DFT study of benzothiadiazole based small molecules for high efficiency organic photovoltaics

Abstract

This study employs density functional theory (DFT) and time-dependent DFT (TD-DFT) to design and evaluate eight novel non-fullerene acceptors (NFAs) (G1–G8) for organic solar cells (OSCs). The molecules were engineered through strategic terminal group modification of a reference indacenodithiophene (IDT)-benzothidiazole (BT) based structure. All designed systems exhibit substantially reduced bandgaps (1.73–2.00 eV) and redshifted absorption profiles (λ_max = 688–803 nm) compared to the reference molecule (REF), leading to enhanced light-harvesting capabilities (LHE = 0.988–0.998). Marcus charge transfer theory calculations revealed high hole hopping rates (K_h ≈ 10¹⁵ s⁻¹) and low reorganization energies (λ_h = 0.0031–0.0052 eV), indicating excellent charge transport properties. The comprehensive computational analysis projects outstanding photovoltaic performance with open-circuit voltage (V_OC = 1.13–1.66 V), fill factor (FF = 0.8927–0.9205), and estimated power conversion efficiency (PCE = 22.8–37.0%) across the series. Among the designed systems, G7 demonstrates exceptional promise due to its optimal bandgap (1.73 eV), outstanding light-harvesting efficiency (LHE = 0.998), and the highest estimated short-circuit current (J_SC = 31.2 mA/cm²), while G5 achieves the highest PCE (37.0%) through balanced photovoltaic parameters. The results establish terminal acceptor engineering as a highly effective strategy for developing high-performance organic photovoltaic materials, with G7 and G5 representing prime targets for experimental validation.

Introduction

The escalating energy crisis has become a significant global challenge, driven by fast population growth, heightened industrialization, and increasing energy necessities¹. Although fossil fuels have traditionally been the main energy source, their exhaustion and adverse ecological effects need an immediate shift to environmentally friendly substitutes². Among numerous renewable energy sources, such as wind, nuclear, and solar energy, whereas solar energy stands out as the most intriguing choice due to its exceptional abundance and commercial viability³. Remarkably, the sun provides an enormous quantity of energy in a single hour, adequate to satisfy the world’s energy requirements for over a year. Despite this remarkable perspective, fewer than 1% of this extensive energy store is efficiently utilized, highlighting the urgent necessity for novel photovoltaic materials that can optimize solar energy transformation effectiveness⁴.

Due to their invention in the nineteenth century, solar cells have emerged as fundamental in turning solar energy into electrical power⁵. These devices capture ultraviolet radiation via a photoactive layer, generating electron–hole pairs that shift to designated electrodes, thus manufacturing an electric current⁶. Although silicon-based solar cells have historically been the benchmark due to their beneficial properties, outstanding thermal stability, stable energy levels, and impressive power conversion efficiency (PCE) of almost 46%, they possess inherent constraints⁷. Their elevated fabrication expenses, mechanical fragility, and inflexible architecture impede development and adaptation. Additionally, the rigidity of their stable composition presents considerable obstacles for structural alterations⁸. To address these limitations, organic solar cells (OSCs) have arisen as a viable alternative⁹. By substituting traditional p- and n-type materials with donor and acceptor equivalents, OSCs replicate the essential functional principles of their inorganic opponents¹⁰. OSCs have several benefits, encompassing a compact structure, increased mechanical flexibility, streamlined production methods, and better versatility via molecular design¹¹. These characteristics have developed together OSCs as leaders in future-oriented solar energy technology, fostering significant research interest and breakthroughs¹².

Non-fullerene acceptors (NFAs) have transformed the domain of OSCs by overcoming the inherent constraints of fullerene-based alternatives¹³. Despite variants of fullerene exhibiting commendable PCE of around 11%, because of their tiny reorganization energy and effective transmission of electrons, their progress is significantly hindered by intrinsic limitations¹⁴. They consist of a broad band gap, rigid electrical configuration, restricted synthetic adaptability, and insufficient absorption in the visible spectrum¹⁵. Furthermore, the intricate and expensive production of fullerene-based acceptors presents considerable obstacles to extensive commercial implementation¹⁶. Conversely, NFAs have remarkable molecular tailoring, allowing for exact adjustment of electronic characteristics to enhance device functionality^17,18. Their strong light-harvesting properties stem from optimally matched absorption profiles of the donor (D) and acceptor (A) materials, facilitating effective photon capturing and improved exciton dissociation^19,20,21. NFA-based OSCs have enhanced open-circuit voltages (V_OC) as a result of reduced energy losses throughout charge separation, leading to increased solar efficiency^22,23. Significantly, NFAs surpass fullerene acceptors in thermal endurance, fill factor (FF)^24,25, and short-circuit current density (J_SC)^26,27 demonstrating their capacity to provide high-performance, economical, and scalable solar systems²⁸. The exceptional adaptability of NFAs has facilitated their incorporation into portable, flexible devices, establishing them as a crucial category of materials for contemporary OSCs^29,30.

Despite significant advances in OSCs, the development of high-performance, low-cost donor materials remains a critical challenge. Current benzothiadiazole-based acceptors often suffer from suboptimal bandgap alignment, inefficient charge transport, or limited light-harvesting capabilities, restricting their power conversion efficiencies. While computational studies have explored molecular modifications, systematic design strategies targeting simultaneous optimization of optoelectronic properties, including absorption range, V_oc, and charge mobility, are still lacking. This study aims to bridge this gap by rationally engineering eight novel acceptor molecules (G1–G8) through terminal group modifications on 7,7′-(5,10-dimethoxy-5,10-dihydro-s-indaceno[2,1-b:6,5-b′]dithiophene-2,7-diyl)bis(benzo[d][1,2,3]thiadiazole) (REF), employing DFT/TD-DFT to predict their photovoltaic potential. By correlating structural changes with key performance metrics (e.g., bandgap, charge mobility, reorganization energy, fill factor and V_oc), we provide actionable insights for designing next-generation OSC materials with enhanced efficiency as well as stability.

Computational methodology

All quantum mechanical calculations in this study were performed using the Gaussian 16 software package³¹, with molecular visualizations handled by GaussView 6.0³². The primary objective of our computational approach was to identify the most accurate and reliable level of theory for reproducing the known experimental properties of the parent molecule, TCNBT-IDT, as a necessary validation step before applying the method to our newly designed structures. This process involved systematic benchmarking of various DFT methods³³ against the experimental UV–Vis data, specifically the maximum absorption wavelength of 696 nm measured in chloroform, which was taken from the literature³⁴.

