3.1. Method selection and structural optimization
In this study, we utilized various DFT functionals, namely B3LYP, CAM-B3LYP, MPW1PW91, PBEPBE, and ωB97XD, to optimize the Ref molecule in CHCI3 solvent using a common basis set. The absorption maxima spectra of the Ref molecule, obtained from the mentioned methods in the chloroform solution, were as follows: 799.18 nm (B3LYP), 551.80 nm (CAM-B3LYP), 738.00 nm (MPW1PW91), 1051.82 nm (PBEPBE), and 504.26 nm (ωB97XD) (Fig. 4). It is worth noting that these results slightly deviate when considering the molecules without solvent. In the absence of a solvent, the UV-visible maximum absorption values were 741.81 nm (B3LYP), 530.31 nm (CAM-B3LYP), 690.26 nm (MPW1PW91), 488.86 nm (PBEPBE), and 965.83 nm (ωB97XD) (Fig. 3b). Interestingly, the MPW1PW91 functional exhibited the maximum absorption (λmax) value of 738.00 nm, which is closest to the experimentally observed λmax (664 nm) of the Ref molecule graphically represented in (Fig. 3a). Hence, MPW1PW91 with the 6-31G (d, p) pople basis set was selected for further analysis.
Furthermore, Table 1 provides the measurements of the length of bonds (Lc-c) in angstroms (Å) and the angle of dihedral (θ◦) for all the optimal geometries. The pair of bond strengths of the molecules under investigation, namely Ref and A1-A5, exhibited a range spanning between a value of 1. to 1.44 Å. It is noteworthy that the interatomic distance between two carbon atoms bonded by a single bond (C–C) is commonly seen to be approximately 1.54 Å, whereas the interatomic distance between carbon atoms bonded by a double bond (C = C) is normally around 1.34 Å. The observed results suggest the existence of substantial conjugation, as the measured lengths of bond in all the examined molecules are within the range between that of single bonds and double bonds.
In relation to the dihedral angle, all of the molecules that were examined displayed differences within the range of 0.05° to 18.68°. The more planar structure of A3 is supported by the validation of its lower the dihedral angle (θ°) compared to Ref. The planarity seen in A3 can be attributed to the smaller acceptor moieties present in this molecule in comparison to the other novel compounds[59]. The optimized arrangement has a planar structure when observed laterally, so promoting conjugation, facilitating substantial π-π stacking across considerable distances, and perhaps augmenting intra-molecular charge mobility. In contrast, the heightened dihedral angle seen in molecules A1, A2, A4, and A5 provides evidence in favor of their twisted conformation, which could potentially enhance the dissociation of excitons (electron-hole pairs). The introduction of sterically hindered large groups in the acceptor constituents of these compounds has the potential to induce structural distortion as a result of steric hindrance.
Frontier molecular orbitals (FMOs)
An understanding of the HOMO and LUMO levels can shed light on the distribution of electrons in molecules and intramolecular charge transfer (ICT). These orbitals provide valuable insights on the characteristics of the molecule’s optoelectronic states under investigation. The acceptor elements' chemical reactivity and stability, when connected to the molecule, play a pivotal role in dictating the magnitude of the HOMO-LUMO energy gap, denoted as Eg. The HOMO energy level is increased by electron-donating groups, whereas the LUMO energy level is decreased by electron-withdrawing groups. However, the effectiveness of solar devices has a negative correlation with the energy gap.
The illustration of the spatial distribution of the FMOs diagram across various structures is presented in Fig. 5b. The charge transport properties of organic compounds are similarly influenced by frontier molecular orbitals (FMOs). The LUMO is responsible for controlling the movement of electrons, whereas the HOMO is responsible for governing the movement of holes. In order to enhance device performance and mitigate recombination losses, it is imperative to provide effective charge transport. It is crucial for efficient charge transfer that the donor material's highest occupied molecular orbital (HOMO) and the acceptor material's LUMO, or lowest unoccupied molecular orbital, are in the correct positions relative to one another. Efficient transfer of photoexcited electrons can be achieved through the presence of a donor and acceptor with closely matched energy levels. The enhancement of the device's efficiency can be achieved through the adjustment of the energy offset between both FMOs, hence influencing the force that is responsible for charge transfer.
