1 Introduction

Organic molecules with a delocalized π-electron system have drawn significant advantages for their high efficiency, flexibility, and unique features where the functional groups can be substituted and the properties can be tuned easily according to the requirements [1]. Significant efforts have been focused on studying the electronic and structural properties of donor–acceptor (D–A)-substituted conjugated π-electron systems with an intention to use them in light harvesting, data processing application, modern communication, and photonic technologies [2,3,4,5,6,7]. Benzo-fused heterocycles are a class of organic chromophores where the electron-donating and electron-accepting nature of the side chain or functional group can alter the energy gap appropriately, which contribute to efficient intramolecular charge transfer (ICT) and thus improve charge transport [8]. The hetero-aromatic system end-capped with an electron acceptor (A) and an electron donor (D) widely represent a class of systems known as push–pull molecules. They have gained much attention due to their remarkable feature in material science especially in the field of nonlinear optics, optoelectronics, and their efficient charge transfer properties [9, 10]. The development of organic π-conjugated donor–acceptor–donor (D–A–D) systems composed of thiophenes (donor) and electron-deficient molecule (phenyl) provides an efficient approach to increase the absorption band through intramolecular charge transfer (ICT) [11]. This approach offers a better matchup of the solar spectrum and thus attains the high efficiency in photovoltaic cells (PVC) [12]. Recently, many researchers [13, 14] have demonstrated that the incorporation of heteroatoms and the side chain into the π-conjugated electron-deficient five-membered ring causes push–pull effect that alters their electronic properties [7].

Generally, ICT occurs in push–pull systems containing electron donor and electron acceptor [15]. The ICT in these D–A systems leads to distinct optical and electronic properties. By suitable combination of the donor and acceptor groups, the ICT character of the push–pull system can be controlled [16]. The combination of donor and acceptor components affects the frontier orbital levels, thereby making them appropriate candidate materials to tune the optoelectronic properties [16]. Usually, electron donors are substituents with inductive (+ I) effects such as CH3, NH2, OH, and benzo-fused thiophenes, whereas the electron acceptors represent substituents with inductive (− I) effects such as NO2, CN, CHO, COOH, CF3, etc. [9]. Resonance effect in substituents also plays an important role by participating in the π-conjugated network of the main chromophore upon photoexcitation [17]. Typical substituents include amino groups and sub-conjugated systems which form extended conjugation with the main chromophore such as CHO, COCH3, COOH, C6H5, and thiophene.

The study reports the effect of introducing various electron donor and acceptor groups to the benzo[1,2-b:4,5-b′]dithiophene (BDT) unit on the electronic, optical, redox, and charge transfer properties at a microscopic level. Among many chromophores, BDT [10, 18] derivatives are appropriate candidate in optoelectronic devices owing to their high electron density and planar structure. In this regard, organic push–pull systems are designed with the various donors and acceptors attached to BDT molecule, and the comprehensive structure and photoelectric properties are studied using the density functional theory and time-dependent density functional theory methods [16, 19, 20]. The D–A structure is created by breaking the delocalization pattern by introducing donor and acceptor at the two thiophene rings. In the present study, a series of BDTs with different electron acceptor groups at ortho (conformer a)- and meta (conformer b)-position to the sulfur atom in the thiophene rings have been investigated. This approach can efficiently fine-tune the “push–pull” effect of BDTs, by simply changing substituents according to their varying electron-donating or electron-withdrawing power. The frontier molecular orbitals, HOMO–LUMO energy gaps, absorption and emission spectra, reorganization energies, and charge transfer have also been investigated. Further natural population analyses have been carried out to understand the nature of delocalization and ground state interactions. The 1H and 13C NMR chemical shift, vibrational frequency, and nucleus-independent chemical shift (NICS) calculations support the structure and push–pull character of these BDTs.

