First-principles exploration of truxene–BODIPY architectures as alternative non-fullerene acceptors in organic photovoltaics

Abstract

In this work, we report for the first time a new class of truxene–BODIPY donor–π–acceptor (D–π–A) architectures as non-fullerene acceptors (NFAs) for organic solar cells (OSCs). This novel molecular design direction integrates a modified truxene core with BODIPY derivatives via π-spacers, providing a rational strategy to develop efficient small-molecule acceptors. A combination of density functional theory (DFT) and time-dependent DFT (TDDFT) was employed to investigate their structural, electronic, optical, and photovoltaic properties. Key descriptors such as ionization potential, electron affinity, dipole moment, reorganization energy, and charge transfer rates were evaluated to understand charge transport behavior. Notably, the analysis of reorganization energy confirmed that all designed molecules preferentially support electron transport, validating their role as effective acceptor materials. Frontier molecular orbital (FMO) and density of states (DOS) analyses revealed favorable donor–acceptor orbital alignment, promoting efficient intramolecular charge transfer. Excited-state absorption studies, carried out in both gas and solvent phases, demonstrated strong and tunable absorption in the visible to near-infrared (NIR) region, with a significant red-shift observed upon donor–acceptor blending. Among all blends, the C4/3p system achieves the highest predicted power conversion efficiency (PCE) of 21.18%, highlighting the critical role of D/A compatibility. Overall, this study illustrates the potential of rationally engineered truxene–BODIPY systems as promising non-fullerene small molecule acceptors for next-generation organic photovoltaics.

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1 Introduction

In materials science, organic semiconductors have drawn a lot of interest because of their lower cost, flexible functionalization, and promising electrical characteristics. The creation of small molecules and conjugated polymers with controllable energy levels, low optical bandgaps, and desirable electrical characteristics has been made possible by advances in chemistry.^1,2

Organic solar cells (OSCs) with bulk heterojunction (BHJ) active layers are emerging as highly promising candidates for affordable solar energy solutions. This is due to their notable benefits, including low-cost solution-based manufacturing, lightweight and flexible large-area applications, semi-transparency, and suitability for indoor photovoltaic devices.³ The BHJ active layer, composed of donor and acceptor organic semiconductors, plays a crucial role in sunlight absorption and exciton generation. Traditional OSCs utilize blends of electron-donor materials with fullerene-based acceptors (FAs) to form efficient BHJ structures.⁴ FAs have been widely used due to their high electron mobility and ability to facilitate charge separation in OSCs. However, limitations, viz. weak absorption in the visible region and morphological instability, have driven the search for alternative acceptor materials.⁵

One comprehensive benchmark study on FAs analyzed a large dataset of fullerenes (C20 to C60) and calculated 12 fundamental properties including binding energy, HOMO–LUMO gap, and solubility, revealing key structure–property relationships. This study found that electronic properties like the HOMO–LUMO gap can be tuned without significantly affecting stability or solubility, and identified an ideal HOMO level (−5.15 eV) and LUMO level (−2.78 eV) for fullerene acceptors in organic solar cells (OSCs). The popular C60 fullerene shows a power conversion efficiency (PCE) around 8% according to theoretical models, aligning with experimental observations. Most benchmark studies focus on fullerenes like C60, C70, and C84 and their derivatives paired with polymer donors in OSCs. Nevertheless, despite the synthesis of several fullerene derivatives, these acceptors suffer from intrinsic shortcomings, including their limited absorption of the solar spectrum, difficulties in functionalization to modify energy levels and absorption, comparatively high production cost, poor air stability, and unfavorable mechanical properties due to film brittleness.^6–9

Developing novel non-fullerene acceptors (NFAs) offers advantages over FAs, including tunable bandgaps for broader NIR absorption and adjustable energy levels for high V_oc and low energy loss.¹⁰ Structural flexibility in NFAs enables better matching with donors, promoting efficient charge transfer and improved blend morphology.^5,11–13 Recent advancements in single-junction OSCs based on non-fullerene small molecule acceptors (NFSMAs) and conjugated polymer donors have led to impressive PCEs of 17–18%, along with excellent stability.^14,15 This progress has been driven by the development of new material strategies and optimized device configurations. However, despite these achievements, polymer-based OSCs still face challenges such as low yield and poor reproducibility. In contrast, small molecule (SM) materials provide unique advantages, such as easy purification and well-defined molecular structures, making them promising candidates for enhancing the efficiency and consistency of OSC devices. Furthermore, the optical and electrochemical properties of SMs can be fine-tuned through appropriate structural modifications to optimize the photovoltaic parameters of OSCs for a specific acceptor, which is an adjustment that is more challenging in OSCs utilizing conjugated polymers as donors.^16–18 In recent years, extensive research efforts have been dedicated to enhancing the power conversion efficiency (PCE) of OSCs based on organic SMs. Various donor and acceptor materials, including porphyrins, coumarins, indoline, phenothiazine, etc., have been explored within OSC architectures.^19–27 Notably, the PCE of SM-based OSCs has exceeded 14% and 15% using all-small-molecule binary and ternary active layers, respectively, positioning them as strong contenders for commercial energy conversion applications.²⁸ Given these advancements, the design of novel SMs remains a promising avenue for further improving PCE while ensuring long-term stability – both crucial factors for the successful commercialization of OSC technology. The emergence of NFSMAs has revolutionized the development of OSCs.²⁹ Recent progress in Y-series non-fullerene acceptors has led to remarkable improvements in organic solar cell performance, with power conversion efficiencies approaching 20%. These advances are largely driven by structural optimization of their electron-deficient fused-ring cores (e.g., benzotriazole, benzothiadiazole, quinoxaline), combined with tailored side-chains and end-groups, which enhance optoelectronic properties, morphology, and donor compatibility.^30–32 Notably, the narrow-bandgap acceptor Y6 has significantly advanced both the efficiency and stability of OSCs.³¹ Innovations such as 3D twisted oligomeric acceptors, asymmetric guest components in ternary blends, and polymerized Y-series derivatives have further improved solubility, charge transport, thermal stability, and device robustness. Despite these achievements, challenges remain. Complex synthesis, solubility limitations, scalable processing, and nanoscale morphology control continue to constrain broader applications.^33–35 In parallel, perylene diimide (PDI)-based acceptors have attracted significant attention due to their strong electron affinity, chemical stability, and tunable optoelectronic properties. However, monomeric PDIs generally achieve modest efficiencies (PCE < 10%) because of poor face-on stacking and limited charge transport. The critical research gap lies in developing novel fused, bridged, and multi-core PDI architectures that provide controlled aggregation, improved crystallinity, and tailored energy levels. Addressing scalable processing and morphology control in both Y-series and PDI systems is essential to realize stable, high-performance organic solar cells.^36–38

