Introduction

In the designing of electro-optical materials carbazole core plays a key role acting as the donor part of D- π-A system with BODIPY [1], coumarin [2], styryl [3], quinoxaline [4] and cyanine [5] as acceptors. The carbazole moiety can be easily functionalized at 3-, 6- or 9- positions and covalently linked to other molecular moieties [6]. Substituted carbazoles are known to possess desirable photophysical properties [7, 8] as the requirement for functional applications.

The quinoxaline ring at 3 and 6 positions of carbazole acts as an acceptor through covalent bond or π bridge which leads to D-π-A system with fluorescent properties [9]. The molecules having D- π-A bridge are good candidates for electronics as well as biological applications such as dye sensitizer solar cell (DSSC) with light harvesting properties [10], organic light emitting diode OLED [11], lasers [12], optoelectronics [13], semiconductors [14], sensors [15–18] and bio-imaging [19, 20]. Electron accepting quinoxaline moieties have been exploited for the construction of electron transporting materials suitable for OLED fabrication [21–23]. Exceptionally, carbazole and oxadiazoles, quinoxaline or dicyanovinyl conjugates have been demonstrated to function as dual transport materials with promising emission characteristics [24, 25]. Such small arrangement of molecules, respond to photoexcitation with an intramolecular charge transfer from the donor to the acceptor moiety through π-conjugation [26].

A simple experimental method used to determine optical second order polarizability of the molecules on the basis of second harmonic generation (SHG) was developed by using a two-level quantum mechanical model [27–30]. We have selected this method which is based on solvatochromism, and solvent dependence of the UV-visible absorption and emission spectrum of the synthesized quinoxaline derivatives [28, 31, 32]. The solvatochromic method for determination of first order hyperpolarizability β ijk or β xxx (β CT) was successfully applied first by Paley et al. [27].

The geometry of synthesized compound was optimized with density functional theory (DFT) [33]. The time dependent density functional theory (TD-DFT) computation has been utilized to predict photophysical properties and polarizability values [34]. The DFT and solvatochromism based on conventional correlation between the NLO properties and their parameters like the linear polarizability (α), and first (β 0 ) and second (γ) hyperpolarizabilities of π-conjugated system.

In this paper we are reporting synthesis of 9-ethyl-3,6-di(quinoxalin-2-yl)-9H–carbazole derivatives with orderly change in substituents on quinoxaline ring. The geometry of all the carbazole based quinoxalines were optimized with DFT using B3LYP method and 6-31G(d) basis set. TD-DFT computation has been utilized to predict photophysical properties and nonlinear optical properties of the synthesized quinoxaline and the theoretical values are correlated with experimental values.

Experimental Section

Materials and Equipment

All the reagents and solvents were purchased from the S. D. Fine Chemicals Pvt. Ltd. and used without purification. All the solvents used were of spectroscopic grade. Melting points were recorded by open capillary on Sunder Industrial Product and are uncorrected. UV-Visible absorption measurements were carried out using a Perkin Elmer spectrophotometer with 1 cm quartz cells. The excitation wavelengths were taken as the absorption maxima (λmax) of the compounds. The scan range was 250 to 650 nm. Fluorescence emission spectra were recorded on Cary Eclipse fluorescence spectrophotometer (Varian, Australia) using 1 cm quartz cells. 1H NMR spectra were recorded on VNMR 500-MHz instrument using TMS as an internal standard in CDCl3 and DMSO as a solvent.

Computational Methods

The ground state (So) geometry of the 6a-6c in their C1 symmetry were optimized using the tight criteria in vacuum as well as in different solvents using DFT [35]. The vibrational frequencies at the optimized structures were computed using the B3LYP/6-31G(d) method to verify that the optimized structures correspond to local minima on the energy surface [36–38]. The vertical excitation energies at the ground-state equilibrium geometries were calculated with TD-DFT. All the computations were carried out in vacuum phase and also in solvent of different polarities using the Polarizable Continuum Model (PCM) [39, 40]. All the electronic structure computations were carried out using the Gaussian 09 program [33].

