On the study of dye-sensitized solar cells with high light harvesting efficiency and correlation of its chemical reactivity parameters with overall performance

In this study, thirteen donors with the same spacer and acceptor have been tested to model dyes for dye-sensitized solar cell. Amongst the thirteen donors, 7,7,13,13-tetramethyl-8,9,12,13-tetrahydro-2H,5H,7H,11Hpyrano[2′,3′:4,5]pyrano[2,3-f]pyrido[3,2,1-ij]quinoline-2,5-dione is found to possess the highest oscillator strength amongst the other dyes in first excited state. This donor has been studied further with five different acceptors to make ten dyes (by also considering their conformers formed by twisting the dye by 180∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$180^\circ$$\end{document} about the bond joining the donor with the spacer) to make dyes of type-I, among which the dye with rhodanine acetic acid acceptor and its conformer have the lowest HOMO–LUMO energy gap Eg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {E_{{\text{g}}} } \right)$$\end{document}, highest absorption wavelength in the absorption spectrum with high oscillator strength and low exciton binding energy in the first excited state as compared to the other eight dyes considered here. The rhodanine acetic acid-based dyes have shown to outperform all the other four acceptor-based dyes in terms of chemical reactivity parameters. All the ten dyes when tested further with the inclusion of an extra benzene spacer show enhanced overall performance, with the rhodanine acetic acid-based dyes showing the most planarity, highest absorption wavelength, more suitable reactivity parameters, etc. Correlation studies between the solar cell parameters and chemical reactivity parameters have also been conducted where a direct relationship between the chemical hardness of the dye and open circuit voltage has been observed.