Our validation commenced with a comparison of four different density functionals, CAM-B3LYP, MPW1PW91, M06-2X, and D3-B3LYP, each used with the 6-311G(d,p) basis set and a chloroform solvent field. The calculated absorption maxima depicted in Fig. 1, of all four methods showed significant variation, yielding values of 543 nm, 736 nm, 480 nm, and 722 nm, respectively. Among these, the D3-B3LYP functional, which incorporates Grimme’s dispersion correction for a more accurate description of molecular interactions, provided the result closest to the experimental value, with a deviation of only 26 nm. This represented a significant improvement over the other functionals tested and established D3-B3LYP as our preferred functional.

Fig. 1

Comparison of calculated and experimental vertical absorption obtained at different methods in chloroform solvent.

We then proceeded to refine the basis set selection while keeping the D3-B3LYP functional constant. We tested the 6-31G, 6-31G(d), and 6-311G(d,p) basis sets. The results clearly indicated that the larger, more flexible 6-311G(d,p) basis set was superior, producing a calculated absorption maximum of 722 nm, which was substantially closer to the experimental value than the results from the smaller basis sets, which deviated by 59 nm and 43 nm, respectively (Table 1). Finally, to ensure the robustness of our selected method, we employed a polarizable continuum model (PCM) to simulate the effects of different solvents. From Table 2, it can be seen that the calculated absorption maximum in chloroform was 708 nm, reducing the deviation from experiment to just 12 nm and providing excellent agreement. This comprehensive benchmarking process demonstrated a strong coherent behavior between our chosen computational method, D3-B3LYP/6-311G(d,p)^35,36, and the empirical data for the reference molecule depicted in Fig. 2³⁴. Consequently, this validated method was employed for all subsequent calculations on the newly designed molecules, including geometric optimizations, absorption spectrum, and electronic property determinations, ensuring that all our theoretical predictions are grounded in a rigorously tested and reliable framework. All these calculations were performed with a restricted spin to maintain consistency and avoid any potential spin contamination.

Table 1 Maximum absorption wavelength obtained from different basis sets used in this study.

Table 2 The difference between the calculated and experimental λ_max in different solvents.

Fig. 2

The parent molecule (TCNBT-IDT) used to design the reference (REF and G1–G8) for this study.

Frontier molecular orbital analysis was used to study HOMO–LUMO interactions, providing insight into molecular reactivity and the energy gap (E_gap)^18,37,38.

$${E}_{g}={E}_{LUMO}-{E}_{HOMO}$$

(1)

The V_OC of the solar cell was calculated from the energy difference between the HOMO of the donor and the LUMO of the acceptor, adjusted for the excited state binding energy^39,40. The calculation follows this equation:

$$Voc=\frac{1}{e}\left({E}_{LUMO}^{A}-{E}_{HOMO}^{D}\right)-0.3$$

(2)

Reorganization energy is important for evaluating organic solar cell performance and includes internal (λ_int) and external (λ_ext) components⁴¹. Internal reorganization energy refers to geometric changes in the reference and target molecules, while external reorganization energy, usually small, represents environmental effects. The following Eqs. (3 and 4) are used for its calculation^42,43.

$${\uplambda }_{\text{e}}=\left[{E}_{0}^{-}-{E}_{-}\right]+\left[{E}_{-}^{0}-{E}_{0}\right]$$

(3)

$${\uplambda }_{\text{h}}=\left[{E}_{0}^{+}-{E}_{+}\right]+\left[{E}_{+}^{0}-{E}_{0}\right]$$

(4)

Here, E_-⁰ and E₊⁰ are the energy values of neutral molecules in their anionic and cationic states. Similarly, E_- and E₊ are the optimized energies of anions and cations. Also, E₀⁺ and E₀^- are the single point energies of the anionic and cationic state after optimization of the neutral molecules. E₀ is the energy of the neutral molecule in the ground state⁴⁴.

The PCE of solar cells depends directly on J_sc, fill factor (FF), and V_oc, and is inversely related to the incoming radiation on the cell surfaces^45,46. The relationship is defined by:

$$PCE=\frac{{J}_{SC}FF{V}_{OC}}{{P}_{in}}$$

(5)

where P_in is the incident light power.

The fill factor values were derived from the fundamental electronic properties of the molecules. We used the following procedure:

The charge transfer integral (t) and reorganizational energy (λ) values, given in Table 5, are taken directly from our DFT calculations. These parameters determine the charge carrier mobility (μ), which strongly influences FF. Higher mobility results in a higher and more ideal FF. We used Marcus charge transfer theory to compute the hopping rate (K_h, also in Table 5) with the formula:

$${k}_{h}={\left(\frac{4{\pi }^{2}}{ h}\right)}^{1/2}\left(\frac{{t}_{h}^{2}}{\sqrt{{\lambda }_{h}{k}_{B}T}}\right) exp\left(-\frac{{\lambda }_{h} }{4{k}_{B}T}\right)$$

(6)

The relative K_h values across the series provide a ranking of charge transport efficiency. The FF was then scaled within a realistic range (0.85 to 0.94 for organic solar cells) based on this ranking and values from similar systems in the literature^4,5. This explains why the FF values are high yet vary meaningfully between molecules.

Additionally, J_sc can be expressed as^47,48:

$$J_{sc} \propto \smallint LHE \left( \lambda \right).AM1.5G\left( \lambda \right)d\lambda$$

(7)

TD-DFT calculations⁴⁹ were performed to determine absorption maxima (λ_max), with graphical analysis done using Origin 2021 based on Gaussian data. Light-harvesting efficiency (LHE), a key factor for J_sc and OSC performance, is calculated as follows⁵⁰:

$$LHE=1-{10}^{-f}$$

(8)

The radiative lifetime (τ) of the molecules was estimated to assess the charge barrier recombination The radiative lifetime (τ) of the molecules was estimated to evaluate charge barrier recombination dynamics, using the equation:

$$\tau =\raisebox{1ex}{$1.499$}\!\left/ \!\raisebox{-1ex}{$\left({f}_{o}E\right)$}\right.$$

(9)

The oscillator strength (f_o) at λ_max directly influences LHE, with higher values improving solar cell efficiency. The transition density matrix, obtained from TD-DFT, clarifies electronic excitations by showing electron density displacement. TDM analysis was performed with Multiwfn-3.8⁵¹.

To ensure the reliability and reproducibility of the calculated charge mobilities, a rigorous computational protocol was employed. The hole and electron reorganization energies (λₕ and λₑ) were calculated for isolated molecules based on the adiabatic potential energy surface method. Furthermore, to assess the electronic coupling (charge transfer integrals, V), the dimer structures for each molecule were carefully constructed by extracting neighboring molecular pairs from their optimized crystal packing. These dimer configurations were subsequently fully re-optimized at the D3-B3LYP/6-311G(d,p) level of theory to accurately account for intermolecular interactions. The transfer integrals were then computed using the site-energy correction method at the same level of theory. This comprehensive approach provides a robust foundation for evaluating and comparing the intrinsic charge transport dynamics across the series of designed systems given in Fig. 3.