Relative Quantum Yield Calculations

Quantum yields (ϕ) of compounds 6a–6c in various solvents were evaluated. Relative quantum yields were measured using quinine sulfate in 0.1 N H2SO4 as standard (ϕ = 0.546). Quantum yields were calculated using the comparative method [41, 42]. Absorption and emission characteristics of the standard (in 0.1 N H2SO4) and the compounds in various solvents were measured at different concentrations (1, 2, 3, 4, and 5 μM). Emission intensity values were plotted against absorbance values and linear plots were obtained. Gradients were calculated for the standard and the compounds in each solvent keeping slit width constant at 5. Relative quantum yields of the synthesized compounds in various solvents were calculated by using the Eq. 1 [41, 42].

$$ {\upphi}_x={\upphi}_{st}\ X\ \frac{Grad_x}{Grad_{st}}\ X\ \frac{\eta_x}{\eta_{st}} $$
(1)

where,

\( {\upphi}_x \) :

Quantum yield of compound

\( {\upphi}_{st} \) :

Quantum yield of standard sample

\( {Grad}_x \) :

Gradient of compound

\( {Grad}_{st} \) :

Gradient of standard sample

\( {\eta}_x \) :

Refractive index of solvent used for Compound

\( {\eta}_{st} \) :

Refractive index of solvent used for standard sample

Quantum yields of all the dyes in various solvents are tabulated in Tables 1 , S1 and S2 .

Table 1 Effect of solvent polarity on photophysical properties of 6a
Full size table

Experimental

Preparation of 9-ethyl-9H-carbazole 2

The compounds 5 and 7 were prepared by the reported method [12].

Preparation of 1,1′-(9-ethyl-9H-carbazole-3,6-diyl)bis(2-bromoethanone) 4

The compounds 4 were prepared by the reported method [43].

General Procedure for Synthesis of Carbazole Substituted Quinoxaline 6a-6c

A mixture of 1,1′-(9-ethyl-9H-carbazole-3,6-diyl)bis(2-bromoethanone) 4 (0.5 g, 0.0014 mol), substituted ortho-phenylenediamine 5a (0.308 g, 0.0028 mol) and potassium carbonate (0.579 g, 0.0042 mol) in DMF (15 ml) was stirred at 90 °C for 3–4 h. After completion of the reaction, the mass was poured into the 50 mL ice cold water. The resulting solids 6a-6c were filtered; washed with water and purified by column chromatography on 100–200 mesh silica with chloroform/methanol as eluent. The synthesized compounds are well characterized by FT-IR, 1H NMR, 13C NMR and Mass ( Supporting Information ).

  1. 1.

    9-Ethyl-3,6-di(quinoxalin-2-yl)-9H-carbazole 6a

Color: Yellow solid, Yield: 72%, M.P.: 222-224 °C.

FT-IR (cm−1): 1593 (-C = N-), 1541 (-C = C-), 1486 (-Ar).

1H NMR (500 MHz, DMSO-d 6): 1.41 (t, 3H), 4.60 (q, 2H), 7.81 (td, 2H), 7.88 (m, 4H), 8.12 (d, 2H, J = 7.1 Hz), 8.17 (d, 2H, J = 7.3 Hz), 8.56 (d, 2H, J = 6.9 Hz), 9.40 (s, 2H), 9.79 (s, 2H).

13C NMR (125 MHz, DMSO-d 6): 14.37, 38.00, 110.81, 120.90, 123.62, 126.26, 128.05, 129.34, 131.00, 141.86, 142.10, 144.41, 152.18.

Mass: 455 (M + 1).

  1. 2.

    9-Ethyl-3-(6-methylquinoxalin-2-yl)-6-(7-methylquinoxalin-2-yl)-9H carbazole 6b:

Color: Yellow solid. Yield: 56%.

M.P.: 202-204 °C.

FT-IR (cm−1): 1600 (-C = N-), 1540 (-C = C-), 1487 (-Ar).

1H NMR (500 MHz, CDCl3): 1.51 (t, 3H), 2.62 (s, 6H), 4.44 (q, 2H), 7.56 (m, 4H), 7.96 (s, 1H), 8.00 (d, 2H, J = 8.6 Hz), 8.07 (d, 1H, J = 8.3 Hz), 8.38 (d, 2H, J = 7.9 Hz), 9.05 (s, 2H), 9.42 (s, 2H).