The present work investigates the chemical structures (A1-A5) that are characterized by an indacenodithiophene core. Because it is attached to two terminals acceptor units by means of benzothiadiazole bridges, this core performs the function of a donating group. The electron density originates from the central core and extends towards the terminal acceptor groups that are capped at the ends. This arrangement, characterized by a planar and symmetrical structure, promotes enhanced charge transfer inside the complex. The electronic cloud in the HOMO orbital primarily accumulates around the fused-ring core, while in the LUMO orbital, the charge density moves towards the end-capped moieties as a result of the electron-withdrawing effect exerted by the electron-deficient groups. The electron density distribution in Fragment Molecular Orbitals (FMOs) is a result of the combined contributions from the donor, bridge, and acceptor components.
The HOMO values of the architectural molecules exhibit an ascending order, namely A1, A2, A3, A4, A5, and Ref. In a similar vein, when the LUMO values are organized in ascending order, the resulting sequence is as follows: A2, A5, A1, A3, Ref, and A4. In relation to the energy band gap (Eg) values, the ascending order is as follows: A2, A5, A1, Ref, A3, and A4. The majority of the analyzed chromophores displayed a more limited spectrum of energy gaps in comparison to the reference molecule as depicted in Fig. 6. The aforementioned observation can be ascribed to the existence of electron-deficient groups located at the terminal locations of the molecules. One notable feature of A2, an architectural molecule, is its comparatively lower energy level of the lowest unoccupied molecular orbital (LUMO), which can be attributed mostly to the inclusion of nitrile functional groups. The aforementioned moieties demonstrate a notable attracting effect, leading to the creation of a band gap characterized by the most minimal energy level. Conversely, the significant energy band gap observed in A4 can be ascribed to the inclusion of 5-membered rings containing carbonitrile acceptors and ethyl groups positioned at the terminals. The presence of ethyl groups, which donate electrons, is primarily accountable for the decreased pulling effect and the shortened conjugation length found in these structural components.
Table 2
The energies of HOMO, LUMO as well as parameters like bandgap (Eg), ionization potential (IP), and electron affinity (EA) of both Ref and A1-A5 were assessed through theoretical calculations
Molecules | EHOMO (eV) | ELUMO (eV) | Eg (eV) | IP (eV) | EA (eV) |
Ref | -5.370 | -3.256 | 2.114 | 5.370 | 3.256 |
A1 | -5.501 | -3.545 | 1.956 | 5.501 | 3.545 |
A2 | -5.650 | -3.832 | 1.818 | 5.650 | 3.832 |
A3 | -5.407 | -3.275 | 2.132 | 5.407 | 3.275 |
A4 | -5.252 | -3.020 | 2.232 | 5.252 | 3.020 |
A5 | -5.612 | -3.765 | 1.847 | 5.612 | 3.765 |
Determining the charge transfer features of photovoltaic systems are the electron affinity (EA) and ionization potential energy (IP). Chromophores containing an electron-donating group have lower ionization potential (IP) values as a result of the relatively less stable HOMO level. Conversely, chromophores incorporating electron-withdrawing moieties demonstrate higher IP values due to the significantly stabilized HOMO level. The EA and (IP) values for the compounds under study are presented in Table 2.
3.3 Density of States (DOS)
In order to verify the accuracy of the (FMO) analysis, we assessed the Density of States (DOS) for each molecule under investigation. The DOS plots were segmented into red-, blue- and magenta-colored lines, which represent the acceptor, donor, and bridge fragments, respectively as shown in (Fig. 7). These lines indicate the contribution of each fragment towards the FMOs and are referred to as the Partial Density of States (PDOS). The black lines depicted on the plots serve to illustrate the Total Density of States (TDOS). These graphs have two sides: a left side that displays electron density at HOMO energy levels and a right side that forecasts the same at LUMO energy levels. The middle region, which is relatively flat, corresponds to the energy gap between the frontier molecular orbitals (FMOs). This region is strongly correlated with the energy values (Eg) derived from the analysis of the FMOs, as shown in Table 2. We also evaluated the quantitative contribution of each fragment and recorded the results in Table 3. According to the results of our research, both the donor and the linkers (bridges) played an important part in the expansion of the HOMO. It was observed that both the donor and the π linkers made significant contributions to raising the HOMO In comparison to the reference compounds, the synthesized molecules demonstrated a reduction in the proportion of acceptor involvement in the (HOMO). In a similar manner, it can be demonstrated that the percentage increases in acceptor participation for A1-A5, relative to the reference molecule (Ref), were approximately three times higher for the (LUMO). In contrast, there was a significant decrease observed in the role of the donor fragment across all molecules. The observed outcome aligns with the outcomes derived from the Frontier Molecular Orbital (FMO) research, suggesting that the primary influence on the HOMO energy level stems from the donor and pi linkers. Conversely, the attached acceptors are found to be accountable for the LUMO energy level. The observed effect is more prominent in the recently developed compounds compared to our reference molecule.