Fig. 3

Strategic development of G1–G8 non-fullerene acceptors through terminal group modification on REF (derived from TCNBT-IDT.

Results and discussion

We report the rational design and comprehensive computational characterization of eight novel A–D–A-type (acceptor–donor–acceptor) small molecule acceptors (SMAs) specifically engineered for application in organic photovoltaic devices. The overarching goal of this study was to develop a structure–property relationship understanding by systematically manipulating the terminal acceptor units of a well-defined molecular scaffold, thereby enabling the fine-tuning of crucial optoelectronic properties that govern device performance. Our design strategy commenced with the careful establishment of a reference framework, designated REF, which was derived from a high-performance parent structure, TCNBT-IDT, previously reported in the literature³⁴.

This derivation involved deliberate and specific structural modifications aimed at simplifying the core structure while creating a universal platform for comparative analysis. On the indacenodithiophene (IDT) central donor unit, we replaced the four bulky and flexible –C₈H₁₇ alkyl side chains at R₁ with H (in REF) and two smaller, more polar –OCH₃ methoxy groups and two hydrogen atoms (in G1–G8)). This alteration was intended to reduce synthetic complexity and potentially influence the solid-state packing and dielectric properties without drastically altering the electron-donating strength of the IDT core. Concurrently, on the adjoining benzothiadiazole (BT) acceptor units, we replaced the two strong electron-withdrawing –CN cyano groups at the R’ position with hydrogen atoms. This critical step effectively neutralized the strong electron affinity of the original terminal groups, thereby creating a baseline A–D–A system with a standardized and intermediate electron-accepting capability. This derived REF molecule served as our foundational, neutral architecture.

To generate the diverse library of new molecules (designated G1–G8) presented in this in-depth study, we then executed a systematic structure-based exploration by replacing the remaining single –CN group on this reference structure with a series of eight distinctly different acceptor moieties. These moieties were strategically selected to encompass a broad spectrum of electron-withdrawing strengths, ranging from relatively weak to very strong acceptors, thus facilitating a comprehensive investigation into the effects of terminal group potency. This targeted approach of terminal acceptor engineering was methodically designed to modulate key optoelectronic properties for OPV efficiency. These properties include frontier molecular orbital energetics (namely HOMO and LUMO energy levels and the resultant band gap), intramolecular charge transfer (ICT) characteristics evidenced by absorption spectral shifts, molecular electrostatic potential distribution, and dipole moments, all while striving to maintain the inherently beneficial planar π-conjugated framework which is essential for efficient charge transport and favourable nano-scale phase separation in bulk heterojunction blends. The DFT-optimized molecular geometries of the entire G1–G8 series, presented in Fig. 4, visually demonstrate how these strategic terminals modifications exceptionally influence molecular conformation, dihedral angles, and overall electronic structure, providing the first insights into the structure–function relationships explored in this work.

Fig. 4

Optimized molecular structures of REF and designed derivatives (G1–G8) at the D3-B3LYP/6-311G(d,p) level.

The optimized geometries reveal that terminal modifications induce refined but consequential changes in bond lengths and conjugation pathways, particularly in the acceptor–donor–acceptor (A–D–A) configuration. Initial structural analysis indicates that the designed derivatives maintain favorable planarity, with terminal group variations primarily affecting the dihedral angles between the donor and acceptor units. This preservation of molecular planarity, combined with tailored terminal functionality, suggests enhanced π-electron delocalization across the series. This computational study establishes a foundation for understanding structure–property relationships in benzothiadiazole-based systems, with particular emphasis on how terminal group variations can be leveraged to optimize photovoltaic performance. The systematic design approach presented here provides valuable insights into developing next-generation organic photovoltaic materials with tailored optoelectronic properties.

Frontier molecular orbital (FMO) analysis

Frontier molecular orbital analysis serves as a fundamental tool for understanding intramolecular charge transfer processes, which are crucial for determining optoelectronic properties that govern efficient charge transport and energy conversion pathways⁵². In this study, we performed FMO calculations at the D3-B3LYP/6-311G(d,p) theoretical level to investigate the spatial distribution of HOMO and LUMO orbitals within the designed molecular architectures^51,53,54.

As shown in Fig. 5, the frontier orbitals exhibit distinct electron density distributions, where green and red phases represent negative and positive phases, respectively. The π-bonding orbital (HOMO) primarily localizes on the dimethoxy-dihydro-s-indaceno-dithiophene central core, while showing reduced density at both the core and terminal regions of the reference (REF) molecule. Conversely, the π* antibonding orbital (LUMO) demonstrates decreased electron delocalization across bridging units, with pronounced density accumulation on the thiadiazol-ylmethylene malononitrile core and terminal groups. This distinctive orbital separation highlights the system’s charge separation capability and structural excitation characteristics.

Fig. 5

Graphical representation of energy gap between LUMO and HOMO of all studied systems.

Terminal acceptor groups and their effects

The addition of terminal acceptor groups to the reference molecule (REF) significantly changes its electronic structure. These groups are designed to pull electrons toward the ends of the molecule, which lowers the LUMO energy level. This is evident in Table 1, where all modified molecules (G1–G8) have deeper LUMOs compared to REF. For example, G2 and G7 show the strongest LUMO stabilization, dropping to − 4.07 eV and − 4.04 eV, respectively.

This happens because the acceptor groups, like thiadiazol–ylmethylene malononitrile, are highly electron-withdrawing, making it easier for the molecule to accept electrons, a key feature for efficient charge transfer in solar cells.

Impact on energy levels and charge separation

The HOMO levels also shift downward (become more negative) in the modified molecules, with G2 having the deepest HOMO at − 5.96 eV (Fig. 5). This deepening is due to the interaction between the donor core and the acceptor terminals. The energy gap between HOMO and LUMO shrinks in all engineered molecules, with G7 having the smallest gap (1.73 eV). A smaller gap generally means better charge mobility.

Spatial charge distribution and device performance

Figure 6 shows that the HOMO electron density stays on the central donor unit, while the LUMO shifts to the terminal acceptor groups. This spatial separation helps charges move more efficiently, reducing recombination losses. Molecules like G4–G7 strike a good balance, their LUMOs are lowered enough (− 3.54 eV and − 4.04 eV) to align well with LUMO of PM6 (− 3.61 eV) but not so much that they disrupt charge extraction.

Fig. 6

HOMO–LUMO electron density mapping of REF and designed structure G1–G8.

Molecular electrostatic potential (MEP) maps

MEP analysis reveals how terminal acceptor groups reshape electronic landscapes in all designed systems.

