Efficient and tunable enhancement of NLO performance for indaceno-based donor moiety in A-π-D-π-D-π-A type first DSSC design by end-capped acceptors

The organic dyes with non-fullerene acceptors (NFAs) have aided in the creation of competitive organic solar cells (OSCs) with long-term sustainability. A series of NFA dyes (IDIC-R1–IDIC-R9) have been designed by varying the end-capped fluorinated moieties (PD1–PD6) at indaceno (IDIC) core. All the calculations were performed by density functional theory (DFT) and time-dependent DFT (TD-DFT)–based approaches. All the geometries were optimized at B3LYP/6-31G + (d,p) of DFT level at their ground state energies. Out of several density functionals, the CAM-B3LYP with 6-31G + (d,p) basis sets was selected after a benchmark study to carry out further calculations. All the dyes had their bandgaps in 0.11–3.12 eV while their starting reference dye had a bandgap value of 2.01 eV. Their ionization potential (IP) implied that these dyes have strong tendency to lose electrons. The λmax of the dyes was slightly redshifted from the IDIC (476 nm) and IDIC-R (479 nm) when changing solvent polarity from methanol to DCM and then chloroforms. The natural bond orbital (NBO) analysis showed the (S63)LP → (C61-C62)π* with highest stabilization energy. Their electron injection analysis showed that these dyes can be a good anode material against the aluminum and gold electrodes. The intramolecular charge transfer (ICT) process and stability of the dyes were investigated using frontier molecular orbital (FMO) and natural bond orbital (NBO) analysis. Among all dyes, IDIC-R8 has the highest linear polarizability and second-order hyperpolarizability (βtotal). All the dyes demonstrated promising non-linear optical (NLO) properties due to their low charge transfer barriers. Scientists would be able to exploit these properties to identify the best NLO materials for existing applications.


Introduction
The organic dyes are the most promising groups for optical chemistry [1] with excellent photo-physical properties inside the near-infrared region (NIR) [2] with intramolecular charge transfer (ICT) [3] features. Changing a multifunctional component in the synthesis of fluorescent organic dyes is an excellent way to adjust their absorption and/ or emission wavelengths [4] for dye sensitized solar cell (DSSC) applications [5]. The organic solar cells (OSCs) [6] as optical probes are also useful in photovoltaic (PV) [7] and optical applications [8]. The materials with good nonlinear optical (NLO) properties have received interest due to their potential use in high-tech applications [9] by having fast response time [10]. They have also been extensively customized for optical storage systems and as photodetector switches [11]. A comparative analysis of organic and inorganic NLO materials reveals that organic systems have various benefits over inorganic materials including a fast response time, high structural flexibility, high processing effectiveness, and a high non-linear polarization rate [12].
The organic dyes with a high interconnecting electron density as well as electronic density may be desirable features for second-and third-order NLO materials [13]. Powerful electron-withdrawing moieties have also been added to the ends of A-D-A-D-A type dyes to provide highly efficient non-fullerene acceptors (NFAs) that have exhibited a variety of PV features [14]. With enhanced DSSC capabilities, the effects of various supplementary donor (D) units before and after binding upon the photogenerated electrons have been investigated [15]. Changing the chemical structure to produce major NLO response is thus an intelligent method [16] in which highly interconnected electron density may be a superior requirement for its tunable response [17]. The D and acceptor (A) moieties are also responsible for the required ground state charge balance to tune the NLO performance [18].
The NFAs have attracted the curiosity of many researchers to their enhanced PV features [19]. In order to get around the limits of fullerene-based dyes, researchers are currently working to create inexpensive NFAs for OSCs in PV devices [20]. They have surpassed their fullerene counterparts in terms of light absorption and D-A combination variety [21]. Theoretical studies on these A units and thiophene bridging units are the focus of the current investigation. The proposed molecules' various optoelectronic properties were computed which had just been published with promising findings. These A units displayed broad spectra, a smaller band gap, and the greatest open-circuit voltage values, according to the results. They have widely been used as a D units to pair with different A units to create a range of D-A conjugated materials, which have emerged one of the key categories for OSCs [22]. A wide variety of NFAs have now been studied for their electro-and PV properties over the last 10 years due to its notable electron carrier possibilities.
The outcomes of the NLO attributes investigation with the title NFA dyes have not been communicated still. To bridge this research gap, the theoretical simulations based on density functional theory (DFT) were used to examine NLO characteristics. Predicated on these interesting aspects of cross-linked NF-based molecules, we chose NFA dyes in this study to investigate their NLO capabilities theoretically. The dimalononitrile-based moiety of 2,2ʹ-( (4-heptyl-4,9,9-trihexyl-4,9- [23] is a promising building component for the development of organic devices. Different NFA units have been developed by combining them with conjugated π-spacers to design NFA-based IDIC-R1-IDIC-R9 new dyes. Before designing these dyes, the starting material (IDIC) was modified structurally to design a reference dye IDIC-R for the sake of its compact molecular packing with improved derive parameters related to solar cells (Fig. 1). Because it elucidates the effects of the D, multiple A units, and π-spacers in NFA dyes, this study is crucial for estimating NLO implementation. Natural bond orbital (NBO) analysis, global reactivity parameters (GRPs), frontier molecular orbitals (FMOs), densities of states (DOSs), and ultraviolet-visible (UV-Vis) absorption spectra were derived using DFT and TD-DFT predictions for NLO features. The NFAs are thought to have a significant influence on the non-linear optical field. Because it elucidates the effects of the D, multiple A units, and π-spacers in NFA dyes, this study is crucial for estimating their NLO implementation.