Table 3
The percentage of each fragment involved in generating the FMOs.
Molecules | FMO | Acceptor | Donor | Bridge |
Ref | HOMO | 16.1 | 61.8 | 22.1 |
LUMO | 26.1 | 18.2 | 55.6 |
A1 | HOMO | 12.4 | 64.7 | 23.0 |
LUMO | 42.0 | 15.9 | 42.1 |
A2 | HOMO | 13.5 | 64.3 | 22.2 |
LUMO | 49.4 | 15.0 | 35.6 |
A3 | HOMO | 9.9 | 67.2 | 22.9 |
LUMO | 30.5 | 17.7 | 51.7 |
A4 | HOMO | 10.3 | 67.3 | 22.4 |
LUMO | 37.9 | 14.4 | 47.6 |
A5 | HOMO | 13.2 | 64.5 | 22.3 |
LUMO | 47.4 | 15.3 | 37.3 |
3.4 Optical properties and dipole moment
The quantum spectrum of absorption possesses the ability to forecast the photo-electronic properties of molecules. Chromophores, in turn, can be activated by absorbing photons with energy levels that align with their band gaps [46]. To assess the efficacy of a molecule in collecting solar energy and facilitating charge transfer (CT), it is imperative to ascertain key attributes such as absorbance profile (λmax), the energy of excitation (Ex), the dipole moment (µ), and oscillation intensity (f)[46]. Tables 4 and 5 present the optically derived data for the compounds under investigation (Ref, A1-A5) in both gas and solvent (chloroform) environments, as determined by computational methods. The absorption of the molecules that were built was examined via the MPW1PW91 method, employing a 6-31G (d, p) basis set. This particular approach was chosen because to its ability to produce absorption values that closely align with those found by experimental means. The energy required for excitation (Ex) refers to the energy that is consumed during a transition process, whilst the transition probabilities are referred to as oscillation strength (f). It is postulated that an intramolecular charge transfer, also known as ICT, process that is efficient would have a substantial oscillation strength, a relatively low excitation energy, and a broader absorption spectrum characterized by a higher molar absorption coefficient (λmax)[60].
Table 4
The present study encompasses the investigation of several molecules in a gaseous medium, whereby both experimental and theoretical approaches were employed to determine key parameters such as maximum absorption (λmax), excitation energy (Ex), oscillation intensity (f), assignment, and dipole moment (µ).
Molecules | Calc. λmax (nm) | Excitation energies [Ex] (eV) | Oscillation strength [f] | Major MO assignment | Dipole moment [µ] (D) |
Ref | 690 | 1.796 | 2.482 | H → L + 1 (70.0%) | 0.0001 |
A1 | 745 | 1.665 | 2.352 | H → L + 1 (70.1%) | 8.1107 |
A2 | 789 | 1.571 | 2.514 | H → L (69.7%) | 11.0596 |
A3 | 683 | 1.817 | 2.459 | H → L + 1 (69.9%) | 3.6388 |
A4 | 679 | 1.826 | 2.052 | H → L + 1 (69.8%) | 0.0016 |
A5 | 780 | 1.589 | 2.480 | H → L + 1 (69.8%) | 7.5578 |
Energy levels of the best chromophores (Ref and A1-A5) were calculated using density functional theory (DFT) and the MPW1PW91/6-31G (d, p) basis set utilizing TD-SCF calculations. We used the IEFPCM solvation model and chloroform as the solvent to do the computations for both the gaseous and solvent phases. Figure 8 (a, b) is a graphical representation of the absorption spectrum of both types of molecules. In both its gaseous and solvent forms, the Ref molecule exhibits a maximum wavelength (max) of 690 nm and 738 nm, respectively. The wavelength range of maximum absorption (λmax) for the A1-A5 molecule is 679–789 nm in its gaseous state and 699–874 nm when dissolved in a solvent. In all forms, the ascending order of the maximum eigenvalue (λmax) is as follows: A4 < A3 < Ref < A1 < A5 < A2. The visible spectrum absorption of Ref and A1-A5 molecules is primarily observed in the near-infrared (IR) region. Notably, the newly produced molecules A1, A2, and A5 demonstrate a considerable redshift in comparison to the reference molecule. This redshift is attributed to the presence of exceptional acceptors located at the terminal sites.
The presence of a polar solvent explains the observed bathochromic shift in the solvent phase as contrasted to the gas phase. This solvent preserves the LUMO of the polar excited state, which narrows the band gap and extends the range of wavelengths at which light is absorbed. There is a direct inverse relationship between wavelength and energy. Out of all the compounds that have been examined, it has been determined that molecule A2 exhibits the highest value of λmax, with measurements of 789 nm in a gaseous state and 874 nm in a solvent.
