Introduction

One of the greatest innovative technologies and scientific difficulties in the contemporary era has been the creation of highly efficient solar photovoltaic (PV) systems due to the growing environmental pollution and the depletion of fossil fuels (coal, oil, and gas). Since Grätzel and O'Regan published their first successful demonstration of dye-sensitized solar cells (DSSCs) as a low-cost alternative to the highly efficient PV cells in 1991, DSSCs have gained considerable attention as a potential low-cost PV cell replacement.1,2,3,4 Ru-based complexes are reported to have the best solar power conversion efficiency (PCE), which is over 12% under a calibrated AM 1.5 radiation, despite their high cost and environmental concerns.5 However, the Ru-compounds are very costly, with a low molar extinction coefficient and difficult purification steps. However, there is a critical need for metal-free organic dyes targeted at DSSCs without noble metals. Researchers are now looking more closely at the connection between dye chemical systems and their PV performance as a result of the recent success of PCE for DSSCs based on organic sensitizers.6,7

The majority of organic sensitizers nowadays have a donor-spacer-acceptor (D-π-A) molecular architecture, where the electron-donor (D) and electron-acceptor (A) are both coupled to the π-spacer molecular system. In addition to the wide range of molecular systems available, it has great efficiency, cheap cost, good flexibility, and abundance of raw materials. But there are still issues to be overcome with the decreased energy efficiency of metal-free organic dyes, thermal energy-harvesting devices and electrochemical stability. To achieve high performance of the PV devices, it is important to discover D-π-A types of dye sensitizers. For DSSCs, organic dye molecules containing a variety of heterocyclic building blocks have been described, including triphenylamine, fluorine, carbazole, tetrahydroquinoline, anthracene, N,N-dialkylaniline, merocyanine and coumarin.8,9,10,11,12,13,14,15,16

Particularly, the most widely used phenothiazine (PTZ) and its derivatives are utilized in industrial dyes, optical brightening agents (OBAs), scintillators, fluorescent brightening agents, extremely bioactive substances, and many other things. Because it plays a significant role in electrochemistry and numerous photophysical and photochemical oxidation devices, the synthetic derivative of PTZ has been gaining interest for more than half a century.17,18 Because of their low processing cost, ab initio calculations and molecular simulations have emerged as crucial tools for solving molecular problems and interpreting experimental data.19,20,21,22,23,24,25 The enhancements in CPU resources now make it possible to simulate the electrical characteristics of large-scale dye material behaviours.26,27,28,29 One of the most popular methods for these computations is time-dependent self-consistent-field (TD-SCF), which offers significantly better agreement with observed data for a justifiable computational conclusion, especially when hybrid exchange–correlation (XC) functionals are employed.30,31,32 It is acknowledged that the thiazine class of heterocyclic chemicals, such as PTZ derivatives, may prove difficult to study using quantum theory. The dye sensitizer (E)-3-(10-butyl-10H-phenothiazin-3-yl)-2-cyanoacrylic acid (T2-1) published by Sun and co-authors in 2007 comprises PTZ and 2-cyanoacrylic acid, which serve as electron-D and electron-A (D-A) groups. 33 This kind of sensitizer causes a shift in surface charge that significantly decrease dye recombination in its excited state and hence improves the solar PV efficiency in their DSSCs. A well-known family of electron-rich heterocyclic thiazine compounds called PTZ dye has become established in organic solar cells due to its special features. In DSSCs, for instance, PTZ-based D-A-π-A dyes of PZ-1-4 have been developed and are known for their high photocurrent performance.34

In light of the study approach previously stated, we attempted to combine all the intriguing characteristics of PTZ derivatives in comparison to the T2-1 molecule. Appropriately varied π-conjugated spacers (SZ-1–SZ-5) molecular structures were depicted in Scheme 1. According to the plan, the π-spacer groups provide a chance to carry out computational research using D-π-A architecture for the development of more effective PTZ dye. Additionally, the effect of SZ-1–SZ-5 dyes on semiconductor and PV characteristics was examined. We seek to establish the essential connections between the structure–property of various π-spacer dyes and the development of optoelectronics with high energy conversion efficiencies using theoretical simulations.35,36,37

Scheme 1
figure 1

Structures of designed metal-free organic dyes.

