Designing and theoretical study of fluorinated small molecule donor materials for organic solar cells

A recently synthesized photoactive donor named fluorinated thienyl–substituted benzodithiophene (DRTB-FT), modified with four novel end capped acceptor molecules, has been investigated through different electrical, quantum, and spectrochemical techniques for its enhanced electro-optical and photovoltaic properties. DRTB-FT was connected to 2-methylenemalononitrile (D-1), 2-methylene-3-oxobutanenitrile (D-2), 2-(2-methylene-3-oxo-2,3-dihydro-1H-inden-1-ylidene) malononitrile (D-3), and 3-methyl-5methylene-2-thioxothiazolidin-4-one (D-4) as terminal acceptor moieties. The architectural D-1 and D-3 molecules owe reduced optical band gap of 2.45 and 2.28 eV benefited from A-D-A configuration and have broaden maximum absorption band (λmax) at 617 and 602 nm in polar organic solvent (chloroform). Reduced optical band gap sets the ease for enhanced absorption. Reorganization energy of electron (λe) of D-3 molecule (0.00397 eV) was smaller among all which disclosed its greater mobility of conducting electrons (ICT). Larger values of dipole moment (μ) of D-1 (5.939 Debye) and D-3 (3.661 Debye) molecules in comparison to R indicated greater solubilities of the targeted molecules. Among the tailored molecules, D-3 showed the lowest binding energy of 0.25 eV in solvent phase and 0.08 eV in gaseous phase. The voltaic strength of the designed molecules was examined with respect to fullerene derivative (PC61BM) which exposed that D-1 is the best choice for achieving higher PCE. TDM (transition density matrix), DOS (density of states) analysis, and binding energies all were estimated at MPW1PW91/6-31G (d, p) level of DFT (density functional theory). All the architecture molecules show reduced band gap and high electron transfer rate due to the lowest reorganization energy (RE) of electron. The results show that there is greater contribution of acceptor and conjugated donor core towards the total absorption into the visible region of the spectrum. When tailored molecules D-1, D-2, D-3, and D-4 were blended with fullerene derivative polymer (PC61BM), they give high values of voltage at zero current level (Voc) compared to R. All the architecture molecules show reduced band gap and high electron transfer rate due to the lowest reorganization energy (RE) of electron. The results show that there is greater contribution of acceptor and conjugated donor core towards the total absorption into the visible region of the spectrum. When tailored molecules D-1, D-2, D-3, and D-4 were blended with fullerene derivative polymer (PC61BM), they give high values of voltage at zero current level (Voc) compared to R.


Introduction
The world is facing serious energy shortfalls as a result of escalating energy demands due to rapid industrialization, enhancements in lifestyle, and increase in population [1]. Though much of the energy requirements are being fulfilled by non-renewable energy resources such as fossil fuels (petroleum fractions, natural gas, and coal) [2], the reserves of these non-renewable resources are being continuously depleting. Moreover, they have posed some glaring consequences to the environment due to emission of CO 2 during combustion and to humans by creating an imbalance between energy needs and supply [3]. In short, we will soon run out of these exhaustible energy sources. Scientist are endeavoring to find the substitutes which are not only cost-effective but triumph in minimizing the energy gap between demand and supply [4].
Various renewable energy resources like solar energy, tidal energy, biomass, and wind energy are potential candidates to be used as substitutes for fossil fuels [5]. Among these, solar energy being environmentally amiable, harnessed through the sun using photovoltaics, has been considered a smart choice [6]. Although single crystalline, multi-crystalline, and amorphous inorganic systems have obtained reliable efficiency levels of the order of 25%, these have various shortcomings including uneconomical fabrication, resource scarcity of the required material, less thermal stability, and brittleness [7]. After their serendipitous discovery, organic photovoltaics have been extensively investigated owing to remarkable features like solution processability, structural diversity, flexibility, low weight, transparency, cost-effectiveness, and easy control of energy levels in contradiction to inorganic photovoltaics [8,9]. Organic photovoltaics (OPVs) generally comprised donor conjugated polymers, oligomers, and conjugated pigments, blended with fullerene derivatives (acting as acceptors) in bulk heterojunctions [10]. These are well known for their optical properties, efficient charge transfer abilities, and remarkable efficiencies in the range of 10-12% [11].
Investigations explore that naphthalene-and perylenebased diimides (NDI and PDI) as acceptor moieties in various bulk heterojunctions have shown power conversion efficiencies of 16 and 17.23% respectively [12,13]. Non-fullerene organic acceptors have successfully replaced the fullerene derivatives on account of their large-scale production, commercialization, better morphology, photostability, and improved PCE of the order of 14-17% for single junction and two terminal (2T) tandem OPVs [14].
An effective strategy for broadening optical absorption is to improve the intramolecular push-pull effect. Yong Cui and coworkers employed a useful molecular design strategy by introducing halogen atom into non-fullerene end capped acceptor moieties which reduced the band gap, broaden the optical absorption, and caused significant increase in charge mobility and open circuit voltage due to less non-radiative energy loss which in turn boost the power conversion efficiency to 16.5% [15,16].
Recently, Chunyan Liu et al. synthesized a small photoactive donor DRTB-FT by substituting fluorothienyl into benzodithiophene core and investigated it both experimentally and theoretically [17]. A lower HOMO bonding molecular orbital wavefunction of −5.64 eV and a high open circuit voltage of 1.07 eV were attained with 7.66% power conversion efficiency which was attributed to the fluorination of molecule [18].