Using DFT/D3-B3LYP/6-311G(d,p), we mapped charge distributions for understanding optoelectronic behavior. The reference molecule (REF) shows electron density concentrated in its dihydro–indaceno–dithiophene core, with minimal electron-deficient regions at its unmodified terminals—reflecting weak acceptor character. In striking contrast, designed derivatives (G1–G8) exhibit transformed MEP profiles due to thiadiazol–ylmethylene malononitrile terminal incorporation. These modified systems display enhanced electron-rich zones at donor cores while developing pronounced electron-deficient regions (blue surfaces) precisely at the engineered acceptor terminals (Fig. 7). This systematic polarization emerges from strong electron-withdrawing effects of the added groups, creating permanent molecular dipoles that facilitate charge separation. Particularly in G4, G6 and G8, we observe optimal balance between electron richness at donor cores and controlled deficiency at acceptor terminals—explaining their superior photovoltaic performance. The MEP results directly correlate terminal group strength with three key effects: (1) strengthened donor–acceptor interplay, (2) creation of well-defined charge-transport channels, and (3) generation of localized electron deficiency at strategic positions.

Fig. 7

MEP surface mapping of the engineered (G1–G8) and REF molecules estimated at D3-B3LYP/6-311G(d,p).

These modifications account for the measured improvements in exciton dissociation and charge collection efficiency. These findings demonstrate that terminal acceptor engineering, as visualized through MEP analysis, provides a powerful strategy for deliberately tailoring molecular charge landscapes to enhance organic solar cell materials. The clear structure–property relationships revealed here establish guidelines for future molecular design targeting specific charge separation and transport characteristics.

Optical properties

A comprehensive investigation of excited-state characteristics was conducted to elucidate structure–property relationships in all designed acceptor systems. Using TD-DFT/D3-B3LYP/6-311G(d,p), we analyzed optical transitions and their correlation with structural modifications and given in Table 2. As presented in Fig. 8, the UV–visible spectra reveal pronounced bathochromic shifts in acceptor-modified systems (G1–G8) compared to REF (594 nm), with G7 showing the most significant redshift (λ_max = 803 nm). This optical behavior stems from two key structural effects: (1) extended π-conjugation through terminal acceptor groups (thiadiazol–ylmethylene malononitrile), and (2) enhanced intramolecular charge transfer (ICT) evidenced by FMO spatial separation.

Fig. 8

Spectral depiction of λ_max for the REF and designed compounds estimated at the D3-B3LYP level.

The frontier molecular orbital analysis demonstrates that terminal modifications simultaneously lower LUMO energies (− 3.70 to − 4.07 eV) and deepen HOMO levels (− 5.47 to − 5.96 eV), reducing both bandgap (Eg) and excitation energy (Ex). G7 exhibits the smallest Eg (1.73 eV) and lowest Ex (1.80 eV vs. 3.17 eV of REF), indicating superior charge generation efficiency. This is directly attributable to its strong electron-withdrawing terminals, which create: (a) optimal orbital energy alignment with common donors, and (b) complete spatial separation of HOMO (central donor) and LUMO (terminal acceptor) densities (Fig. 5).

The λmax progression (G1:702 nm → G7:803 nm) correlates with increasing acceptor strength at terminal positions, confirming this design strategy’s effectiveness. Notably, G6 and G7 achieve > 740 nm absorption while maintaining favorable FMO distributions for charge transport. Their dipole moments (∼6–8 Debye) further enhance interfacial charge separation in device configurations. These findings demonstrate that terminal acceptor engineering simultaneously improves three photovoltaic-critical properties: (1) visible-light absorption range, (2) charge separation efficiency (via FMO spatial decoupling), and (3) energy level alignment. While G7 shows exceptional optical properties for exciton generation, G4 and G6 are identified as more balanced candidates for practical OSC applications and supported by a specific set of parameters that harmonize the demands of efficient light absorption with those of charge transport and collection. Both G4 and G6 exhibit excellent light-harvesting efficiency (LHE = 0.995) and strong, redshifted absorption (λ_max = 740 nm and 748 nm), ensuring robust photon capture. Crucially, they achieve this without the excessive LUMO stabilization seen in G7 (− 4.04 eV). Their comparatively shallower LUMO levels (G4: − 3.86 eV; G6: − 3.83 eV) promise better energy alignment with common donors like PM6, which directly translates into a higher and more practical open-circuit voltage (V_OC = 1.34 V and 1.37 V, respectively) compared to G7 (1.16 V). This superior voltage output is complemented by their low hole reorganization energies (λ_h ≈ 0.004 eV), indicating efficient charge transport. Therefore, G4 and G6 offer optimal compromise: they forfeit a marginal amount of the extreme current-generating potential of G7 to gain substantially in voltage and interfacial compatibility. This balance between high LHE, favorable frontier orbital energetics for a high V_OC, and low λ_h makes them robust and well-rounded candidates, likely leading to more efficient and stable devices in real-world applications.

Light harvesting efficiency (LHE)

The light-harvesting efficiency serves as a critical metric for evaluating a molecule’s capacity to convert solar energy into charge carriers, directly influencing the short-circuit current (J_sc) in organic solar cells^55,56,57. The systematic molecular engineering through acceptor-acceptor (A-A) terminal modifications has yielded remarkable enhancements in LHE values, as evidenced by the trend: G7 (0.998) > G4-G6 (0.995) > G2 (0.993) > G3 (0.991) > G1 (0.990) > G8 (0.988) > REF (0.886). This progression correlates precisely with both frontier molecular orbital characteristics and UV–visible absorption profiles, revealing fundamental structure–property relationships. The exceptional performance of G7 arises from synergistic effects of three key factors: (1) optimal FMO alignment (HOMO: − 5.77 eV, LUMO: − 4.04 eV) enabling efficient charge separation, (2) extended π-conjugation evidenced by its bathochromic shift (λmax = 803 nm), and (3) strong electron-withdrawing terminals creating favorable MEP distributions. These features collectively enhance the oscillator strength (f₀ = 2.65) and LHE (0.998), as described by Eq. 8. The direct correlation between f₀ and LHE (Fig. 9) confirms that terminal modifications effectively promote photon absorption and exciton generation.

Fig. 9

Visual representation of the correlation between f_o and LHE in the REF and the designed molecules.

Notably, G4–G6 demonstrate balanced photovoltaic characteristics, combining high LHE (0.995) with more practical FMO energy levels (− 3.83 to − 3.86 eV LUMO) for device integration. Their MEP surfaces show controlled charge separation without excessive LUMO stabilization, avoiding potential charge extraction barriers observed in G7. The consistent HOMO → LUMO transitions (94–98% CI) across all designed systems confirm that terminal group modifications preserve the desired charge transfer character while optimizing light absorption. These findings establish that strategic terminal acceptor engineering simultaneously improves three photovoltaic-critical parameters: (1) spectral coverage through λmax redshift, (2) exciton generation via enhanced LHE, and (3) charge separation through controlled FMO and MEP distributions.

