Introduction

Captivating advantages of high molar extinction coefficient, flexible assembling, low-cost fabrication, and environmental cleanliness has helped metal-free organic dye-sensitized solar cells (DSSCs) to gain considerable interest as an alternative renewable energy source over the last decade1,2,3,4,5,6,7. In DSSC system, an organic photosensitizer is anchored to the wide band gap semiconductor and possesses a donor-π-acceptor (D-π-A) structure motif with well-developed intramolecular charge transfer (ICT) characteristics. The photoactive sensitizer of DSSCs absorbs sunlight in the form of the photon and photo excited dye injects electrons to the conduction band (CB) of the semiconductor such as TiO2. The performance of DSSCs relies on fundamental quantum properties like the lowest unoccupied molecular orbital (LUMO), the highest occupied molecular orbital (HOMO), and their distributions in the photosensitizers. Most significantly, the kinetics of the electron-transfer processes at the interface between the dye and the semiconductor as well the dye bound to the semiconductor surface and the hole-transporting substance8,9. Thus, it is imperative that the microscopic interfacial properties of organic metal-free dyes on TiO2 photoanodes need to be thoroughly investigated. This will elucidate the details of charge transfer and anchoring state at the interface, band gap offset of dyes, HOMO and LUMO shift, and their redistribution.

Computational approaches have become an integral part of research in material science following their successes in drug design and discovery process. In silico modeling to design, followed by quantum and electrochemical parameters calculation, represents the complete scheme for the rational solar cell development prior to experiment10,11,12,13. Our research group has efficiently employed quantitative structure-property relationship (QSPR) approach for modeling and virtual screening of polymer-based solar cells for the very first time14. It was followed by first QSPR modeling of arylamine organic dyes (AOD) for DSSCs explicit to cobalt electrolytes that were recently reported5. In our previous study, we have modeled 273 AODs from 11 diverse chemical classes explicit to iodine electrolyte followed by quantum chemical analysis employed to understand the primary electron transfer mechanism and photophysical properties. Further, identified features from QSPR models were applied in designing of 10 dyes - each for Tetrahydroquinoline (THQ), N,N-dialkylaniline and Indoline, respectively maintaining required electrochemical parameters with encouraging enhancement in predicted percent power conversion efficiency (PCE) value13. It is important to mention that finally, based on requisite electrochemical and photo-physical parameters seven lead dyes have been screened from the ten designed dyes for each chemical class. Expanding the research work to the next level, in the present study, we have investigated the seven THQ lead dyes to explore the interfacial properties as well as further photophysical properties of the isolated dyes. Compare to Rubidium based organic dyes; metal free organic dyes are receiving more endorsement to devise DSSCs due to the advantages of molecular engineering including the possibility of tuning donor-acceptor of dyes, their broad optical absorption, and exceptional electrochemical properties15,16,17.

Though a substantial number of studies have been directed towards metal-based organic dyes, only a limited work6,18,19 reported on non-metal organic dyes-sensitizers. Computational approaches focused on the semi-classical20 and Density Functional Theory (DFT) approaches combined with Time-Dependent DFT (TD-DFT)12,21,22,23,24, have been used to explore the electron injection process at the interface of metal and non-metal based organic dyes. First principle approaches were carried out to study the characteristics of the designed THQ dyes before and after the adsorption on TiO2 surface to compare qualitatively different aspects of the complex phenomena. Initially, we have analyzed the crucial parameters of the isolated dye like open-circuit voltage, short-current density, electron injection efficiency, reorganization energy, injection time, and intramolecular charge transfer (ICT) parameters by DFT and TD-DFT calculations. On the next level, structural and electronic properties, charge density and electrostatic potential energy differences of the adsorbed system, variations in the band gap and projected density of state were computed with the use of plane-wave DFT including Hubbard correction. The encouraging outcomes of the performed study allow selecting new efficient THQ dye sensitizers for DSSCs to obtain higher photo-to-electron conversion efficiency.

Results

Optoelectronic properties of isolated dyes

The seven lead dyes from the THQ family studied by us are represented in Fig. 1. The structural and electronic properties of the designed THQ dyes were computed in gas and solvent phase to get deep insight into investigated phenomena. After the photo-excitation of dye in DSSCs, JSC and VOC are the most relevant parameters to calculate theoretically with precision to compare its performance as an efficient sensitizer. Electron injection mainly depends on the absorption capacity of photon, ground state oxidation potential and optimum HOMO-LUMO energy gap of the respective dye. Parameter like JSC can be estimated in terms of ΔGinject and the computed critical energy parameters25 of the present study are tabulated in Table 1 for B3LYP/6–31 g(d, p) level of theory in gas phase and with TD CAM-B3LYP/6–31 g(d, p) level of theory in acetonitrile solvent (Applied equations for computation are discussed in Methods section).

