wavelength range extends to 750 nm. T1, T2 and T3 show electronic transitions at 727, 680–637 and 654 nm, respectively, with small oscillator strength (f ≤ 0.001), mainly arising from TTF rings 1, 2, and 3 to NO, from TTF rings 1–3 to NO (at positions R1 and R2) and from rings 5 and 6 to NO (at position R3) respectively. The HOMO → LUMO excitations of T1, T2 and T3 are located at 307, 456 and 418 nm, respectively, mainly ascribed to a π → π* charge transfer (CT) character. The electronic transitions of T5 are assigned as a CT from rings 1, 2, 5, and 6 to four NO units (677, 637 and 455 nm) and from rings 1, 2, 5, and 6 to the 4S–Ge unit (at 400 and 289 nm). For T4, the electronic transition appears in the 676, 455 and 316 nm from rings 1–2 to NO (at positions R1 and R2) and from rings 5–6 to S–NO (positions R1 and R2) π → π* CT character, besides the electronic transition at 290 nm (f = 0.132) from rings 5–6 to NO (at position R3) and to the 4S-Ge unit.

For the T6 to T10 compounds, the HOMO → LUMO transition at ∼399 nm is a charge transfer from rings 6 and 5 to 4S-Ge. The bis-TTF-Ge T6 is also ascribed to the same CT character at 292 nm (f = 0.141). For T8 the absorption bands located at 304 and 243 nm, with large oscillator strength, mainly arise from rings 1 and 2 to 4S-Ge and CN (at position R3). For bis-TTF-Ge T10, it involves three CT characteristic bands at 363, 279 and 241 nm from rings 1–3 to C–S–COCN units attached to ring 1, from TTF rings to 4S-Ge (f = 0.198) and from ring 6–5 to C–S–COCN (at R1 and R2 positions) and C3–C4 atoms attached to ring 6 (f = 0.129), respectively. For T7 and T9, the absorption at 276 nm (f = 0.234 and 0.191, respectively) have a mixed character of charge transfer from rings 5 and 6 to S–CN units at the R1 and R2 positions of type n → π* and π → π* electronic transition.

For T14 and T15, the electronic transition at 374 and 351 nm, respectively, is mainly ascribed to the n → π* and π → π* CT mixed character from rings 4, 5 and 6 to S–COCN unit at position R3. The transition at 400 nm of T14 and T15 mainly comes from rings 1–3 to S-COCN (at R1 and R2 positions). The electronic transition of T13 at 398 and 359 nm arises from rings 5 and 6 to 4S-Ge and from rings 1, 2, 5 and 6 to two COCN units CT, respectively.

For T16, T17 and T19 the HOMO → LUMO transition at ∼401 nm is CT from rings 6 and 5 to the 4S-Ge unit. For T16 and T19 the HOMO−2 → LUMO and HOMO−1 → LUMO+4 excitations are CT from rings 1 and 2 to 4S-Ge unit and from rings 1–3 to 4–6, respectively (see Table S1 and Fig. S2, ESI†). Bis-TTF-Ge T18 exhibits absorption at 398 nm (HOMO → LUMO) with a charge transfer from rings 1, 2, 5 and 6 to the 4S-Ge unit. The T20 compound has three absorption bands at 397, 304 and 278 nm with a charge transfer character from rings 6 and 5 to 4S-Ge, from rings 6 and 5 to the four units S–CHO and from rings 1, 2, 5 and 6 to the 4S-Ge unit, respectively.

The bis-TTF-Ge with NH₂ and NMe₂ electron donors show three main absorption bands. The most intense absorption band of Ti (i = 26 to 35) is at 269 nm, with the largest oscillator strength, mainly coming from intra-rings charge transfer (ICT). The band at ∼404 nm is formed by a charge transfer from rings 1 and 2 to 4S-Ge unit from HOMO → LUMO. The absorption band at ∼310 nm shows that the electronic transitions have a mixed character of charge transfer from rings 1–3 to rings 4–6 of type n → π* and π → π* electronic transition.

For T21, the electronic transition at 434 and 295 nm is assigned as a CT from rings 1 and 2 to S–NO₂ and from rings 5 and 6 to S–NO₂, respectively. For T23, there is a charge transfer from rings 1, 2, 5 and 6 to S–NO₂ (at the R4 position) and to the 4S-Ge unit.