2 Computational methods

Various ortho- and meta-substituted BDT models are generated with different donor and acceptor groups. All the models were optimized in gas phase without any constraints at the tight convergence criteria using long-range corrected CAM-B3LYP [21, 22] hybrid functional and 6-31 + G(d,p) all-electron basis set for all atoms as implemented in the Gaussian 09 package [22]. The minima nature of the structure is confirmed from the computed real frequencies based on the harmonic vibrational analysis. The charge distribution in all optimized BDT models are investigated by the natural orbital method [23, 24]. The charge distribution is considered by dividing the BDT into different ring units (ring A: thiophene unit attached to donor substituent, ring B: central fused benzene unit, and ring C: thiophene unit attached to acceptor substituent), and at donor and acceptor substituents, respectively, as in Fig. 1. The oxidation and reduction properties of the BDT models were studied by calculating the vertical and adiabatic ionization potential (VIP and AIP), vertical and adiabatic electron affinity (VEA and AEA), and reorganization energy for oxidation and reduction (λele and λhole) process using the equations given below,

$${\text{VIP }} = E^{\prime}_{(N - 1)} - E_{(N)}$$
$${\text{AIP }} = E_{(N - 1)} {-}E_{(N)}$$
$${\text{VEA }} = E^{\prime}_{(N + 1)} {-}E_{(N)}$$
$${\text{AEA }} = E_{(N + 1)} {-}E_{(N)}$$
$$\lambda_{{{\text{ele}}}} = {\text{ AEA }}{-}{\text{ VEA}}$$
$$\lambda_{{{\text{hole}}}} = {\text{ AIP }}{-}{\text{ VIP}}$$

where E(N) is the energy of an optimized neutral molecule with N electrons, E′(N-1) is the energy of a cation present at optimized neutral geometry, E(N-1) is the energy of an optimized cation with (N − 1) electrons, E′(N+1) is the energy of an anion present at optimized neutral geometry, and E(N+1) is the energy of an optimized anion with (N + 1) electrons.

Fig. 1
figure 1

Schematic representation of benzo[1,2-b:4,5-b′]dithiophene (BDT) core considered in this work. The ortho (positions 6 and 2)- and meta (positions 7 and 3)-position in the thiophene ring are substituted with various substituents [donor: CH3, NH2, and OH; acceptors: CF3 (1a/1b), NO2 (2a/2b), CN (3a/3b), COOH (4a/4b), and CHO (5a/5b)]. The skeletal atoms and ring labels used for NPA, NICS, 1H and 13C NMR calculations are shown

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Hardness (η) and softness (σ) are related to the energy gap between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) calculated by the equations given below [25],

$${\text{Hardness}},\,\;\eta = \frac{{{\text{HOMO}} - {\text{LUMO}}}}{2}$$
$${\text{Softness}},\;\sigma = \frac{1}{\eta }$$

Nucleus-independent chemical shift (NICS) [26] values were calculated for the optimized ground and excited state geometries at CAM-B3LYP/6-31 + G(d,p) level of theory using the gauge-independent atomic orbital method (GIAO) [27] method. The NICS(0) and NICS(1) values were measured as a negative magnitude of isotropic chemical shielding values (in ppm) [26] by placing the ghost atoms at the center of the ring plane and 1 Å above this point. 1H and 13C NMR chemical shielding values are calculated in GIAO method by considering tetramethyl silane as reference at the same level of theory. The electron–hole distribution, electron density difference (EDD), charge transfer (CT) length, and Chole and Cele (centroids of hole and electron) were all generated and visualized by the Multiwfn 3.8 program [28,29,30].

The first vertical excitation energy corresponding to the lowest absorption energy (Eabs) based on the optimized ground state geometry (S0) was calculated by the TDDFT method [31, 32]. According to Kasha’s rule [33], the emission energy (Eflu) is determined as the S1 → S0 transition, where the first singlet excited state (S1) is typically important to emit fluorescence and is obtained by optimizing the S1 state. The Stokes shift is calculated as the difference between the lowest absorption and emission energy.