Methodology
The current investigation was carried out by operating the Gaussian 09 package [24]. All the molecular geometries of the dyes were optimized at Becke, 3-parameter, Lee-Yang-Parr (B3LYP) density functional (DF) with 6-31G + (d,p) basis sets. All the optimizations were performed at 300 atm pressure with 2.0 psi pressure which were adjusted by including in the basis sets "functional/basis set freq temperature = 300.0 pressure = 2.0." Several long-range and range-separated DFs were applied on the output files of optimized geometries to benchmark their absorbance maxima (λ max ) [25] of new dyes. Out of this benchmarking, the DF of CAM-B3LYP with 6-31G + (d,p) basis gave the closest λ max and was selected for further studies. The parameters for FMO, NBO, density of state (DOS), projected UV-Vis absorbance [26], and NLO characteristics of NFA dyes with a very A-π-D-π-D-π-A architecture were determined. The bandgap was calculated using an FMO analysis, which enabled the lowest amount of energy necessary for the transition from their highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbitals (LUMO) to be computed. Their hyper-conjugative connections were analyzed by utilizing their NBO analysis. The DOS calculations were used to calculate the dispersion of energy states between their FMOs. The UV-Vis absorption spectra were obtained to investigate their ICT, dipole moment (µ nor ), and linear polarizability including first hyperpolarizability (α) and second hyperpolarizability (β tot ). The findings were obtained from output files applying the GaussView [27], Avogadro [28], and Chemcraft [29] software packages.
When a single-molecule system acquires an additional surface charge density from its surroundings, it monitors energy constancy, as defined by Parr [31]. It is a feature of reactivity that allows for quantitative classification of Light harvesting efficiency (LHE) is also another crucial segment that influences optical performance. The charge transfer (CT) sensitivity of dyes with a high LHE content is greatest. The LHE of dyes can be computed using the formula (8).
The calculation below is commonly used to calculate open circuit voltage (V oc ), an essential parameter for measuring the cost-efficiency of semiconductor applications.
Equations (10) and (11) were used to compute the NLO responses of dyes as α β tot by using their tensors [32] of polarizability.