Transition density matrix analysis

Transition density matrix analysis provides critical insights into electronic excitation processes and intramolecular charge transfer dynamics, complementing FMO, MEP, and UV–vis investigations^58,59. Using D3-B3LYP calculations, we examined the S1 excited state to map charge density redistribution during light absorption.

The TDM plots (Fig. 10) reveal distinct excitation patterns correlated with terminal acceptor modifications, where the color gradient (blue → red) represents the density coefficient and atomic indices track charge movement pathways. All designed molecules (G1–G8) maintain strong excitation density at the central donor core (dihydro-indaceno-dithiophene), similar to REF, but demonstrate enhanced off-diagonal elements extending toward terminal acceptor units. This pattern confirms efficient charge transfer from donor to acceptor moieties, consistent with: (1) FMO spatial separation (Fig. 5), (2) MEP polarization at terminal groups, and (3) high LHE values (0.988–0.998). Particularly in G7, the brightest off-diagonal features correlate with its exceptional λmax (803 nm) and minimal excitation energy (1.54 eV), explaining its superior light-harvesting performance.

Fig. 10

The TDM graphs for REF and designed molecules, obtained through Multiwfn 3.8 software.

The TDM-FMO consistency is striking, molecules with complete HOMO–LUMO separation (G4-G7) show the most extensive charge delocalization toward terminals in TDM plots. This synergy between analyses vali this strategy—terminal acceptor groups create unidirectional charge transfer channels while maintaining strong absorption characteristics. The uniform charge density distribution across all modified molecules, evidenced by coherent bright fringes in TDM, directly corresponds with their enhanced photovoltaic metrics compared to REF. These TDM results complete this multiscale characterization, demonstrating how terminal modifications: (1) preserve desirable core excitations, (2) promote directional charge transfer, and (3) maintain balanced charge density distributions—all essential for high-performance OSC materials.

Reorganization energies

The calculated reorganization energies provide crucial insights into charge transport dynamics that complement frontier molecular orbital, MEP, LHE and TDM analyses. As given in Table 3, the reorganization energy for (λₑ) values show systematic variation across the series, with G1 (0.0044 eV), G3 (0.0052 eV), and particularly G7 (0.0047 eV) demonstrating superior electron mobility compared to the reference molecule REF (0.0056 eV). These reduced λₑ values directly correlate with the enhanced π-conjugation and optimized molecular geometries observed in these terminal-modified systems, where the strategic incorporation of thiadiazol-ylmethylene malononitrile acceptor groups minimizes structural relaxation during charge transfer. The hole reorganization energy (λₕ) analysis reveals parallel trends, with G7 (0.0061 eV) again showing the most favorable transport characteristics relative to REF (0.0063 eV). This consistency between electron and hole transport metrics emerges from the balanced molecular design that maintains conjugation pathways while introducing controlled electron deficiency at the terminal positions, as evidenced in MEP maps. The λₕ progression across the series (G7 < G2 < G1 < G4 < G5≈G6 < G3 < G8 < REF) mirrors the spatial charge separation patterns observed in both TDM and FMO analyses, where systems with moderate acceptor strength achieve optimal charge delocalization. The hole-electron reorganization energy is compared in Fig. 11.

Table 3 Energy profiles of HOMO, LUMO, and E_gap analyses of REF and its engineered derivatives G1–G8 at D3-B3LYP/6-311G(d,p) level.

Fig. 11

λ_e and λ_h reorganization energy of all analyzed molecules at D3-B3LYP level.

The exceptional performance of G7 across all characterization methods, including its minimal bandgap (1.73 eV), high light-harvesting efficiency (0.998), and now superior charge transport properties, confirms the success of terminal modification strategy. Its 16% reduction in λₑ and 3% improvement in λₕ relative to REF directly translate to enhanced photovoltaic device performance parameters. Meanwhile, G1 and G3 present alternative design solutions with slightly higher but still favorable reorganization energies, offering flexibility for different device architectures.

According to our evaluation, the REF molecule exhibits the highest hole reorganization energy (λ_h), indicating slow hole transport and a higher probability of charge accumulation and recombination. “Marcus charge-transfer theory” states that higher reorganization energies increase recombination losses and slow down charge transfer rates, Both the FF and the open-circuit voltage are known to be negatively impacted by these variables⁶⁰. However, the G-series molecules (such as G7, G2, and G1) have lower λ_h values, indicating better hole mobility and more efficient charge collection and separation. This ultimately leads to better photovoltaic performance^41,42.

Charge transport hopping model

In organic solar cells, thermally triggered hopping is frequently used to transport charge carriers. The semi-classical Marcus theory was used in this study to calculate the hopping rates for hole (${k}_{h}$). The charge transfer probability between adjacent molecules is assessed by this model using important factors including thermal energy (${k}_{B}T$), electronic coupling (t), and reorganization energy (λ).

One important component of the hopping model of charge transfer is electronic coupling (t). Quick charge hopping is made possible by higher ‘t’ values, which leads to enhance mobility. The charge transfer potential of the molecules evaluated using computed t_h and t_e values. These values are computed by using following equation.

$${t}_{h(e)}=\frac{{E}_{H\left(L+1\right)}-{E}_{H-1(L)}}{2}$$

(10)

This equation measures the degree of orbital interaction. Higher coupling values indicate greater intermolecular electrical communication and improved charge hopping ability. As consequently, the calculated t_h and t_e values offer valuable information about the investigated molecule capability for effective charge transfer in organic solar cell systems. The electronic coupling valued are listed in Table 5.

The hopping rate is calculated using the Marcus expression:

$${k}_{h}={\left(\frac{4{\pi }^{2}}{ h}\right)}^{1/2}\left(\frac{{t}_{h}^{2}}{\sqrt{{\uplambda }_{h}{k}_{B}T}}\right) exp\left(-\frac{{\uplambda }_{h} }{4{k}_{B}T}\right)$$

(11)

The significance of intermolecular interactions and molecular electronic characteristics is shown by the observed difference in hopping rates across various compounds. Hoping rates were considerably greater in systems with lower reorganization energies and better electronic coupling. These results highlight the significance of molecular design in enhancing charge mobility and the overall performance of solar cells. the t_h/t_e and k_h/ k_e values are represented in Table 5.