For T25, it is interesting to find that there is a CT from rings 2 and 3 to two units C–S–NO₂ (at R1 and R2 positions), from rings 1–2 and 5–6 to the 4S-Ge unit and from rings 4–6 to the C–S–NO₂ unit (at R1 and R2 positions) at 524, 394 and 325 nm, respectively; besides n, π → π* mixed CT from 1–3 to 4–6 rings and from rings 2–3 and 5–6 to C–S–NO₂ (at ring 6). For T22, the electronic transition arises from rings 1–2 to S–NO₂ and from rings 4–6 to S–NO₂ (at R1 and R2 positions), from rings 5–6 to 4S-Ge and from rings 1–2 to 4S-Ge. For bis-TTF-Ge T24, the electronic transition is mainly ascribed to a n, π → π* mixed character from rings 2–3 to S–NO₂ (at R1 and R2 position), from rings 4–6 to S–NO₂ (at R1 and R2 positions) and to S–NO₂ at the R3 position.

TD-DFT calculations on bis-TTF-Ge T0–T36 compounds show that the wavelength of the largest oscillator strength located at ∼266 nm, are due to n → π* and π → π* mixed character type intra-TTF electron transition (see Table S1 and Fig. S1, ESI†). Furthermore, these excitations show a relatively small d^CT and a large S_r index, indicating that the hole and electron are very close. For example, for T0, T36, T13, T18, T23 and T16 the electron density difference maps (EDDM) of this transition, shown in Fig. 4, reveals a significant intramolecular CT (ICT) and, for all compounds, is reported in the ESI† in Fig. S2.

Fig. 4 Electron density difference maps of T0, T36, T13, T8, T23 and T16 compounds from the ground state to the crucial excited state S0 → Sn (S17, S17, S2, S19, S25 and S18 respectively), plotted using 0.008 a.u. isovalues.

On the other hand, the TD-DFT results show that the electronic transition HOMO → LUMO for T2, T4, T11, T12, T21, T22 and T24 (R = NO, COCN and NO₂; position is a, b and d) is a strong non-local excitation as indicated by the overlapping index between the hole and the electron which is zero (S_r = 0, Table S1, ESI†).

Overall, T22, T24 and T25 show red-shift wavelength absorption compared to T23 and T12. On the other hand, the absorption wavelengths of T6 to T10 are close to T16 to T20. Furthermore, this study displays that the bis-TTF-Ge with electron-acceptor substituents (NO₂ and NO) shows a red-shift wavelength absorption compared to the Ti with donor electron substituents. In general, from this calculation, we can conclude that the electronic transition characters and the absorption wavelength of Ti compounds can be tuned through the introduction of the electron donors or electron acceptor substituents at different positions.

Nonlinear optical properties

In current years, quantum chemical calculations have become a widely accepted method for predicting new NLO materials.^20,21 For the NLO calculation we carried out a test on T36 with the 6-311++G and 6-311G(d,p) basis set, but did not find significant differences (see Fig. S3, ESI†). This is no surprise because of the quasi linear shape of the molecules and the 6-311G(d,p) basis is a good choice for the title compounds. On the other hand, we calculated the dynamic hyperpolarizabilities at the λ value of 1064 nm (ω = 0.04282 a.u.), which is sufficiently apart from the observed lowest-energy absorption of the title compounds (the λ_Max values are in the range 250–270 nm). It is known that it is difficult to compare the calculated dynamic first hyperpolarizabilities to the experimental data measured under resonance conditions.⁸³ However the tendency is very similar between experimental and theoretical values,⁷⁷ and one has hyperpolarizabilities (experimental) > hyperpolarizabilities (dynamic) > hyperpolarizabilities (static) and our calculation shows the same tendency: hyperpolarizabilities (dynamic) > hyperpolarizabilities (static).

The second-order nonlinear responses calculated in the static (λ = ∞) and dynamic (λ = 1064 nm) regimes for the 37 derivatives are summarized in Table 2. The reported quantities include the hyper-Rayleigh scattering (β_HRS) hyperpolarizabilities and the associated depolarization ratio (DR).

Table 2 Static (λ = ∞) and dynamic (λ = 1064 nm) HRS first hyperpolarizability (β_HRS, a.u.) and depolarization ratio (DR), as well as calculated dipole moment (D, Debye), calculated at the CAM-B3LYP/6-311g(d,p) level in Ti (i = 0–36) compounds