Figure 1
figure 1

The sketch of all the investigated Tetrahydroquinoline dyes.

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Table 1 Estimated critical energy parameters (in eV) and electron injection time (in ns) with B3LYP/6–31 g(d, p) level of theory in gas phase.
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The obtained values of ΔGinject for all of the cases are negative which implies the spontaneity of the electron injection process. Also, Islam et al. proved that the injection efficiency of the electrons in the excited state (Φinject) tends to approach 1 when ΔGinject is greater than 0.20eV26. THQ1 (−1.18 eV) is showing the highest efficiency while THQ7 (−0.93 eV) displays the lowest one. The sequence of dyes considering ΔGinject is: THQ1 > THQ2 > THQ5 > THQ8 > THQ3 > THQ9 > THQ7. Comparable assessments of dyes regeneration efficiency have been calculated (See equation in methods section) and the computed values of ΔGregn of all the dyes are negative which implies the feasibility of the process. The values of ΔGregn vary from 9.79 to 10.9 eV that is much higher than the accepted value of ΔGinject and confirming that the dye regeneration process is more favorable compared to electron injection27. The THQ9 with the lowest ΔGregn value suggests that it will minimize the undesirable charge recombination between oxidized dye and photoexcited electrons of the dye molecule efficiently, due to the presence of diketopyrroleopyrrole (DPP) unit with one benzene ring.

The open circuit voltage (VOC) that can be expressed28 by the Equation (1), depends on the recombination of the dye with electrolyte. This type of recombination could provide insufficient blocking effect due to relatively low adsorption density of dyes29. Thus to enhance the effect, the shape and structures of the dye need to be optimized. Ning et al. suggested that upshifting of the sensitizer ELUMO will increase the VOC and reduce the charge recombination30. Our computed results showed that THQ2 has highest while THQ9 has lowest VOC value among the studied dyes. Analyzing individual dye structures, we can firmly state that presence of DPP unit is responsible for lowering VOC values for THQ5, THQ7-THQ931,32 and absence of DPP fragments in THQ1-THQ3 resulted in higher VOC values.

$${V}_{OC}={E}_{LUMO}-{E}_{CB}^{Ti{O}_{2}}$$
(1)

Electron recombination is one of the most important factor which reduce VOC by two ways: (i) redox couple of electrolytes, and ii) oxidized dyes2. Richards et al.33 established that electron recombination to the electrolyte dominated by the free iodine concentrations and thus I2 is more inclined to bind with heteroatoms (like O, N, S etc.) of dye molecules via non-covalent halogen bond interaction. To estimate the electron recombination on TiO2 surface, we considered three different configurations of the isolated-dye…I2 complex. Three configurations are: (a) I2 (IA − IB) binds with the N of CN moiety; (b) S atom of thiophene ring (S1) near acceptor units binds with I2 (IC − ID) atom; and (c) S atom of thiophene ring (S2) far form acceptor units binds with I2 (IE-IF) atom. The optimized structures of dye…I2 complex for all the seven dyes are depicted in Fig. 2 while the bond lengths of I-X (X = I, N, S) are listed in Table S1 (supplementary material). In dye…I2 complex, intramolecular I-I bond lengths are larger than the covalent radii (2.86 Å), which imply the iodine dimers are weekly bound and the distance of CN and iodine (CN–IA) atom is smaller than the net van der Waals radii 3.53 Å but larger than the net covalent radii 2.03 Å. Also, the bond lengths between thiophene S and iodine (S–IC/E)are larger than the covalent radii, while smaller than the net van der Waals radii (3.78 Å) of the binding atoms. Similar outcomes was also observed by Xu et al.34.

Figure 2
figure 2

Optimized structures of all isolated dye-I2 complex. Color code: Gray, Yellow, Red, Blue and Purple representing C, S, O, N, and I atoms.