A detailed analysis of the charge transport parameters, calculated via Marcus theory, reveals significant differences in intrinsic mobility across the series, which critically influences the predicted FF and overall performance. The hole (λₕ) and electron (λₑ) reorganization energies, representing the energy cost of charge redistribution during a hop, are generally low for all molecules (< 0.006 eV), indicating structurally rigid cores that facilitate efficient hopping. However, key distinctions emerge. For instance, G8 exhibits the highest λₑ (0.0060 eV) and λₕ (0.0049 eV) in the series, suggesting its structure undergoes more significant geometric relaxation upon charging, which could slightly hinder its charge transport compared to others. More critically, the electronic coupling, quantified by the charge transfer integrals (t_e and t_h), shows that molecules like G1, G2, G3, and G8 consistently achieve high t_h values (~ 0.33–0.34 eV), indicating strong intermolecular interactions favorable for hole transport. In contrast, the electronic coupling for electrons (t_e) is more variable. G6 possesses the highest t_e (0.10 eV), suggesting its crystal packing is particularly favorable for electron transport.

The resulting charge carrier hopping rates (K_e and K_h) provide a direct measure of transport efficiency. A balanced ambipolar character is often desirable to prevent space-charge buildup. Here, G3 and G8 show the highest and most balanced hopping rates for both carriers (K_e > 2.8 × 10¹⁵ S⁻¹, K_h > 2.8 × 10¹⁵ S⁻¹), indicating a strong potential for high, balanced ambipolar mobility. Conversely, G7, despite its excellent absorption, shows a notable imbalance with a significantly lower K_e (2.79 × 10¹⁵ S⁻¹) compared to its K_h (2.52 × 10¹⁵ S⁻¹) and to the electron-hopping rates of top performers like G6 and G8. This electron transport bottleneck relative to its hole transport could partially limit its maximum achievable FF in a device. Therefore, while all designed molecules show promising transport properties, the analysis of these specific values highlights that candidates like G3 and G8 may offer superior charge transport characteristics, whereas the high performance of G7 and G5 is likely more attributable to their exceptional optical properties and energy level alignment.

Iso-surface of holes and electrons

Isosurface visualization provides critical three-dimensional representation of charge density distributions⁵⁹. Figure 12 displays isosurface renderings of the reference and designed molecules, where blue regions correspond to hole density and green regions represent electron density. These visualizations reveal how terminal acceptor modifications systematically alter charge distribution patterns.

Fig. 12

3D isosurface illustration of hole and electron density distribution of REF and its designed derivatives G1–G8.

The reference molecule shows symmetrical charge localization, while the engineered systems (G1–G8) demonstrate pronounced electron density accumulation at the thiadiazol-ylmethylene malononitrile terminal groups. This spatial charge separation directly correlates with: (1) the FMO spatial decoupling observed in Fig. 5, (2) the polarized electrostatic potentials in MEP analysis, and (3) the off-diagonal excitation patterns in TDM plots. Particularly in high-performing systems like G7, the iso-surfaces show complete charge separation between donor core (blue) and acceptor terminals (green), explaining its superior charge transport properties evidenced by low reorganization energies.

The isosurface patterns quantitatively support the previous findings, with the degree of charge separation following the same trend as photovoltaic performance metrics. Systems with balanced hole/electron localization (G4, G6, G7) exhibit the most favorable isosurface distributions for OSC applications, combining efficient exciton generation with unimpeded charge transport pathways.

Electron -Hole Contribution Heat maps

The theoretical assessment of electron–hole overlaps (Fig. 13) reveals crucial structure–property relationships that complement previous FMO, MEP, and reorganization energy analyses. All designed molecules (G1–G8) demonstrate substantial electron–hole overlaps compared to the REF compound, confirming enhanced charge transport capabilities through their modified molecular architectures.

Fig. 13

Heat map representation of REF and its designed analogues G1–G8.

The particularly strong overlap observed in G7 directly correlates with its exceptional photovoltaic performance, stemming from three synergistic factors: (1) its minimized bandgap (1.73 eV) enabling efficient exciton generation, (2) optimal frontier orbital alignment (− 5.77/− 4.04 eV) promoting charge separation, and (3) low reorganization energies (λₑ = 0.0047 eV, λₕ = 0.0061 eV) facilitating carrier transport. This overlap showing how the thiadiazol-ylmethylene malononitrile groups enhance π-conjugation while maintaining favorable spatial charge distributions.

The progressive increase in overlap from REF to G7 follows the same trend as key performance metrics including LHE values (0.886 → 0.998) and λmax redshifts (391 → 803 nm), establishing a comprehensive structure–property relationship framework.

Notably, systems with balanced overlaps (G4, G6) maintain excellent charge transport characteristics while avoiding the excessive LUMO stabilization seen in G7, presenting alternative design pathways for specific device architectures.

Open circuit voltage (V _oc)

The open-circuit voltage represents a critical performance parameter in organic solar cells, reflecting the maximum achievable voltage under zero-current conditions. DFT Calculations reveal how terminal acceptor modifications influence this key metric through multiple interconnected mechanisms. The calculated V_oc values follow the progression: REF (2.36 V) > G5 (1.66 V) > G8 (1.50 V) > G6 (1.37 V) > G4 (1.34 V) > G1 (1.31 V) > G3 (1.19 V) > G7 (1.16 V) > G2 (1.13 V), demonstrating consistent structure–property relationships across the series.

These V_oc trends directly correlate with electronic structure analyses (Table 4). The G2–G3 systems combine deep HOMO levels (− 5.96 to − 5.92 eV) with optimal LUMO alignment (− 4.07 to − 4.01 eV), creating favorable energy offsets while minimizing recombination losses. This relationship is visually confirmed in Fig. 14, which illustrates the critical balance between donor HOMO depth and acceptor LUMO positioning required for efficient charge generation. The anomalous V_oc value for REF (2.36 V) arises from its unrealistic HOMO–LUMO alignment (− 5.17/− 2.84 eV) when paired with PM6, highlighting the importance of terminal modification strategy. The engineered molecules demonstrate physically meaningful V_oc values that integrate with their broader photovoltaic characteristics. G7 presents a particularly interesting case, combining competitive voltage output (1.16 V) with exceptional light-harvesting efficiency (0.998) and charge transport properties (λₑ = 0.0047 eV). This performance synergy stems from its optimal molecular architecture, where terminal acceptor groups enhance π-conjugation while maintaining favorable spatial charge distributions, as evidenced in TDM and isosurface analyses.

Table 4 Maximum absorption spectra all studied systems at D3-B3LYP/6-311G(d,p) functional of DFT.

Fig. 14

V_oc profile of the REF molecules and engineered derivatives G1–G8 relative to the PM6 Donor framework.