	Ti	μ	DR^λ=∞	β ^λ=∞HRS	DR^λ=1064	β ^λ=1064HRS
	T0	2.048	1.503	75	1.407	137
a	T1	0.797	3.817	440	4.629	1266
b	T2	0.955	5.247	782	7.147	3397
c	T3	0.014	1.862	314	1.720	1015
d	T4	0.702	3.505	464	5.108	2469
e	T5	1.005	2.34	317	1.541	1140
a	T6	4.492	3.679	263	4.278	501
b	T7	7.508	5.729	416	6.576	742
c	T8	1.436	2.053	152	1.812	246
d	T9	4.290	3.907	231	3.067	383
e	T10	5.674	1.781	173	1.407	390
a	T11	4.271	4.731	644	5.215	1566
b	T12	6.626	5.387	627	7.022	1374
c	T13	1.070	2.316	371	2.322	858
d	T14	3.643	1.915	324	1.859	807
e	T15	3.440	2.739	234	1.845	629
a	T16	3.294	2.693	180	3.256	360
b	T17	5.625	3.913	265	5.131	576
c	T18	1.829	1.688	116	1.676	206
d	T19	2.623	2.633	150	3.137	331
e	T20	1.501	1.633	104	1.326	271
a	T21	4.106	3.92	713	4.27	2859
b	T22	6.091	4.499	800	1.145	9638
c	T23	2.939	2.378	709	1.902	2726
d	T24	2.583	2.527	829	1.754	12 600
e	T25	2.836	1.952	761	0.749	19 810
a	T26	4.838	2.447	103	1.942	185
b	T27	3.384	4.077	327	3.741	602
c	T28	1.694	2.793	118	1.914	194
d	T29	2.717	4.596	295	4.054	581
e	T30	4.024	1.538	115	1.422	183
a	T31	4.919	2.813	110	2.158	189
b	T32	2.567	4.724	192	4.061	369
c	T33	0.912	4.829	110	2.265	173
d	T34	2.014	6.843	185	5.122	364
e	T35	1.388	3.059	111	2.779	158
e	T36	4.024	1.538	116	1.422	183

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For bis-TTF-Ge T26, T28, and T30 their β^λ=∞_HRS values are close to the value of T31, T33 and T35 (∼111 a.u.) which indicates that when the NH₂ (at a, c and e positions) is replaced by the NMe₂ group the effect on the β_HRS value is not significant. On the other hand, the β^λ=∞_HRS value calculated for T26, T28, T30–T31, T33 and T35 are relatively close to the value of T0 (75 a.u.). We can observe that the dynamic regime has the same behavior as the static regime for NH₂ and NMe₂ donor groups. Furthermore, the hyperpolarizability β^λ_HRS (λ = ∞, 1064 nm) of T27 and T29 are three times larger than that of the T26, T28 and T30. For T32 and T34 the β^λ_HRS values are about twice that of T31, T33 and T35. We can observe that the introduction of donor substituents (NH₂ and NMe₂) at b and d positions can increase the hyperpolarizability of bis-TTF-Ge. For T1–T5 (acceptor NO unit) the β^λ_HRS (static and dynamic) of T2 is found to be about twice larger than that of T1, T3, T4, and T5.

For bis-TTF-Ge T11–T12, the β^λ_HRS values are larger than those of T13, T14 and T15, respectively. Comparing β^λ=1064_HRS values of T11–T12 and T0, it can be seen that the T11–T12 values are about 11 times larger than that of T0. For bis-TTF-Ge substituted by CN and CHO units, the β_HRS (static and dynamic) values are also larger in the substitution at b and a positions than for d, c and e. For T6–T10, T11–T15 and T16–T20 compounds, we observe that the β^λ=∞_HRS and β^λ=1064_HRS values of bis-TTF-Ge substituted by the acceptor COCN group are larger than that of bis-TTF-Ge substituted by CN and COH group at the same substituent position, respectively.

In static and dynamic regimes, the compounds T21–T25 exhibit larger hyperpolarizability values than the other bis-TTF-Ge compounds, which show that the introduction of the acceptor NO₂ group can effectively enhance β^λ_HRS values. This observation is in line with Gong et al.'s study of helicenes⁸⁴ and linear [3]spirobifluorenylene.⁸⁵ On the other hand, the β^λ=∞_HRS decreases slightly from T29 ≈ T27 to T25, T21 and T23, respectively, indicating that the substituent position (number) of NO₂ substitutions in bis-TTF-Ge have little effect on the β^λ=∞_HRS values. On the other hand, the β^λ=1064_HRS values decrease in the order T25 > T24 > T22 > T21 ≈ T23, indicating that the β^λ=1064_HRS increases with the number of NO₂ groups in the bis-TTF-Ge compound (see Fig. 5). The β^λ=1064_HRS value of T25 is about 7 times larger than that of T23. Furthermore, the β^λ=∞_HRS value calculated for T0 (and T36) is about 11 times smaller than that of T21–T25 and β^λ=1064_HRS of T25, T24, T22 and T21 is 145, 92, 70 and 20 times larger than that of T0, respectively.