Introduction
Solar energy is one of the most sought sources of energy that demands its fruitful harnessing as a way to meet the ever growing needs of energy in modern world.Solar cell offers itself as an environment friendly means to harness this solar power for utilization in electrical circuits.Among the existing photovoltaic technology, dye-sensitized solar cell is known to be a greener alternative to the conventional semiconductor-based solar cells on account of its ease of fabrication and offering high photoconversion efficiency (PCE) [1][2][3].This has gained the attention of researches worldwide ever since its inception in the year 1991 by Grätzel and O'Brian [2].The structure of dye-sensitized solar cell consists of a semiconductor electrode, a dye, a redox couple and a counter-electrode [4].The dye absorbs radiation from sunlight which causes electrons in it to be excited to the unoccupied molecular orbitals of the dye wherefrom the electrons pass on to the conduction band edge ( E CB ) of the semiconductor surface.The E CB is expected to be at a lower potential (energy) than that of the energy of the lowest unoccupied molecular orbital (E LUMO ) of the dye.These electrons after reaching the semiconductor surface can be conducted to an external circuit whereby the electrons are then looped back into the solar cell via the counter-electrode [5,6].To replenish the dye of its lost electrons, a redox couple acts as a mediator between the counter-electrode and the dye of which the redox potential, E redox , should be at a higher potential than that of the highest occupied molecular orbital energy E HOMO of the dye [7].Metal-based dyes such as those containing ruthenium have shown much promise towards building highly efficient dyes (PCE > 10%) which offer favourable electrochemical properties and high stability in the oxidized state [8].Recently, these metal-based dyes are gradually being replaced by metal-free organic dyes as the extraction of rare metals like ruthenium is expensive as well as hazardous to the environment.Metal-free organic dyes are known to offer ease of fabrication, structural flexibility, high molar extinction coefficients, tunability of its electronic and optical properties [9,10] etc., due to which these have gained recognition and shown much scope towards building efficient, cheap and reliable constituent of a dye-sensitized solar cell (DSSC).
The basic skeleton of a dye in a dye-sensitized solar cell comprises mainly three parts: the donor (D) moiety that donates electrons to the rest of the dye upon excitation from solar radiation and the -spacer that conducts electrons donated by the donor towards the acceptor (A) moiety which pulls the electrons passed on by the remaining parts of the dye.These three parts constitute the basic structure of a D − − A dye [11,12].Generally, the acceptor moi- ety is also accompanied by an anchoring group which can bind the dye to the semiconductor surface.Studies on more complicated D − D − − A , D − A − − A [13][14][15][16], etc., also exist which offer tuning of the solar cell parameters on adding auxiliary donors and acceptors.Commonly used donors such as triphenylamine (TPA) [17][18][19], carbazole [20,21], indoline [22,23], etc., are well known for their electron-donating capabilities and numerous works exist where these donors have shown themselves as worthy candidates to be used in dye-sensitized solar cells.Yet, consistently, attempts are being made to find donors that can provide higher performance by either adding extra moieties to the said donors that can enhance their donating capabilities or explore newer donors.In a study by Nabil et al. [24], six different electron-rich donor groups have been explored and one such donor (7,7,13,13-tetramethyl-8,9,12,13 named as donor N1 is suggested in that study which when employed as donor imparted a high dipole moment to the dye, highest oscillator strength (which pertains to highest light harvesting efficiency (LHE) to the dye) and highest hyperchromic shift amongst all dyes taken in their study, thus making it worthy of ample consideration in designing of a dye, especially when the excited state properties of the dyes are considered.
A suitable donor when compiled with a suitable acceptor promises a dye with superior performance, and for this to be the case, often donors are tested with different acceptors and making comparisons on their overall efficiency, thus making their judicious selection necessary.The use of fullerene as an acceptor has served as a milestone in the designing of dyes for DSSCs [25,26] on account of fullerene possessing highly delocalized -electrons on its spherical surface which facilitates its ability to withdraw -electrons from the dye.But even so, its utilization is limited as fullerene is not easy to synthesize.Searching for less rare acceptors which can efficiently accept electrons but are also easy to synthesize is necessary.In this study, five different acceptor moieties have been considered and tested for their suitability as acceptor in the dye among which conformation effects have also been studied by rotating the donor along the D − π bond, thus giving us ten dyes of type-I.From studies by Bartkowiak et al. [27], 2-thiohydantoin with carboxymethyl co-anchoring group (henceforth known as acceptor A-1) as an acceptor in dyes for DSSCs has shown a photoconverison efficiency (PCE) of 2.59% despite having very simple structure.This PCE of 2.59% is highest amongst all dyes considered in their study and is a promising value for lightweight dyes.This acceptor has been adopted in this study, and the dye constructed therefrom is named as dye D-1 and its conformer DC-1.Studies performed with rhodanine acetic acid acceptor (henceforth known as acceptor A-2) have shown high PCE of > 9% in indoline-based dyes [28,29] and have been adopted in this study to construct dyes D-2 and its conformer DC-2.Dyes with catechol (A-3), salicylic acid (A-4) and phosphoric acid (PO 3 H 2 ) (A-5) show these acceptors as being selectively suitable for certain donors [30] and have been adopted as acceptors in dyes D-3, D-4 and dye D-5 and their corresponding conformers DC-3, DC-4 and DC-5, respectively.
To be efficient in its functioning, a dye requires itself to be conductive when it comes to the flow of electrons from the donor onto the acceptor.Thus, a suitable spacer can make a great difference in the overall efficiency of the dye.A molecule to be used as spacer in a dye is expected to be highly conductive and generally is a -conjugated system which aids in the transfer of electrons through it [31].Numerous works have been carried out with molecules such as thiophene as the spacer molecule that is known to lower the chemical hardness of the dye as the number of thiophene rings are increased, thus improving its conductivity [32,33].In this study, thiophene has been taken as the spacer motif for all dyes considered.Furthermore, the inclusion of an electron-donating group (benzene) as an extra spacer has also been discussed.The dyes D-1, D-2, D-3, D-4, D-5 and their corresponding conformers DC-1, DC-2, DC-3, DC-4 and DC-5 (henceforth known as "type-I" dyes) with an extra benzene group added have been named as dyes DB-1, DB-2, DB-3, DB-4, DB-5 and their corresponding conformers DBC-1, DBC-2, DBC-3, DBC-4 and DBC-5, respectively (henceforth known as "type-II" dyes).Figure 1 gives a schematic representation of the type-I dyes, while Fig. 2 gives a schematic representation of the type-II dyes.Through conceptual density functional theory (CDFT) studies, chemical reactivity parameters of the dyes such as ionization potential, electron affinity, chemical potential, electrophilicity index, etc., can be determined which are known to greatly influence the charge dynamics as well as stability of a dye and influence its photoconversion efficiency.Through correlation studies, the nature of this influence can be understood [34][35][36][37][38][39][40][41][42][43].