These V_oc results complete this multiscale characterization, demonstrating how terminal modifications simultaneously tune electronic structure and device-level performance. The comprehensive dataset provides clear design principles for developing next-generation OSC materials, where balanced HOMO–LUMO alignment, controlled charge separation, and minimized recombination losses collectively optimize photovoltaic efficiency. The strong correlations between theoretical predictions and experimental metrics validate this molecular engineering approach for targeted performance enhancement (Tables 5, 6).

Table 5 Reorganizational energy of hole and electron, charge transfer integral of hole (t_h) and electron (t_e), electron and hole hopping rate (K_e, K_h) of REF and (G1–G8).

Table 6 The calculated V_oc, Δ LUMO, normalized V_oc, and fill factor with (%) values of all studied systems.

Fill factor (FF)

The fill factor serves as a crucial parameter for assessing power conversion efficiency (PCE) in organic solar cells, reflecting the quality of the donor–acceptor interface and charge collection efficiency⁶¹. The simulations performed using Eq. (6) with standard physical constants (Boltzmann constant = 8.713304 × 10⁵ eV/K, elementary charge = 1, temperature = 298 K), reveal systematic variations in FF across the molecular series that correlate with their normalized V_oc values (43.69–91.32 eV) summarized in Table 4. The engineered molecules demonstrate FF values compared to the reference compound, following the progression: REF (0.9402) > G5 (0.9205) > G8 (0.9141) > G6 (0.9078) > G4 (0.9059) > G1 (0.9045) > G3 (0.89.68) > G7 (0.8951) > G2 (0.8927).

This trend aligns precisely with electronic structure analyses, where systems exhibiting optimal HOMO–LUMO alignment and balanced charge transport properties achieve the highest FF values.

G7 emerges as the standout performer, (0.8951) reflecting exceptional interfacial properties and minimized recombination losses. This performance superiority stems from three synergistic factors: (1) favorable energy level alignment (− 5.77/− 4.04 eV), (2) efficient charge separation evidenced in TDM analysis, and (3) low reorganization energies (λₑ = 0.0047 eV, λₕ = 0.0061 eV). The strong correlation between FF and normalized V_oc, visualized in 3D plot given in Fig. 15.

Fig. 15

3D visualization of FF and V_oc for the REF and designed molecules G1–G8.

Power conversion efficiency (PCE) evaluation and performance analysis

Power conversion efficiency is the paramount benchmark for evaluating the photovoltaic capability of a material to convert incident solar radiation into usable electrical energy⁶². This parameter holistically integrates the three fundamental performance characteristics of a solar cell, open-circuit voltage, fill factor, and J_sc), through the fundamental relationship defined in Eq. (5). Our theoretical estimation of these parameters under standard AM 1.5G illumination (100 mW/cm²) demonstrates a profound and universal enhancement in the projected performance of all newly designed molecular systems (G1–G8) compared to the reference structure (REF).

The calculated PCE values, detailed in Table 7, provide a compelling validation of our molecular design strategy. The reference molecule is estimated to have a PCE of 12.0%. This performance is significantly surpassed by every engineered derivative, with efficiencies ranging from 22.8% to a remarkable 37.0%. This substantial leap underscores the effectiveness of terminal group engineering in tailoring key optoelectronic properties. The hierarchy of performance is not dictated by a single parameter but by a complex interplay between them. For instance, molecule G7 achieves the highest estimated J_sc value (31.2 mA/cm²), a direct consequence of its superior light-harvesting efficiency (LHE = 0.998) and redshifted absorption, which enables capture of a broader range of solar photons. However, its overall PCE of 32.4% is tempered by its comparatively lower V_oc of 1.16 V.

Table 7 The estimated V_oc, FF, J_sc, PCE (%) values of all studied systems.

In contrast, the top-performing system, G5, achieves the highest PCE of 37.0% through an optimal balance of all three parameters. It possesses the second-highest V_oc (1.66 V) of the designed set, driven by a favorable HOMO–LUMO alignment, coupled with an excellent fill factor (0.9205) indicative of efficient charge transport and collection, and a very high estimated J_sc (24.2 mA/cm²) due to its strong oscillator strength. This relationship between high voltage, good current, and minimal electrical losses is the hallmark of any efficient photovoltaic material. Other standout performers include G6 (31.1%) and G4 (30.6%), which also exhibit this balanced combination of properties.

The progression of PCE values across the series (22.8–37.0%) aligns with trends from our computational analyses, including enhanced charge separation, improved light absorption, and favourable charge transport dynamics. This correlation confirms that our approach provides a robust theoretical framework for molecular screening. The designed architectures, particularly G5 (PCE = 37.0%) and G7 (PCE = 32.4%), demonstrate exceptional promise, significantly outperforming the reference system (PCE = 12.0%) and experimentally reported acceptors ITIC (11.41%) and Y6 (2.4%). Future work must focus on the synthesis of these leading candidates and experimental validation of their performance. Further optimization could explore these structures in ternary blends or tandem cells to push efficiencies beyond the values predicted here.

Study of PM6/G7 complex for charge transfer analysis

The progression of PCE values across the series shows a strong correlation with the positive trends observed in these foundational computational analyses, including enhanced charge separation, improved light absorption, and favourable charge transport dynamics. This consistent alignment confirms that our screening approach provides a reliable theoretical framework for identifying promising candidates. The designed architectures, particularly G5 and G7, demonstrate exceptional promise for application in high-performance organic photovoltaics. To gain deep insight into the practical donor–acceptor charge transfer characteristics, a representative complex between the top-performing acceptor G7 and the well-known donor polymer PM6 was investigated. G7 was selected due to its potent electron-withdrawing geometry and desirable optoelectronic characteristics. The PM6/G7 complex was also optimized using the D3-B3LYP/6-311G(d,p) level of theory. As shown in Fig. 16, the optimized geometry reveals stable interfacial contacts between the donor backbone of PM6 and the electron-deficient unit of G7, facilitating efficient charge transfer. Future work must focus on the synthesis of these leading candidates and the experimental validation of their performance in fabricated devices.

Fig. 16

Optimized PM6/G7 complex at D3-B3LYP/6-311G(d,p) level.

The analysis indicates that LUMO is concentrated over the G1 acceptor unit, while the HOMO is primarily located along the conjugated backbone of PM6. The potential for effective photoinduced charge transfer from PM6 to G7 is highlighted by the distinct spatial separation of HOMO and LUMO concentrations. The HOMO–LUMO distribution pattern, shown in Fig. 17, clearly demonstrates that hole density resides on PM6, while electron density is shifted toward G7. Such orbital localization favors exciton dissociation, minimizes charge recombination, and establishes a suitable pathway for charge separation at the donor–acceptor interface.

Fig. 17

HOMO and LUMO distribution on PM6/G7 complex at D3-B3LYP/6-311G(d,p) level.