13C NMR (125 MHz, CDCl3): 13.91, 21.87, 38.08, 109.37, 120.26, 125.66, 127.99, 128.52, 131.23, 132.45, 139.41, 139.72, 140.65, 140.89, 141.27, 141.64, 141.70, 142.51, 142.59, 143.39, 151.57, 152.24.

Mass: 480 (M + 1).

  1. 3.

    3-(6-Chloroquinoxalin-2-yl)-6-(7-chloroquinoxalin-2-yl)-9-ethyl-9H-carbazole 6c :

Color: Greenish yellow solid, Yield: 52%, M.P.: 218–220 °C.

FT-IR: 1598 (-C = N-), 1539 (-C = C-), 1483 (-Ar), 829 (-C-Cl).

1H NMR (500 MHz, CDCl3): 1.56 (t, 3H), 4.51 (q, 2H), 7.63 (d, 2H, J = 8.5 Hz), 7.68 (d, 1H, J = 7.1 Hz), 7.71 (d, 1H, J = 6.8 Hz), 8.14 (d, 2H J = 2 Hz), 8.16 (d, 2H, J = 9.4 Hz), 8.42 (t, 2H), 9.10 (s. 2H), 9.51 (d, 2H, J = 6.6 Hz).

13C NMR (125 MHz, CDCl3): 13.94, 38.17, 109.60, 120.47, 123.95, 125.95, 126.048, 128.02, 128.21, 130.02, 130.25, 130.49, 131.36, 136.16, 139.60, 142.08, 142.75, 143.42, 144.20, 152.93.

Mass: 521 (M + 1).

Results and Discussions

Synthesis

Compounds 6a-6c were synthesized by using carbazole (1) as starting material (Scheme 1). The first step involved N-substitution of carbazole 1 by the diethylsulphate resulted into intermediate 2. Friedel-Crafts reaction was carried out on intermediate 2 at the 3- and 6- positions by using bromoacetyl bromide to give intermediate 4. This intermediate 4 was treated with different substituted ortho-phenylenediamine derivatives in presence of potassium carbonate in DMF at room temperature to yield 6a-6c. All the synthesized compounds were purified by column chromatography on silica with chloroform/methanol as eluent.

Scheme 1
scheme 1

Synthesis of carbazole based quinoxaline derivatives

Full size image

Absorption and Emission Spectra in Different Solutions

Absorption and emission spectra of compounds 6a-6c were recorded in varying polarity solvents (Figs. S1-S3 ) and the relevant parameters were compiled in Tables 1 , S1 and S2 . Compounds 6a-6c showed a broad and relatively intense absorption band around 390–410 nm attributable to the electronic transition originating from the π-molecular orbitals. But in acetonitrile they showed hypsochromic shift of lower degree around the 360–370 nm. The red-shifted absorption was observed for the arylamine derivatives (6b and 6c) with expressive involvement of conjugative delocalization in the ring from donor (carbazole) to acceptor (quinoxaline) [44]. Different substitution at 6th position of aryl ring of the arylamine showed effect on absorption maxima. Hydrogen atom substitution showed hypsochromic shift as compared to chloro and methyl substitution on 6th positions. This may be due to good +I (inductive effect) of methyl group [45] and +M (mesomeric effect) of chloro group [46] as compared to hydrogen. The introduction of methyl and chloro groups as electron-donating substituents increases the electron density of quinoxaline ring. On comparing dyes 6b and 6c there may be reduction of accepting ability of quinoxaline core, which cause blue shift in absorption for methyl (6b) as compared to chloro-substituted quinoxalines (6c).

All the dyes studied in this work exhibited a slight red shift in emission maxima from non-polar to polar solvents. This result indicates that compounds exhibited positive solvatochromism, leading to gradual increase in the Stokes shift on increasing the solvent polarity. This mainly originates from the difference in the dipole moments of the molecule in the ground state and the excited states, interactions such as dipole-dipole, hydrogen bonding and solvation. The dipole moment ratios from ground state to excited state μe/μg are calculated and tabulated (Table S3 ). The red-shifted emission observed for the arylamine derivatives (6b and 6c) expressed the involvement of conjugative delocalization in the ring. The effects of solvent polarity on the emission are shown in Figs. S1-S3 for the compounds 6a-6c.