Although the efficiencies of earlier NFSMAs were rather modest, their chemical architectures provide a broad range of tunability.³⁹ The PCEs of NFSMA-based OSCs have risen above 18% due to the development of A–D–A and A–DA′D–A-type acceptors, such as ITIC and BZIC.^{14,15,30,31,40–45} Recent computational studies highlight how small structural modifications can make a big difference in the performance of organic semiconductors. For instance, adjusting the terminal groups of non-fused ring acceptors has been shown to tune reorganization energies, absorption behavior, and exciton binding energies, leading to improved photovoltaic outcomes.⁴⁶ Similar design approaches have been used in nonlinear optical (NLO) materials, where changes to π-spacers and terminal acceptors around a quinoxaline core were found to strongly influence absorption, polarizability, and hyperpolarizability values.⁴⁷ More recently, S-shaped non-fused acceptors with different end-capped substituents demonstrated how such targeted substitutions can control reorganization energies, exciton binding energies, and light absorption, ultimately boosting predicted photovoltaic efficiencies.⁴⁸ Another recent work on A–D–A-type NFAs with extended fused-ring donors highlights how strategic donor–core engineering can further enhance optoelectronic properties and device performance,⁴⁹ motivating our exploration of truxene–BODIPY architectures. Together, these examples underline a clear message that precise chemical tailoring remains one of the most effective ways to design next-generation, high-performance organic photovoltaic materials.

Truxene has been recognized as a highly promising candidate for developing high-performance optoelectronic materials. Its rigid, coplanar framework and distinctive C_3h symmetry contribute to the formation of a well-delocalized conjugated electronic structure and enhanced molecular dimensionality. Additionally, the bulky truxene units introduce significant steric hindrance, which helps prevent aggregate formation on the semiconductor surface while also improving solubility.^50–52 For instance, the truxene-functionalized star-shaped molecule FTr-3PDI-Se was developed to function as an electron acceptor, achieving a high open-circuit voltage of 1.12 V and a PCE of 1.6%.^53,54 Another innovative approach involved the design of two star-shaped non-fullerene acceptors, TBT-1 and TBT-2, based on a truxene core conjugated with BODIPY units. These acceptors demonstrated strong absorption in both visible and near-infrared regions, leading to PCE values of 13.41% and 11.75% when blended with donor polymers.^55,56 Although truxene has been widely studied for organic solar cell applications, most research focuses on its star-shaped structure. Limited studies have explored its potential in a linear D–π–A architecture, where it can serve as an excellent donor moiety.

4,4-Difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) dyes are widely studied for their exceptional optical characteristics, such as high molar extinction coefficients, excellent fluorescence quantum yields, narrow optical band gaps, advantageous redox properties, and superior thermal and photostability. Additionally, their absorption and emission properties can be modulated to extend the UV-visible to near-infrared regions of the solar spectrum.⁵⁷ BODIPY derivatives offer tunable energy levels through structural modifications to their core, making them promising candidates for organic photovoltaic applications. Despite this advantage, their incorporation into BHJ devices remains limited, with reported power conversion efficiencies (PCEs) ranging from 2.8% to 9%.^58,59

Studies employing truxene and BODIPY have focused on their donor roles, where their electron-rich structures favor hole transport and light harvesting. However, as acceptors, these units offer a complementary advantage: truxene provides structural rigidity and prevents aggregation, while BODIPY stabilizes the LUMO and enhances electron affinity. Therefore, combining these two in a linear donor–π–acceptor framework might enable favorable intramolecular charge transfer with reduced band gaps, setting them apart from previous and common star-shaped truxene or BODIPY donor systems. To date, the role of the truxene–BODIPY combination as a non-fullerene acceptor has not been systematically investigated, representing a novel design direction distinct from their traditional applications.

Considering the above facts, here, we have modified the molecular design from a previously reported study, which developed BODIPY-based donor molecules substituted with truxene and triphenylamine (TPA) units for application in binary and ternary organic solar cells. The reference study achieved PCEs of 11.37% and 13.32% using their donor molecules in combination with PC71BM and Y6 as acceptors.⁶⁰ In contrast, our work focuses on designing truxene–BODIPY-based acceptor molecules by introducing structural modifications aimed at reducing the band gap and improving efficiency. By employing a donor–π–acceptor (D–π–A) architecture with thiophene and benzene as π-spacers, we have explored the potential of these newly designed acceptors in BHJ active layers. This approach not only expands the applicability of truxene–BODIPY derivatives in OSCs but also provides valuable insights into structure–property relationships for high-performance organic photovoltaics. The schematic diagram of these designed acceptor molecules is presented in Fig. 1. As shown in the figure, truxene, functionalized with –NH₂ groups at two of its ring ends, has been chosen as the donor unit. The third ring end of truxene has been connected to a π-spacer, where we incorporated either thiophene or benzene, resulting in two distinct molecular types. As the acceptor unit, we utilized BODIPY derivatives and systematically modified their terminal positions by substituting four different functional groups at the ‘X’ position. This approach led to the design of eight novel truxene–BODIPY-based acceptor molecules, enabling a systematic investigation of the impact of π-spacer and acceptor modifications on the electronic and optical properties of these molecules.

Fig. 1 Schematic diagram of the designed compounds.

To improve the efficiency of OSCs, this research focuses on the design and characterization of new NFSMAs that promote efficient charge transfer and transport. While the initial absorption of solar radiation occurs in the donor material, our investigation focuses on tuning the molecular structure of the acceptors to optimize the subsequent charge separation and collection at the donor/acceptor (D/A) interface. We have examined how these designed acceptors influence the charge transfer processes, using a previously reported donor as the light-harvesting component. Additionally, we have investigated the charge transport and photovoltaic properties of these novel acceptors when paired with the standard donor, employing quantum chemical methods to analyze their geometric structures, electronic properties relevant to charge transfer, and the charge transfer mechanisms. It is noted that in this design the truxene core has reactive methylene and amino groups, which in experiments could have been replaced with protective groups like methyl to avoid unwanted reactions. In our theoretical study, we have not included these substitutions, as they have not significantly impacted the frontier orbital energies or intramolecular charge-transfer behavior that are central to our design. Still, our results have remained relevant for experimental work, where such protective modifications can be made without changing the key electronic properties.