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Computational Aspects

The Gaussian 09w38 software package carried out all computations using a hybrid Becke-3-Lee–Yang–Parr (B3LYP) functional with a 6-31G(d,p) basis set. Utilizing the hybrid B3LYP theory and quantum chemical computations, the ground state geometries (S0) of all the specified dyes were calculated.39,40 To calculate the electronic absorption and emission spectra with the excited state of all SZ-1–SZ-5 dyes, time-dependent DFT (TD-DFT) computations were used. Those spectra were pictured by GaussSum version 3.0 software. The energy gap (Eg) and electron densities of the highest occupied molecular orbital (HOMO) and lowest unoccupied MO (LUMO) levels of the SZ-1–SZ-5 molecules were calculated using the same method. The above approaches are also used to estimate the polarizability of the first static (hyper) polarizability of the non-linear optical (NLO) investigation for its optoelectronic properties. Moreover, the oscillator strength (f) acquired by using the TD-DFT approach is used to compute light harvesting efficiency (LHE).

Results and Discussion

Screening of π-Conjugated Bridge

A major problem with the D-π-A framework for the PV performance of DSSCs, as we described in the previous section, led us to change the π-spacer in particular. We calculated SZ-1 to SZ-5 dyes based on T2-1 dye in order to demonstrate good PV performances of the various conjugated systems of PTZ-based metal-free dyes. The subsequent inclusion of various functional groups, including thieno[3,4-d]pyrimidine, thieno[3,4-b][1,4]dioxine, 2,5-thiophenedicarboxaldehyde, benzo[c][1,2,5]thiadiazole and [1,2,5]thiadiazolo[3,4-g]quinoxaline. Figure 1 illustrates the influence of the superior π-spacer portions on the structural geometries for all the SZ-1 to SZ-5 dyes. Table I displays the calculated geometrical parameters of some important torsion angles or dihedral angles of the molecules. The computed results shown in Table I demonstrate that the SZ-1–SZ-5 dyes have superior delocalized electron distributions compared to T2-1 dye and are hence more amenable to better intramolecular charge transfer (ICT) capabilities.

Fig. 1
figure 1

Optimized ground state geometries of the dye molecules in solvent phase obtained at the B3LYP/6-31G(d) level of theory.

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Table I Some specific dihedral angles of the optimized dyes
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Electronic Structure of the Dyes

To examine the optical and electrical characteristics of SZ-1–SZ-5 molecules, the TD-DFT approach was used. Using the conductor-like polarized continuum model (CPCM), the initial self-consistent field (SCF) predicted by hybrid B3LYP level theory at 6-31G(d,p) basis sets was used to determine the solvation of free energies. The ultraviolet–visible (UV–Vis) spectral analysis of the developed dyes must be associated with considerable absorption capacity and must fit as closely as feasible with the solar radiation spectrum. Figure 2 shows the simulated absorption spectra of the SZ-1–SZ-5 dyes. Table II shows the results of TD-DFT calculations on the excitation energies (E), f and electronic transitions to provide insight into the electronic and photophysical characteristics of SZ-1–SZ-5 molecules and T2-1. Using T2-1 as a reference dye molecule, the normalized absorption wavelengths from 300 nm to 800 nm are also determined in order to take a relative position of the strong absorption quality and ability of all provided dyes in the visible range. These dye molecules absorb light at two separate wavelengths (\(\lambda_{\max }\)) in the UV and visible light spectrum. The π-π* electronic transitions are responsible for the shorter \(\lambda_{\max }\) range between 300 nm and 400 nm, while it is acknowledged that the organic D-A electron transfer state occurs in the longer \(\lambda_{\max }\) range of 600–900 nm. According to calculations, the highest \(\lambda_{\max }\) for SZ-3 occurs at 810 nm, with an electronic excitation energy of 1.531 eV. When compared to the T2-1 dye, the HOMO → LUMO with f of 0.197 are responsible for a 100% substantial contribution to this electronic transition. Additionally, the second-best \(\lambda_{\max }\) peak at 680 nm (SZ-1) with an f of 0.181 is assumed to be mostly caused by the HOMO → LUMO transition. To put it another way, it was discovered that the length of π-conjugation increased and the optical absorption range shifted to higher \(\lambda_{\max }\) as a result of metal-free organic substitution. These PTZ derivatives are good options for increasing solar light harvesting in the infrared (IR) region of the solar spectrum for use in PV solar cells.