The compounds 6a-6c exhibited broad emission bands with maxima at 6a 498 nm, 6b 488 nm and 6c 514 nm in DMSO, which can be indicative of the intramolecular charge-transfer (ICT) transition due to the dipolar interaction. All the compounds showed moderate quantum efficiencies in nonpolar solvents but in case of polar solvents, the quantum yield decreased which may due to the dipolar interaction between molecule and solvents.

Dipole Moment Changes of the 6a-6c on Photoexcitation

The ICT feature of the compounds 6a-6c can be evaluated by Lippert–Mataga plots [Eq. (1)] [38–40]. The positive solvatochromism indicates that excited states of molecules are more stable in polar solvents. This can happen due to the ICT. These common solvent effects on the molecules were described solvatochromism properties by Lippert-Mataga Eq. 2. Lippert-Mataga equation (Eq. 2) was used to estimate change in dipole moment on photoexcitation as a function of the solvent polarity.

$$ \begin{array}{l}\Delta \upnu =\frac{2\Delta f}{4{\pi \varepsilon}_0\hslash {ca}^3}{\left({\mu}_{e-}{\mu}_g\right)}^2+ b\hfill \\ {}\Delta f=\frac{\varepsilon -1}{2\varepsilon +1}-\frac{n^2-1}{2{n}^2+1}\hfill \end{array} $$
(2)

where,

∆ν :

νabs - νem stands for Stokes shift,

νabs and νem :

are absorption and emission (cm−1),

ℏ :

Planck’s constant,

c:

velocity of light in vacuum,

a:

Onsager cavity radius,

b:

constant,

∆f :

orientation polarizability,

μg :

ground-state dipole in the ground-state geometry,

μe :

excited-state dipole in the excited-state geometry,

ε 0 :

permittivity of the vacuum,

(μe-μg)2 :

proportional to the slope of the Lippert-Mataga plot.

The Lippert-Mataga plots of the Stokes shift of compounds 6a-6c against orientation polarizability showed very good regression (Fig. S4 ).

The polarity plots of the compounds 6a-6c show good regression factors with good charge transfer. In 6a regression factor was 0.74 and in 6b was 0.77 with good charge transfer. In 6c very good regression was observed (about 0.81 with good linearity). The dipole moment changes in compounds 6a-6c inferred that the ICT features in the molecules are significant. The compounds 6a-6c have μe/μg ratio calculated by various method like Bilot-Kawski, Bakhshiev and Liptay. The fact that the values are less than unity implies that the excited state is less polar (Table S3 ). These results are due to the electron withdrawing quinoxaline moiety on carbazole ring at 3rd and 6th position, which induce ICT.

Oscillator Strength and Transition Dipole Moment

Oscillator strength is dimensionless quantity that expresses the probability of absorption and emission properties in energy levels, which helps to understand charge transfer within the molecules. It was simply described by number of electron transition from ground to excited state. Oscillator strength (f) can be calculated using the following Eq. 3 [41].

$$ f=4.32\times {10}^{-9}\int \varepsilon \left(\nu \right) d\nu $$
(3)

where ε is the extinction coefficient (L mol−1 cm−1), and ν represents the wavenumber (cm−1). From this equation we have calculated oscillator strength for the synthesized carbazole based quinoxaline derivatives 6a-6c and tabulated in Table S4 .

By using the value of f, we have calculated transition dipole moment, which was the difference in electric charge distribution between a ground and excited state of the molecule. The transition dipole moment for absorption (μa) was the measurement of the probability of radiative transitions which have been calculated in Debye unit in different solvent environments using the Eq. 4 [47]. The transition dipole moment was increased with increase in the oscillator strength for all compounds 6a-6c

$$ {\mu}_a^2=\frac{f}{4.72\times {10}^{-7}\times \nu} $$
(4)

where,

μa :

is transition dipole moment (D),

f :

is oscillator strength,

ν :

is wavenumber (cm−1).