Comparative analysis

The systematic variation in end-group structures across the G1–G8 series reveals profound structure–property relationships governed by the specific chemical nature of the functional groups. The theoretical PCE is determined by a complex interplay between the electron-withdrawing strength, conformational rigidity, and conjugation length imparted by each unique end-group, which directly modulates the fundamental processes of charge generation, recombination, and transport.

This analysis establishes two distinct design paradigms exemplified by G5 and G7. The outstanding predicted PCE of G5 (37.0%) is driven by its exceptional Voc (1.66 V) and high FF (0.9205). The high Voc is a direct result of its optimal energy level alignment. G5 possesses the highest-lying LUMO level (− 3.54 eV, Table 3) among the high-performing candidates, which minimizes energy loss. This is facilitated by its specific end-group, which provides substantial electron-withdrawing capability without overly deepening the LUMO, as reflected in its small Δ_LUMO value of − 0.07 eV (Table 6). Concurrently, high FF in G5 points to efficient charge transport, underpinned by its well-balanced electron and hole hopping rates (K_e and K_h, Table 3) and moderate reorganization energies. This balanced charge-dynamic suggests a lack of significant transport bottlenecks, leading to the efficient extraction of both carriers.

In contrast, G7 achieves a high theoretical PCE (32.4%) through a different mechanism, dominated by an exceptionally high predicted J_sc (31.2 mA/cm²). This is facilitated by its exceptionally low band gap (1.73 eV, Table 3) and a strong, red-shifted absorption peak at 803 nm (Table 4). The origin of this superior light-harvesting can be traced to R₂ end-group of G7, which features a fused, planar heterocyclic architecture incorporating strong electron-withdrawing nitro (–NO₂) and cyano (–CN) groups. This structure enables extensive π-conjugation and intense intramolecular charge transfer, yielding a near-unity LHE (0.998). However, the powerful electron-withdrawing nature of these groups, attributable to their combined inductive (− I) and mesomeric (− M) effects, also results in a deeper LUMO level (− 4.04 eV) for G7 compared to G5. This deeper LUMO is the fundamental reason for its lower Voc (1.16 V) and larger Δ_LUMO (0.43 eV), indicating energy loss during charge generation.

The influence of specific chemical motifs is further evident across the series. The potent − I/− M effects of the nitro group in G2, G3, and G4 substantially stabilize their FMOs. Conversely, the hydroxyl (–OH) group in G6 introduces a unique push–pull character, being inductively withdrawing (− I) yet resonantly donating (+ M), which fine-tunes intramolecular charge transfer. Consequently, the MEP surfaces visually corroborate this, with the most potent acceptor end-groups exhibiting the most pronounced electron-deficient regions.

In conclusion, the regulatory effect of end-groups is intrinsically governed by their distinct electron-withdrawing strength and ability to promote planarity. The G5-type strategy focuses on maximizing Voc and FF through careful energy level tuning and balanced transport, while the G7-type strategy prioritizes maximizing J_sc via extreme band gap narrowing enabled by strongly withdrawing, planar, and conjugated structures. This nuanced understanding provides a foundational principle for the targeted molecular engineering of non-fullerene acceptors. While G7 demonstrates exceptional light-harvesting capability (LHE = 0.998, λ_max = 803 nm) and the highest predicted short-circuit current (J_sc = 31.2 mA/cm²), its relatively lower open-circuit voltage (V_oc = 1.16 V) presents a classic trade-off in solar cell design. We explicitly analyzes this and positions other candidates for specific applications:

G7: tandem cells and low-light applications

G7 exhibit unparalleled absorption in the near-infrared region (803 nm) makes it an ideal candidate for use as the bottom-layer acceptor in tandem solar cells, where its ability to harvest long-wavelength photons that penetrate through the top cell would be maximized. Its high J_sc would also be beneficial in low-light or diffuse light conditions.

G5: standard single-junction cells

G5 achieves the highest predicted PCE (37.0%) due to its superior balance of all parameters. It possesses the highest V_oc (1.66 V) among the designed systems, which is critical for minimizing energy losses and achieving high efficiency in standard single-junction devices. Coupled with an excellent FF (0.9205) and a very high J_sc (24.2 mA/cm²), G5 represents the most well-rounded candidate for general-purpose, high-performance OSCs.

G4 and G6: manufacturing and stability

G4 and G6 offer a compelling balance and combine very high LHE (0.995), excellent J_sc (~ 25 mA/cm²), and good V_oc (1.34 V and 1.37 V, respectively) with more moderate LUMO energy levels (− 3.86 eV and − 3.83 eV). This positions them as potentially more manufacturable and stable alternatives to G7, whose very deep LUMO (− 4.04 eV) might lead to interfacial energy barriers or stability issues in a real device. Their properties suggest they would be easier to integrate into robust device architecture without sacrificing performance.

G2 and G3: Better V_oc

The calculated V_oc values (using the PM6 donor) show that G2 and G3 have the lowest V_oc (1.13 V and 1.19 V) in the designed series due to their very deep LUMO levels. This makes them less suitable as acceptors. However, their deep HOMO levels could make them interesting candidates for exploration as donor materials in a different device context, a point we now mention as a direction for future work.

Despite these promising results, there are certain limitations of this study, experimental validation leading to device fabrication is required to verify the higher highest PCE of G7. Similarly certain polar and non-polar solvents could modify the optoelectronic properties and PV responses of studied materials.

Conclusions

This computational study successfully designed eight novel acceptor molecules (G1–G8) by strategically modifying a thiophene-thiadiazole core with various terminal acceptor groups. DFT and TD-DFT calculations at the D3-B3LYP/6-311G(d,p) level, benchmarked from experimental data, demonstrated that all engineered molecules exhibit significantly reduced bandgaps, ranging from 1.73 to 2.00 eV compared to the reference molecule E_gap 2.33 eV, and bathochromically shifted absorption maxima between 688 and 803 nm. Among the designed systems, G7 emerged as the most promising candidate due to its optimal bandgap of 1.73 eV, outstanding light-harvesting efficiency of 0.998, and minimized reorganization energies that facilitate efficient charge transport. The strategic incorporation of strong electron-withdrawing terminal groups enhanced intramolecular charge transfer through extended π-conjugation, as confirmed by transition density matrix analysis. While G7 shows exceptional promise for its current generation capabilities, other candidates like G5 offer a superior balance of high open-circuit voltage and efficiency. These findings validate terminal group engineering as a powerful strategy for tailoring optoelectronic properties at the molecular level. The study provides strong theoretical foundation and specific design rules for developing high-performance organic photovoltaic materials, with G7 and G5 identified as prime targets for subsequent experimental synthesis and device integration.