3 Results and discussion

3.1 Electronic structural and optical properties of 1,5-dihydros-indacene and benzo[1,2-b:4,5-b′]dithiophene chromophore

The 1,5-dihydros-indacene and benzo[1,2-b:4,5-b′]dithiophene molecules were optimized to understand the influence of sulfur atom in the ring. The presence of sp3 carbon in 1,5-dihydros-indacene makes the structure non-planar with bond distance of Csp3-Csp2 (1.51 Å) and Csp2-Csp2 (1.34–1.47 Å). Computed natural charges show intramolecular charge transfer from center of the ring to terminal rings (Fig. 2). Further, the computed NICS(0) and NICS(1) values of indacene molecule indicate that five-membered rings A and C are non-aromatic with − 0.14 and − 2.99 ppm values, while six-membered ring is aromatic with − 8.26 and − 10.01 ppm values, respectively. The substitution of –CH2 group by sulfur atom in BDT makes the structure planar with C–S bond distance 1.75 Å. Further, the sulfur lone pair of electron is found to participate in the conjugation (Fig. 2); as a result, the chemical stability is found to increase in BDT molecule by 0.24 eV compared to indacene molecule. The heteroatom polarizes the molecule where the negative charge is more concentrated at the central ring (− 1.03 e) compared to the terminal rings (− 0.57 e). The MO picture shows extended delocalization; as a result, the terminal thiophene rings (− 9.30 and − 7.80 ppm) and the central phenyl ring (− 10.64 and − 11.34 ppm) become aromatic with larger negative NICS(0) and NICS(1) values. TDDFT computation shows that the absorption maximum occurs at 273.97 nm for indacene and 233.82 nm for BDT. In both the molecules, absorption occurs due to π → π* transition. The blueshift observed for BDT is the result of larger stabilization of HOMO due to hetero atom substitution. This wavelength has been further tuned by introducing the push–pull effects by substituting donor and acceptor groups at the terminal rings (ortho- and meta-position to sulfur atom).

Fig. 2
figure 2

Optimized molecule and molecular orbital pictures of a 1,5-dihydros-indacene and b benzo[1,2-b:4,5-b′]dithiophene (BDT). Computed bond distances (in Å), natural charges in e (bold italics) averaged to each rings, NICS(0) and NICS(1) (orange font in ppm) values are given

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3.2 Electronic structural and optical properties of donor- and acceptor-substituted BDT

3.2.1 Structural properties

The optimized geometries of the BDT models clearly show negligible change in planarity and bond distances irrespective of the substituents size and position (Fig. 3, S1, and S2). However, the substituents enhance the intramolecular hydrogen bonding interaction between the acceptor units and the H-atoms in the ring (distances are found to vary from 2.30 to 2.77 Å, in Figs. 3, S1, and S2). These weak interactions stabilize the conformer b (substituent at meta-position) marginally more than conformer a by CH3: 1.07–2.00 kcal mol−1, NH2: 0.46–1.05 kcal mol−1, OH: 0.66–2.01 kcal mol−1 as mentioned in Table 1 for all substituent (NH2-5a as an exception). Further, the intramolecular hydrogen bonding redshifted the functional group stretching frequencies of acceptor substituents in conformer b compared to conformer a. The computed vibrational frequencies of acceptor groups (υ in cm−1) for all the BDT models are given in supplementary information (Table S1 in SI). The charge transfer nature, chemical reactivity, kinetic stability, chemical hardness and softness of the molecules are understood from the energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) as given in Table 1. Among conformer b, the chemical stability of various donor-substituted molecules follows the trend, NH2 < OH < CH3 irrespective of the acceptors. This can be explained based on the improper dihedral angle (ω) defined between donor and acceptor units as given in Table S4 in supplementary information. In CH3-substituted BDTs, the angle ω is co-planar ~ 180° with respect to the BDT ring, and hence, there is a larger π-electron delocalization, whereas for NH2- and OH-substituted BDTs, the angle ω deviates from co-planarity ~ 30–40° (NH2) and ~ 30° (OH), respectively. In case of different acceptors, the NO2-substituted models are chemically least stable and the CF3-substituted models are chemically most stable compared to other models by 0.92 eV (NH2), 0.89 eV (CH3), and 0.85 eV (OH), respectively. The HOMO–LUMO gap lies over a range of 5.45–6.69 eV for conformer b. It is interesting to note that the absence of push–pull groups on either ends results in BDT to be chemically more stable with wide HOMO–LUMO gap (7.04 eV). The eigenfunction plots given in Fig. 4 and supplementary information Fig. S3 clearly indicate that the substitution of CH3 as donor has negligible contribution toward HOMO and LUMO, while electron-accepting group at thiophene ring has a significant contribution. For NH2- and OH-substituted models, the donor groups (NH2 and OH) also show a considerable molecular orbital contribution. Specifically, CF3 substituent has minimal contribution in HOMO and LUMO, while NO2 group extends maximum contribution as shown in Fig. 4. As a result, CF3-substituted BDTs has large HOMO–LUMO gap than other models studied here. Interestingly, the position of substituent is found to alter the energy gap, where ortho-substituted conformer a extends strong overlap than meta-substituted conformer b. The same phenomenon is also reflected in the hardness and softness values. The molecule CH3-1b has the highest hardness value (η = 3.35 eV), and the molecules NH2-2a and NH2-2b are the softest molecules with σ = 0.37 eV. The computed natural charges illustrate the push–pull effect of various substituents where the polarity is stimulated at the donor and acceptor ends. For CH3-substituted BDTs, the CH3 group exhibits a partial positive charge of 0.06 and 0.05 e at conformers a and b. The rings A and C possesses a negative charge and acts as donor units where ring C is a strong donor compared to ring A. Irrespective of the donor and acceptor substituents, the central ring B possesses an overall partial negative charge of 0.5 e and serves as a linker between rings A and C, thus stabilizing the push–pull effect at the thiophene units. In case of NH2- and OH-substituted BDTs, both NH2 and OH groups possess a partial negative charge (NH2: 0.02 e and 0.05 e at conformers a and b, OH: 0.18 e and 0.21 e at conformers a and b). Consequently, ring A display a partial positive charge while ring C exhibits a partial negative charge. This facilitates intramolecular charge transfer from one unit to another. In case of different acceptor substituents, the CF3 and NO2 substituents tend to cause maximum charge polarization but show an opposite behavior. The CF3 group leads to maximum negative charge at ring C with a positive charge at CF3 group while in contrast NO2 results in a positive charge at ring C and a maximum negative charge at NO2 end. When CH3 acts as a donor, the conformer a is found to possess more charge at the donor end, while for NH2 and OH, conformer b possesses more charge at the donor end. This indicates substituent positional effects on the nature of charge distribution for different donor moieties. Hence, the arrangement of the electron donors and acceptors around the BDT is important when designing a push–pull molecule.