2 Theoretical background

When photons are absorbed by the donor material, one electron is excited and an exciton is formed. This is the first step in the working mechanism of organic solar cells. This exciton then diffuses to the donor–acceptor interface, where favourable energy level offsets cause it to separate into charges, producing free charge carriers. In the end, charge collection and electrical current generation result from these divided charges being carried towards the electrodes via their respective materials. A lower LUMO level for the acceptor, adequate photon energy, and suitable electrode work functions in relation to the active layer energy levels are all necessary for efficient functioning.^61,62 For an organic molecule to function effectively as an acceptor material in an organic solar cell, it needs to possess a specific set of properties that facilitate the crucial steps of the photovoltaic process. A suitable acceptor molecule for organic solar cells needs to have modified energy levels for efficient charge injection and separation, strong and broad light absorption, effective exciton generation and diffusion, favorable charge separation and high charge carrier mobility.^63,64

The performance of organic photovoltaic materials is intrinsically tied to their electronic properties, including ionization potential (IP), electron affinity (EA), and charge transport behavior. These key parameters dictate the success of charge injection and movement, ultimately defining device efficiency.^65–67 To gain critical insights into these properties for our designed molecules, we determined their vertical and adiabatic IP and EA values using the well-defined equations (eqn (1)–(4)) from our previously published work.⁶⁸

It has been observed that reactivity descriptors help to predict how molecules will behave under various conditions, including their stability and tendency to undergo chemical reactions, which is vital for selecting materials that will last longer and perform better in solar cells. These chemical reactivity parameters, including electronegativity (χ), chemical potential (μ), hardness (η_h), softness (S), and electrophilicity (ω), can be directly calculated from adiabatic IP and EA values using the following equations:^69–72

where IP(v) and EA(v) are vertical ionization potential and vertical electron affinity, respectively.

Prior studies have demonstrated that the energy levels of the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) directly impact charge injection capabilities.⁷³ To evaluate the charge transport properties, the reorganization energy (λ) is often considered. It accounts for structural relaxation effects when a charge is added to or removed from a molecule. The contributions to λ primarily stem from molecular geometry reorganization, which affects the efficiency of hole and electron transport. Therefore, we calculated the reorganization energies for both holes and electrons in our designed molecules. This has been carried out by employing the specific methodologies detailed in eqn (5) and (6) of our previously reported study.^68,74

Charge transport in molecular systems is commonly understood through two primary frameworks: coherent band theory and incoherent hopping. Band theory describes delocalized charge carriers moving freely across well-ordered systems. Conversely, the hopping model is more applicable to disordered systems, where localized charges transfer via thermally activated jumps between neighboring molecules.⁷⁵ Given the inherent disorder in our practical system, we have adopted the hopping mechanism to elucidate charge transport. Within this context, Marcus theory offers a theoretical framework for quantifying the charge transfer rate (k_CT), considering both the electronic coupling between adjacent molecules and λ, which is expressed using the following equation:^66,74

where k_B, T, V, and ħ represent the Boltzmann constant, absolute temperature, the electronic coupling matrix element between two entities, and reduced Planck's constant, respectively.

To compute the electronic coupling matrix element (V), our designed molecules have been arranged in a stacked, face-to-face configuration with an intermolecular separation of 3.5 Å. This stacked dimer has been optimized prior to the calculation of V. The following equation has been subsequently utilized to determine the parameter V, often referred to as the charge transfer integral, for both holes (V⁺) and electrons (V⁻) between adjacent molecules:⁷⁴

Here, E_H, E_L, E_H−1, and E_L+1 denote the energies of the HOMO, LUMO, HOMO−1, and LUMO+1 of the molecule in its neutral, closed-shell state, respectively.

In OSCs, the power conversion efficiency (η) is influenced by several key parameters, including the open-circuit voltage (V_oc), short-circuit current density (J_sc), and fill factor (FF). These parameters are typically estimated using empirical relationships based on both experimental observations and theoretical models. Among them, the energy level alignment between donor and acceptor materials is crucial for determining V_oc, as an optimal energy offset promotes efficient charge separation while minimizing recombination losses. Typically, the power conversion efficiency (η) of a photovoltaic device is calculated using eqn (8):⁷⁶

Here, P_in represents the input power of the incident sunlight. For the solar spectrum, a standard value of P_in is taken as 100 mW cm⁻² under AM 1.5G illumination.⁷⁷

The spectroscopic limited maximum efficiency (SLME) model is commonly used to estimate the PCEs of solar cells. In this study, the SLME model is employed to calculate the short-circuit current density (J_sc) using eqn (9):^78,79

In this equation, P is the maximum power density, J is the total current density, and V is the potential across the absorbing layer. J₀ represents the reverse saturation current, k is the Boltzmann constant, T is the temperature, and e is the elementary charge.

The short-circuit current density J_sc depends on the intensity and spectral range of solar absorption. It is governed by the external quantum efficiency (η_EQE) of the device and the photon flux (S(λ)) across the wavelength range. This relationship is expressed using eqn (10):^80,81

Here, (η_EQE) is the product of exciton diffusion efficiency (η_ED), light harvesting efficiency (η_λ), charge collection efficiency (η_CC), and charge transfer efficiency (η_CT).

This equation highlights the importance of the absorption ability in enhancing solar cell performance. η_λ can be related to the oscillator strength (f_OSC) at a specific wavelength, as shown in eqn (11):⁸¹

η_λ = 1 − 10^−f_osc. (11)

The fill factor significantly influences η and can be estimated using eqn (12):^19,82

where v_oc is a dimensionless voltage that can be calculated as:^19,82

In this equation, e, k_B, and T represent the elementary charge, Boltzmann constant, and absolute temperature, respectively. The open-circuit voltage V_oc itself can be determined using the following relation expressed as eqn (14):⁸³

eV_oc = |E^donor_HOMO − E^acceptor_LUMO| − 0.3 eV. (14)

Here, E^donor_HOMO and E^acceptor_LUMO are the HOMO energy of the donor and the LUMO energy of the acceptor, respectively. The term 0.3 eV is an empirical value that accounts for energy losses typically observed in bulk heterojunction organic solar cells.

By leveraging density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations, the electronic structure and photophysical properties of the designed molecules are systematically investigated. These computational approaches enable the prediction of key parameters, ensuring a comprehensive understanding of the charge transport and optical properties relevant to organic photovoltaic applications.

3 Selection of computational methodology

All calculations in this study have been carried out using the Gaussian 09 (revision D.01) program package, while GaussView has been used for visualization and analysis.⁸⁴

To determine the appropriate level of theory for DFT calculations, we have performed a benchmark calculation using a reference molecule (6a) that shares structural similarities with our designed molecules. This molecule has been selected from a previously reported experimental work.⁶⁰ The functional validation test has been conducted to identify the most suitable functionals for subsequent ground-state and excited-state calculations.