Computational details
All calculations have been performed under the framework of density functional theory (DFT) [44] methodology using the B3LYP [45,46] exchange-correlation functional along with 6-311g + (d,p) basis set as implemented in the Gaussian 09 quantum chemistry package [47].Frequency calculations have been done for the verification of the optimized structures, and time-dependent density functional theory (TDDFT) calculations for the first twenty excited states have been performed to characterize the excited state properties.
The total energy of the neutral ( E N ), anionic ( E N+1 ) and cationic ( E N−1 ) systems has been used for calculating the vertical ionization potential (IP) and vertical electron affinity (EA) using the relations [35,42,43,48] which can be used to calculate the chemical potential ( ) given by the relation [34,35,42,43,49] and chemical hardness ( ) by the relation [50]   (3) = − IP + EA 2  The chemical potential and chemical hardness can be used to calculate the electrophilicity index ( ) given by [50,  51]: Multiwfn software [52] has been used for obtaining the excited state properties of the dyes and chemical reactivity parameters.
The photoconversion efficiency (PCE) of a dye used in a DSSC is given by the relation [53][54][55] (4) where J Sc represents the short circuit current density, V OC is the open circuit voltage, FF represents the fill factor of the solar cell and I input is the intensity of the incident radiation on the solar cell.The J SC that plays a major role in the light harvesting efficiency of the dye can be evaluated using the relation J SC = ∫ LHEΦ inject collect d .Here LHE represents the light harvesting efficiency that can be obtained from the oscillator strength (f ) of the dye given by Φ inject is the electron injection efficiency, and collect is the charge collection efficiency.
Φ inject is related to the free energy of electron injection ΔG inject and is expressed by [56] where where ΔE is the electronic vertical transition energy associated with max (maximum absorption wavelength) and E dye OX = −E HOMO is the ground state oxidation potential of the dye.
Using data from TDDFT analysis on the dyes, the LHE and the ΔG inject can be evaluated, the product of which can give an idea about the J SC .