Fig. 3
figure 3

Optimized geometries of various NH2-substituted BDT models. a and b represent different conformers for the BDT models with NH2 group anchored at positions 6 and 7, and acceptor at positions 2 and 3. The important bond distances and weak interaction (in Å) are given (1a/1b: CF3, 2a/2b: NO2, 3a/3b: CN, 4a/4b: COOH, 5a/5b: CHO). The optimized geometries of CH3- and OH-substituted BDTs are given in supplementary information (Figs. S1 and S2)

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Table.1 Computed relative energies (ΔE in kcal mol−1), HOMO–LUMO energy gap (Δ in eV), natural charges (in e), hardness (η), and softness (σ) index (in eV) of various BDT models
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Fig. 4
figure 4

Computed molecular orbital pictures of conformers a and b of various CH3- and NH2-substituted BDT models plotted with an isocontour value of 0.02 Å−3. The orbital pictures of OH-substituted BDT models are given in supplementary information (Fig. S3)

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Accordingly, the change in electron density distribution is reflected in the NICS values and the results are given in supplementary information (Table S2 in SI). The larger negative NICS(1) value compared to NICS(0) indicates the larger contribution from π-orbitals. Considering the aromatic character of free thiophene (− 13.6 ppm) [34], the aromatic character of rings A and C in BDT is slightly reduced as donor and acceptor substituents are anchored to thiophene units. The aromaticity of ring C is enhanced compared to that of free benzene (− 9.7 ppm) due to the push–pull effect that tend to increase the aromatic character of central fused benzene [26]. This is accounted based on the high negative charge at the ring B that increases its aromatic nature by 1–2 ppm. The NICS(0) and NICS(1) values were computed for excited geometry and a similar trend in aromaticity in the rings were observed. However, the aromatic nature is found to increase by 0.2–1 ppm during excitation. This indicates the higher delocalization at the excited state compared to the ground state. (Values for excited molecules are given in Table S2 in SI.)

Finally, the NMR chemical shielding values are calculated to check the reliability of the optimized structures, aromatic nature and to quantify the push–pull nature of these BDTs. It is important to recall that the chemical shift of protons usually shifted to high δ values due to the substitution of electron-withdrawing groups and shifted to low δ values in case of electron-donating group (Table S3 in SI). The protons in positions 4 and 8 are deshielded compared to other protons attributed to the highly aromatic six-membered ring. Further, the delocalization along with push–pull effect in the molecules is evident from the chemical shift of protons. There is a slight downfield shift of protons at positions 2 and 3 (2-H and 3-H) compared to that of protons at positions 6 and 7 (6-H and 7-H). This is due to the electron-withdrawing and electron-donating groups at rings C and A, respectively. The presence of nitro and aldehyde groups in CH3-2b (9.79) and CH3-5b (9.62) makes the protons (2-H and 3-H) highly deshielded with a larger chemical shift value than other BDTs. The protons of CH3 donor are slightly deshielded in conformer b (3.3) compared to conformer a (3.2). Overall, the computed NMR chemical shift values accounts for the shielding and deshielding nature of protons due to the push–pull electronic environment in these BDTs. The 13C NMR chemical shift values are given in Table S5 of supplementary information which is found to follow the same trend as 1H NMR. These data are useful to validate the results by comparing with experimental data. Similar observation holds good for NH2- and OH-substituted BDTs.