Fig. 2
figure 2

UV–vis absorption spectra of organic dyes in THF solution.

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Table II Computed electronic transitions, absorption maxima (\(\lambda_{\max }\) in nm), oscillator strengths (f in a.u.), electronic excitation energies (E in eV) and orbital contributions (%) of SZ-1–SZ-5 dyes using TD-DFT at B3LYP/6-31G(d,p) level
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The emission spectra (\(\lambda_{emi}\)) of dye sensitizers based on PTZ were determined using TD-DFT computations. All dyes were exposed to emission spectra using the optimized geometry of the excited state and the corresponding values of electronic transition, \(\lambda_{emi}\) and other parameters are tabulated in Table III. The estimated emission spectra of PTZ-based SZ-1–SZ-5 dye sensitizers in THF solvent are displayed in Fig. 3. These dyes will have good fluorescence intensities since the S1-S0 electronic transitions were found to have high \(\lambda_{emi}\) and excitation energy. The strong absorption band in SZ-3 is attributed to the π-π* electronic transition because it was discovered that SZ-3 has a greater \(\lambda_{emi}\) at 950 nm, which is 419 nm higher than the T2-1 absorption \(\lambda_{\max }\). Table IV demonstrates that good electron injection and CT properties of the DSSCs are anticipated for all PTZ dye compounds.

Table III Calculated oxidation and reduction potential energies (\(E^{dye}\), \(E_{{}}^{{dye^{*} }}\) in eV), vertical transition energy (E in eV), free energy of electron injection ( in eV), regeneration ( in eV), open-circuit photovoltage (\(eV_{OC}\) in eV), light-harvesting efficiency (LHE in a.u.), first-order hyperpolarizability (β in e.s.u.) and dipole moment (\(\mu_{normal}\) in debye) of SZ-1–SZ-5 dyes
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Fig. 3
figure 3

Emission spectra of the all dyes in THF solution.

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Table IV Computed electronic transitions, emission spectra (\(\lambda_{emi}\) in nm), oscillator strengths (f in a.u.), electronic excitation energies (E in eV) and orbital contributions (%) of all designed molecules using TD-DFT at B3LYP/6-31G(d,p) level
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Intramolecular Charge Transfer Analysis

The electronic structure and molecular distribution pattern of the SZ-1–SZ-5 dyes have been further studied using the frontier MO (FMO) theory. The HOMO and LUMO of MO theory are of particular relevance in this regard since they may be advantageous in the potential CT processes. The charge distribution in the MOs is dispersed on the HOMO and LUMO levels during the photoexcitation process, and it is also partially distributed to the π-spacers. The electronic density maps of the HOMOs and LUMOs are shown in 3D-optimized structures in Fig. 4. The image clearly shows that the HOMO to LUMO electron transition can predict the emergence of desirable charge-separated states for the specified dyes and that the HOMO-LUMO energy levels are related to CT processes from D to A. According to the MO theory, the overlap between the HOMO and LUMO transition determines the distribution of electron density in the σ1s MO, and the D-A moiety exhibits the strongest induction effects and π-spacer groups. As a result, we conclude that the conduction band edge (CBE) of TiO2 material exhibits substantial interactions between the electron-D and A.

Fig. 4
figure 4

Electron distributions of the HOMOs and LUMOs.

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Because it is considered to be more suitable for solar cell applications, the LUMO energy level was compared with the potential CBE of TiO2. These measurements reveal a shorter electron transport time and longer lifetime of photoexcited charge carriers. We have taken into consideration a CBE of TiO2 at the calculation values that are comparable to the experimental data (−4.0 eV). The electrolyte redox potential (I/I3−) and the HOMO level capacity to penetrate the mesoporous semiconductor layer are both highly effective and have good long-term stability. Low dye regeneration contribute to faster photoelectrons injection into the CB. All the SZ-1–SZ-5 dyes meet the molecular excited energy states necessary for their ability to function as photosensitizers. The LUMO level is specifically situated above the oxide CBE of the TiO2 surface, enabling the CT process from the dye sensitizers to the semiconductor and electrolyte. Furthermore, the efficient regeneration of oxidized states is made possible by the fact that the HOMO level is lower than the (−4.8 eV) redox shuttle. Because all of the proposed molecules have identical relative transition energy levels, it is impossible to predict which one will effectively offer a CT to the oxidation state. With a LUMO of −4.93 eV, the SZ-3 dye is closest to the TiO2 conduction band, as seen in Fig. 5.