Results and discussion
The study commences with considering thirteen different donors (structures are given in figure S1) and testing them for their suitability as donors in D − − A systems to be used in dye-sensitized solar cells considering the same -spacer and acceptor motifs.For this test, thiophene has been taken as the common -spacer and 2-thiohydantoin as the common acceptor motif.Amongst the dyes considered, the dye with donor N1 has shown itself to possess the highest oscillator strength followed by donors diphenyl ethylene benzene [57], 3-oxo-[1, 2, 4]-triazolo[3,4-a]isoquinoline [24] and piperdine-phenyl [57] in the lowest excited state (first excited state) which pertains to the maximum probability of light absorption and high light harvesting efficiency.This indicates the much expected higher ability of donor N1 towards absorbing the incoming radiation thereby making it the most suitable donor for further studies.The donors used in the thirteen dyes along with their excitation energies, oscillator strengths and absorption wavelength in the first excited states have been provided in Table S1.hybridized bonds.In the case of bond length L 2 (bond length between -spacer and acceptor), dyes D-2 and DC-2 show lower values of bond lengths about 1.43 Å, while the other dyes have higher bond lengths.As apparent from Figs. 3 and 4, the bond length L 2 has a -bond nature in dyes D-1, DC-1, D-2 and DC-2 as compared to the other dyes that indicates a resonating character of the electrons from the spacer towards the acceptor.With the inclusion of an extra benzene spacer, the bond lengths L 1 and L 2 show only slight variation in the type-II dyes.The dihedral angle 2 remains similar in case of dyes DB-2 and DBC-2 and slightly increases in the case of DB-1 and DBC-1, while in the case of remaining dyes, the angle is increased substantially.This causes all the dyes except DB-2 and DBC-2 to become much less planar.This phenomenon can be understood from the acceptors catechol and salicylic acid present in dyes DB-3, DBC-3, DB-4 and DBC-4 consisting of a six-membered carbon ring-like benzene which being bonded to the benzene spacer gets non-planar due to steric hindrance among the two rings.On the other hand, the planar structure of dyes DB-1, DBC-1, DB-2 and DBC-2 indicates electron delocalization between the benzene spacer and the acceptor moiety.The bond lengths L 1 , L 2 along with the dihedral angles 1 and 2 for all the dyes taken in the study are provided in Table 1.The dihedral angle 2 of dyes D-5, DC-5, DB-5 and DBC-5 has not been shown as the acceptor moiety (A5) is not an aromatic molecule (Fig. 5).
Considering the dyes to be used in DSSCs with TiO 2 sem- iconductor as the photoelectrode and I − 3 ∕I − as redox couple, the ten dyes (type-I) and their benzene included counterparts (type-II) have their E LUMO above the conduction band edge (E CB ) of the TiO 2 semiconductor (−4.00 eV) [4, 58] which would facilitate efficient transfer of charge from the dye's excited state onto the TiO 2 semiconductor and E HOMO suffi- ciently below the redox potential of I − 3 ∕I − (−4.80 eV) which should help in proper replenishing of charges in the dye from the counter-electrode [59,60].The E HOMO and E LUMO along with the energy gap E g of the dyes, with and without an extra benzene spacer, are enlisted in Table 2.
From the sensitizing mechanism, where the dyes irradiated by sunlight pass on electrons from the LUMO of the dye onto the conduction band edge of the TiO 2 semiconductor electrode, the open circuit voltage eV OC can be given by the relation eV OC = E LUMO − E CB .Table 2 shows dyes with acceptor A1 and A2 have the lowest eV OC in their category, while the dyes with acceptor A3 show the highest eV OC amongst dyes in their category.The value of eV OC obtained from the difference between E LUMO and the E CB does not take into consideration the recombination effects of the redox electrolyte.As will be apparent from the later section, despite the dyes with acceptor A2 being the superior ones in terms of chemical reactivity parameters and excited state properties amongst the type-I and type-II dyes which is not endowed with a high value of eV OC , this can be attributed to the lower E LUMO of the dyes.From the results of Nabil et al. [24], a BP-2 dye analogue with the same donor D-1 when tested at B3LYP/6-311G(d,p) level of theory shows the dye to possess an E HOMO of − 6.62 eV, an E LUMO of − 2.36 eV and an energy gap of 4.25 eV.These results yield an eV OC of 1.36 eV which is higher than all dyes taken in the present study except for dyes D-3, DC-3, DB-3, DBC-3, DB-4 and DBC-4.This can be attributed to these dyes having higher E LUMO , thus making the dyes a good donor of electrons.On the inclusion of an extra benzene spacer, the eV OC values of all dyes are seen to increase DB-3) .This increase in the value of eV OC can be understood from the fact that an electron-donating group like benzene when added to a system imparts additional electrons to the system, thereby increasing its HOMO and LUMO energy (except DB-3).Meanwhile, the HOMO-LUMO gap is seen to decrease or remain constant except in case of dyes DB-1 and DBC-1.The Boltzmann weighted averages of E HOMO , E LUMO , E g and eV OC of the dyes and their conformers are given in Table S2.The frontier molecular orbitals (FMO) (Fig. 6, S2 and S3) of dyes show a shift from being spread throughout the dye (as in HOMO) to being shifted towards the acceptor of the dye (as in LUMO) except in dyes containing acceptor A3 (figure S2 (e), (f), (g), (h) and figure S3 (e), (f), (g), (h)).FMOs of dyes D-2, DC-2, DB-2 and DBC-2 are provided in Fig. 6.