The carbazole-based quinoxaline derivatives 6a-6c have good transition dipole moment. Observed results show that the carbazole and quinoxaline moieties have good charge transfer within the small system. We obtained transition dipole moment up to 6 D for 6a-6c molecules from the relationship between the Stokes shifts (cm−1) and the solvation parameter tabulated in Table S4 .

DFT Calculations

To investigate the structure-electronic property relationship in the carbazole based quinoxaline, we have performed DFT calculations in Gaussian. We optimized the molecular structure of compounds 6a-6c in maximum solvent using B3LYP method and 6-31 g(d) as basic set. The lowest energy transitions resulting from the theoretical study along with their energy, oscillator strengths, absorption emission maxima, and the compositions in terms of molecular orbital contributions.

Optimized Geometries of 6a-6c

Ground state geometries of the carbazole based quinoxaline derivatives were optimized at B3LYP/6-31G(d) basic set. A small twisting was observed between C15-C14-C44-C58 (6a: 20.3, 6b: 20.18 and 6c: 18.25) (Fig. 1 ) in toluene. From the optimized geometries, it is clear that the slight twisting of the donor carbazole moiety from the quinoxaline ring by an angle 20o in all the derivatives. The distribution of HOMO and LUMO are well separated within the molecule 6a-6c and a significant overlap is present.

Fig. 1
figure 1

Dihedral angles and bond angles in 6a-6c

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Electronic Vertical Excitation Spectra (TD-DFT)

The absorption band at lower energy with higher oscillator strength is due to ICT and is characteristic of donor-π-acceptor molecules. These ICT bands for all the dyes mainly occurred due to the electronic transition from HOMO to LUMO. The compound 6a shows blue shifted absorption in acetonitrile (362 nm) and red shifted absorption in DMSO (394 nm). The vertical excitation of 6a was computed and it shows blue shift absorption in dioxane (404 nm) and slightly red shift in DMSO (413 nm). Similar solvatochromic results were obtained for compounds 6b and 6c. The trend observed in vertical excitations of carbazole based quinoxaline compounds were very similar to the absorption spectra (Table 1 and S1, S2 ).

Frontier Molecular Orbitals

The frontier molecular orbitals were studied to understand the electronic transition and charge delocalization within these π-conjugated systems The energy band gap in 6a 2.29 eV, 6b 2.31 eV and 6c 2.15 eV in toluene.

The electronic distributions in the HOMO and LUMO for the all compounds (6a-6c) are presented in the (Fig. S5-S7 ) with oscillator strength and band gap (eV) in toluene. The HOMO diagram of 6a and 6b shows that the electron density is delocalized over the carbazole ring, with maximum components arising from the carbazole nitrogen from the π conjugation to the end of quinoxaline ring. In the LUMO, maximum electron density localized on quinoxaline ring (Fig. S5-S7 ). In case of 6c, HOMO has maximum electron density localized at chlorine on the quinoxaline ring. The LUMO showed maximum electron density located on the quinoxaline ring and carbazole ring is totally unaffected by electron delocalization (Fig. S7 ). The observations indicate that quinoxaline core enhances the electron-accepting ability and drifts the electron-density toward it and the effect is highly dependent on the powerful donor like carbazole ring. Stronger donor such as carbazole pushes more electron density towards the quinoxaline core. The trend observed for the absorption maxima of the carbazole based quinoxaline derivative in all the solvent is well supported by the vertical excitation theoretical computations and results are good agreement with the experimental absorption.

Nonlinear Optical (NLO) Properties by Solvatochromic and DFT Method

The nature and the length of π-conjugated system for NLO properties were investigated by using DFT method. Optimized geometries at B3LYP/6-31G(d) levels were used for evaluation of NLO properties of all dyes. Due to an effective ICT, the quinoxaline derivatives must show significant NLO properties. The strong ICT containing quinoxaline derivative and their first and second order NLO properties were studied.

Molecular Nonlinearity

Organic molecule with small π-conjugated system is well known for NLO property. These systems have strong π-configuration with ICT characteristics and commonly provide good arrangement for electrons to excite from ground to excited state on photo-excitation. NLO properties do not depend only on the nature of the strong conjugation, but also on the substituent positions and the geometry of the molecule. Carbazole linked to quinoxaline possess rotating single bonds in the π-conjugation resulted into change in the dihedral angles, which enhance the polarizability of these molecules.