For ground-state calculations, the geometry optimization of the 6a molecule has been performed using various functionals available in GaussView, namely B3LYP, B3LYP-D3, B3PW91, PBEPBE, CAM-B3LYP, HSEH1PBE, and ωB97XD, in combination with the 6-31G(d) basis set. The Δ_H–L value has been computed for each case and compared with the experimentally reported value of the 6a molecule. Among all functionals tested, the HSEH1PBE/6-31G(d) level of theory has provided the closest agreement with the experimental Δ_H–L value. Consequently, we have adopted the HSEH1PBE/6-31G(d)^85–88 level of theory for further ground-state calculations and geometry optimizations of our designed molecules.

Similarly, for excited-state calculations, TD-DFT computations have been performed on the 6a molecule using the same set of functionals and basis set. The maximum wavelength (λ_max) has been obtained for each case and compared with the experimentally reported λ_max value of the 6a molecule. The B3LYP-D3/6-31G(d)⁸⁹ level of theory has yielded results that are most consistent with the experimental values. Therefore, B3LYP-D3/6-31G(d) has been chosen for all further excited-state calculations of our designed molecules.

The validation tests used to determine the appropriate functionals for ground-state and excited-state calculations are illustrated as bar graphs in Fig. 2 and 3, respectively.

Fig. 2 Validation of functionals for ground state calculations.

Fig. 3 Validation of functionals for excited state calculations.

For calculations in the solvent phase, we have utilized the conductor-like polarizable continuum model (CPCM)^90–92 with DMF⁶⁰ as the chosen solvent. To determine the electronic coupling matrix element (V), we have employed the M06-2X-D3/6-31G(d) level of theory. This method incorporates dispersion corrections, making it suitable for investigating charge transfer characteristics.

4 Results and discussion

The optimized structures of the designed molecules are presented in Fig. S1 of the SI. Here, we have systematically investigated the structural, electronic, optical, and photovoltaic properties of the designed molecules to evaluate their potential applicability in OSCs. The following subsections present a detailed analysis of these properties.

4.1 Structural and geometrical properties

4.1.1 Dihedral angle. The dihedral angle is regarded as a crucial parameter because it influences the molecular planarity, which is directly linked to the electronic properties and charge transport efficiency of the molecules.⁹³ We have calculated the dihedral angles between the donor–π-spacer (ϕ₁) and the π-spacer–acceptor (ϕ₂) of the designed molecules. The dihedral angle values of the studied compounds are presented in Table 1. From this table, it can be observed that our designed compounds exhibit relatively low dihedral angles, suggesting a relatively planar molecular structure. While these values are low, the fact that they are not very close to zero allows them to advantageously mitigate self-aggregation.^94,95 The ϕ₁ and ϕ₂ values suggest that slight deviations from planarity mitigate self-aggregation, a strategy also effective in asymmetric NFAs with non-fused bridges.⁹⁶ Aggregation often leads to larger domains of pure donor or pure acceptor materials, reducing the crucial donor–acceptor interfacial area. Exciton dissociation (the separation of the electron and hole) primarily occurs at these interfaces. A smaller interface means fewer excitons can be effectively split.^97,98

Table 1 Dihedral angle values of the studied compounds

Compounds	Phase	ϕ 1 (°)	ϕ 2 (°)
3i	Gas	−24.63	44.07
	Solvent	−23.08	42.66
3j	Gas	−24.78	40.69
	Solvent	−22.62	37.49
3k	Gas	−23.55	44.03
	Solvent	−22.12	44.31
3l	Gas	−24.86	42.35
	Solvent	−23.04	41.03
3n	Gas	−35.31	52.50
	Solvent	−33.63	51.46
3o	Gas	35.19	49.92
	Solvent	33.96	49.21
3p	Gas	−35.96	−51.36
	Solvent	−33.91	−50.58
3q	Gas	34.99	−51.33
	Solvent	33.35	−49.39

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The data in Table 1 reveal that the dihedral angle between D and the π-spacer is less than that between the π-spacer and A. This implies that the A moiety plays a role in lowering self-aggregation by introducing a slight deviation from planarity. The dihedral angles between D–π-spacer and π-spacer–A units also suggest that slight deviations from planarity mitigate self-aggregation, a strategy also effective in asymmetric NFAs with non-fused bridges.⁹⁶ The ϕ₁ and ϕ₂ for all compounds show relatively small changes between gas and solvent phases, suggesting good conformational stability across environments. Compounds 3i–3l exhibit lower dihedral angles (around ±22° to ±44°), indicating better planarity compared to 3n–3q, which show significantly higher dihedral angles (±33° to ±52°), suggesting increased twisting between molecular fragments. The effect of solvent is minimal but consistent, slightly reducing the dihedral angles across the series, which may marginally enhance planarity and conjugation in the solvated state.

4.1.2 Bond length alteration parameter (BLA) and average inter-ring bridge bond distance (Δl). In the field of organic electronics and optoelectronics, BLA is recognized as a critical parameter for characterizing conjugated organic molecules. BLA describes the non-uniformity in bond lengths within the conjugated backbone, conventionally determined by calculating the difference between the average lengths of the carbon–carbon double and single bonds. This alternation pattern exerts a considerable influence on the electronic and optical behavior of conjugated materials like polymers and organic dyes. A diminished BLA is associated with a more delocalized electronic charge distribution across the conjugated system, reflecting a higher extent of conjugation. This elevated conjugation level generally translates to improved charge transport properties, facilitating the more facile movement of electrons throughout the molecule.^66,74 The calculated values of BLA for all the designed molecules are presented in Fig. 4. It is observed from the figure that the BLA values of all our designed compounds are either 0.02 Å or 0.03 Å, which are close to zero. Such low BLA values indicate a high degree of π-electron delocalization across the molecular framework, characteristic of aromatic or quinoid resonance structures. This delocalization is generally associated with enhanced conjugation, which can improve the charge transport and optoelectronic properties of the molecules. However, BLA analysis shows that all of the designed molecules maintain very similar backbone characteristics. This is expected, since they share the same truxene–π–BODIPY framework. The small changes that do appear are mainly due to the different substituents and π-spacers, which slightly influence conjugation along the backbone. Overall, the consistently low BLA values across the series confirm that the π-conjugation is preserved, supporting efficient charge delocalization. This structural consistency provides a stable foundation for comparing how electronic and optical properties are tuned by the specific modifications introduced in our design.

Fig. 4 Calculated BLA parameter values of the designed compounds.