3.2.2 Ionization potential, electron affinity, and reorganization energy

Vertical ionization potential (VIP) indicates the energy required by a molecule to lose an electron and form a cation. The smaller the VIP of molecule, the more easily it loses electron and turn into a hole carrier. Vertical electron affinity (VEA) is the energy required by a molecule to accept an electron. Larger the VEA value, the more readily it accepts electron and serves as an electron transport material. The VIP and VEA of the BDT models are tabulated in Table 2. The COOH-containing BDTs show low IP compared to other molecules. The trend in VIP values observed for various donors is as follows, NH2-4b (7.32 eV) < CH3-4b (7.62 eV) < OH-4b (7.64 eV). The hole transport barrier varies from 0.30 to 0.38 eV (4b < 5b < 1b < 3b < 2b). The NO2-substituted BDTs show larger VEA value in comparison with other molecules and observe to follow the order, NH2-2a (1.24 eV) < OH-2a (1.35 eV) < CH3-2a (1.37 eV). The electron transfer capability of the BDTs is enhanced more for conformer a in the presence of NO2 group. The COOH-substituted BDTs are good hole transport materials irrespective of conformers. (IP value varies within 0.02–0.06 eV for both conformers.) The low VIP and high VEA of NO2-substituted BDTs can be correlated based on the strong electron acceptor ability of NO2 and hence have good charge transfer capability.

Table.2 Computed adiabatic ionization potential (AIP), adiabatic electron affinity (AEA), vertical ionization potential (VIP), vertical electron affinity (VEA), and reorganization energy for hole (λhole) and electron (λele) in eV for various BDT conformer
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Marcus theory [35] is used effectively to predict the charge transport property of a material. According to Marcus theory, the charge transfer rate constant κ is given by,

$$\kappa = A\exp \left[ {\frac{ - \lambda }{{4K_{B}T}}} \right]$$

where A is electron coupling, T is temperature, KB is Boltzmann constant, and λ is reorganization energy. From the above equation, an important parameter to determine charge transport is λ. The smaller the value of λ, the better the charge transport capability. The reorganization energies are calculated for hole (λhole) and electron (λele) using Eqs. (5) and (6), respectively, which estimate the charge transport for holes and electrons [36, 37]. The reorganization energies of hole and electron for various BDTs are listed in Table 2. The electronic reorganization energies of CN-substituted BDTs are smaller than that of other molecules and hence serve as good electron transport systems. For CH3 donor, the hole reorganization energies of CN-substituted BDT is small compared to other molecules, whereas for NH2 and OH donors, the NO2-substituted BDTs of conformer a show small value of λhole. The electron and hole reorganization energies are comparatively small for BDTs containing CH3 donor. The CN-containing BDTs with CH3 donor serve as an efficient ambipolar transport system. In case of CH3-containing BDTs, the λhole and λele values of conformer b are relatively small compared to conformer a (except CH3-2b).

3.2.3 Electron excitation analysis

The hole and electron distribution can be quantitatively characterized that are useful for identifying type of electron excitations. In this regard, a multitude of hole–electron descriptors were used such as Δρ, Sr, D, qCT, μCT, H, t, Δr, and Λ indices to understand the charge transfer [38,39,40,41,42]. Hole–electron descriptor details are given in supplementary information.