The moment of dipole attraction (µ) is a fundamental characteristic that can offer valuable insights into the molecular morphology by characterizing its level of solubility and polarity [48, 49]. The polarity of chromophores is reflected by their dipole moment, whereby greater values are indicative of enhanced solubility in polar organic solvents. Furthermore, it is observed that molecules have a tendency to arrange themselves in an antiparallel manner, whereby the opposite poles of the molecules exhibit an attractive force towards one another. The process of self-assembly facilitates the improvement of intermolecular order while simultaneously minimizing disarray [61]. The dipole values of the compounds being investigated are shown in Tables 4 and 5, for both their gas and solvent (chloroform) forms. In the gaseous state, the dipole moment of each molecule exhibits a range of values, spanning from 0.0001 to 11.0596 Debye (D). Conversely, in the solvent phase, the dipole moment spans from 0.0001 D to 13.4372 D. In both forms, the increasing order of dipole moment is Ref < A4 < A3 < A5 < A1 < A2. The utilization of a polar solvent in the solvent form enhances the polar nature of the molecules, leading to elevated dipole moment values in comparison to the gaseous state. Among the compounds under investigation, A2 exhibits the highest charge partition, mostly attributed to the exceptional electron-withdrawing capability of the groups located at its terminal locations. Hence, there is potential for improving charge transport within the active material of solar cells by the manipulation of molecular shape.
Table 5
Both experiments and theoretical calculations were used to estimate the maximum absorbance (max), the energy of excitation (Ex), oscillation intensity (f), assignment, and the dipole moment () of all molecules studied in a chloroform solvent.
Molecules | Exp. λmax (nm) | Calc. λmax (nm) | Excitation energies [Ex] (eV) | Oscillation strength [f] | Major MO assignment | Dipole moment [µ] (D) |
Ref | ~ 664 | 738 | 1.680 | 2.776 | H → L + 1 (70.3%) | 0.0001 |
A1 | - | 810 | 1.530 | 2.568 | H → L + 1 (70.1%) | 9.7701 |
A2 | - | 874 | 1.419 | 2.682 | H → L + 1 (69.7%) | 13.4372 |
A3 | - | 726 | 1.707 | 2.704 | H → L + 1 (70.0%) | 3.5730 |
A4 | - | 699 | 1.773 | 2.257 | H → L + 1 (69.2%) | 0.0020 |
A5 | - | 861 | 1.440 | 2.664 | H → L + 1 (70.0%) | 8.6560 |
3.5 Molecular electrostatic potential maps (MEPs)
The study employed the MEPs (Molecular Electrostatic Potentials) of Ref's MEPs, along with recently synthesized molecules (A1-A5). The analysis was conducted using the MPW1PW91/6-31G (d, p) level of DFT theory. These MEPs are graphical representations of molecules, employing distinct colors to denote diverse electrostatic potential areas on the molecules. Additionally, simulated MEP plots were generated for the molecules, revealing areas of intense negative charge in blue and strong positive charge in red. This is illustrated in Fig. 9.
The arrangement of both negative and positive charges inside a molecule can be deduced from MEPs. In organic solar cells, excitons (bound electron-hole pairs) are produced upon light absorption and must dissociate into carriers of free charge (electrons and holes). MEPs can help assess the likelihood of charge transfer processes and identify regions where charge separation is likely to occur. Most organic solar cells have two main components: a donor material (which donates electrons) and an acceptor material (which accepts them). Energy level alignment and the driving force for charge transfer at the interface are both heavily influenced by the MEPs of the donor and acceptor molecules. The effectiveness of charge separation and the overall functioning of the device can be better understood by studying the donor and acceptor MEPs. When it comes to the efficiency of an OSCs, the active layer's molecular arrangement and orientation matters a great deal. Understanding the active layer's shape, packing motifs, and intermolecular interactions with the help of MEPs can shed light on charge transport paths, exciton diffusion lengths, and other crucial characteristics affecting device performance.
The MEP plots exhibit a notable prevalence of the red color in the middle donor region, whereas the blue color is primarily concentrated in the terminal moieties. The electronic clouds that exhibit a vibrant blue color predominantly symbolize the oxygen atoms located at the terminal positions of the molecules. In a similar vein, the nitrogen atoms present in dicyanides exhibit robust negatively charged electron clouds, which give rise to nucleophilic reaction sites as a result of their positioning at the terminal positions within the molecules. On the other hand, the red hues observed in the MEP maps at the oxygen and sulfur atoms can be attributed to the existence of positively charged carbon atoms around the oxygen atom within the molecular core. These carbon atoms effectively neutralize the negative maximum associated with the oxygen atom.