Fig. 5
figure 5

FMO energy level diagram of the SZ(1–5) dyes.

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Density of States

Using density of states (DOS) calculations of the SZ-1–SZ-5 molecules along with their estimation onto the component parts of developed dyes and compared with T2-1 dye, we are able to obtain a clearer understanding of the electron injection mechanism. The T2-1, or the point at which the energy band gaps of HOMOs and LUMOs are zero, is represented by the black line. Consequently, clarification of the differences in energy conversion due to macrocycle cavity replacement and elongating the bond distances of the π-conjugation system of the D-π-A dyes is required in the current density spectrum. The DOS of a molecular system denotes the region of power-level states per interspaces that are attainable states that electrons can occupy. Since there are multiple energy levels available for electron occupation in the high-energy area of the DOS at a given energy stage, superlinear scaling with the extremely efficient conversion is possible. The computed DOS spectrum of the dye molecules is intended to demonstrate the influence of the metal alternative as well as the greatest effect of lengthening the strong π-conjugation. As seen in Fig. 6, the DOS becomes more abundant close to Fermi degrees when moving from SZ-1 to SZ-5 molecules, where additional profound vales arise on the two sides close to the Fermi levels. This illustrates the main impact of increasing the strong bond distance of the π-spacer system on enhancing the performance of solar cells.

Fig. 6
figure 6

DOS spectrum of the SZ(1–5) dyes.

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Nonlinear Optical Properties

The quality of intermolecular interactions, total cross sections of different scattering and frequency-mixing methods, as well as the NLO properties of the molecular system, can all be used to determine the first static hyperpolarizabilities.41,42 According to reports, a novel hemicyanine sensitizer framework with outstanding photoelectric conversion typically possesses great optical properties. Calculations were made for the electro-optics and hyperpolarizabilities of SZ-1–SZ-5 compounds in order to examine the links between molecular structures. Hyperpolarizabilities can be calculated using TD-DFT-dependent sum-over states (SOS), coupled-perturbed Hartree–Fock (CPHF) and finite perturbation (FP) theory. However, very large basis sets for dyes cannot afford to use CPHF, FP, and SOS procedures since they are too expensive. Here, using B3LYP at the 6-31G(d,p) level of theory, we numerically differentiate to derive the static first-order hyperpolarizability, which can be calculated by Eq. 1.43

$$ \beta = \left[ {\left( {\beta_{xxx} ,\beta_{xyy} ,\beta_{xzz} } \right)^{2} + \left( {\beta_{xxy} ,\beta_{xzz} ,\beta_{yzz} ,} \right)^{2} + \left( {\beta_{xxz} ,\beta_{zyy} ,\beta_{zzz} } \right)^{2} } \right]^{1/2} $$
(1)

where \(\beta_{xxx} ,\beta_{xyy} ,\beta_{xzz} ,\) \(\beta_{xxy} ,\beta_{xzz} ,\beta_{yzz} ,\) \(\beta_{xxz} ,\beta_{zyy} ,\beta_{zzz}\) are the tensor components of first hyperpolarizability of designed dyes, respectively. Hyperpolarizability is inversely proportional to E. Table III shows that the hyperpolarizability value of an SZ-3 molecule is 2.765 × 10–28 e.s.u. (E is 1.27 eV obtained from TD-DFT method).

Photovoltaic Properties

In general, photosensitizers determine the PCE of DSSCs. The spacer effects of the D-π-A structure are the primary structural component of the most effective metal-free dyes. Different π-bridge groups inside the D-π-A structure can change the photophysical characteristics of planned dyes. As a result, TD-DFT computation is employed in this study, which is an effective way of identifying the optimum electronic structural features of SZ-1–SZ-5 dyes in comparison to other sophisticated quantum chemical techniques. The orbitals have been shown to be ideal for the features of computational survey and interpretations.