We have determined the average inter-ring bond distance, denoted as Δl, for all the designed molecules. In these conjugated organic systems, the inter-ring bridge bond distance refers to the length of the covalent linkage connecting adjacent aromatic rings.⁶⁸ The computed Δl values are graphically presented in Fig. 5. As can be seen from the figure, the Δl values for all studied compounds lie within the range of 1.45–1.47 Å, which is intermediate between the typical C=C double bond distance (1.33 Å) and the C–C single bond distance (1.54 Å). This suggests partial double bond character and indicates the presence of extended π-conjugation across the molecular framework.

Fig. 5 Calculated average inter-ring bond distance of the designed compounds.

4.1.3 Reduced density gradient (RDG). The reduced density gradient (RDG) offers an intuitive visual method for investigating non-covalent interactions, which are crucial for molecular stability. This dimensionless scalar field is defined by the equation:
where |∇ρ(r)| is the magnitude of the electron density gradient and ρ(r) is the electron density. The RDG essentially quantifies the rate of change of electron density in space relative to the density itself.⁹⁹

In non-covalent interaction (NCI) analysis, the RDG is used to create 2D graphs that help distinguish between repulsive steric clashes, stabilizing hydrogen bonds, and weak van der Waals forces within molecules. Multiwfn 3.8 software is employed to generate these scatter plots, providing a visual representation of these interactions in the studied compounds.

Fig. 6 displays these scatter plots alongside density gradient isosurfaces for all the designed molecules. The plots show the signed electron density (sign(λ₂) × ρ) on the x-axis and the RDG on the y-axis, effectively distinguishing different interaction types within each molecule. The nature of these interactions is determined by the sign of the second eigenvalue (λ₂) of the electron density Hessian: positive values (λ₂ > 0) indicate repulsive interactions, while negative values (λ₂ < 0) signify attractive interactions.^100,101

Fig. 6 RDG plots of the designed compounds.

Analysis of Fig. 6 reveals that attractive forces dominate steric effects in all the designed dye molecules, contributing to their stability. Furthermore, the prominent spikes on the left and right sides of the plots, corresponding to more negative and positive sign(λ₂)ρ values (specifically −0.05 and +0.05 a.u.), show a consistent pattern. The blue region on the left, representing attractive interactions, is consistently more pronounced than the red region on the right, representing repulsive interactions, across all plots. This consistent observation further supports the conclusion that the designed molecules exhibit substantial stability due to the prevalence of attractive non-covalent interactions, clearly visualized by the RDG plots. While the RDG plots of the designed molecules look broadly similar because of their common D–π–A backbone, we do notice small shifts in the spike positions. These subtle changes arise from the different substituents or π-spacers and point to slight variations in weak intramolecular interactions. Overall, however, the close similarity across the series confirms that the molecular framework remains structurally stable. This was the main purpose of carrying out the RDG analyses that is to ensure that the backbone is robust, so that any differences observed in the optoelectronic properties can be attributed to the intentional chemical modifications rather than to structural instability.

4.2 Electronic properties

4.2.1 Ionization potential (IP) and electron affinity (EA). The ability of organic materials to conduct charge depends on how easily they can donate or accept electrons. For an organic material to function as a p-type semiconductor, it should have a low ionization potential (IP) to facilitate easier hole injection into the HOMO. Similarly, for an n-type semiconductor, a high electron affinity (EA) is necessary to enable efficient electron injection into the LUMO.⁷⁴ The calculated vertical and adiabatic ionization potentials (IPs) and electron affinities (EAs) provide valuable insights into the electronic properties and potential charge injection or extraction capabilities of the studied compounds. The values of IP(v), IP(a), EA(v), and EA(a) for the studied compounds in the gas phase have been calculated and are presented in Table 2. From this table, it is apparent that the vertical IPs, which represent the energy required to remove an electron without geometry relaxation, range from 5.95 eV (3k) to 6.37 eV (3j), indicating a moderate resistance to oxidation. The adiabatic IPs, which account for geometry relaxation upon ionization and are generally more relevant for thermodynamic considerations, show a slightly lower range of 6.06 eV (3n) to 6.17 eV (3j). The vertical EAs, representing the energy gained upon adding an electron without geometry changes, range from 2.11 eV (3n) to 2.41 eV (3j). The adiabatic EAs, which include geometry relaxation upon electron addition, are slightly higher, ranging from 2.23 eV (3n) to 2.52 eV (3j). Compound 3j exhibits the highest values of EA(v) and EA(a), suggesting a favorable electron injection into its LUMOs. Comparing the vertical and adiabatic values, the relatively small differences suggest that only minor structural rearrangements occur upon ionization or electron attachment, which can be favorable for efficient charge transport. The observed variations in IPs and EAs across the series of compounds (3i–3q) likely arise from subtle differences in their molecular structures.

Table 2 Calculated values of vertical (v) and adiabatic (a) IPs and EAs of the studied compounds in the gas phase

Compounds	IP(v)	IP(a)	EA(v)	EA(a)
3i	6.17	6.10	2.20	2.32
3j	6.37	6.17	2.41	2.52
3k	5.95	6.11	2.32	2.39
3l	6.21	6.12	2.39	2.49
3n	6.13	6.06	2.11	2.23
3o	6.31	6.11	2.33	2.44
3p	6.33	6.08	2.25	2.33
3q	6.17	6.08	2.32	2.43

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4.2.2 Global chemical reactivity parameters. To further assess the electronic reactivity and stability of the designed molecules, global chemical reactivity parameters have been computed using the vertical IP and EA. Studying chemical reactivity parameters is important for designed molecules in OSCs because these parameters predict molecular stability and compatibility, which are critical for device longevity and performance.⁷² To assess the chemical reactivity and suitability of the designed compounds for OSC applications, we evaluated a set of global descriptors, viz. electronegativity (χ), chemical potential (μ), chemical hardness (η_h), global softness (S), and the electrophilicity index (ω). As summarized in Table 3, the χ values range narrowly from 4.15 eV to 4.35 eV, indicating similar electron-attracting tendencies across the series of designed compounds. Compound 3j showed the highest χ (4.35 eV), suggesting excellent electron-attracting character and effective charge transfer behavior when blended with a donor. Correspondingly, the μ value, which is the negative of electronegativity, ranges from −4.15 eV to −4.35 eV. Molecules with more negative μ are better electron donors, whereas those with less negative μ are better acceptors. Compound 3j had the lowest μ (−4.35 eV), reinforcing its potential as a highly efficient electron acceptor. The η_h values lie between 1.82 eV and 1.92 eV, corresponding to moderate resistance toward electronic deformation and charge transfer. Compound 3n exhibits the highest η_h (1.92 eV), indicating enhanced stability and potentially longer device lifetimes but less reactivity in terms of charge transfer. As expected, S values are inversely related to η_h and span from 0.2604 to 0.2747 eV⁻¹. Compound 3l had the highest S (0.2747 eV⁻¹), indicating favorable dynamic response to charge fluctuations, which is beneficial for efficient charge transport. The ω, which quantifies the molecule's ability to stabilize added electronic charge, ranges from 4.48 eV to 5.17 eV. Among the studied molecules, compound 3j exhibits the highest (5.17 eV) ω value, suggesting a strong electron-accepting ability and enhanced reactivity, which are the features desirable for acceptor materials in OSCs. Compounds 3l and 3o also exhibit higher ω values (5.10 eV and 4.98 eV), reinforcing their potential in facilitating efficient charge separation. In contrast, compound 3n, with the lowest ω (4.48 eV) and highest η_h values (1.92 eV), appears to be chemically more stable, which may benefit long-term device durability.