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The trend of CN–IA bond lengths is: THQ9 > THQ7 > THQ8 > THQ2 > THQ1 > THQ3 > THQ5 while the length of IA-IB is following: THQ5 > THQ3 > THQ1 > THQ2 > THQ8 > THQ7 > THQ9. Moreover, the sequence of S1–IC bond length (except THQ1 and THQ2) is THQ5 > THQ7 > THQ8 > THQ9 > THQ3 and the trend for IC-ID is: THQ3 > THQ9 > THQ7 > THQ8 > THQ5. In both cases, the interaction of dye and iodine is increasing with the increase of separation distances of iodine. On the other hand, THQ1 and THQ2 are showing different trend in case of S2–IE bonds. It might be possible due to the presence of two different thiophene rings, as strongly supported by literature34. Based on above analysis, it is quite difficult to choose which dye will transfer the I2 away from the semiconductor (TiO2) surface and help to reduce the charge recombination by inhibiting the local concentration of I2 on TiO2.

Built-in push-pull structure in the designed dyes possesses significant charge separation that confirms the high overall efficiency of photo-to-electron conversion35. Index of spatial extent method is used to describe the ICT process qualitatively. Spatial index including distance between two barycenters of the density depletion and density accumulation distribution upon excitation (DCT) in Å, transferred charge (qCT) in e, and overlap integral (S) are reported in Table 1. Analysis of data suggested that chromophore in dye with larger overlap integral increases the amount of charge transfer with longer DCT which confirms proper charge separation of donor and acceptor moieties35. The predicted trend of S is as following: THQ9 > THQ7 > THQ8 > THQ2 > THQ1 > THQ3 > THQ5, while DCT displays the following tendency: THQ7 < THQ9 < THQ3 < THQ2 < THQ1 < THQ5 < THQ8. The increased value of S implies that the addition of DPP unit as an additional donor and acceptor moiety makes the smooth flows of electron transfer from the ground state to excited state. However, from the above sequence, it is not possible to select which lead dye will be more efficient for DSSCs based on ICT. Again, upon the analysis of the amount of charge transferred, the qCT sequence of dyes is as following: THQ1 > THQ9 > THQ2 > THQ3 > THQ7 = THQ8 > THQ5. There are some literature evidences that also claimed advantages of DCT and S which may reduce the charge recombination of the sensitizers, besides excellent charge separation34,36. If one investigates the Fig. S1 reported in Supplementary material, the overlap integral space can be visualized clearly upon electronic excitation. The blue and green colors indicate the centroid of hole (C+) or donor and the centroid of electron (C−) or acceptor.

Furthermore, all designed dyes had been checked based on the Marcus theory37 by calculations of the charge transfer rate using the following equation:

$${k}_{ET}=\frac{1}{\sqrt{{\lambda }_{total}}}\sqrt{\frac{\pi }{{\hslash }^{2}{k}_{B}T}}|{V}^{2}|\exp \{-\frac{{\lambda }_{total}}{4{k}_{B}T}\}$$
(2)

In equation (2) except reorganization energy, λtotal, all the parameters on the right-hand side are constant. Thus electron transfer rate constant (kET) depends only on λtotal, which is the sum of hole reorganization (λh) and electron reorganization (λe) energy, whose values can be estimated by the Equations (3) and (4), respectively.

$${\lambda }_{h}=({E}_{0}^{+}-{E}_{+}^{+})+({E}_{+}^{0}-{E}_{0}^{0})$$
(3)
$${\lambda }_{e}=({E}_{0}^{-}-{E}_{-}^{-})+({E}_{-}^{0}-{E}_{0}^{0})$$
(4)

where, \({E}_{0}^{+}\,({E}_{0}^{-})\) denotes the energy of cation (anion) calculated from the optimized structure of the neutral molecule; \({E}_{+}^{+}\,({E}_{-}^{-})\) is the energy of cation (anion) calculated from the optimized cation (anion); \({E}_{+}^{0}\,({E}_{-}^{0})\) is the energy of neutral molecule computed from the cationic (anionic) state; and \({E}_{0}^{0}\) is the energy of neutral molecule at the ground state.