Excited state properties
A dye on photoexcitation causes its electrons to reach higher energy levels which leads to transfer of energy from the dye to its vicinity-a process called photosensitization which is often accompanied by transfer of electrons.These photoexcitations in the dye require perturbation with certain wavelength that match with the excited state energy levels of the dye.TDDFT results bear information of the UV-visible absorption spectra of the dye whereby it pinpoints the specific wavelength that can excite the dye molecule to its possible higher energy state and also sheds light onto the maximum probability of absorbance towards light of certain wavelength by specifying their oscillator strength (Table 3).
The TDDFT results of the ten dyes of type-I show their highest oscillator strengths in the first excited state with dyes D-1, DC-1, D-2 and DC-2 showing the highest oscillator strength among these dyes along with the highest absorption wavelength.As will be discussed in the later section, the decrease in the values of oscillator strength and absorption wavelength may be attributed to the change in reactivity parameters of the dye on flipping the donor motif.On the other hand, when the extra benzene spacer is substituted into the dyes, their oscillator strength in the first excited state is enhanced in all dyes except DBC-2 which shows a slight decrease.All dyes show redshift in the maximum absorption wavelength on addition of extra benzene spacer except for DBC-1 which shows a slight decrease.Table S3 enlists the Boltzmann weighted averages of oscillator strengths, excitation energies and absorption wavelengths of the dyes and their conformers.
With the first excited state being the most influential one that decides the overall functioning of the dye under solar irradiation [61,62], the analysis of carrier dynamics that occur at the first excited state would be fruitful towards gaining insights about the functioning of the dyes.As the dye makes a transition from the ground state to an excited state, its charge density topology changes vastly.The charge density difference between the ground state and the excited state is given by Δ (r) = excited (r) − ground (r) , where ground is the charge density at the ground state and excited is the charge density in the excited state.With intramolecular charge transfer occurring between different parts of the dye upon excitation, the Δ can be divided into positive and negative parts (holes and electrons, respectively), the area weighted integral of which constitutes of what is known as the positive and negative barycenters, respectively.The distance between these two barycenters will give us the charge transfer length [63].The charge transfer length values are provided in Table 4.In the present study, all dyes show efficient charge transfer with dye D-2 showing a moderate value, while the dyes DC-2, D-3 and DC-5 show highest charge transfer lengths.On the inclusion of an extra benzene spacer, the charge transfer length is increased in dyes DB-1, DBC-1, DB-2, DBC-2 and DB-3, while dyes DBC-3, DB-4, DBC-4, DB-5 and DBC-5 show a decrease in the charge transfer length.With the charge density topology getting segregated into electron-rich and electron-deficit (considered to be accommodated by holes) regions, a coulomb attractive energy would develop between them [64,65].This energy is known as the exciton binding energy (E b ) and is one of the key parameters that determine the carrier dynamics in a dye [66].It is to be noted that the exciton binding energy E b in the present study has been calculated using the coulomb integral between the density distribution of holes and electrons given by the relation: where hole/electron represent the density distribution of hole/ electron on the molecule.With lower exciton binding energy, the dye can easily separate holes and electrons.Amongst the dyes taken in the study, dyes DBC-2 and DB-2 show the lowest exciton binding energy.With the inclusion of an extra benzene spacer, the exciton binding energy gets decreased in all dyes.This can be attributed to the lengthening of dyes due to the extra spacer moiety [67,68].Boltzmann weighted averages of charge transfer lengths and exciton binding energies of the dyes and their conformers in first excited state have been provided in Table S4.

Chemical reactivity parameters
Conceptual density functional theory (CDFT) [69] offers calculation of reactivity parameters of the dyes from DFTbased calculations of ionic-and neutral-based quantities [70,71].Table 5 enlists the chemical reactivity parameters of all the dyes.Amongst the dyes without benzene spacer (type-I), dyes D-3 and DC-3 show the lowest ionization potential which indicates towards their superior hole-generating (10) property.On the inclusion of an extra benzene spacer, the vertical ionization potential in all dyes is further decreased which indicates towards improved performance in all dyes.Among type-I dyes, dye DC-2 shows the highest vertical electron affinity followed by its isomer counterpart D-2.This indicates their higher ability of accepting electrons, pointing towards their higher efficiency.With the inclusion of an extra benzene spacer, dyes with acceptors A1, A2 and A4 show an increase in the value of vertical electron affinity which are seen to decrease in A3-and A5-based dyes.For the dye to function as an efficient sensitizer, it is desirable that the dye should possess lower chemical hardness which represents lower resistance to intramolecular charge transfer.
A lower chemical hardness relates to higher conductivity in the dye which in turn should facilitate towards efficient charge transfer to the TiO 2 semiconductor surface.This is also reflected in the chemical potential of all the dyes (both type-I and type-II) having their chemical potential ( ) above the chemical potential of TiO 2 60 (− 5.245 eV) as adopted in a work by Sadki et al. [72], which indicates that the dyes can transfer electrons onto the TiO 2 semiconductor until equilibrium is reached.A dye with higher electrophilicity is known to be energetically stable when getting additional electrons from the environment.A similar trend is also followed by their electrophilicity index where the dyes D-2 and DC-2 having higher values would indicate their higher stabilization energy.These higher values of electrophilicity and vertical electron affinity may be understood from the higher electron accepting capabilities of rhodanine acetic acid used as an acceptor in dyes D-2 and DC-2.This electron-accepting power is further enhanced by the addition of an extra benzene spacer between the thiophene spacer and the accepting moiety in all dyes except DB-4.
On the addition of an extra benzene spacer motif, the chemical hardness of all dyes is further reduced, thereby indicating their better charge conduction owing to the presence of resonating -bonds in the benzene molecule.Boltzmann weighted averages of chemical reactivity parameters of the dyes and their conformers have been provided in Table S5.