Fig. 5 Static and dynamic hyperpolarizability values for T21–T25 calculated at the CAM-B3LYP/6-311g(d,p) level.

From this study, we observed that the substituent position b has a stronger effect on the enhancement the β^λ_HRS value than the a, c, d and e substituent positions. Comparing T0 and the bis-TTF-Ge substituent position b, it is found that the β^λ=∞_HRS values of T2, T12, T7, T17, T27 and T32 is about 10, 8, 6, 4, 4 and 3 times larger than that of T0, respectively, and the β^λ=1064_HRS value of these compounds is about 25, 10, 5, 4, 4 and 3 times larger than that of T0, respectively. We conclude that the highest hyperpolarizability value can be obtained by the introduction NO₂, NO or COCN acceptor groups at the b position for bis-TTF-Ge.

The experimental study of Bao et al.,⁸⁶ shows that the different numbers (mono-, di-, tri-, and tetra-) of ester substituents as well as their position (trans and cis) have a significant influence on the NLO properties of tetraphenylporphyrins. They indicate that the compounds with four ester groups present a small value of hyperpolarizability. In the static regime, the same results are observed for title compounds, excepting the bis-TTF-Ge substituted with NO₂ group (see Fig. 5 and Table 2).

Generally, in the dynamic regime, the hyperpolarizability is 2–5 times larger than that in the static regime, excepting T22, T24 and T25, where β^λ=1064_HRS is about 26, 15 and 12 times larger than the β^λ=∞_HRS, respectively. The static hyperpolarizability of T1 to T35 is about 2–11 times larger than that of T0.

On the other hand, the TD-DFT results of T22, T24 and T25 show that the λ_0→1 (between 524 and 554 nm) corresponds to the two-photon resonance value (1048–1108 nm). This value is very close to near-resonant wavelength (1064 nm) causing resonance. The two-photon resonance value of T25 is 1048 nm and that of T22 and T24 is 1108 and 1096 nm, respectively. The resonance value of T25 is the closest to the near-resonant wavelength of 1064 nm and that of T22 and T24 is the most shifted from the near-resonant wavelength. This is the reason why the value of β^λ=1064_HRS of T25 is larger than the value of β^λ=1064_HRS of T24 and T22, respectively. Accordingly, the wavelength resonance is one of the reasons why the value of β^λ=1064_HRS is much larger than that of β^λ=∞_HRS.

On the other hand, the urea molecule is one of the prototypical compounds used in the study of the second-order NLO response of molecules. Therefore it is used frequently as a threshold value for comparative purposes.^87,88 The HRS hyperpolarizability of urea was calculated at the same level of theory. From our results we observe that the all bis-TTF-Ge derivative showed values for the static and dynamic HRS hyperpolarizability higher than the T0 (β^λ=∞_HRS = 75 a.u. and β^λ=1064_HRS = 137 a.u.) and urea (β^λ=∞_HRS = 38 a.u. and β^λ=1064_HRS = 40 a.u.).

The depolarization ratio (DR) is an essential parameter for displaying the contribution of the hyper-Rayleigh scattering response. As revealed by the static and dynamic DR values collected in Table 2, the NLO responses of T1, T2, T4, T6, T7, T9, T11, T12, T17, T21, T22, T27, T29, T32, T33 and T34 compounds display a dominant dipolar character, with the exception of T9, T33 compounds (λ = 1064 nm) dominated by their octupolar component. On the other hand, in our studied bis-TTF-Ge T3, T5, T8, T10, T13, T15, T18, T20, T23, T24, T25, T26, T28, T30, T31, T35 and T36 the octupolar component is dominant. From this study we observed that the (static and dynamic) DR values are more strongly sensitive to the substitution positions than to the nature of the substituent (donor and acceptor). This reveals that the a, b and d substitution positions lead to a dominant dipolar nature of the NLO response; the b substitution positions show a larger DR value in the static and dynamic regimes. On the other hand, the title compounds with c and e substitution positions are octupolar molecules. For the e substitution positions, the DR value (λ = ∞, 1064 nm), close to 1.5 (T10, T18, T20, T30, T36 and T0) characterizes typical octupolar systems. Furthermore, we observed that the DR value at λ = 1064 nm of T0, T10, T20, T22, T25, T30 and T36 is less than 1.5, indicating that those compounds are close to resonance.