Linear Optical Properties by Solvatochromism

Calculation of αCT and μCT from the Solvatochromic Data

The linear polarizability α CT was evaluated experimentally for the the dyes 6a-6c. The values are obtained by two-level model using UV-vis absorption/emission spectroscopy. The solvatochromic method can also be utilized in determination of the dipole moment of the lowest lying charge transfer excited state. α CT are calculated by using the Eqs. 5 and 6. And all α CT  values are calculated for quinoxaline derivatives (6a-6c), and are tabulated in (Table 2 S5, S6 ).

$$ {\alpha}_{CT}={\alpha}_{xx}=2\frac{\mu_{eg}^2}{E_{eg}}=\frac{2{\mu}_{eg}^2{\lambda}_{eg}}{hc} $$
(5)

where,

x:

direction of charge transfer,

ℎ:

Planks constant,

c:

velocity of light in vacuum,

λ eg :

The wavelength of transition from the ground state to excited state,

\( {\mu}_{eg}^2 \) :

The transition dipole moment, that is related to the oscillator strength f.

$$ {\mu}_{e g}^2=\frac{3{e}^2 h}{8{\pi}^2 mc}\times \frac{f}{{\overset{-}{\nu}}_{e g}} $$
(6)

where,

m:

mass of electron,

f :

oscillator strength,

\( {\overset{-}{\nu}}_{eg} \) :

Absorption frequency,

e:

charge on electron,

Table 2 Measured linear optical properties and static first hyperpolarizability of 6a in different solvent
Full size table

The oscillator strength can be obtained by integrated absorption coefficient.

Calculation of β0 from the Solvatochromic Data

The two level model used to determine solvent dependent hyperpolarizability is based on the Oudar equation.

$$ {\beta}_{C T}={\beta}_{xxx}=\frac{3}{2{h}^2{C}^2}\times \frac{{\overset{-}{\nu}}_{eg}^2{\upmu}_{eg}^2\Delta {\mu}_{C T}}{\left({\nu}_{eg}^2-{\nu}_L^2\right)\left({\nu}_{eg}^2-4{\overset{-}{\nu}}_L^2\right)} $$
(7)

where,

x:

direction of charge transfer,

ℎ:

Planck’s constant,

c:

speed of light in vacuum,

μ:

transition dipole moment,

νeg :

transition frequency,

νL :

frequency of the reference incident radiation to which the β value would be referred,

Δμ CT :

difference between the charge transfers excited state and ground state dipole moment.

The static βCT is obtained from the above Eq. 7 as under the static conditions the value of νL = 0. The values for first hyperpolarizability obtained using the solvatochromic method (Table 2 , S5 , S6 ) is based on several assumptions, and thus allow only approximate estimate of dominant tensor of total hyperpolarizability along the direction of charge transfer, which is the major contributor to the total hyperpolarizability. Though the values are approximate it has advantages over the other well-known expensive method.

Calculation of solvatochromic descriptor of 〈γ〉SD from the solvatochromic data

The third order hyperpolarizability 〈γ〉SD at molecular level originating from the electronic polarization in the non-resonant region can be treated by a three-level model [48–52]. The quasi-two-level model in place of the three level model using the density matrix formalism to a simpler Eq. 8 [53, 54].

$$ <\gamma >\alpha \frac{1}{E_{eg}^3}{\mu}_{eg}^2\left(\varDelta {\mu}^2-\varDelta {\mu}_{eg}^2\right) $$
(8)

The value \( \frac{1}{E_{eg}^3}{\mu}_{eg}^2\left(\Delta {\mu}^2-\Delta {\mu}_{eg}^2\right) \) appearing in the Eq. 8 may be termed as third order “solvatochromic descriptor”. The values for quinoxaline 6a-6c in various solvents are given in (Table 2 , S5 , S6 ). The values calculated are static dipole moment (μ), the mean polarizability (α0), the anisotropy of the polarizability (∆α) the mean first hyperpolarizability (β o) and static second hyperpolarizability (γ), of the quinoxaline 6a-6c molecule in different polarity of solvents.