Computational details
Gauss view 5.0 [20] was used for construction of reference R and designed molecules D-1, D-2, D-3, and D-4 and to envisage the outcomes of quantum chemical investigations. For geometry optimization of reference molecule R and designed molecules D-1-D-4, GAUSSIAN 09 [21] program package was employed. First of all, geometrical optimization and frequency studies of molecule R were executed with a range of density functional methods such as B3LYP [22], CAM-B3LYP [23], MPW1PW91 [24], and WB97XD [25] for the quest to choose the method whose maximum absorbance is in better agreement with the experimental maximum absorption (λ max = 541 nm) [18]. The outcomes confirm that the experimental results are in better agreement with density functional theory (DFT) results (λ max = 578 nm) at MPW1PW91/ 631-G (d, p) level in chloroform solvent indicated in Fig. 6a. Since the functional MPW1PW91 has more agreement of absorption maxima value with experimental λ max value, it was chosen for further calculations. The integral equation formalism polarizable continuum model (IEFPCM) [25] has been utilized to check the effect of solvent on the absorption maxima value. For plotting data and graphical representation of data, origin 6.0 software [26] has been employed. Frontier molecular orbitals (FMOs), density of state (DOS), and transition density matrix (TDM) analysis have been done for charge dispersion and contribution of different moieties to the total absorption [27], with the same functional at the same level of theory. DOS and TDM maps have been plotted by PyMOlyze 1.1 [28] and Multiwfn 3.3.9 Revision software [29] accordingly. Charge mobilities and dipole moments (μ) were calculated with MPW1PW91 functional together with 631-G (d, p) basis set. Reorganization energies of electrons (λ e ) and holes (λ h ) were then calculated from the single point energy calculations and energy calculations after optimization of cations and anions as explained in Eqs. (1) and (2) given below [30].
In the above equation, E 0 − is the energy of anion of neutral geometry, E 0 + is the energy of cation of neutral geometry, and E 0 is the energy of neutral molecule. E _ is the energy of anion in ionic geometry and E + is the energy of cation in ionic geometry.