Difference between the λh and λe is also important to determine the equilibrium properties for hole- and electron transport while smaller λtotal accelerates the charge-carrier transport rates and vice-versa. The value of calculated λtotal is found within a range of 0.48 eV to 0.65 eV with following trend: THQ9 = THQ8 < THQ5 < THQ7 < THQ1 = THQ2 < THQ3. Also, the lifetime (\({\rm{\tau }}\)) of first excited state (S1) is a crucial factor to modulate the charge transfer phenomenon efficiently. This can be estimated by the relationship from Chaitanya et al.38 \(\tau =1.499/(f{E}^{2})\); where E (cm−1) is the excitation energy for S1 and f is the oscillator strength for the respective state. The dye with a more extended lifetime in the first excited state is predicted to transfer charge efficiently39. Our calculations of charge transfer shows the following trend: THQ5 (3.42 ns) > THQ7 > THQ9 > THQ8 > THQ3 > THQ2 > THQ1 (1.42 ns). The difference between the redox potential and the EHOMO13, as well the energy gap of the sensitizer affect the lifetime to reduce undesirable reaction like charge recombination40. On the basis of Marcus theory and lifetime in the excited state, we can preliminary comment that among the seven designed lead dyes THQ5, THQ7, THQ8, andTHQ9 are more proficient than THQ1, THQ2, and THQ3.

Based on the above analysis, we can firmly confirm that all of the designed dyes have the desirable optoelectronic properties including electron injection and lifetime in the excited state, open circuit voltage, ICT parameters, and regeneration of the dye itself. However, we are not able to conclusively comment on the overall performance because the effectiveness of isolated dye is not the only factor to determine the efficiency of DSSCs. The adsorption characteristic of the dye, the interface of dye@TiO2 and charge transfer phenomenon are also important factors to determine the efficiency of DSSCs, which are computed and thoroughly discussed in the next section.

Structural and electronic properties of dye-TiO2 system

To elucidate the stability and interfacial charge transfer phenomenon of the designed THQ dyes on anatase TiO2 (101) surface, we have calculated the adsorption energy, 3D charge density difference (CDD) plot, Bader charge analysis, planar averaged electrostatic potential and CDD with respect to Z-direction, and partial density of states (PDOS) using first principle approach.

Adsorption energy varied with different binding modes of anchoring group of dye and TiO2 surface. In literature, three different types of binding such as monodentate, chelated and bridged bidentate41 are prevailed and later one being the most stable12,23,42. Thus in the present study, the equilibrium interface geometry and adsorption energy of the dyes on anatase TiO2(101) surface were calculated based on the bridged bidentate bonding. Optimized configurations of the interface for all the dyes are illustrated in Fig. 3. It is notable to mention that the adsorption energy, charge density, and Bader charge analysis had been computed based on the deprotonated dye (negatively charged) and protonated TiO2 (101) surface (positively charged)43,44. Geometrical parameters and adsorption energy for the different systems were calculated and reported in Table 2. Adsorption energy is one of the measures to describe the strength of interaction or electronic coupling between TiO2 surface and a dye. In our study, THQ9 is showing highest adsorption energy (−3.77 eV) whereas THQ5 having the least (−1.42 eV) energy. The adsorption energy is calculated according to the Equation (5):

$${\rm{\Delta }}{E}_{ads}={E}_{dye+Ti{O}_{2}}-[{E}_{dye}+{E}_{Ti{O}_{2}}]$$
(5)

where, ΔEads, Edye+TiO2, Edye, Edye+TiO2 are the adsorption energy, energy of the system, free dye energy and TiO2(101) slab energy, respectively. The adsorption energy has been computed by the equation (5) with the use of van der Waals density functional, optB86b-vdW, implementing Hubbard corrections (Table 2). The average bond length between Ti and O of the –COOH group is approximately the same value for all of the systems42. Plane averaged electrostatic potential of TiO2 slab is lower than that of the dye molecule, suggesting charge transfers from dye molecule to TiO2, in line with results reported in Table 2. The electrostatic potential differences between dye and TiO2 slab also has a good agreement with the Bader charge transfer. The efficiency of DSSCs highly relies on both the rate of electron injection and the efficient regeneration of dye. Not only that, but also the HOMO and LUMO levels of the dye sensitizers are lower and higher enough than the redox couple and TiO2 conduction band, respectively, as reported in Table 1.