3.6 Reorganization energy (RE)
The estimation of chromophore CT attributes relies on the important parameter known as reorganization energy (RE), which can be determined by measuring the mobility of charge carriers. Upon exciton separation, the hole and electron move towards their respective electrodes, causing the molecule's structure to deform, and the energy required to rearrange the distorted molecule is termed reorganizational energy. There are two distinct categories of reorganization energies (REs): internal RE (λint), which is shaped by the internal molecular morphology, and external RE (λext), which is dictated by external factors such as the polarization of the surrounding environment. Marcus' theory employs equations (1) and (2) to calculate internal RE, while external RE is disregarded [50]. The relationship between the mobility of charges and the reorganizational energy is inversely proportional. Thus, for building efficient OSCs, high charge mobility is desired, necessitating the lowest possible reorganization energy.
Table 6
Electron and hole reorganization energies (in electron volts, eV) for R and M1-M4 molecules.
Molecules | λe (electron) | λh (hole) |
Ref | 0.3523 | 0.2910 |
A1 | 0.3079 | 0.3105 |
A2 | 0.2385 | 0.2156 |
A3 | 0.2845 | 0.2930 |
A4 | 0.2936 | 0.2765 |
A5 | 0.2423 | 0.2602 |
Using the MPW1PW91/6-31G (d, p) method in conjunction with density functional theory, we calculated the energies of optimized geometries for neutral, anionic, and cationic states. This allowed us to determine the hole (λh) and electron (λe) mobilities. The computed mobilities are summarized in Table 6. Notably, all synthesized molecules exhibit lower reorganization energies (RE) for electrons compared to the reference molecule. The sequence for electron mobility (λe) across all investigated molecules is (sequence), while the sequence for hole mobility (λh) is (sequence). According to our analysis, molecule A2 demonstrates the smallest reorganization values for both electrons (λe = 0.2385) and holes (λh = 0.2156).
This indicates that A2 possesses enhanced charge mobility in comparison to the other molecules under evaluation. When reorganization values are minimal, it signifies that the molecule can effectively accommodate and redistribute charges, facilitating the smooth movement of electrons and holes within its structure. In the case of A2, its low reorganization values indicate its ability to efficiently enable the flow of both electrons and holes, making it highly conducive for charge transport.
3.7 Exciton Binding Energy (Eb) and Transition Density Matrix (TDM)
The concept of (Eb) refers to the amount of energy required to separate an electron and the hole that are initially bound together as an exciton. Excitons are generated in the domain of organic solar cells subsequent to the receipt of photons. However, in order to facilitate the production of electric current, it is imperative that the excitons undergo dissociation, resulting in the release of charge carriers, specifically electrons and holes. This dissociation phenomenon, commonly referred to as exciton dissociation or charge separation, is made possible through the existence of donor and acceptor materials within the device. The charge carriers, after photoexcitation, are constrained as excitons, and they must be effectively dissociated for electricity generation. Researchers are striving to enhance the efficiency and performance of these devices by manipulating the exciton binding energies of engineered materials. Acceptors with lower Eb values can help achieve this, making it crucial that the exciton's Eb is low enough for efficient dissociation.
Eb = Eg – Ex (3)
Table 7
Bandgaps (Eg), excitation energies (Ex), and exciton binding energies (Eb) of Ref and A1-A5 in gaseous and solvent (chloroform).
Molecules | Eg (eV) | Ex (eV) Gaseous | Ex (eV) Solvent | Eb (eV) Gaseous | Eb (eV) Solvent |
Ref | 2.114 | 1.796 | 1.680 | 0.318 | 0.434 |
A1 | 1.956 | 1.665 | 1.530 | 0.291 | 0.426 |
A2 | 1.818 | 1.571 | 1.419 | 0.247 | 0.399 |
A3 | 2.132 | 1.817 | 1.707 | 0.315 | 0.425 |
A4 | 2.232 | 1.826 | 1.773 | 0.406 | 0.459 |
A5 | 1.847 | 1.589 | 1.440 | 0.258 | 0.407 |
Using Eq. (3), the Eb values for A1-A5 and Ref molecules were tabulated in Table 7, where Eg is the bandgap, and Ex is the excitation energy. The descending order of Eb in all molecules is A4 > Ref > A3 > A1 > A5 > A2 for the gaseous state, and A4 > Ref > A1 > A3 > A5 > A2 for the A4 > Ref > A3 > A1 > A5 > A2 for the gaseous state, and A4 > Ref > A1 > A3 > A5 > A2 for the solvent state. The Eb is higher in the solvent form due to the stronger interaction and binding of the chloroform solvent with the excitons.