Frontier molecular orbitals (FMOs)
Quantum mechanical investigation of frontier molecular orbitals is an important tool for electronic excitation property analysis. Time-dependent density functional theory well explains these properties. Planer configurations, extended-πconjugation, and introduction of electron donating or withdrawing moieties are the strategies that lead to significant charge mobilities, narrowing of energy band gap, and better absorption properties due to increase in λ max value of molecules [31]. These mechanisms enhance the electron donating ability of HOMO by raising the energy level of the occupied orbitals and accepting abilities of LUMO by lowering the energy level of the unoccupied orbitals which may prove useful in enhancement of delocalization of π electrons on the FMO. Charge flow pattern of reference molecule R and designed structures D-1-D-4 is shown in Fig. 3. HOMO of reference molecule R is uniformly distributed on the donor core, while LUMO is homogeneously dispersed all over the molecule showing the less delocalization and wider energy band gap. Among the designed molecules D-1, D-2, D-3, and D-4, HOMO is more concentrated on donor core while the LUMOs have different pattern. LUMOs of D-1, D-2, and D-4 to a greater extent are dispersed on end capped acceptor moieties and to a very less extent on the donor core. Massive delocalization can be seen on the right acceptor of LUMO of D-3. The energy order of E HOMO bonding energy orbitals was found to be −5.75 Energy band gap is a true replica of absorption and delocalization of electrons. The lesser the band gap, the higher will be the delocalization and the λ max of molecule will move to the red shift (bathochromic effect) [32]. HOMO-LUMO energy gap of reference and designed molecules arranges themselves in the order of 2.62 > 2.54 > 2.53 > 2.45 > 2.28 for R, D-2, D-4, D-1, and D-3 respectively. The HOMO-LUMO energy gap, along  Table 1 and their graphic description is in Fig. 4. All the designed molecules show lower energy band gap than the reference molecule which lead to the better delocalization of electrons from HOMO to LUMO due to the comparatively strong withdrawing effect of end capped acceptor moieties. D-3-designed molecule has the lowest band gap of 2.28 eV due to extended π conjugation in the end capped acceptor moiety and negative inductive effect of 2-(2-methylene-3-oxo-2,3-dihydro-1H-inden-1ylidene)malononitrile. In tailored molecule D-1, the cyano group acts as pi-acceptor functionality removing electron density from adjacent pi-system.

Density of states analysis
Density of states analysis reinforces the results of frontier molecular orbitals (FMOs). The electron density of the designed organic solar cell molecules was computed with PyMOlyze software suit. At particular energy level, DOS corresponds to number of different states of molecular orbital. With the aid of partial density of states contribution of each molecular orbital constituting the system, total density is analyzed. Individual contribution of principle fragments of a molecule (donor, acceptor, and sometime spacer) to the total absorption band and electronic distribution is analyzed [33]. Green lines indicate the maximum electron density on the donor core and red lines exhibit the same at acceptor moieties in the DOS graph.
For this reason, a molecule is fragmented into donor and acceptor fragments to check their individual contribution to the total absorption as indicated in Fig. 5. From the DOS graph, it is envisaged that the donor core of fluorinesubstituted benzodithiophene contributes significantly to the total population in reference R and each designed molecule.
The negative energy values side along x-axis correspond to HOMO (valence band), while the positive energy values side along the same axis indicate LUMO (conduction band).
Between the conduction and valence band is band gap (E g ). In HOMO, the orbital contribution of donor part was much larger than that of acceptor moieties in all tailored molecules D-1-D-4 plus reference molecule R. The LUMO of R has comparable effect of donor and acceptor moieties towards total absorption. In LUMO of D-1-D-4, the orbital contribution effect of acceptor moieties is prominent and this effect is more pronounced in D-3 as represented in Fig. 5.

Opto-electronic properties
Theoretical maximum absorbance (λ max ) for the designed D-1, D-2, D-3, D-4, and R molecules was calculated for 10 states to better understand the electronic excitation from ground to excited state at MPW1PW91/6-31G** level of density functional theory in solvent phase. Chances of electronic transition (% ETC) of the four designed and one reference molecules are 81%, 90%, 63%, 86%, and 91% respectively in chloroform/ IEFPCM conditions. Stability and de-stability of HOMO and LUMO have greater impact on electronic excitation between FMOs and %ETC. Larger excitations are related to the less stable HOMO. On the other hand, stable LUMO accommodates electrons for prolonged period in the acceptor group which laid the foundation for maximum efficiency of the material. Maximum absorbance (λ max ) for the designed D-1, D-2, D-3, D-4, and R molecules was found to be 617 nm, 602 nm, 602 nm, 601 nm, and 578 nm respectively. The increasing order of maximum absorbance (λ max ) is 578 nm < 601 nm < 602 nm = 602 nm < 617 nm for R < D-4 < D-2 = D-3 < D-1 respectively.
The best absorption properties have been seen for D-1 than for the reference molecule R and designed molecules due to extended π-conjugated system in methylene malononitrile end capped acceptor moieties which leads to π → π* transition and has bathochromic effect in the visible region of the spectrum. It is also inferred that π electrons show strong interaction with chloroform solvent on the account of polarity. Furthermore, oscillator strength in chloroform solvent varies from 1.4359 to 3.1180. Oscillator strength is proportional to the probability that a photon will be absorbed during excitation from ground state to excited state. Oscillator strength is in direct relation with light harvesting efficiency [34]. Comparison of oscillator strengths in solvent phase and gaseous phase exposes that light harvesting efficiency is greater in solvent phase than in gaseous phase. Excitation energies of molecules were found to be in the range of 2.01-2.14 eV. Experimental and theoretical λ max values, %ETC, excitation energies, and oscillator strength of the designed and reference molecules in solvent and gaseous phase have been tabulated in Tables 2 and 3 respectively. After computing the values in the range of 350-800 nm, we obtain the simulated UV/Visible spectrum shown in Fig. 6.    that due to charge separation, polarity is created which is stabilized by polar solvent that causes a shift in the absorption.