Table 2 Calculated adsorption energy (in eV) and bond lengths (in Å) of the most stable structure of dye@TiO2 systems by DFT + U method with optB86b-vdW density functional.
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Next, to gain insight into the dye-surface interactions, we have examined the charge redistribution between the dye and surface after and before the adsorption of dye at the same relative ionic positions and have shown the results in the Fig. 4(a). Here we have only discussed THQ1 dye, which is similar to other systems. Evaluating the figure, it is clear that there is definite charge injection from the dye molecule to the interface. For the better understanding, we consider the charge-density difference and the average of this quantity over the (x, y) plane is depicted in Fig. 4(b) suggesting that the charge at the interface originates from the dye molecule. This phenomenon is also confirmed through the 3D charge density difference plot illustrated in Fig. 4(c). Bader charge analysis45,46 results are illustrated in Table 3. This indicates that the charge transfer from the dye to interface region originates from the dye. The accumulation of charge at the interface is also in line with the trend mentioned above, except for THQ7, which comes after THQ9 but above THQ5 and THQ8. When rate of charge transfer reaches equilibrium state, net charge collection at interface leads to the formation of built-in electric field and helps to continuous electron injection from the dye to interface and interface to the TiO2 surface after the dye excitation. Quite similar results are obtained from analysis for other dyes as illustrated in Figs S2–S7 in Supplementary material file.

Figure 3
figure 3

Optimized by DFT + U method with optB86b-vdW density functional stable geometrical structures of studied dye@TiO2 systems.

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Figure 4
figure 4

For THQ1 (a) Planar averaged charge density of dye@TiO2 system after absorption (red), isolated dye (dashed) and surface (dotted) at the same relative positions. It is clear that there is no significant charge redistribution away from the interface region. Inset: magnifying the interface region and yellow part showing the amount of injected charge. (b) Planar average charge density difference as a function of position in the Z-direction, in Å. (c) 3D charge density difference with an isovalue of 0.006e/Å3. Blue and red color represents charge accumulation and depletion in space. The vertical cyan line indicates the interface line of dye@TiO2 system.

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Table 3 Ab initio (VASP) calculated band gaps (in eV) after adsorption of the Dye/TiO2 system and Bader charge (in e−). dgap (in eV) indicates the difference before and after adsorption.
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The differences of planar average charge density difference and planar average electrostatic potential differences are plotted in Fig. 5 with respect to Z-direction. The Fig. 5(a) depicts the important features of the interface in order to compare the electron injection efficiency of the dye. Among seven dyes, charge accumulation at interface of THQ1 is the highest while THQ8 showing the least of charge accumulation. The trend of accumulation is as following: THQ1 > THQ2 > THQ3 > THQ9 > THQ5 = THQ7 > THQ8. It is important to mention that THQ1 and THQ2 possess the largest amount of charge accumulation at interface as well as the highest free energy change for electron injection efficiency (see Table 1). The Fig. 5(b) represents the planar average self-consistent electrostatic potential difference as a function of the position in the Z-direction. Potential for all three components are dipole corrected. At interface the formation of well-shaped potential-well explains the charge transfer phenomenon that is in line with the previous discussions.

Figure 5
figure 5

(a) Comparison of planar averaged charge density differences and (b) planar averaged electrostatic potential differences as a function of position in the Z-direction (in Å) of all different dyes. Grey and cyan shaded stripes are representing the approximate position of the interface and –COOH group of dye, respectively.

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To further elucidate the electronic properties/band alignment of the dye@TiO2 interfaces, it is insightful to analyze the PDOS of adsorbed complexes. PDOS of the different interfaces is displayed in Fig. 6. After the adsorption of dye, for all considered systems, the conduction band minima (CBM) and valence band maximum (VBM) of TiO2 showed upward shift relative to Fermi level. After adsorption, the band gap of the complexes is reduced due to the introduction of sharp occupied molecular energy levels in the band gap regions from the dye. It is supported by the facts that narrow band-gap extends the absorption region and controls the photo adsorption efficiency while the energy difference between \({E}_{CBM}^{Ti{O}_{2}}\) and ELUMO of the dye regulates injection efficiency or short circuit current density. The computed band gap of TiO2(101) surface decreased from 1.70 eV to 0.40 eV (THQ7/TiO2, THQ8/TiO2) for dye@TiO2 system; while the range is 0.40 (THQ7/TiO2, THQ8/TiO2) to 1.25 eV (THQ3/TiO2) for all studied composite Dye@TiO2 systems. Band gaps for THQ1, THQ2, THQ3, THQ5, and THQ9 are 0.90 eV, 1.01 eV, 1.25 eV, 0.53 eV and 0.42 eV, respectively. The narrow band gap of specific dyes can be explained due to the lower order occupied orbitals of the dyes. Thus this characteristic helped in moving the conduction band towards lower energy. For all the cases, LUMO of the adsorbed dyes is coupled with the CBM of TiO2 surface that allows intermolecular electrons to be excited to the surface and increases the overlap between the LUMO and CBM, improving the electron injection process. Also, inner LUMO of the dye expedites electron injection process. In Fig. 6, it can be confirmed that the DOS of the dye has a strong overlap with the valence band of the TiO2 semiconductor, which means that dye introduces few pi-occupied levels on top of the TiO2 valence band. The newly pi-occupied levels from the dye become the new top-part of the valence region. In case of DI293 (highest experimental %PCE dye from our model dataset13), the band gap is 1.0 eV (see Fig. S8 in Supplementary material file). Moreover, the DOS of adsorbed dye molecules shift to higher energy (compared to before adsorption), illustrated a significant amount of charge transfer from dye to TiO2 surface. This is because of the HOMO of dye shifted to band gap regions while LUMO shifted toward the conduction band about 0.18–0.58 eV (Table S2 reported in Supplementary material). Based on PDOS, it is crucial to highlight that, our designed dyes (except THQ2 and THQ3) have lower band gap than DI293 with highest photo-conversion efficiency value obtained in modeling study, suggesting that their photon absorption efficiency would be higher than that of the DI293. Insertion of DPP47 moiety, also with the double bonded oxygen as an additional donor and acceptor, enhances the photovoltaic efficiency of the designed dye. The above results strongly support the conclusions of our previous study13.