Table 3 Global chemical reactivity parameters calculated for the designed compounds

Compound	χ (eV)	μ	η h (eV)	S (eV^−1)	ω (eV)
3i	4.21	−4.21	1.89	0.2646	4.69
3j	4.35	−4.35	1.83	0.2732	5.17
3k	4.25	−4.25	1.86	0.2688	4.85
3l	4.31	−4.31	1.82	0.2747	5.10
3n	4.15	−4.15	1.92	0.2604	4.48
3o	4.28	−4.28	1.84	0.2717	4.98
3p	4.21	−4.21	1.88	0.2659	4.71
3q	4.26	−4.26	1.83	0.2732	4.96

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4.2.3 Effect of solvent on dipole moment. The dipole moments of the studied compounds have been calculated in both gas and solvent phases to understand the influence of solvation on their electronic distribution. As presented in Table 4, all compounds exhibit a noticeable increase in both ground-state (μ_g) and excited-state (μ_e) dipole moments upon solvation, reflecting substantial stabilization due to solvent polarization. Similar trends are observed across the series, with all compounds experiencing an enhancement of dipole moments in the excited state in both states. This indicates that the solvent environment plays a significant role in stabilizing the charge-separated states by enhancing molecular polarity. The nearly parallel increase in both μ_g and μ_e in both gas and solvent states further suggests that the structural reorganization between ground and excited states is minimal in solvent, which may favor consistent charge transport characteristics in device applications.

Table 4 Calculated values of μ_g and μ_e in gas and solvent states

Compounds	Phase	μ g (D)	μ e (D)
3i	Gas	15.54	15.51
	Solvent	18.62	18.59
3j	Gas	17.08	16.96
	Solvent	22.35	22.20
3k	Gas	16.29	16.25
	Solvent	19.35	19.37
3l	Gas	17.05	16.99
	Solvent	21.43	21.41
3n	Gas	14.38	14.35
	Solvent	16.85	16.81
3o	Gas	15.22	15.22
	Solvent	18.84	18.72
3p	Gas	15.25	15.21
	Solvent	18.79	17.94
3q	Gas	15.53	15.48
	Solvent	18.80	18.79

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4.2.4 Frontier molecular orbital (FMO) analysis. FMO analysis is a key factor influencing the charge transport properties in OSCs. The FMO energies of the investigated compounds are closely linked to their electronic properties.¹⁰² The ground-state calculations provide the highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), and Δ_H–L energy values for all the studied compounds, as summarized in Table 5 for both the gas and solvent phases. From Table 5, it can be observed that all the designed compounds exhibit relatively low Δ_H–L values. These low Δ_H–L values indicate that the designed compounds have the potential to function as π-semiconducting materials. The HOMO energy levels for the studied compounds range from −5.02 eV to −4.87 eV, while LUMO levels lie between −3.80 eV and −3.28 eV. The corresponding HOMO–LUMO energy gaps (Δ_H–L) vary from 1.14 eV to 1.53 eV, reflecting differences in conjugation and electron delocalization among the molecules. Compounds 3j, 3l, 3o, and 3q exhibit narrower band gaps (1.14–1.31 eV), indicating stronger intramolecular charge transfer and improved visible-light absorption, which are advantageous for enhanced photovoltaic performance in organic solar cells. Among these, 3o shows the smallest gap (1.14 eV), suggesting it may have the most red-shifted absorption and superior light-harvesting capability. All molecules show deeply lying HOMO and LUMO levels, suggesting good chemical stability and potential compatibility with a variety of photovoltaic materials. The calculated HOMO levels show minimal variation across the series, indicating that the donor strength of the truxene core remains largely unaffected by either substituents or π-spacers. In contrast, the LUMO levels are more responsive to chemical modifications. Substitution at the BODIPY unit, such as the introduction of formyl groups, significantly lowers the LUMO energy (0.2 eV), thereby enhancing electron affinity. The choice of π-spacer also influences the frontier orbitals. Thiophene-linked systems generally exhibit slightly lower LUMO levels than phenyl-linked counterparts, reflecting enhanced acceptor character. These results highlight that BODIPY substituents are the dominant factor in tuning energy alignment, while π-spacers provide additional fine control over the electronic properties.

Table 5 Calculated values of the HOMO, LUMO and Δ_H–L for the gas phase of the studied compounds

Compounds	HOMO (eV)	LUMO (eV)	Δ H–L (eV)
3i	−4.95	−3.42	1.53
3j	−5.02	−3.80	1.22
3k	−4.93	−3.43	1.50
3l	−4.98	−3.67	1.31
3n	−4.89	−3.28	1.52
3o	−4.94	−3.80	1.14
3p	−4.87	−3.39	1.48
3q	−4.91	−3.66	1.25

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The FMO diagram is an essential tool for understanding how charge separation occurs within a molecule. By visualizing the spatial distribution of the HOMO and the LUMO, we can trace the likely pathway of electron transfer. We have examined the FMO plots of our designed molecules, as depicted in Fig. 7. From this figure, it is clear that specifically the HOMO is predominantly located on the truxene unit, which functions as the electron-donating segment of the molecule. Conversely, the LUMO is primarily distributed across the π-conjugated spacer and the BODIPY derivatives, which constitute the electron-accepting portion. This distinct spatial separation of the HOMO and LUMO provides visual confirmation of the intramolecular charge transfer pathway, indicating that, upon excitation, electrons are expected to move from the truxene donor unit, through the π-spacer, and onto the BODIPY acceptor unit. The localization of the HOMO on the donor and the LUMO on the acceptor minimizes the spatial overlap between these orbitals. This reduced overlap is generally beneficial for charge separation as it can lead to a smaller reorganization energy upon charge transfer and potentially lower the rate of charge recombination by spatially separating the positive and negative charges after photoexcitation.

Fig. 7 FMO diagrams of the designed compounds.