The transition density matrix (TDM) analysis is another technique for evaluating the creation, mobility, and separation of excitons, as well as how donors and acceptors interact in Indacenodithiophene-benzothiadiazole-based molecules. The TDM plots plays a crucial role in elucidating the electronic transitions occurring between molecular orbitals. It offers valuable information regarding the formation of excitons. Through the analysis of the TDM, can enhance their comprehension of various aspects such as exciton generation and decay mechanisms, exciton diffusion lengths, and the overall dynamics of excitons within organic materialsBy analyzing electron-occupied modelled orbitals, Time-domain spectroscopy (TDM) is a technique used to visualize the electron density distribution within a molecular structure and track the temporary positions of holes and electrons throughout the process of excitation.
The generation of unbound charges and the facilitation of charge transport through effective transfer of charges and separation of the excitons at the interface between the donor and acceptor are crucial. The Time-Dependent Density Matrix (TDM) provides insight into how the efficiency of the separation of charges is influenced by the characteristics and intensity of the electronic coupling among the acceptor and donor molecules. Tailoring the molecular architecture of organic materials based on the knowledge acquired about TMD can enhance charge transfer and reduce recombination losses. The energy of the Transition Dipole Moment (TDM) was calculated using the TD-DFT/MPW1PW91/6-31G (d, p) method. The resulting data was shown as a two-dimensional colored graph using the Multiwfn 3.8 software (Fig. 10). The two-dimensional plots of Time-Domain Multiplexing (TDM) demonstrate that the molecules under investigation are dispersed across three distinct segments, namely A, B, and D. These segments correspond to the acceptor, the bridge, and donor regions, respectively. The molecules have a consistent distribution of electron density from the central donor core to the outside acceptor units, suggesting their suitability for application in organic solar cells (OSCs).
3.8 Light harvesting efficiency (LHE)
LHE refers to a materials ability to collect light and produce a charge or induce it into the conduction band. OSCs rely on the absorption of sunlight by organic molecules to generate excitons (bound electron-hole pairs). A higher light harvesting efficiency ensures that a greater fraction of incident photons is absorbed, increasing the number of excitons generated. This, in turn, leads to a higher probability of charge separation and improved current generation. It is a critical factor for any material utilized in solar cells. By employing DFT approach, researchers can gain insights into and optimize the electronic structure, optical characteristics, exciton dynamics, interface influences, and charge transport mechanisms. The ultimate objective is to enhance the efficiency of light absorption and overall performance of these devices, thereby improving their light harvesting capabilities.
LHE can be calculated using Eq. (4), which involves the oscillation strength (f).
LHE = 1 – f –10 (4)
Table 8 shows the computed LHE values for Ref and A1-A5 molecules. The values are almost similar for all the molecules in both gaseous and solvent form depicted in Table.8.
As per Eq. (5), there exists a direct relationship between LHE and short-circuit current JSC.
JSC = \(\underset{\lambda }{\overset{0}{\int }}LHE.{\phi }_{injected}.{\eta }_{collect}.d\lambda\) (5)
The short-circuit current (JSC), provided by the Eq. (5), is calculated by integrating the product of LHE, φinjected, and ηcollect over the wavelength range (0 to λ). Here, φinjected is the electron injection, and ηcollect represents the persistent charge collection. Since the aforementioned equation links LHE directly to JSC, it was concluded that any alterations in LHE would have a direct effect on JSC.
Table 8
Theoretically investigated values of LHE (gaseous and solvent phase) for Ref and A1-A5 molecules.