On the other hand, we studied the correlation between the energy gaps (hardness) of the title compounds and their hyperpolarizability in the static regime. The results show that β^∞_HRS values are increased with the decrease of the bis-TTF-Ge energy gaps (the correlation factor is 0.832, see Fig. S4, ESI†). Taking T24 as an example, the energy gap of T24 is the smallest (1.819 eV) but its hyperpolarizability value is the largest (β^∞_HRS = 829 a.u.), which is in good agreement with the literature.^89,90

In order to understand the nonlinear optical origins of studied compounds, the excitation energy (ΔE_0→n) and wavelength (Δλ_0→n), oscillator strengths (f_0→n), transfer distance charges (d^CT), charge transfer (q^CT) and transition dipole moment (Δμ_0→n) calculated for the crucial singlet excited states are summarized in Table 3, with more details in Table S1 (ESI†), and the corresponding electron density difference maps (EDDMs) are shown in Fig. S2 (ESI†).

Table 3 Vertical transition energy (ΔE_0→n, eV) and wavelength (Δλ_0→n, nm), oscillator strengths (f_0→n, dimensionless), charge transfer (q^CT, |e|), charge transfer distance (d^CT, Å), and dipole moment variation (Δμ_0→n, D) associated with the S0 → Sn (S_0→n) transition, as calculated at the CAM-B3LYP/6-311g(d,p) in Ti compounds

Ti	S0→n	ΔE0→n	Δλ0→n	f 0→n	q ^CT	d ^CT	Δμ0→n
T0	S0→1	3.096	400	0.003	0.821	0.035	0.054
T1	S0→1	1.706	727	0.001	0.891	8.636	36.946
	S0→7	3.218	385	0.079	0.707	9.586	32.559
T2	S0→13	3.892	318	<0.001	0.999	16.977	81.427
	S0→16	4.303	307	0.126	0.618	6.649	19.741
T3	S0→1	1.896	654	0.001	0.888	11.586	49.439
	S0→13	3.999	310	0.162	0.508	2.906	7.095
T4	S0→17	3.921	316	<0.001	0.997	17.038	81.612
	S0→20	4.010	309	0.125	0.576	6.199	17.151
T5	S0→1	1.831	677	<0.001	0.805	6.489	25.050
	S0→5	2.725	455	0.046	0.794	1.452	5.526
T6	S0→1	3.070	404	0.003	0.872	6.729	28.067
	S0→7	4.003	307	0.167	0.631	7.18	20.478
T7	S0→1	3.051	406	0.002	0.871	6.634	27.747
	S0→7	4.028	308	0.163	0.623	5.961	17.829
T8	S0→1	3.132	396	0.004	0.792	1.963	7.467
	S0→7	4.074	304	0.429	0.513	0.320	0.784
T9	S0→5	3.421	362	0.042	0.781	4.721	17.702
	S0→12	4.304	288	0.178	0.593	3.380	9.545
T10	S0→1	3.086	402	0.005	0.747	6.418	23.035
	S0→13	4.305	288	0.204	0.594	4.507	12.859
T11	S0→13	4.238	293	0.141	0.601	4.082	11.783
T12	S0→20	4.200	295	0.205	0.708	7.483	25.392
T13	S0→17	4.309	288	0.764	0.575	1.699	4.684
T14	S0→9	3.790	327	0.100	0.752	4.598	16.609
T15	S0→8	3.528	351	0.041	0.912	6.937	30.399
T16	S0→1	3.082	402	0.003	0.838	6.540	26.862
	S0→7	4.020	308	0.221	0.610	3.628	10.635
T17	S0→1	3.065	404	0.003	0.869	6.778	28.212
	S0→7	4.032	307	0.173	0.650	8.709	27.195
T18	S0→1	3.119	398	0.003	0.800	1.281	4.946
	S0→7	4.018	309	0.295	0.558	0.723	1.945
T19	S0→1	3.117	398	0.004	0.831	5.726	22.867
	S0→8	4.091	303	0.172	0.669	5.704	18.314
T20	S0→1	3.125	397	0.004	0.786	3.243	4.816
	S0→7	4.074	304	0.386	0.581	0.315	0.879
T21	S0→1	2.854	434	0.083	0.831	5.372	21.438
	S0→14	4.207	295	<0.001	0.999	15.939	76.256
T22	S0→6	3.421	362	<0.001	0.969	15.746	73.084
	S0→11	3.971	312	0.113	0.883	6.229	26.408
T23	S0→1	2.867	432	0.123	0.829	3.650	14.512
T24	S0→2	2.869	432	0.034	0.828	5.318	22.476
	S0→8	3.603	344	<0.001	0.999	15.685	75.300
T25	S0→2	2.366	524	0.036	0.383	7.626	30.538
	S0→9	3.811	325	<0.001	0.916	13.204	58.126
T26	S0→1	3.083	402	0.003	0.875	6.448	26.428
	S0→7	4.030	308	0.332	0.536	4.420	11.286
T27	S0→1	3.020	411	0.002	0.877	6.741	28.401
	S0→7	3.993	311	0.135	0.744	8.137	29.066
T28	S0→1	3.050	406	0.002	0.852	6.211	25.277
T29	S0→1	3.026	410	0.002	0.874	6.746	28.277
	S0→7	4.002	309	0.151	0.738	8.838	31.299
T30	S0→1	3.039	408	0.002	0.873	6.537	27.177
	S0→7	4.016	309	0.146	0.734	6.854	24.012
T31	S0→1	3.081	402	0.003	0.870	6.972	29.120
	S0→7	4.023	308	0.319	0.593	7.924	22.565
T32	S0→1	3.027	410	0.002	0.893	7.276	31.218
	S0→7	3.998	310	0.201	0.749	9.054	32.562
T33	S0→1	3.089	401	0.003	0.843	4.628	18.658
	S0→7	4.021	308	0.420	0.522	3.447	8.593
T34	S0→1	3.026	410	0.003	0.896	7.178	30.898
	S0→7	3.981	311	0.219	0.689	8.247	27.285
T35	S0→1	3.055	406	0.003	0.869	5.083	21.208
	S0→7	3.989	311	0.315	0.568	2.059	5.619
T36	S0→1	3.083	401	0.003	0.843	4.578	18.492