We are aware that the intensity of incident light (\(P_{INC}\)), open-circuit voltage (\(V_{OC}\)), fill factor (FF) and short-circuit current density (\(J_{SC}\)) all affect the PCE of solar cell characteristics, and they can be calculated by Eq. 2.44

$$ \eta = \frac{{V_{OC} J_{SC} FF}}{{P_{INC} }} $$
(2)

The following Eq. 3 can be used to estimate \(V_{OC}\) in DSSCs,

$$ V_{OC} = \frac{{E_{CB} }}{q} + \frac{kT}{q}\ln \left( {\frac{{n_{C} }}{{N_{{_{CB} }} }}} \right) - \frac{{E_{redox} }}{q} $$
(3)

where the \(V_{OC}\) of a DSSC is determined by the energy LUMO difference between the quasi-Fermi level of p-type semiconductor substrate CBE of TiO2 and the redox potential of the electrolyte. It is assumed that the I−/I3− solution will be utilized as the redox electrolyte in DSSCs. ΔCB is the main influencing factor of \(V_{OC}\), which is calculated using the following Eq. 4,

$$ \Delta CB = - \frac{{q\mu_{normal} \gamma }}{{\varepsilon_{0} \varepsilon }} $$
(4)

where q is the elementary charge, γ is the molecular outermost level concentration, \(\mu_{normal}\) denotes the total dipole moment (\(\mu_{normal}\)) of different π-conjugated dye molecules perpendicular to the surface of the TiO2 and ε0, ε is the dielectric constant. It is obvious that a high \(\mu_{normal}\) will cause the CBE to shift more, which results in a higher value for \(V_{OC}\). Compared to T2-1, the SZ-3 dye molecule (7.8431 D) has the highest \(\mu_{normal}\) of an excellent electronic transition, as indicated in Table IV, which may contribute to the high PCE of DSSCs. The formula from the literature was used to compute the maximum theoretical \(eV_{OC}\) of the dyes, and the corresponding values are provided in Table III.45 From the table, SZ-1–SZ-5 dye values are 0.84, 1.21, 0.93, 0.96 and 0.62 eV, respectively. Table III shows that the absolute \(eV_{OC}\) values of SZ-1–SZ-5 indicate a promising and capable electron injection mechanism. Taking into account values of \(eV_{OC}\) , all the dyes may have higher \(V_{OC}\) of the organic solar cell. These findings show that all sensitizers may make excellent candidates for DSSCs.

The following Eq. 5 can be used to express \(J_{SC}\) parameters, which is another method of increasing PCE.46

$$ J_{SC} = \int\limits_{\lambda } {LHE(\lambda )\Phi_{inject} \eta_{collect} d\lambda } $$
(5)

where LHE(λ) is a measure of light harvesting efficiency related to UV–Vis wavelength, \(\Phi_{inject}\) is the electron injection efficiency from the excited state dye and \(\eta_{collect}\) refers to the charge collection efficiency. Since the designed organic sensitizers are the only difference between DSSC electrodes, \(\eta_{collect}\) can be assumed to remain constant.47 The f of the absorption spectra allows for the calculation of LHE(λ).48 Table III indicates that the LHE of SZ-3 dye molecules (0.37 a.u.) has a high value when compared to other dyes. The driving force for the fast electron injection (ΔGinject) from excited dyes to the CBE of TiO2 was directly related to these values. According to the literature, to achieve good performance, ΔGinject must be more than 0.2 eV.49 This can be summarized by the following Eq. 6.50

$$ \Delta G_{inject} = E^{{dye^{*} }} - E^{{TiO_{2} }} $$
(6)

where \(E_{{}}^{{dye^{*} }}\) represents the reduction potential of the dyes, ECB is the energy value of CBE (−4.0 eV) and the electronic state energies. Table IV lists the calculated ΔGinject values for all the dyes examined. We can see that these excited state dyes have an adequate driving power for rapid charge injection because the corresponding values of ΔGinject for SZ-1–SZ-5 are significantly better than 0.2 eV. However, a high value may come before energy redundancy, which can be provided by a smaller ΔGinject and larger thermalization losses.51,52 The dye regeneration efficiency (\(\Delta G_{reg}\)), which can be determined using Eq. 7, also affects \(J_{SC}\) of DSSCs.53

$$ \Delta G_{reg} = E_{redox} - E^{dye} $$
(7)