Reorganization energy (RE)
Reorganization energies (energy required to structurally reorganize donor and acceptor upon electron transfer) of electron and hole are significant measure of charge transfer process. DFT method at MPW1PW91/6-31G** basis set was employed to investigate the (exciton) electron and hole transport properties. Reorganization energies are influenced by molecular packing, substituent effect of the end capped moieties, and extended delocalization of charge. The Marcus theory explains that two parameters, (i) internal reorganization  energy and (ii) external reorganization energy, are to be considered to estimate reorganization energy of exciton [35]. Actually, charge separation takes place when photon of light is absorbed that ensures the transformation of absorbed photon's energy into charge transfer energy. Larger values of reorganization energy correspond to greater change in structure when electrons get transported from the donor end to acceptor end or from neutral molecule to ionic one. RE determines longevity of charge separated states. Reorganization energy has an indirect relation with charge transfer. The smaller the value of reorganization energy, the more efficient charge will be transferred. The reorganization energies of electron (λ e ) of all molecules were found to be in the order of 0.00397 eV < 0.00572 eV < 0.00648 eV < 0.00731 eV < 0.00749 eV for D-3, R, D-1, D-4, and D-2 respectively. Among all the molecules, only the D-3-designed molecule has the lowest reorganization energy which favors good charge transfer rate and charge transfer properties. While, the reorganization energies of hole (λ h ) were 0.00553 eV < 0.00611 eV < 0.00612 eV < 0.00622 eV < 0.00624 eV for R, D-1, D-4, D-2, and D-3 respectively. These results suggest that the designed molecules D-1 to D-4 are better for hole transport as their reorganization energies of hole are comparable to R, whereas the designed molecule D-3 is the best choice for electron transport in OSCs as its λ e value is the smallest among all others. Reorganization energies of electron and hole are summarized in Table 4.

Dipole moment
Dipole moment values are the estimation of polarity and extent of symmetry in the geometry of molecules. We can assess that lower values of dipole moment are due to the larger symmetry present in the molecule. During excitation, electrons get excited from the ground state to the excited state. So, there is unsymmetrical distribution of electron that makes the excited state more polar. With the excited state being less stable, electrons return to the ground state configuration. Dipole moment of a molecule is the measure of solubility of the molecule in polar solvents. The greater are the values of dipole moment, the more will be the solubility that facilitates the solution processability of organic solar cell materials. Charge transfer abilities of organic solar cell material are also greatly influenced by the dipole moment. Electronic excitation and dipole moment are proportional to each other. A comparison of ground state dipole moment (μ g ) and excited state dipole moment (μ e ) is shown in Table 5. We have assessed the excited state dipole moment of molecules in polar chloroform solvent using the IEFPCM model at MPW1PW91/6-31G** basis level of density functional theory.
During simulation analysis, all the designed molecules show greater solubilities in polar organic chloroform solvent. Apart from this, dipole moment values in excited states are even greater than in ground states that are attributed to the greater polarity due to electronic excitation and charge separation. The increasing order of solubilities at the ground state is given as 0.853 Debye (R) < 1.556 Debye (D-4) < 2.456 Debye (D-2) < 3.661 Debye (D-3) < 5.939 Debye (D-1), while in the excited state the same order of 1.072 Debye (R) < 2.050 Debye (D-4) < 2.654 Debye (D-2) < 4.463 Debye (D-3) < 7.455 Debye (D-1) is followed but with increased solubilizing strengths. D-1 shows maximum dipole moment value that is attributed to the more polar cyanide moieties of end capped acceptor groups. Introduction of fluorine atoms (fluorination) also leads to the greater change in dipole moment [36].