Solar cell parameters
Using Eqs. 7 and 9, the LHE and ΔG inject of the dyes can be evaluated using which the product ΔG inject × LHE can give an idea about the short circuit current density J SC and can be used for comparison amongst the dyes (Table 6).
Amongst the ten dyes in type-I, the dye DC-2 shows the highest value of ΔG inject × LHE which indicates towards its highest short circuit current in type-I, while its conformer analogue D-2 and dyes D-1 and DC-1 show nearby values and the remaining dyes show lower values.On the inclusion of an extra benzene spacer, a similar trend is again seen in all the dyes.The inclusion of benzene spacer is shown to increase the light harvesting efficiency.
From Eq. 6, a product of eV OC with ΔG inject × LHE can give an idea about the photoconversion efficiency (PCE) of the dyes.Among type-I dyes, DC-3 shows highest PCE and DC-2 shows lowest PCE.In case of type-II dyes, DBC-3 and DBC-2 show highest and lowest PCE, respectively.Boltzmann weighted averages of ΔG inject , LHE, LHE × ΔG inject and eV OC × ΔG inject × LHE of the dyes and their conformers have been provided in Table S6.

Comparison of reactivity parameters with solar cell parameters
As apparent from Eq. 6, a dye that imparts higher eV OC to the solar cell will cause it to have a higher PCE.Yet, for a dye to be efficient in transfer of charges to the semiconductor surface, it must be endowed with a lower chemical hardness.On a one-to-one comparison of eV OC with the chemical hard- ness for dyes in type-I, a directly proportional relationship is seen between the chemical hardness and eV OC with a slope of 0.78 with an R 2 value of 0.96 and error of 6.23% in the linear graph.The graph of chemical hardness vs. eV OC is given in Fig. 7a.It is apparent from Fig. 7a that a dye endowed with a higher chemical hardness (or lower conductivity) will cause the solar cell to have a higher eV OC .On the other hand, chemical hardness shows an inverse relationship with the short circuit current ( LHE × ΔG inject ) giving a slope of -0.91 with an R 2 value of 0.99 and error of 2.34% (Fig. 7b).This is understandable as a dye with higher conductivity (lower chemical hardness) shall facilitate transfer of charges thereby allowing higher J SC .
Also, on comparison of electrophilicity index with eV OC in Fig. 7c, an inverse relationship is observed with a slope of -0.97, R 2 value of 0.99 and error of 3.90%.This points towards the mutually contradictive relationship between these two parameters where both electrophilicity and eV OC are preferred to be high for the better functioning of the dye.And similar to the case of chemical hardness, electrophilicity index also shows a linear relationship with the product ΔG inject × LHE having a slope of 0.60, R 2 value of 0.93 with an error of 5.70% (Fig. 7d).
On the inclusion of an extra benzene spacer in all dyes, the same linear relationship between the chemical reactivity parameters with eV OC and ΔG inject × LHE is still followed.For the case of type-II dyes, the graph of eV OC vs. chemical hardness (Fig. 8a) has a slope of 0.98 with an R 2 value of 0.76 and error of 19.22%, ΔG inject × LHE vs. chemical hardness (Fig. 8b) has a slope of -0.80 with an R 2 value of 0.85 and error of 11.74%, eV OC vs. electrophilic- ity index (Fig. 8c) has a slope of -1.03 with an R 2 value of 0.98, error of 4.99% and ΔG inject × LHE vs. electrophilic- ity index (Fig. 8d) has a slope of 0.80 with an R 2 value of 0.97 and error of 4.54%.
From the graphs obtained, it is apparent that with the inclusion of an extra benzene spacer, the slopes of all the graphs (except ΔG inject × LHE vs. chemical hardness) get