where \(E^{dye}\) is the oxidation potential of the dyes and \(E_{redox}\) is the redox potential of the dyes (at −4.8 eV). According to the review by Robson, the charge/electron movement in the TiO2 surface and the \(\Delta G_{reg}\) of the oxidized dyes can greatly increase the high conversion efficiency of the DSSCs.54 The augmentation of regeneration, which is found to facilitate the increase of \(J_{SC}\), occurs because of the stronger electron driving forces for electron injection of the SZ-3 dye and regeneration of the oxidized dye. The best candidate among all the SZ-1–SZ-5 dyes is the SZ-3 molecule, which has the best performance on PV parameters such as \(\lambda_{\max }\), LHE, \(J_{SC}\), \(\mu_{normal}\), \(eV_{OC}\) and achieves tolerable stability between conflicting factors. In light of this, the SZ-3 molecule will be a strong candidate for excellent performance in DSSCs.

Impact of the Semiconductor

We next compute the DOS spectrum of the dyes tied to Ti complexes together with their prediction onto the various components of the SZ-1–SZ-5 molecules to gain a better understanding of the electron injection mechanism. The centre of the Ti semiconductor HOMO-LUMO energy levels, which is put at 0 eV in Fig. 7, is known as the quasi-Fermi level of a solid state. The HOMOs and LUMOs were studied and are shown in Fig. 8 to help understand the type of electron density. This graph shows that the PTZ group is primarily stabilized by the HOMOs, while the semiconductor is primarily stabilized by the LUMOs.

Fig. 7
figure 7

DOS of all dye@TiO2 complexes.

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Fig. 8
figure 8

Representation of the all dye@TiO2 complexes of HOMOs and LUMOs were obtained at the TDB3LYP/6-31G(d) level.

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We use this work as a chance to theoretically calculate the dyes associated with the Ti complex. In order to ensure that all of the dyes are neutral groups, we assume that the dyes are restricted to a bridge Ti atom and the SZ-1–SZ-5 groups. Using the DFT ground state approach, Peng and colleagues discovered a similar impact in this model.55 The following are the results of the full theoretical approach. We analyse the impact of the Ti semiconductor collision on the \(\Delta G_{inject}\) parameter and compute the semiconductor effects on the important parameters. The charge injection forces and electron transfer are connected to the \(\lambda_{\max }\),\({E}_{ox}^{dye}\) \(E^{dye}\) and \(E^{{dye^{*} }}\) \({E}_{ox}^{dye*}\) needed to evaluate the free energy change. We have estimated all of the PV parameters shown in Table V using both the Ti model and the calculated variation of the \(\Delta G_{inject}\),\({E}_{ox}^{dye}\), \(E^{dye}\) and \(E^{{dye^{*} }}\) (in eV). The positions of the LUMO energy level and the CB of Ti-based materials are particularly crucial for the highest solar energy transfer process of PV devices because the higher energy levels of the electrons are influenced by injection rates. Unfortunately, it is exceedingly difficult to obtain accurate estimates of these energies, the absolute values, and the position of the LUMOs above or below the CB edge compared to the Ti-CB state at the current levels of theory.

Table V Simulated oxidation and reduction potential energies (\(E^{dye}\), \(E_{{}}^{{dye^{*} }}\) in eV), vertical transition energy (E in eV), free energy of electron injection (in eV), regeneration (in eV), open-circuit photovoltage (\(eV_{OC}\) in eV), oscillator strength (f in a.u.) and light-harvesting efficiency (LHE in a.u.) of the SZ-1–SZ-5 with Ti dyes
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Conclusions

In conclusion, theoretical research was conducted to investigate the use of DFT and TD-DFT calculations to estimate the structural, electronic and photophysical properties of PTZ-based SZ-1–SZ-5 molecules for DSSCs. When compared to T2-1 dye, the metal-free SZ-1–SZ-5 dyes performed well in terms of their \(J_{SC}\), \(eV_{OC}\) properties. Our findings showed that the HOMO-LUMO gap in these dyes was lower than that in molecules reported in the literature. Specifically, SZ-3 dye exhibits a reduction in the HOMO-LUMO energy gap, an increase in optical activity and noticeably enhanced PV characteristics. The improvement of DSSCs based on PTZ dye was therefore thought to have been greatly influenced by the results of this investigation. Finally, PTZ derivatives demonstrate how π-spacer groups can be appropriately adjusted for use with organic PV in DSSC applications by changing their D-π-A structure.