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The charge transfer involves both n → π* and π → π* transitions, the main factor being the conjugation of the p electrons through the delocalization domain.

From the EDDM of bis-TTF-Ge substituted with acceptor groups (T1–T5 (R: NO), T11–T15 (R: COCN) and T21–T25 (R : NO₂)), it can be observed that there is obvious CT from the TTF fragment to the substituted groups (R) at the other TTF fragment. These transitions are dominated by an electronic excitation from the HOMO to the LUMO and have high charge transfer parameters (q^CT, d^CT and Δμ_0→n) character which is the necessary condition to obtain a high NLO response. On the other hand, the CT characters of T6–T10, T16–T20 and T26–T36 are from the TTF fragment (rings) to the 4S-Ge unit and these transitions are also associated with a HOMO → LUMO excitation with fewer charge transfer parameters than the other compounds (see Table 3, Fig. S2 and Table S1, ESI†). For instance, the dipole moment variation of T21 (76.26 D) is due to a transferred excitation charge q^CT = 0.999 |e| and a larger associated CT distance (d^CT = 15.94 Å, S_r = 0) than that of T31 (q^CT = 0.87 |e|, d^CT = 6.97 Å; S_r = 0.367 and Δμ_0→1 = 29.12 D). The relatively small d^CT and Δμ_0→n values are obtained for bis-TTF-Ge with the substitution donor or acceptor at position c. This can be attributed to the CT from the TTF to the substituted group on the same fragment; see for example T23 in Fig. 6. In contrast, T0 undergoes a moderate CT excitation (q^CT = 0.821 |e|) with a weak CT distance and small dipole moment variation (d^CT = 0.035 Å and Δμ_0→1 = 0.054 D) (see Fig. 6). Furthermore, the title compounds show a nice correlation between HRS hyperpolarizability and the largest dipole moment variation (Fig. 7). Also, there is a good correlation between β^λ=∞_HRS and β^λ=1064_HRS, except for T2, T4 and T5 (Fig. 8).

Fig. 6 Electron density difference maps of T0, T2, T21, T22, T31 and T36 compounds from the ground state to the crucial excited state S0 → Sn (S1, S13, S1, S1, S1 and S14, respectively), plotted using 0.008 a.u. isovalues.

Fig. 7 Correlation between HRS hyperpolarizability (β^λ=∞_HRS) and dipole moment variation (Δμ_0→i), (T3, T4, T11, T13 and T23 are exceptions).

Fig. 8 Correlation between static and dynamic hyperpolarizability, T2, T4 and T5 are exceptions.

Two-level model analyses for hyperpolarizability

The sum-over-states (SOS) method is one of the most commonly used methods for theoretical estimation of hyperpolarizability.^91–96 The full form of the SOS formula of component ABC of hyperpolarizability is defined as
where ω is the energy of external fields, and ω = 0 corresponds to the static electric field; Δ_i stands for excitation energy of state i with respect to the ground state (0). P̂ is the permutation operator that acts on the xyz indices of the β-components. μ^x_ij is the x component of the transition dipole moment between state i and state j.