Figure 6
figure 6

The partial density of states (PDOS) of adsorbed complexes at different interfaces. The vertical dashed line indicates that the Fermi level is set at zero energy.

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Discussions

In summary, we have performed systematic, comprehensive investigations to evaluate seven ‘lead THQ dyes’. These dyes were selected by our group in previous study as characterized by high-predicted %PCE. The current work was carried out to reveal the relation between dyes’ structure and their photo-conversion efficiency. The optic-electronic properties of the isolated dyes were computed by DFT and TD-DFT with solvent effect, whereas necessary. Interfacial properties of the adsorbed dye on TiO2 (101) surface was investigated with the use of first principle approach with van der Waals density functional, in conjunction with on-site Coulomb interaction for Ti 3d orbital. Outcomes from the first step can be summarized as follows: THQ9 emerged among the top three dyes concerning charge transfer characteristics (S, τ, qCT, λtotal) while giving lower value for open circuit voltage (VOC), and electron injection energy (ΔGinject) than other considered dyes. Furthermore, three different binding modes and their structural attributes of dye–I2 complex are evaluated to address electron recombination process. Analyzing dye regeneration efficiency, THQ3 shows the highest value. Based on calculations for the isolated dyes, it can be concluded that all of the considered dyes possess potential properties to become an efficient dye-sensitizer for DSSCs. Introspecting the geometrical interface structures, PDOS, planar averaged charge density and potential energy difference of dye@TiO2 system; we infer that there is robust electronic coupling between all dyes and TiO2 surface. The PCEs of THQ7, THQ8, and THQ9 dyes are better than for the other four dyes when dye@TiO2 are considered, due to their lowest adsorption energy, lower band gap and higher Bader charge. Interestingly, the other four dyes also possess all required electrochemical parameters to act as efficient and improved dye sensitizers for DSSCs, compared to the products available on the market. Therefore, the insertions of double bonded oxygen to the aromatic carbon certainly improve the photovoltaic performance and energy conversion efficiency of sensitizers. In conclusion, based on the comprehensive analysis, modeling and design followed by the structural and electronic properties evaluation of the lead dyes, we proposed them as efficient, potential sensitizers for future DSSCs with improved PCE.

Methods

Geometry optimization and estimation of all photophysical parameters of the isolated dyes were performed in Gaussian09 package48. Ground state and excited state calculations were done with B3LYP and CAM-B3LYP functional within DFT and TD-DFT framework, respectively. It is notable to mention that CAM-B3LYP functional for the TD-DFT method provides reasonable prediction for the excitation energies and the absorption spectra due to its long-range coulomb-attenuating method5,13,49. In all the cases, 6–31 g(d,p) basis set is used for C, H, O, N, and S atoms while LANL2DZ effective core potential (ECP) for I atoms. For the ICT parameters and to visualize centroids calculations were performed by code Multiwfn 3.3.950. The overall efficiency of photo-to-electron conversion in DSSCs is determined by the integral of short-circuit photocurrent density (JSC), open–circuit photo voltage (Voc), fill factor (FF) and incident solar power on the cell1:

$$\eta =FF\frac{{J}_{SC}\times {V}_{OC}}{{P}_{IN}}\times 100 \% $$
(6)