Solvent Dependency of NLO Properties of Carbazole Based Quinoxaline (6a-6c) by DFT

The linear polarizability (α) value of quinoxaline derivatives 6a-6c tabulated in (Table S7 ). The first hyperpolarizability value of compound 6a-6c was ranging from 130 X 10−30 (6a), 126 X 10−30 (6b) and 161 X 10−30 (6c) esu (Table 3) in DMSO. These values are greater than urea (0.38 X 10−30) by 343 (6a), 333 (6b) and 425 (6c) times. The value of asymmetric quinoxaline 6c is larger than the other derivatives, which proved that quinoxaline with asymmetric geometry passes the higher polarizability values.

Table 3 DFT calculated linear first order hyperpolarizability (β o) for 6a-6c (X10−30 esu)
Full size table

Second Order Hyperpolarizability (γ)

The quinoxaline derivatives show very high γ values, by DFT calculation. The carbazole based quinoxaline show 1226.40 X 10−35 esu. (6a), 1251.57 X 10−35 esu. (6b) and 1509.53 X 10−35 esu. (6c) γ values by computationally (Table S8 ).

Charge Transfer Characteristics of 6a-6c

An efficient charge transfer in a Donor–π–Acceptor chromophore is responsible for the manifestation of NLO properties. Degree of delocalization or fractional degree of localization of the excess charge (C 2 b ) and donor–acceptor coupling matrix value (H DA ) was calculated by Eqs. 8 and 9 respectively [55].

$$ {C}_b^2=\frac{1}{2}\left(1-\sqrt{\frac{{\varDelta \mu}_{\ge}^2}{{\varDelta \mu}_{\ge}^2+4{\mu}_{\ge}^2}}\right) $$
(9)
$$ {H}_{D A}=\frac{{\varDelta E}_{\ge }{\varDelta \mu}_{\ge }}{{\varDelta \mu}_{\ge}^D}=\frac{{\varDelta E}_{\ge }{\varDelta \mu}_{\ge }}{\sqrt{{\varDelta \mu}_{\ge}^2+4{\mu}_{\ge}^2}} $$
(10)

where,

ΔE ≥ :

vertical excitation energy

Δμ ≥ :

difference between the adiabatic dipole moments of the ground and excited states

Δμ D ≥ :

difference in adiabatic state dipole moments

μ ≥ :

transition dipole moment

Donor–acceptor coupling matrix distance (R DA ) was calculated by Eq. 11 [56]

$$ {R}_{DA}=2.06\ \mathrm{x}\ {10}^{-2}\frac{\sqrt{\nu_{max}{\epsilon}_{max}{\varDelta \nu}_{12}}}{H_{DA}} $$
(11)

where,

ϵ max :

molar extinction coefficient at maximum absorption

Δν 12 :

full width at half maximum (FWHM) of charge-transfer band

Higher calculated values of C 2 b and H DA for 6a suggested higher coupling between donor and acceptor in polar solvents while reverse situation was observed in 6b and 6c (Table 4). On the other hand R DA values increased from nonpolar to polar solvents indicated good charge separation in polar solvents for all the dyes.

Table 4 Degree of delocalization (C 2 b ), donor–acceptor coupling value (H DA ) and donor–acceptor coupling distance (R DA ) for the dyes 6a–6c in various solvent
Full size table

Conclusion

3,6-di(substituted quinoxalin) carbazole fluorophores were designed and synthesized successfully. Photophysical properties study revealed positive solvatochromism with strong intramolecular charge transfer between the donor carbazole and acceptor quinoxaline through the π-conjugation. Computed vertical excitations using B3LYP/6-31G(d) basic set are in good correlation with the experimental values. Solvent polarity functions correlated well with the ICT phenomenon in these fluorophores. Nonlinear optical properties have been evaluated by solvatochromic method using two-level quantum mechanical model and are found to be in good correlation with density functional theory calculated values. Due to good charge transfer in these novel molecules can be applied to OLED or DSSC applications with suitable molecular structural modifications.