Molecular NLO responses of material is intimately related to the electronic absorption properties and through the two-level model established by Oudar and Chemla the static hyperpolarizabilities β can be expressed as^97,98

where ΔE, f and Δμ are the excitation energy, oscillator strength and difference of dipole moment between the ground state and the excited state, respectively. According to this relation, it is observed that the static hyperpolarizability (β₀) is inversely proportional to ΔE³, demonstrating that lower excited energy (ΔE), greater dipole moment (Δμ) and oscillator strength (f) will lead to the largest β₀ of compounds.

Furthermore, it is well known that the molecular NLO properties calculated using the SOS method are closely related to the number of excited states;⁹⁹ therefore in our study we plotted the relationship between the first hyperpolarizability (β^SOS) and 100 excited states (Fig. S5, ESI†). Generally, these graphs demonstrate that 100 excited states are sufficient for the convergence of the β^SOS value. As shown in Table S2 and Fig. S5 (ESI†) the introduction of the substituent group at the b position can increase the hyperpolarizability values more than at the other positions, and the NO₂, NO and COCN acceptor groups, lead to the largest values. This prediction agrees well with hyperpolarizability calculated by CAM-B3LYP/6-311g(d,p).

In addition, the two-level analysis discloses that the excited state S7 makes a dominant contribution to the hyperpolarizability value of compounds T6, T7, T8, T16–T18, T20 and T26–T35; the crucial excited states S12, S13, S12, S13, S20 and S17 with largest hyperpolarizability in compounds T9, T10, T19, T11, T12, and T13 respectively; these transitions can be assigned to the CT from TTF fragment (rings) to the 4S-Ge unit (see Tables S1 and S2, ESI†). For systems T1–T5 the dominant contribution to hyperpolarizability values can be assigned to S7, S18, S23, S22 and S5, respectively, and are mainly made up of CT from TTF fragment to the NO groups at the other TTF fragment. For compounds T21 to T25 the excited states S1, S11, S1, S2 and S2, respectively, with CT from the TTF fragment to NO₂ groups make large contributions to the hyperpolarizability value. For compounds, T14 to T15 the crucial excited state is S9 and S8 respectively, with CT from the TTF fragment to COCN groups have (see Tables S1, S2 and Fig. S2, ESI†). On the other hand, SOS calculations show that the local excitation transition at ∼266 nm of title compounds (noted in italic in Table S2, ESI†) exhibit a small hyperpolarizability value and a large dipole moment variation. These results agree well with the character of the electronic transition that we have noted before (in the section of nonlinear optical properties and Table 3).

As can be seen from Table S2 and Fig. 9, as a whole, the hyperpolarizability β^SOS_HRS and ratio DR^SOS values (calculated DR^SOS ratio and β^SOS_HRS based on the hyperpolarizability tensor derived by the SOS formula) qualitatively reproduce the general trend of the HRS hyperpolarizabilities and DR character (Table 2) with a few exceptions resulting from the limitation of the SOS method. On the other hand, it is worth stressing that the SOS method obviously overestimates the hyperpolarizability and DR value of Ti compounds (Fig. 9(I) and (II)).

Fig. 9 (I) Calculated static first-hyperpolarizabilities of Ti compounds by using the SOS method and at the CAM-B3LYP/6-311g(d,p) level; (II) depolarization ratios DR of Ti compounds calculated via the SOS method and at the CAM-B3LYP/6-311g(d,p) level.

Furthermore, the frequency dispersion factor (FDF) between static and dynamic at a definite wavelength λ = 1064 nm depicted by the ratio β¹⁰⁶⁴/β^∞, namely FDF_HRS and FDF_HRS,SOS, are calculated from the results in the Table 2 and Table S2 (ESI†), respectively and are presented in Fig. 10. From this Fig. 10, as expected, both FDF_HRS and FDF_HRS,SOS follow the same trend and in addition, the FDF_HRS values are quite close to the FDF_HRS,SOS values, with the exception of T2, T4, T12, T22 and T25. On the other hand, we can observe that the dispersion of optical nonlinearity of T24, T25 and T22 have maximum frequency dispersion factor at λ = 1064.8 nm, confirming their great nonlinear optical properties, in contrast to the other compounds (dispersion factor from ∼1 to 5.5). It is important to highlight that the SOS method consistently produces large hyperpolarizability and small FDF values of compound bis-TTF-Ge. Indeed, all the compounds containing NO₂ substituent(s) (and, to a smaller extent, containing NO) are much more hyperpolarizable at 1064 nm frequency than in static regime, whereas with other substituents, the difference is not significant. This may be related to the NO₂ lone pairs, which may be more mobile through the molecular systems.