The JSC depends on the absorption coefficient of the dye and the interaction between the dye and the nanocrystalline TiO2 surface. It can be computed by the following equation:

$${J}_{SC}=\int LHE(\lambda ){{\rm{\Phi }}}_{inject}{\eta }_{collect}d\lambda $$
(7)

where LHE is light harvesting efficiency at wavelength λ, Φinject is quantum yield for electron injection efficiency and ηcollect is the charge collection efficiency which only depends on the architecture of DSSCs while other parameters strongly depend on the structural and quantum phenomenon of the dye. Katoh et al.51 related injection efficiency to the free energy change for the electron injection (ΔGinject) that can be defined through following equation:

$${\rm{\Delta }}{G}_{inject}={E}_{ox}^{dy{e}^{\ast }}-{E}_{CB}^{Ti{O}_{2}}$$
(8)

where \({E}_{ox}^{dy{e}^{\ast }}\) is the oxidation potential of the dye in the excited state, and \({E}_{CB}^{Ti{O}_{2}}\) is the reduction potential of the conduction band of semiconductor (TiO2). The \({E}_{ox}^{dy{e}^{\ast }}\) can be computed by subtracting absorption energy associated with the maximum wavelength (λmax) from the ground state oxidation potential (\({E}_{ox}^{dye}\)) of the dye that is equal to the negative value of the HOMO energy of the isolated dyes.

$${E}_{ox}^{dy{e}^{\ast }}={E}_{ox}^{dye}-{\lambda }_{max}$$
(9)

Also, dye regeneration efficiency can be measured by the driving force of regeneration (ΔGregn) between electrolyte and oxidized dye via the following expression:

$${\rm{\Delta }}{G}_{regn}={E}^{redox}-{E}_{ox}^{dye}$$
(10)

Calculations of TiO2 surface and the interface of dye@TiO2 were performed using the Vienna ab initio Simulation Package (VASP)52,53,54 code under generalized gradient approximation (GGA). To account for the van der Waal (vdW) interactions, non-local density functional like vdW density functional, optB86b-vdW55, was employed as implemented in VASP by J. Klimeš et al.56,57. A Hubbard onsite Coulomb repulsion term58 was added (DFT + U) to improve the description of the on-site Coulomb interaction in the Ti-d states with an effective U parameter. It is crucial to choose effective U parameter, as the band gap of anatase is directly proportional to the U parameter with the overestimation of lattice description59. Our study also follows the same trend. Based on the previous work60 by our group and Paes et. al.61 study we choose effective U value of 3.5 eV.

In the dye@TiO2 system, we describe C-1s2, O-1s2, N-1s2, Ti-[Ne]3s2 and S-[Ne] core electrons with the projector augmented wave (PAW) pseudopotentials62. The cutoff energy of the plane-wave basis set was 400 eV with a Γ centered Monkhorst-Pack grid of 0.03 Å−1 separation (equivalent to a k-points mesh of 8 × 8 × 11, 2 × 2 × 1 for bulk anatase, and TiO2(101)-c(4 × 2) supercells, respectively). The total energy converged to <1 meV/atom. All the structures considered in this study were fully relaxed until all the forces and energy were less than 0.025 eV/Å and 10−6 eV/atom, respectively. The DFT + U computed optimum lattice parameter of bulk anatase TiO2 were a = 3.85 Å and c/a = 2.52 Å; while the indirect band gap is lower in the order of 2.4 eV (direct band gap 2.9 eV) compared to experimental value of 3.2 eV. The band structure, corresponding Brillouin zone with direct and indirect band e gap are shown in Fig. 7. The anatase TiO2(101) surface was modeled with three O-Ti-O layers along the [001] direction and 15 Å vacuum thickness between slabs resulting in approximately 25 Å dimension in [001] direction.

Figure 7
figure 7

Band diagram and PDOS of bulk TiO2 with an indirect and direct band gap of anatase. The distance between the top of the valence band at X and the bottom of the conduction band at Γ, amounts to 2.4 eV (double ended blue arrow) and from Γ to Γ is 2.9 eV (double ended black arrow) represent the indirect and direct band gap, respectively.

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Data Availability Statement

The results of calculations can be obtained by request from the authors.