4.2.5 Density of states. The density of states (DOS) provides insight into the number of electronic states available at each energy level that electrons can occupy. To gain a more detailed understanding of how different molecular fragments contribute to the electronic structure, we have analyzed the partial density of states (PDOS), which reveals the individual contributions from the donor (D), π-spacer, and acceptor (A) units to the total DOS. The PDOS plots for the studied compounds are shown in Fig. 8. The corresponding spectral data obtained from PDOS spectra for the percentage contribution of D, π and A moieties to the HOMO and LUMO are presented in Table S2 of the SI.

Fig. 8 PDOS plots of the designed compounds.

From the figures, it is clear that the HOMO is mainly contributed by the donor unit, while the LUMO is primarily localized on the acceptor moiety. The π-spacer shows little to moderate involvement in both the HOMO and LUMO, suggesting its role in promoting charge delocalization and facilitating efficient charge transfer between the donor and acceptor ends. This distribution of orbital contributions aligns well with the expected behavior of D–π–A systems and confirms the effective electronic communication across the molecule.

4.2.6 Molecular electrostatic potential surface (MEPS) of the studied compounds. To analyze the charge transfer behavior within the molecule, the MEPS plots of all the designed compounds have been evaluated. The MEPS is a three-dimensional representation that maps the electrostatic potential created by the distribution of electrons and nuclei around a molecule.¹⁰³ The MEPS contour plots have been derived from the total self-consistent field (SCF) density. The positive potential has followed the color order: red < orange < yellow < green < blue. In this scheme, red color indicates electron-rich regions, while blue color corresponds to electron-deficient regions.

From Fig. 9, it can be observed that all the compounds display notable charge separation. The blue regions are predominantly localized on the truxene donor, while the red regions are concentrated on the BODIPY acceptor moiety. Thus, the MEPS contour plots suggest that the designed compounds possess the potential to serve as promising candidates for the development of organic photovoltaic devices.

Fig. 9 MEPS contour plots of the studied compounds.

4.2.7 Charge transport properties of the studied compounds. Studying the charge transport properties is essential for evaluating the suitability of these compounds for photovoltaic applications. Efficient charge transport is vital for minimizing energy losses and optimizing charge extraction in organic photovoltaic devices.

Reorganization energy (λ) is a critical parameter influencing the charge transfer process in organic materials. It is defined as the energy difference between the charged and neutral states of a molecule when considering two distinct geometries. In semiconductors, λ serves a role analogous to the activation energy barrier for electron or hole transfer. For optoelectronic devices to achieve high performance, λ must be minimized, as a lower reorganization energy facilitates a higher charge transfer rate.⁷⁶ In this work, the reorganisation energies for both electrons (λ_e) and holes (λ_h) have been calculated for all the designed compounds. The data in Table 6 show that the λ_e values are lower than the λ_h values for all of the designed molecules. This indicates that the designed compounds function as electron transporting materials.

Table 6 λ _h, λ_e, V₋ and k_CT values of the studied compounds

Compounds	λ h	λ e	V −	k ^−CT (×10^14 s^−1)
3i	0.250	0.212	0.387	6.99
3j	0.386	0.177	0.116	1.84
3k	0.680	0.158	0.049	0.05
3l	0.292	0.286	0.029	0.57
3n	0.245	0.223	0.094	0.36
3o	0.386	0.226	0.096	0.36
3p	0.354	0.163	0.055	0.26
3q	0.272	0.218	0.095	4.12

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To evaluate the electronic coupling matrix element for electron transfer (V₋), we investigated by optimizing a dimer model of the studied molecules. In this model, the molecules have been arranged in a co-facial stacking with a separation distance of 3.5 Å.¹⁰⁴ The computed V₋ values for these orientations are summarized in Table 6. From the calculated k_CT values, it is evident that all the studied compounds exhibit a high electron transfer rate, ranging from 0.05 × 10¹⁴ s⁻¹ to 6.99 × 10¹⁴ s⁻¹. These high electron transfer rate values indicate that the compounds have significant potential to function as electron transporters. Furthermore, as shown in Table 6, compound 3i demonstrates the highest electron transfer rate among all the designed compounds, which is consistent with its highest V₋ value. Compounds 3i–3l, which incorporate thiophene as the π-spacer, generally exhibit lower λ_e values and higher electron transfer rates compared to their benzene-spacer counterparts (3n–3q). This trend indicates that the thiophene spacer enhances electronic delocalization and facilitates faster electron transport. Within each spacer type, the nature of the substituent on the BODIPY acceptor significantly influences the charge transport parameters. For instance, among the thiophene series, 3i shows the lowest reorganization energy and highest k⁻_CT, suggesting that its particular substituent optimally aligns the frontier molecular orbitals for efficient electron transfer. Similarly, in the benzene series, 3q demonstrates superior electron transfer relative to the other derivatives, reflecting the impact of substituent-induced electronic modulation even in a less conjugated spacer system. Overall, these observations highlight that both the π-spacer and terminal substituents on the acceptor unit play a critical role in tuning the charge transport properties of these D–π–A molecules.

4.2.8 Charge density difference (CDD). The charge density difference (CDD) plot serves as an effective visual tool for illustrating electron redistribution in organic molecules, thereby offering valuable insights into the charge transfer processes that are critical for organic photovoltaic applications. CDD analysis enables the identification of molecular regions that experience electron accumulation or depletion upon excitation.¹⁰⁵ To examine exciton dissociation into free charges and their spatial distribution in the investigated D–π–A systems, three-dimensional CDD maps have been generated for the S₀ → S₁ transitions. These plots have been obtained using excited-state calculations with Multiwfn 3.8.¹⁰⁶ The representative CDD maps for the designed compounds are presented in Fig. 10. In these visualizations, the green and blue regions denote electron accumulation and depletion, respectively, resulting from photoexcitation.

Fig. 10 CDD plots of the designed molecules.