Fig. 10 Variation of the frequency dispersion factor of bis-TTF-Ge derivatives calculated by SOS method and at the CAM-B3LYP/6-311g(d,p) level.

To summarize, the large HRS hyperpolarizabilities origin of bis-TTF-Ge substituted with acceptor groups come from the CT from the TTF fragment towards the acceptor group located on the second TTF unit. In the meantime, the values of the CT from the TTF to the acceptor group located on the same TTF fragment are weak, whereas the NLO origin of bis-TTF-Ge substituted with donor originates a CT from TTF fragment to the 4S-Ge unit.

Conclusions

The structural properties, reactivity parameters, and linear and nonlinear optical properties of 37 bis-TTF-Ge derivatives differing by a donor and acceptor substitution on the TTF fragment have been investigated by using DFT and TD-DFT calculations. These calculations were performed at the CAM-B3LYP/6-311g(d,p) level and using the sum-over-states (SOS) approach in both static and dynamic regimes.

Our results indicate that the bis-TTF-Ge hardness can effectively be reduced when substituent positions are substituted with an acceptor group (NO, NO₂, and COCN). Furthermore, the b substituent position leads to a smaller hardness than the d, e, a and c substituent positions. The electronic excitation properties of the title compounds can be described as a mixed transition of intra-TTF charge transfer (ICT) and charge transfer (CT) from TTF to the 4S-Ge unit, TTF to the acceptor group (NO₂, NO and COCN) and TTF to TTF. For example, the electronic transition at ∼266 nm is a local excitation with a relatively small d^ct and large S_r indexes. The transition HOMO → LUMO of bis-TTF-Ge with the acceptor substituent (R = NO, COCN and NO₂) at positions a, b and d is a non-local excitation with large dipole moment variation and a small S_r index (S_r ∼ 0). In the case of bis-TTF-Ge with a donor substituent (R: NH₂ and NMe₂) at positions a, b and d, the transition HOMO → LUMO from the TTF fragment to 4S-Ge shows moderate values of the transition dipole moment and S_r indexes (S_r = ∼0.3) when we compare it with the results of an acceptor substituent.

All bis-TTF-Ge derivatives showed values for the static and dynamic HRS hyperpolarizability higher than T0 and urea.

The quantum chemical calculations indicate that the position and the nature (donor/acceptor) of the substituent have strong effects on the NLO responses. The introduction of a substituent group at the b position induces a greater increase of the first hyperpolarizability and the acceptor NO₂, NO and COCN groups show a large value of HRS hyperpolarizability which indicate that the acceptor group has a stronger effect on the second order NLO than the donor group. On the other hand, the compounds with c and e substitution positions are octupolar molecules and a, b and d substitution positions lead to a dominant dipolar nature of the NLO response.

The large first hyperpolarizability origin comes from the CT from the TTF fragment towards the acceptor group located on the second TTF unit. On the other hand, the β^λ=∞_HRS values of compounds T21–T25 are high and relatively close, indicating that the introduction of the acceptor NO₂ group at any substituent position can effectively enhance the first hyperpolarizability. Interestingly, the β^λ=1064_HRS of bis-TTF-Ge substituted with the NO₂ group increases with the number of NO₂ in the TTF fragment.

Finally, it is important to emphasize that the intrinsic asymmetric geometry of the bis-TTF-Ge can tune the second order NLO response through the nature, position and number of the substituent group at the TTF fragment, as well as by the S_r index.

On the other hand, our study suggests that these compounds can be used as new materials for developing nonlinear second order photonic devices. Furthermore, the bis-TTF-Ge compounds substituted with the an acceptor group may become excellent candidates for second order NLO materials, which will also promote the evolution of high technology applications.

Author contributions

All the authors discussed the results. Dalila Kamli: calculations achievements, data interpretation, draft writing. Douniazed Hannachi: project initiation, conceptualization, calculations supervision, data interpretation, draft writing. Djamila Samsar: calculations, data interpretation, draft writing. Henry Chermette: calculations, data interpretation, draft writing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors gratefully acknowledge the GENCI/CINES for HPC resources/computer time (Project cpt2130), and the PSMN of the ENS-Lyon for computing resources.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2nj03671a

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