Molecules | Oscillation strength [f] (gaseous) | Oscillation strength [f] (solvent) | LHE (gaseous) | LHE (solvent) |
Ref | 2.482 | 2.776 | 0.9998 | 0.9999 |
A1 | 2.352 | 2.568 | 0.9998 | 0.9999 |
A2 | 2.514 | 2.682 | 0.9999 | 0.9999 |
A3 | 2.459 | 2.704 | 0.9999 | 0.9999 |
A4 | 2.052 | 2.257 | 0.9993 | 0.9997 |
A5 | 2.480 | 2.664 | 0.9998 | 0.9999 |
3.9 Open circuit voltage (VOC)
VOC is a fundamental metric that plays a pivotal role in determining the efficiency of solar cells. The term "open-circuit current" refers to the highest current produced by a device in the absence of an applied voltage. The assessment of power conversion efficiency in organic solar cells is facilitated by the utilization of the open-circuit voltage as a significant parameter. The direct proportionality between the voltage in the open circuit of a device and its overall efficiency is generally recognized. The open circuit voltage of a solar cell plays a crucial role in determining the maximum electrical output that can be attained. By increasing the voltage in the open circuit, the efficiency of harnessing the light that is generated can be enhanced, leading to the optimization of the cell's overall performance. The primary component influencing the effective transfer of electrons between the layer that is photoactive to the electrode, as well as the reverse motion of holes, is this crucial element. The enhancement of charge carrier extraction and reduction of losses can be achieved by minimizing the incidence of recombination of charges and leakage channels by an increase in the open circuit voltage. The volatile organic compound (VOC) is subject to the effect of multiple parameters, encompassing materials, levels of energy, light source characteristics, light intensity, temperature, and device shape.
In the context of solar cells, the process of photoexcitation involves the transfer of an electron from the (HOMO) of the donor to the (LUMO) of the acceptor. The open-circuit voltage (VOC) can be calculated by determining the energy difference between the levels of the (HOMO) and the (LUMO) of the corresponding electron donors and acceptors. This can be done by quantifying the difference between these two molecular orbital energies.
The efficiency of a solar cell is directly influenced by the open circuit voltage it exhibits. The two critical factors that are impacted are the (FF) and the short circuit current (Isc). The fill factor is a metric that quantifies the maximum power achievable from a solar cell. It is determined by calculating the percentage of the total input voltage and current. This value is equivalent to the product of the (Voc) and the short circuit current (Isc). A rise in the open circuit voltage of a solar cell results in a corresponding increase in the fill factor, hence leading to an overall enhancement in the PCE of the cell.
Table 9
Open-circuit voltage (VOC), normalized open-circuit voltage (\(\frac{e{V}_{OC}}{{K}_{B}T}\)), and fill-factor (FF) of all the explored molecules.
Molecule | VOC (V) | Normalized VOC | FF | PCE % |
Ref | 1.644 | 63.647 | 0.920 | 18.30 |
A1 | 1.355 | 52.458 | 0.907 | 14.87 |
A2 | 1.068 | 41.347 | 0.888 | 11.47 |
A3 | 1.625 | 62.911 | 0.919 | 18.06 |
A4 | 1.880 | 72.784 | 0.928 | 21.11 |
A5 | 1.135 | 43.941 | 0.893 | 12.26 |
Since all of our compounds are acceptors, we connected our designed acceptors to well-known donor PTB7-Th [51], which has efficient HOMO-LUMO values of − 5.20 eV and − 3.60 eV, respectively.
VOC = \(\frac{{E}_{HOMO}^{DONOR} - {E}_{LUMO}^{ACCEPTOR} }{e}\) – 0.3 (6)
Equation (6) was used to calculate the VOCs of all studied molecules, The variable (e) denotes a molecular charge of 1, while the number 0.3 is generally employed to describe intersurface charge generation. The computed values of the Voc for all molecules are presented in Table 9. Additionally, Fig. 12 displays the energy levels of the HOMO and LUMO for the acceptor molecules, as well as the PTB7-Th donor molecule, together with their respective computed Voc values.
The reference molecule's VOC value is 1.644 V, and the increasing order of VOC values for all designed molecules is A2 < A5 < A1 < A3 < A4. This sequence indicates that A4 has the highest VOC value among all other designed molecules. Therefore, A4 exhibited the highest PCE value (21.11%) to improve photovoltaic properties. PCE values of Ref and all investigated molecules are presented in Fig. 11.
3.10 Fill-factor (FF) and power conversion efficiency (PCE)
The (FF) is an important parameter that is directly related to (PCE) of photovoltaic devices. When it comes to organic solar cells, the fill factor is one of the most important factors that determines the PCE. In most cases, productivity increases coincide with a rise in the fill factor. This is because the voltage drops across the series resistance and charge carrier recombination, two factors that contribute to the overall loss in power conversion, are both reduced with larger fill factors.
Researchers are working to increase the fill factor of organic solar cells in order to boost their PCE by making improvements to the device design, materials, and fabrication processes. Higher fill factors and better performance can be achieved by minimizing recombination losses, maximizing charge carrier mobility, lowering series resistance, and optimizing electrode and interfacial characteristics. However, FF is a complex and poorly understood feature that is mostly determined by the open-circuit voltage (VOC) at the interface of the acceptor and donor molecules. FF can be calculated using Eq. (7).