Modeling of A-π-D-π-D-π-A framework
The dyes comprising D-π-A must have their geometry optimized to achieve a stable alignment in order to have good PV potential [33]. Their structural morphologies must be screened because they are crucial in determining the µ nor , efficient packing ability, as well as other PV-related characteristics. All of these dye-related factors are crucial for obtaining their NLO performances. For D-π-A style fluorescent dyes, filtering of A units is critical for achieving a good NLO performance [34]. The goal of this research was to create a new indaceno moiety-based interesting NLO switches by being structurally tailored with different π-bridges and to forecast their optoelectronic, electrical, and NLO characteristics for the newest optoelectronics. This is where and why such theoretical engineering takes place. These six π-conjugates served as the major end-capped A units, while two types of π-spacers serve as the secondary π-linkers, resulting in a total of nine dye molecules (Fig. 2). Our proposed materials (IDIC-R1 to IDICR9) were made up of three primary components: the D moieties of IDIC and MDI, first and second π-spacers as phenyl, and third π-spacer as 2,2ʹ-bithiophene, which served as a bridging link, and A components (1-oxo-1H-inden-3-yl)propanedinitrile. All the dyes had the dihedral angles spanning 117-118.5° for C-C-C in the framework aromatic (benzene) rings. The binding angle between C-C-N bond was found to be around 106-110°.
The C-N-C bond angle of such MDI corner benzene ring was determined to be identical, ranging between 112 and 114°. The dihedral angles of C-C-N were calculated to be 107-111°. The geometric bond angle between C and C-N was 106-107°. In case of dye IDIC-R1, similar outcomes were observed for the bond angles of C1-C3-C5, C16-N14-C75, and C3-C1-C16, which were 120.23-121.33° (Fig. 3). The bond angles between the bithiophene ring atoms like C83-C81-S82 were at 121.3°. By adding large donor atomic units, the indole structure was considerably changed, but the symmetrical arrangement of the phenyl ring was unaffected. Two phenyl conjugates were used to create dyes with different acceptor atoms. All the dihedral angles of the aromatic rings were 117.65-118.09°.

FMO analysis
A FMO study may be used to evaluate the investigated dyes for their essential quantum chemical properties, such as electronic metrics, chemical stability, energy transfer qualities, and their chemical reactivity [26]. Such studies also regulate electron-hole pair, ω, chemical reactivity, and σ as a pull-push effect. All the dyes with their thermodynamic and chemical stability were inextricably linked to their difference in energy of their FMOs (bandgap = E LUMO − E HOMO ) ( Table 1). It can be rationalized from their bandgap values that the reference dye IDIC-R had a considerably low value than that of its starting materials IDIC and then the new dyes had further a reduction of their values except a few dyes.
Among all, the dye IDIC-R7 had a bandgap value of 5.88 eV, which was greater than the bandgap of IDIC (3.12 eV) while dyes IDIC-R4, IDIC-R5, IDIC-R8, and IDIC-R9 had lower values than the IDIC-R (1.11). Overall bandgap for all proposed dyes were calculated as follows: The D, A, π-spacers, and end A units are all involved in ordering the dyes, which had significantly reduced their bandgap. The reduction in bandgap observed for dyes had demonstrated how a position of a small molecule can affect the energy variations. The dyes IDIC-R7 and IDIC-R8 were changed because of compositional modifications and as a result bandgap values have been further decreased by adding two and one fluoro (F) on its A unit (PD3), where two F units were proven to be more efficient in decreasing the bandgap than one cyano (CN) unit. The analysis of FMOs in conjunction with bandgap revealed that the suggested dyes may perform ICT from D to A units through π-spacers (Fig. 4).
The D, π-spacers, and A units are found to be involved in arranging the bandgap values of these newly designed dyes. The bandgap values have been further decreased to 1.07-1.18 eV by adding two and one F unit on A units, where two F units were proven to be more efficient in decreasing the bandgap than one F unit.
The bandgap value in IDIC-R4 reduced dramatically to 1.67 eV due to the inclusion of one F unit on the A moiety. This increase in bandgap value might be attributable to the F unit since its resonance impact is less amplified than that of the F unit. The dyes IDIC-R2, IDIC-R5, and IDIC-R6 had lower bandgap values since F units constituted D units due to resonance phenomena. Because of the inclusion of nitro groups, bandgap measurements in IDIC-R6 were increased about 0.22 eV. The dye IDIC-R8 had the smallest bandgap value of all because of the clear considerable conjugation involved in phenyl rings as well as the end-capped A segment comprising nitro units. The presence of electronegative entities (F and CN units) on A subunits can effectively lower electrostatic potential concentration from other areas of the A unit, resulting in a decrease in bandgap. With the aid of the π-spacer, the bandgap values characterize the ICT interface from D to A section, providing significant understanding into connected functional linkages of the NLO components. The contour parts of FMOs were employed to determine the transport of electrical charges. In IDIC-R1-IDIC-R4, the LUMOs for the charge density were only visible on the A unit and partially on the second π-spacer. On the first π-spacer, second D units, and A1, the electronic populations in the HOMO were discovered. Electron density from D to A or via the π-spacer was required for NLO stimulation. The dye IDIC-R1 and IDIC-R6 may be considered as feasible NLO contenders because of this influence.