Conclusion
Using density functional theory, 13 donors have been tested for DSSC with the same thiophene spacer and 2-thiohydantoin acceptor.Of the 13 dyes generated, the dye with donor N1 shows the highest oscillator strength in the first excited state.This donor has been taken further for constructing ten dyes using five different acceptors and also considering their conformers by twisting the donor by ∼ 180 • about the bond joining the donor and spacer to make dyes of type-I.Amongst the ten dyes of type-I, the dye with rhodanine acetic acid and its conformer (D-2 and DC-2, respectively) are the most planar with the dihedral angle between spacer and acceptor being < 1 • .These dyes have the lowest energy gap E g , highest oscillator strength in the first excited state with high absorption wavelength ( > 540 nm) .Dyes with acceptor A1 and A2 out- perform all the other dyes in terms of exciton binding energy and reactivity parameters.On the inclusion of an extra benzene spacer, all dyes portray a further enhancement in their parameters with dyes DB-2 and its conformer DBC-2 showing the most planarity, lowest energy gap (E g ) , highest redshift in their absorption wavelength as well as superior reactivity parameters.The ten dyes in type-I show a reduction in their exciton binding energies on the inclusion of an extra benzene spacer.Of the 20 dyes considered in the study, dyes with acceptor A3 show the highest value of eV OC with highest PCE, while the dyes containing acceptor A2 with lower chemical hardness lag behind.This has been attributed to the eV OC of dyes hav- ing a direct relationship with chemical hardness of the dyes.Further, an inverse relationship has been observed for eV OC vs electrophilicity index.On comparisons of ΔG inject × LHE with chemical hardness and electrophilicity index of the dyes, an inverse and direct relationship is observed, respectively.On the inclusion of an extra benzene spacer in the dyes, the slopes of all the graphs (except ΔG inject × LHE vs chemical hardness) are seen to get steeper.

Fig. 5 2 125
Fig. 5 Diagrammatic representation of bond lengths (L 1 and L 2 ) and the dihedral angles ( 1 and 2 ) in dye a D-2 and b DB-2

Page 7 of 16 125 3 . 1
Geometry and electronic structure of the dyesFollowing the selection test for a suitable donor, five dyes with D − − A architecture have been constructed with molecule N1 as the donor motif, thiophene molecule as the spacer and five different acceptor motifs (A-1, A-2, A-3, A-4 and A-5 that make up the dyes D-1, D-2, D-3, D-4 and D-5, respectively) are investigated for properties that indicate towards their suitability as sensitizers for dye-sensitized solar cells.Five conformers of these dyes have also been constructed by rotating the donor moiety of the dyes by ∼ 180 • about the bond joining the donor and the spacer giving in total ten dyes of type-I.Further, an extra benzene spacer has also been added adjacent to the thiophene spacer in all dyes of type-I to generate the dye molecules DB-1, DB-2, DB-3, DB-4 and DB-5 along with their conformers DBC-1, DBC-2, DBC-3, DBC-4 and DBC-5, respectively, that make ten dyes that fall under the category type-II.Comparisons have been made amongst the dyes in both classes (type-I and type-II) regarding their structural, electronic, excited state and chemical reactivity properties.The optimized structures of type-I and type-II dyes are given in Figs. 3 and 4, respectively.Amongst the ten dyes in type-I, the dyes D-2, DC-2, D5 and DC-5 are the most planar with dihedral angles 1 (representing the dihedral angle between the donor and the -spacer) being 1.17 • , 1.42 • , 0.14 • and 1.78 • , respec- tively, while 2 (dihedral angle between the -spacer and the acceptor) to be 0.09 • and 0.27 • , respectively, for dyes D-2 and DC-2, respectively.Other dyes, have similar values of 1 , but have higher values of 2 .These lower values of 1 in dyes D-2, DC-2, D5 and DC-5 and 2 in dyes D-2, DC-2, thereby making them planar structures, should facilitate efficient charge transfer in the dyes.On the other hand, all dyes show a similar value of bond length L 1 (bond length between donor and -acceptor) between 1.45 and 1.46 Å.This indicates towards sp3

Fig. 6 2 125
Fig. 6 Frontier molecular orbitals (FMO) representing the a HOMO of dye D-2, b LUMO of dye D-2, c HOMO of dye DC-2, d LUMO of dye DC-2, e HOMO of dye DB-2, f LUMO of dye DB-2, g HOMO of dye DBC-2 and h LUMO of dye DBC-2

Fig. 7 a
Fig. 7 a Graphical representation of a vs. eV OC and b vs. ΔG inject × LHE , c vs. eV OC and d vs. ΔG inject × LHE of type-I dyes

Fig. 8 a
Fig. 8 a Graphical representation of a vs. eV OC and b vs. ΔG inject × LHE , c vs. eV OC , d vs. ΔG inject × LHE

Table 2 E
HOMO , E LUMO , E g and eV OC of the dyes taken in the present study

Table 3
Oscillator strengths, excitation energies and absorption wavelengths of the dyes taken in the present study

Table 4
Charge transfer lengths and exciton binding energies in first excited state for dyes taken in the study

Table 6
ΔG inject , and LHE of the dyes taken in the study