To account for the push–pull behavior and donor–acceptor nature within the BDTs during the electron excitation, multifarious descriptors based on hole–electron theory have been used (details are given in SI). The computed values in Table 3 provide a quantitative picture on electron transition characteristics. Figures 5, S4, S5, and S6 illustrate the total density difference for ground and excited states (Δρ), DCT values, and Chole/Cele map. The DCT value of NO2-substituted BDT is very small (CH3-2a: 0.996, CH3-2b: 0.813, NH2-2b: 0.843, OH-2a: 1.017, OH-2b: 0.818) compared to other BDTs, and the corresponding Sr index is close to 0.50 to 0.51 Å, implying that about half of hole and electron part matched perfectly. This suggests that the excitation is a typical local excitation (LE). Further, the t index is negative suggesting that the separation of hole and electron distributions is insignificant, which also support LE. The main electronic transition is n → π* due to the lone pair of electrons and π* orbitals on NO2 group. Similar observations hold good for CH3-5b and OH-5b where the DCT values are slightly large 1.231 and 1.397, respectively. The corresponding Sr index is 0.50 and 0.49, and the excitation is a π → π* (occurs on thiophene unit attached to CHO group) and n → π* (on CHO group) LE. The H index of the above-discussed BDTs is not large as the hole and electron of these states are distributed in a local region. An exceptionally high DCT value (3.915 Å) is observed for NH2-2a with Sr index of 0.695 and a positive t index (1.619 Å), which obviously points to a charge transfer (CT) excitation. There is π → π*-type transition from amino group (donor) toward nitro group (acceptor), thus highlighting push–pull effect. In case of other BDTs, the distribution of hole and electron in these molecules is wider (DCT value in the range 1.279 to 4.359 Å), and their Sr and H indices are markedly larger (Sr value varies between 0.695 and 0.841 and H index from 2.658 to 3.170). The electronic transitions are CT type where the direction of electron transfer is from donor end to acceptor end. However, the barycenters are not exactly on the donor or acceptor moieties, but centered on the either thiophene units, which suggests that the charge transfer occurs from thiophene unit attached to a donor to thiophene unit attached to an acceptor via fused benzene (Fig. 5). In the presence of NH2 donor, all the BDTs show CT excitation (except NH2-2b), which is accounted based on the donor–acceptor distances for NO2-substituted BDTs where the dD-A values are 7.766 Å (NH2-2b), 7.775 Å (OH-2b) and 7.883 Å (CH3-2b), respectively. It is evident that the dD-A of NH2-2b is less than that of OH-2b and CH3-2b. The NO2-substituted conformer a exhibits dD-A in the range OH-2a (9.724 Å) < 9.769 Å (NH2-2a) < CH3-2a (9.895 Å) and all of them are found to show CT excitation. Also the improper dihedral angle (ω1) is − 40.31° for NH2-2b which is much deviated from co-planarity compared to NH2-2a (27.63°). Hence NH2-2b favors LE and NH2-2a favors CT excitation. The improper dihedral angles ω1 and ω2 are − 0.08 and 179.86° for CH3-5b (exactly coplanar in case of CH3-5a) and 30.42 and − 149.70° for OH-5b (− 15.66 and 164.40° in case of OH-5a) that suggests a deviation from planarity with respect to the BDT plane compared to conformer a, and hence exhibits LE. The improper dihedrals of all the optimized BDTs are listed in supplementary information (Table S4).

Table.3 Hole–electron descriptors (Sr, H, and t), charge transfer length, charge and dipole moment (DCT, qCT, μCT), and diagnostic descriptors (Δr and Λ) of various BDTs
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Fig. 5
figure 5

Computed total density difference for ground and excited states (Δρ, isovalue set to 0.001 Å), graphical representation of DCT indicating the approximate barycenters of positive (green) and negative (blue) part obtained by increasing the isovalue accordingly and DCT value is also labeled, and centroids of hole and electron (Chole/Cele map, isovalue set to 0.001 Å) of CF3- and NO2-substituted BDTs. The figures for CN-, COOH-, and CHO-substituted BDTs are given in supplementary information (Figs. S4, S5, and S6)

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The Δr index ranges from 0.8 to 3.5 Å, where most of the BDTs exhibit long-range excitation (Δr > 1.5 Å) with a few exceptions such as CF3-substituted CH3-1a, CH3-1b, and OH-1a (Δr < 1.5 Å). The BDTs with NH2 donor display a strong charge transfer irrespective of the acceptors. The Λ-values of all BDTs are in the range 0.4 ≤ Λ ≤ 0.7 where CH3-2a (0.41), CH3-2b (0.43), NH2-2b (0.43), OH-2a (0.42), OH-2b (0.43), CH3-5b (0.38), and OH-5b (0.38) have a relatively small overlap and other BDTs show a larger hole–electron overlapping extent.