Global reactivities
The HOMO → LUMO difference in energy (bandgap) has widely been used to compute the GRPs of newly designed compounds which include IP, EA, χ, η, ω, µ, and σ ( Table 2). Understanding the association between structural system and their chemical reactivity requires the usage of conceptual DFT-based global reactivity descriptors. In addition, these descriptors can be used to create structure-activity interactions. The property to donate electrons is known as IP, while the ability to receive electrons is known as EA. Single molecular dyes with higher are expected to be more thermodynamically stable [35]. So, the overall order of IP for all the dyes were reported as IDIC-R (7.29) > IDIC-R1 (7.21) = IDIC-R2 (7.21) = IDIC-R4 (7.21) > IDIC-R5 From this trend, their EA values were reported in their inverse order as in descending order: IDIC-R5 had the greatest IP value of 7.6 eV, indicating that the D moiety communicated the electrical potential density to the A effectively, whereas IDIC-R6 had the smallest IP value, 6.13 eV. According to thermodynamics, the chemical potential of any entity has been the energy that may be absorbed/released due to a change in density of the specific species, or in a chemical processes or phase transitions [36]. The dye IDIC-R3 had the highest value, which was reduced to 0.11 eV in IDIC-R6. The overall order was noted as IDIC-R3 > IDIC > IDIC-R6 > IDIC-R7 > IDIC-R5 > IDIC-R1 > IDIC-R2 > IDIC-R4 > IDIC-R > IDIC-R9 > IDIC-R8. Electrophilicity index was noted as IDIC-R5 > IDIC-R8 > IDIC-R9 > IDIC-R4 > IDIC-R > IDIC-R2 > IDIC-R1 > IDIC > IDIC-R7 > IDIC-R6 > IDIC-R3. The minimal bandgap revealed that the subsequent ICT interaction took place within the investigated molecule and demonstrated significant kinetics. The GRPs revealed that all the dyes were softer, with an electrophilic entity, and have a high affinity for other solar materials. According to the molecular electrostatic potential framework, the negative and positive locations of the examined chemical are located surrounding electronegative elements and hydrogen atoms.

DOS spectra
Several types of electronic states (per unit volume per unit energy) are inhabited by electrons at a quantized energy level at the Fermi level enabling DOS with an extremely high value to suggest that various sorts of states for energy condition are accessible. A zero score along the axis represents the lack of a state for excited electrons. The DOS  (Fig. 5). These insights show that designing varied dyes by altering different effective A moiety has a significant impact on ionic and electronic cloud transparency in a variety of ways. Each dye is made up of three components: a D, a π-spacer, and an A unit. The maximal charge density of the HOMO was about 6-11 eV on that π-spacer, but the LUMO content at the D section was 1.5 eV, indicating effective ICT from D to A region via the π-spacer. The greatest HOMO density reported in IDIC-R2 is 7 eV, which is 45% on the π-spacer, whereas the greatest LUMO density was found only on the A, which provides 73% of the charge. For IDIC-R3 and later, the A restricts the maximum HOMO density to 7-14 eV, while the π-spacer restricts the highest LUMO concentration to 2.4 eV, enhancing the electron-withdrawing behavior while concurrently prolonging the conjugation. All the DOS examined data strongly supports the FMO conclusions. Another key factor