FF = \(\frac{\frac{e{V}_{OC}}{{K}_{B}T} -\text{ln}\left(\frac{e{V}_{OC}}{{K}_{B}T} + 0.72\right)}{\frac{e{V}_{OC}}{{K}_{B}T} + 1}\) (7)
which includes the normalized VOC (\(\frac{e{V}_{OC}}{{K}_{B}T}\)) and the basic charge (e) which has a constant value of 1. The Boltzmann constant (KB) and temperature (T) are also included in the equation, with KB = 8.61 × 10–5 eV, and T fixed at 300 K. The values of the normalized VOC and FF for the Ref molecule are 63.647 eV and 0.920, respectively. For the designed molecules (A1-A5), the normalized VOC and FF decrease in the sequence A4 > A3 > A1 > A5 > A2, with the same sequence observed for both parameters. The A4 molecule is estimated to have the highest normalized VOC (72.784) and FF (0.928) among all the developed molecules based on the computed values.
A higher PCE value indicates a more efficient energy conversion, which is useful in various situations. Researchers and manufacturers work at increasing PCE values in an effort to make organic solar cells more competitive in the market for clean energy.
The energy harvesting, cost, material optimization, commercial feasibility, and environmental sustainability of organic solar cells are directly impacted by the (PCE). In order to enhance the competitiveness and adoption of this technology, considerable research endeavours have been directed towards augmenting the power conversion efficiency (PCE) of organic photovoltaics, taking into account these aforementioned parameters. The evaluation of PCE is a crucial step in determining the practical applicability of a solar cell material. PCE can be evaluated using Eq. (8),
![](data:image/png;base64,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)
which takes into account the short-circuit current (JSC), open-circuit voltage (VOC), fill factor (FF), along with the constant power of incoming light falling on the cell interface (Pin). The values for FF, VOC, and light harvesting efficiency (LHE) are calculated theoretically. By comparing the results of these calculations with those of the other created compounds, it is clear that the A4 molecule has the highest power conversion efficiency (PCE). The greater fill factor (FF) and normalized voltage open circuit (VOC) values of the A4 molecule lead to this conclusion, while the relatively constant light harvesting efficiencies (LHE) across all molecules support this claim. It's worth emphasizing that PCE is directly correlated with both FF and normalized VOC.
3.11 RDG Exploration
The application of reduced density gradient (RDG) analysis is a valuable technique in the comprehension and enhancement of organic solar cells. This analysis can be conducted using Gaussian software, employing the same degree of theory, by generating a WFN file format to visualize these maps. The investigation of Resonant X-ray Diffraction (RDG) offers valuable insights into the spatial distribution and magnitude of electron density within a molecule. This information is of utmost importance in comprehending the electronic characteristics and mechanisms of charge transfer in organic solar cells. The analysis of Resonance-Enhanced Raman Scattering (RDG) has the capability to elucidate the characteristics and magnitude of intermolecular interactions, including hydrogen bonds, π-π stacking, and the forces of van der Waals. The aforementioned interactions are of significant importance in the arrangement and consolidation of molecules inside the active component of a solar cell, hence influencing the separation and movement of charges, as well as the overall performance of the device.
The (RDG) analysis is accomplished to elucidate the existence of non-covalent interactions (NCIs) due to the development of interacting forces within the molecules (O—S, O—H, F—H, N—S), and sometimes between solvent and organic polymers. RDG is useful to explore the existence of NCIs that comprise hydrogen bonding, LDF (London dispersion forces), Van der Waals forces, and steric hindrance. NCIs prohibit the self-assembly of molecules and maintain the compact packing in molecular structure, induce planarity by restricting the free rotation around the single bond, improve charge transfer, and improve crystallinity. In this way, the optoelectronic characteristics of the molecules are improved to a great extent. NCIs are put into pictorial representation via VMD 1.9 and Multiwfn 3.8 softwares. The positive values of sign(λ2) ρ indicate the existence of strong repulsive interactions, as depicted by red saturation. However, the concentration of green color is the best indication of attractive forces like LDF, while H-bonding is exhibited by blue. These interactions are the best indications of the stability of a molecule, paving the path for the ease of charge transfer. Highly electronegative atoms like F, O, and S strongly interact with green shades. At the same time, the blue saturation is seen between the highly electronegative O-atom and highly electropositive H-atom, thus representing H-bonding. Likewise, the repulsive forces are present between similar structures like five-membered and six-membered rings, as shown in (Fig. 13). All these interactions develop planarity in the molecular structure, thus enabling the molecule to transfer the charge. These insights provide a deeper understanding of the molecular systems involved in organic solar cells and contribute to their optimization and development.