Binding energy and transition density matrix analysis
For the evaluation of electro-optical properties and electronhole pair dissociation potential (efficiency) of organic solar cell materials, binding energy (E b ) is a significant parameter [37]. The Coulombic forces existing between electron-hole pairs are estimated through the binding energy. Due to the low dielectric constant of organic molecules, strong Coulombic forces between the electron and the hole pair lead to the high binding energy which in turn is in inverse relation to the dissociation energy. Coulombic forces and binding energy are directly proportionate.
Binding energy of electron-PyMOlyze, Version 1.1Eq. (3) [38].  where E b represents the binding energy or is the estimation of dissociation energy of exciton, E (LUMO-HOMO) is the band gap energy of optimized organic solar cell material, and E (S1-S0 ) is the single point excitation energy difference of the molecule from ground to excited state. Band gap energies, single point excitation energies, and their corresponding binding energies in solvent phase are given in Table 6.
It has been observed and inferred from the tabulated results that binding energies in solvent phase are higher than in gaseous phase. The higher binding energies in the solvent phase are purely attributed to the solvent interactions that tightly held the electron-hole pairs together. All the architecture molecules have lower binding energy values than R.
In molecular systems, transition density matrix [39] analysis of filled and simulated orbitals is a significant tool for analyzing electronic excitations. Transition density matrix provides a spatial map which reads off characteristic features like coherence and delocalization lengths. Coherence length is actually the separation size or length of distribution of associated electron and hole pair. This characterizing feature is important in demonstrating charge transfer dynamics in light harvesting organic solar cells [40]. Without changing the transition, charge density transformation can be analyzed when electron density is drawn by acceptor moieties from donor core [41]. We visualize the dynamics of shifting of electron density in terms of coherence length indicated by diagonal bright lines in the spatial transition density matrix map shown in Fig. 7.
For better understanding and interpretation of interaction between donor core and terminal end capped acceptor moieties, we segmented the molecule into principle components (benzodithiophene donor core D and acceptor components A). Due to the less contribution of hydrogen atoms towards excitations, we ignored them from all architecture molecules. Among the rest of the atoms, 1-73 atoms in numbering correspond to benzodithiophene donor core D, while atoms that are numbered above 73 fall in the category of acceptors (A) which are arranged along Y-axis (left) and X-axis (bottom) in spatial TDM map, whereas the electron density is on Y-axis (right side). TDM spatial map analysis discloses that electrons are entirely distributed in reference R from donor core to the end capped acceptor moieties as indicated by diagonally bright lines which indicate the coherence between donor and acceptor parts. On the other hand, in tailored molecules D-1, D-2, D-3, and D-4, electron density does not uniformly spread over the entire molecule because end capped acceptor moieties are deficient of electrons so there is a uniform trend of electron transfer from donor to acceptor portions as indicated by bright diagonal fringe.

Open circuit voltage (V oc ) of OSCs
Open circuit voltage of organic solar cell is the maximum voltage of a photovoltaic cell when there is no load connected to the circuit (zero current level). It is the total current drawn from an optical device at the null current level of the device. To estimate the photovoltaic properties of OSC material, open circuit voltage is a significant parameter. Performance and efficiency of the optical system greatly depend upon V oc [42]. Large values of V oc increase the fill factor which have major contribution to the efficiency of the system. In this research work, we estimated the V oc of the reference and architecture molecules theoretically in a simulation analysis with PC 61 BM. To achieve high open circuit voltage values, the HOMO of the donor molecule should be more stabilized with respect to LUMO of the acceptor molecule (PC 61 BM in this case).