UV-Visible analysis
The UV-Vis analysis gives additional evidences for a wide range of electronic events [31] for DSSCs regarding their parameters of incident light absorption at specific wavelength (Fig. 6). In addition, some other relevant features by which several DSSC-related parameters such as their λ max , transition energy (E), and oscillator strength (f os ) can be calculated. Those values were calculated in gaseous phase using TD-DFT simulations to pictograph typical absorption changes in the dyes IDIC-R1-IDIC-R9 with an inverse relationship between their E and λ max . Photovoltaic cells are wavelength selective and respond positively to sunlight in some areas of the spectrum than others, generally a wavelength range of 600-700 nm. Generally, the greater the frequency of light with more energy carried by emitted electrons, the smaller the wavelength of incident beam. Similarly, the absorption λ max , f os , and E for the identical spectral allocations in increasing solvent polarity from methanol through dichloromethane to chloroform were calculated and had a λ max of 476-483 nm with redshift. The average λ max values (nm) were recorded in the  Table 3). The analysis revealed that electron-withdrawing end-capped A units had such a significant influence on peak value. This electron-deficient constituent is responsible for the red shift in absorption spectra. All the dyes IDIC-R1-IDIC-R9 had absorption band widths extending from 480 to 498 mm, which are red shifted in contrast to IDIC. The dyes IDIC-R2 and IDIC-R6 demonstrated a stronger red shift with lowest E values of 1.28 and 0.77 eV, respectively.
Because of the low bandgap, charge separation might be possible there [37]. The dyes IDIC-R1, IDIC-R3, and IDIC-R4 exhibited identical λ max values, with their values of f os at 0.0034-0.39. All the dyes (IDIC-R1-IDIC-R9) showed E ranging from 0.77 to 1.66 eV, which had been lower than the typical value of 1.743 eV. The computed fluorescence emission of such relevant dye structures in chloroform was well given the previously published data. It also implies that the H-bond to the lone pairs of alkene units in S 1 states was disrupted in the solvent trap by the transport of lone pairs to certain ring following excitation.
As a result, the CT functionality is included in the allowed transition. Because of the above discussion, it is possible to conclude that the newly designed dyes have superior optoelectronic characteristics than the reference dye molecule. All the dyes that have recently been created are thought to have high values of E, f os , and absorption coefficients. The dye IDIC-R3 and IDIC-R6 could be used as key fullerene free D subunits in PV systems.
Optical performance is influenced by a segment called light harvesting efficiency (LHE). The greatest charge transfer (CT) sensitivity is found in dyes with a high LHE content. The formula can be used to calculate the LHE of dyes. In spectroscopic calculations, oscillator strength is a non-dimensional variable that reflects the likelihood of incident electromagnetic absorption/emissions during transitions as energy. Non-radioactive decay can beat optical decay if particle emitters with state do have low oscillator intensity. The greater the CT inside the semiconductor, the greater is the LHE. It was calculated using the oscillator intensity of the UV-Vis analysis.

NBO analysis
NBO research assists in the finding of hydrogen bonds in engineered molecules that result from hyper conjugated engagements [38]. It provides a realistic image for investigating intra-molecular delocalization and electron density as the units get beyond electron D to A units. As the energy of stabilization grows, the interaction across the D unit functionalities becomes more essential. Equation (12) is the stabilizing energy formula employing a second-order perturbation approach.

Electron injection and hole analysis
As work function (W) of metal (HIE = E HOMO ) and (EIE = E LUMO ), a hole/electron injection barrier (HIE/EIE) [40] originating from dyes and toward the aluminum (Al) and gold (Au) electrodes is being investigated. In the HIE of new dyes for Au metal, the decreasing rank was as follows: Depending on electron injection and hole analysis, all dyes can operate as good electrochemical devices, and the electrode impact is non-existent. They also represent the same metal trend. However, it can be deduced that Au

Charge tripping analysis
To investigate the possible use of D functions in OSC semiconductors, the IDIC-R8 was coupled with IDIC as a complex and optimized at B3LYP functionality at its energy minima. The complex of both dyes was optimized to its ground state energy by using PBEEPBE basis set at DFT level [41]. We decided to note the pathway of electron transfer for the IDIC-R8 as it had the highest V oc . Also, the dye IDIC had been a well synthetic solar dye that was also frequently used in CT. We applied our produced dyes on the D component to measure the efficiency of ICT. In HOMO, a developed electrical environment is focused over IDIC-R8, but in LUMO, it is concentrated over the IDIC/IDIC-R8 complex, including its final stage A part (Fig. 8).
Because of the efficient flow of electrons from D to A, these dyes are appropriate OSCs to be used in organic semiconductor technologies. Furthermore, its bandgap was found at 1.11 eV which was manageable for plausible electronic transitions. The method was used to forecast transition behavior, particularly from a shorter wavelength to the singlet excited state (S 1 ), as well as D-A unit interactions with charge carrier localization. Hydrogen atoms were left out since their effect on such changes is so minor.