3.2.4 Absorption spectra

TDDFT computations were carried to determine first six singlet excited states. The computed absorption spectra are given in Fig. 6. The absorption spectra clearly show that the absorption wavelength covers wide wavelength region due to push–pull groups anchored to the BDT and range roughly from 180 to 400 nm. The ability to tune the absorption at a particular wavelength is an important characteristic for optoelectronic properties. The absorption maximum has more than 65% contribution from HOMO to LUMO transition (Figs. 7, S7, S8, S9, and S10), while the transition from other delocalized frontier orbitals contribute 35% as shown in the orbital transition diagram (Figs. 7, S7, S8, S9, and S10). Overall, the excitations are mainly due to π → π* transitions for CH3-substituted BDTs, whereas π → π* and n → π* transitions are notable for NH2- and OH-substituted BDTs. The push–pull effect increases the absorption wavelength for all models as expected when compared to the unsubstituted one (λmax = 200 nm). Among the models explored, NO2-substituted BDTs absorb at higher wavelength and follows the order OH-2a (352.58 eV) < CH3-2a (356.93) < NH2-2a (361.66) while CF3-substituted ones absorbs at lower wavelength and the observed trend is OH-1a (287.42) < NH2-1a (292.03) < CH3-1a (294.02) in eV. In case of CH3 donor, irrespective of the nature of acceptor groups, the conformer a is markedly redshifted compared to conformer b. This is due to the strong overlap between sulfur lone pair and donor/acceptor substituents in conformer a. The computed absorption maxima are well correlated with the calculated HOMO–LUMO energy gaps. The HOMO–LUMO gap is large and small for CF3- and NO2-substituted BDT molecules which is responsible for the marked blueshift and redshift in the absorption spectra of these BDTs. The oscillator strengths are highest for the cyano-substituted conformer a and follow the trend NH2 > OH > CH3, due to strong electron-withdrawing effect of CN unit. The least oscillator strengths are observed for nitro-substituted conformer b and tend to follow the order NH2 < OH < CH3 that suggests weak electron-withdrawing effect of NO2 unit in these conformers. The trend in oscillator strengths observed for various acceptors is as follows, CN > COOH > CHO > NO2 > CF3 (CH3-a), CN > CHO > COOH > NO2 > CF3 (NH2-a), CN > COOH > CHO > NO2 > CF3 (OH-a), CN > COOH > CHO > CF3 > NO2 (CH3-b), CN > COOH > CHO > CF3 > NO2 (NH2-b), and CN > CF3 > COOH > CHO > NO2 (OH-b). In summary, irrespective of the conformers cyano is a strong electron acceptor, whereas CF3 and NO2 act as weak electron acceptors when attached to conformers a and b, respectively.

Fig. 6
figure 6

TDDFT computed absorption spectra of various BDTs using CAM-B3LYP functional and 6-31 + G(d,p) basis set

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Fig. 7
figure 7

Computed molecular orbitals involved in transitions for CF3-substituted BDTs plotted with an isocontour value of 0.2 Å−3. Note that for other models the orbital transition diagrams are given in supplementary information, Figs. S7, S8, S9, and S10

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3.2.5 Fluorescence energy and lifetime

The fluorescence energies of all BDTs were calculated using TDDFT method, and the results are summarized in Table 4. The fluorescence energies for the highest oscillator strength are assigned to S1 → S0 transition. The examination of the optimized excited state indicates that the excited state of CH3-substituted BDTs showed negligible structural change with respect to ground state (Table S4 in SI). The excited state of NH2- and OH-containing BDTs points that the structure is more or less co-planar with respect to the BDT molecule compared to the ground state, due to strong electron-donating effect of NH2 and OH unit. The change in trend of fluorescence wavelength and oscillator strength is similar to that of the absorption wavelength. The fluorescence peak appears at longer wavelength compared to the absorption peak. This redshift is explained by an increase in the dipole moment in the excited state of the BDTs relative to its ground state (Table 4). The Stokes shift is large for NO2-substituted BDTs of conformer b due to the steric hindrance of the substituent. The Stokes shift is more enlarged for NH2-2b (0.79) followed by OH-2b (0.63) and CH3-2b (0.51). In NH2-2b, steric hindrance of donor and acceptor substituent is strong in the ground state which is compensated during optical excitation enabling the electron delocalization between donor and acceptor ends. The Stokes shift is small in CH3-2b because the steric hindrance is relatively weak, and only negligible structural changes occur on photoexcitation.

Table.4 Computed absorption and emission wavelength (λ in nm), molecular orbital contribution, oscillator strength (f), absorption and fluorescence energies (Eabs and Eflu in eV), ground state and excited state dipole moments (μGS and μES in Debye), fluorescence lifetime (τ in ns), and Stokes shift (in eV) obtained using TDDFT method
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The fluorescence energies and oscillator strengths were used to calculate the radiative lifetimes that are summarized in Table 4. The radiative lifetime (τ in ns) based on the Einstein transition probabilities is expressed as [43],

$$\tau = \frac{{c^{3} }}{{2E_{flu}^{2} f}}$$

where c is the velocity of light, Eflu is the fluorescence transition energy (in au.), and f is oscillator strength. The predicted radiative lifetimes are shortest for conformer a with strong electron acceptors and longest for conformer b with weak electron acceptors. The shortest lifetimes are observed for the cyano-substituted BDT and increased in the following fashion as NH2-3a < OH-3a < CH3-3a, and their extrapolated lifetimes are 48.86, 56.51, and 75.96 ns, respectively. The lifetime of NH2-3a is 7.56 and 27.10 ns shorter than that of OH-3a and CH3-3a, implying that there is longtime emission of electrons in OH-3a and CH3-3a. In contrast, the florescence lifetimes are significantly increased for nitro-substituted BDT where the values decrease as follows, NH2 (1435.81) > OH (773.43) > CH3 (516.36). Particularly, NH2-3a and NH2-2b exhibit the shortest and longest lifetimes compared to all BDTs studied. These computed data are valuable and would contribute to further design and development of D-A molecules for efficient charge transfer.

3.2.6 Structure–property relationship for optical excitation

The excited state optimization show rotation of the donor and acceptor substituents attached to the BDT molecule. The rotation of the substituent causes it to align with respect to the BDT molecular plane. The improper dihedral angle (ω) is reduced in excited BDT molecules due to substantial rotation during excited state geometry relaxation (Table S4 in SI). The important factor that causes the decrease in ω is the resonance effect between the BDT and the substituent that provides affinity to align with the molecular plane in order to attain enhanced electron delocalization as observed in charge distribution. The decrease in bond length or bond characters from ground and excited states shows the strong bond formation with substituents in excited state (Table S4 in SI). For CH3-substituted BDTs, the optical-induced structural changes between donor and BDT are small while NH2-2b and OH-2b show significant structural change. These facts show that the substituents undergo rotation upon photoexcitation enabling charge transfer, as the substituents tend to become more coplanar with the BDT molecule in the excited state.

4 Conclusions

The computational studies on various BDT models show that for CH3 donor minimal structural change is observed irrespective of the acceptor substitutions, while for NH2 and OH donors the structural changes are significant. A major variation is also observed in the electronic density distribution. All the molecules show excellent π-conjugation. The computed NPA charges and NICS values indicate the intramolecular charge transfer ~ 0.2 e from the terminal five-membered rings to the acceptor unit. The computed NMR chemical shift values confirm the push–pull behavior of these BDTs. The calculated HOMO–LUMO gap, softness, and hardness parameters indicates highly electronegative CF3-substituted CH3-1b is chemically inert and less polarizable while NO2-substituted NH2-2a and NH2-2b become relatively active and more polarizable. Further, the orbital pictures show the strong overlap between ortho-substituted conformers and sulfur lone pair than meta-substituted conformers. The calculated λhole and λele values are small for CH3-3b-substituted models indicating that cyano group serves as an efficient ambipolar transport system. For NH2 and OH donors, the NO2- and CN-substituted BDTs are good candidates for hole and electron transport, respectively. The electron excitation analysis of the BDT models predicts LE for all NO2-substituted systems, except NH2-2a which show CT excitation due to deviation of the substituents from the BDT molecular plane. The absorption spectra obtained from TDDFT method point to π → π* transition in CH3-substituted BDTs, whereas π → π* and n → π* transitions are dominant in NH2- and OH-substituted BDTs. Among the models studied here, NO2-containing BDTs are found to be efficient with longer absorption wavelength. The calculated fluorescence lifetimes were found to be the shortest and longest for cyano- and nitro-substituted BDTs. Finally, the structure–property relationships were explored which revealed a marked reduction of improper dihedral angle (ω) in excited state molecule due to the bond rotation during excited state geometry relaxation. Our study provides useful insights into the structure–property relationship, electronic, and charge transfer properties that would be certainly handy to the experimentalist to carry the quest for better molecules with enhanced properties.