NLO response
Non-linear optical (NLO) response is effective in organic molecules with sufficient electrical connection across their various moieties (Fig. 9) [4]. Many computational and experimental investigators have focused on materials engineering, thermodynamics, and their chemistry to quest for new and efficient NLO responsive materials [42]. Interdisciplinary efforts to create NLO materials have been initiated Fig. 7 The V oc of newly designed dyes (IDIC-R1-IDIC-R9) with IDIC-R in chloroform as the need for photonic manipulation, harmonic production, frequency melding, and accompanying statistics rises [43]. During the present study, the electronic features were used to estimate the amplitude of optical engagements to monitor a sequential linear relationship (polarizability) and non-linear responses (hyperpolarizabilities) [44]. The calculated α total and β total values of the dyes were recommended. All tensors stated were employed as a reference material for a measurement of initial hyperpolarizability and magnetic moments, and they were determined to be greater than those for the literature. All dyes were discovered to have more µ nor than urea (1.  IDIC-R3 (354). The larger the µ nor value, the lower the bandgap, resulting in an excellent NLO value observed. The recommended compound IDIC-R5 was proven to have the greatest mean polarizability. In addition, 3485 D, a noteworthy rise in its value, was identified. The inclusion of three nitro groups boosted electron-withdrawing ability by enriching the electrical structure surrounding the A unit.
The intensity of substituents applied to the A unit (PD6) influenced a molecule with its non-linearity. When replacements occur, conjugated contribution grows and becomes more dominant. The overall worth was arranged in decreasing order. The dye IDIC-R5 is more functional than IDIC-R6. The dye IDIC-R5 offers the highest overall value when compared to other created dyes.
A comparison study was carried out using urea as a reference component, yielding a β tot value of 714 D. The dye IDIC-R1 and IDIC-R6 showed hyperpolarizability values that were 8.33 and 1.27 times greater, respectively, than the standard. The NLO responses exhibited in IDIC-R1 to IDIC-R9 are bigger because of stronger electron-withdrawing entities in the acceptor half, which may minimize the HOMO → LUMO band gap, boost the ICT between both orbitals, and then further polarize the molecule. When the bandgap between the HOMO and LUMO orbitals were inverted, all the recommended dyes exhibited second-order hyperpolarizability numbers. The dye IDIC-R8 is the most valuable. The current work dives into the fascinating NLO recordings of conjugated push-pull organic compounds for modern optical applications. Furthermore, because of their significant NLO sensitivity, the created dyes can be used as study targets.

Conclusions
Organic compounds that have significant non-linear optical (NLO) properties are widely employed in the optical device sector. Nine newly designed, Pull-Push, organic dyes (IDIC-R1-IDIC-R9) with A-π-D-π-D-π-A framework were theoretically generated from A and D components with π-spacers by changing the different substituted opportunities to automate their band gap and their NLO responses. The influence of various A units on non-linear kinetic energy modes is examined. FMO tests revealed that all the created dyes had a very small bandgap which had a reflection of their effect in their other PV properties. These GRP values were shown to be associated with a shorter bandgap, with lower values and higher σ scores. Furthermore, when compared to the reference molecule, all the dyes had greater λ max values and slightly lower energy of electronic transitions. An NBO investigation demonstrated the creation of electrostatic repulsion in molecules between the D and A species. Such charge separation might be the result of a significant NLO reaction due to ICT from D to A. The initial hyperpolarizability indices of the dyes IDIC-R1-IDIC-R9 were eight times higher than those of the reference molecule. The most valuable dye is IDIC-R8. Our findings should help in the development of organic dyes with desirable characteristics for improving optical device efficiency. Also, a pull-push effect can be generated to enhance the NLO responses by using π-poor versus π-rich electronic dyes toward the dyesensitized solar cells. Among all the dyes, IDIC-R8 produced the highest V oc value and at the same time it also had the highest second-order NLO response to imply that this dye structure can be a good candidate to be synthesized experimentally. Due to their appealing characteristics including cheap cost, simplicity of manufacture, transparency, and high performance under normal situations, these improvements may serve as the foundation for the global acceptance of DSSCs as energy harvesters.