4.2.9 Spectral absorption properties of the studied compounds in the gas phase. To gain deeper insights into the electronic properties of the designed compounds, vertical excitation energies for 30 excited states have been computed using TD-DFT at the B3LYP-D3/6-31G(d) level of theory. The key results, including the maximum absorption wavelength (λ_max), oscillator strength (f_OSC), transition configurations, percentage contributions, and the excitation energy of the first excited state (E_g), are summarized in Table 7. The corresponding UV-vis absorption spectra are shown in Fig. 11. All the compounds exhibit λ_max values within the visible range, underscoring their potential as light-absorbing materials in optoelectronic applications. Similar to benzoselenadiazole-based A2–D–A1–D–A2 systems,¹⁰⁷ our truxene–BODIPY derivatives achieve broad absorption through strategic π-spacer and acceptor modifications, critical for maximizing photon harvesting. The dominant transitions are primarily characterized by single-electron excitations from H−2 or H−3 to the L, often contributing over 90%, indicating that these absorptions arise from well-defined orbital transitions. Among the studied compounds, 3k displays the highest λ_max of 599.24 nm, along with a strong oscillator strength (f_OSC = 0.843) and a highly pure H−2 → L transition (99.95%), making it a promising candidate for efficient light-harvesting. Notably, 3o shows the lowest excitation energy (E_g = 1.34 eV), suggesting ease of electronic excitation. Compounds 3p and 3k also show additional transitions such as H−2 → L+1 with substantial oscillator strengths, indicating potential for broad-spectrum absorption. These observations collectively point to the favorable optical characteristics of the studied molecules, supporting their applicability in the development of advanced optoelectronic devices. All molecules exhibit strong absorption in the visible to NIR region, with red-shifted λ_max values observed for thiophene-linked compounds compared to the benzene-linked compounds. This red-shift originates from the greater planarity of the thiophene spacer, which facilitates conjugation and reduces the HOMO–LUMO gap. The high molar absorptivity across the series ensures efficient photon capture, a key requirement for NFAs. These results underline that subtle spacer tuning can be used to extend light harvesting into the NIR region without compromising structural stability.

Table 7 λ _max, oscillator strength (f_OSC), configuration, %contribution of electronic transitions and excitation energy for the first excited state (E_g) values of the studied compounds in the gas phase

Compounds	λ max	f OSC	Configuration	%Contribution	E g
3i	532.31	0.645	H−3 → L	89.64	1.72
	512.87	0.553	H−2 → L	90.82
	393.97	0.297	H−5 → L	83.27
3j	574.24	0.590	H−2 → L	98.85	1.40
	456.69	0.296	H−3 → L	90.79
	415.15	0.108	H−4 → L	80.42
3k	599.24	0.843	H−2 → L	99.95	1.70
	551.84	0.766	H−3 → L	98.01
	399.54	1.247	H−2 → L+1	36.59
3l	573.63	0.615	H−3 → L	95.64	1.50
	523.81	0.592	H−2 → L	97.61
	416.12	0.194	H−4 → L	82.69
3n	507.34	0.316	H−3 → L	97.89	1.73
	499.31	0.592	H−2 → L	99.11
	379.52	0.391	H−6 → L	45.98
3o	580.60	0.272	H−2 → L	98.97	1.34
	442.46	0.340	H−3 → L	89.54
	389.03	0.127	H−11 → L	87.37
3p	585.45	0.923	H−2 → L	99.95	1.70
	519.01	0.448	H−3 → L	98.15
	399.68	1.75	H−2 → L+1	38.99
3q	561.39	0.271	H−3 → L	98.86	1.46
	509.75	0.646	H−2 → L	98.28
	404.69	0.152	H−4 → L	71.24

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Fig. 11 UV-vis spectra of the studied compounds in the gas phase.

4.2.10 Effect of solvent on spectral absorption properties. We have explored how the solvent environment influences the light-absorbing properties of the studied compounds using TDDFT calculations in conjunction with the CPCM model, with dichloromethane (DCM) as the chosen solvent. The principal results, including the maximum absorption wavelength (λ_max), oscillator strength (f_OSC), the characteristics and contributions of key electronic transitions, and the first excited-state energy (E_g), are presented in Table 8.

Table 8 λ _max, oscillator strength (f_OSC), configuration, %contribution of electronic transitions and excitation energy for the first excited state (E_g) values of the studied compounds in the solvent phase

Compounds	λ max	f OSC	Configuration	%Contribution	E g
3i	699.02	0.261	H−1 → L	98.38	1.62
	569.13	0.740	H−2 → L	96.51
	536.71	0.652	H−3 → L	98.48
3j	642.29	0.799	H−2 → L	99.57	1.19
	479.04	0.395	H−3 → L	96.61
	334.17	0.720	H−2 → L+1	84.06
3k	644.11	0.971	H−2 → L	99.66	1.59
	689.31	0.852	H−3 → L	97.06
	417.01	1.339	H−2 → L+1	43.44
3l	638.63	0.763	H−2 → L	98.98	1.31
	565.86	0.692	H−3 → L	99.55
	442.80	0.101	H−4 → L	51.79
3n	529.09	0.377	H−3 → L	97.26	1.67
	525.46	0.706	H−2 → L	99.17
	386.96	0.403	H−6 → L	40.26
3o	643.35	0.355	H−2 → L	98.96	1.17
	467.44	0.462	H−3 → L	95.85
	411.09	0.194	H−8 → L	75.18
3p	611.68	0.343	H−2 → L	98.58	1.32
	554.62	0.760	H−3 → L	98.12
	426.38	0.181	H−4 → L	63.68
3q	611.68	0.343	H−2 → L	98.58	1.72
	554.62	0.760	H−3 → L	98.13
	426.38	0.181	H−4 → L	63.68

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A comparative analysis with the gas-phase results as presented in Table 7 reveals a consistent red shift in λ_max values for all compounds in the DCM environment. This observed bathochromic shift indicates that the solvent preferentially stabilizes the excited states over the ground state. In many cases, this shift is also accompanied by an enhancement in oscillator strength, suggesting that the compounds exhibit improved light absorption efficiency in DCM. For example, compound 3j shows a pronounced absorption peak at 642.29 nm with an oscillator strength of 0.799, primarily arising from an electronic transition between the H−2 and L orbitals.

Notably, the key electronic transitions generally exhibit high percentage contributions from individual configurations, pointing to clean and well-defined excitations. The E_g values differ across the compound series, likely influencing the slight variations observed in the absorption onsets within the solvent, as illustrated in the spectra shown in Fig. 12.

Fig. 12 UV-vis spectra of the studied compounds in the solvent phase.

4.2.11 Transition density matrix (TDM) analysis. The transition density matrix (TDM) is a quantum chemical method used to study and interpret electronic excitations in molecular systems. It illustrates the spatial arrangement and interaction of electron–hole pairs formed during an electronic transition, typically from the ground to an excited state.¹⁰⁸ The TDM heat map visually represents the transition density matrix by using color coding to indicate the magnitude and sign of its elements. In this work, Multiwfn 3.8 is used to generate these heat maps. The associated electron density plots employ a color gradient (ranging from blue to green to red) to depict regions with different electron potentials. Intense or bright areas on the map indicate zones with high electron density and active electronic transitions.^100,106 This analysis has been carried out to investigate the charge distribution and coherence among the donor (D), π-spacer, and acceptor (A) units in their excited states. The corresponding heat maps are presented in Fig. 13. Contributions from hydrogen atoms is minimal and therefore excluded, allowing a focused examination of the D, π-spacer, and A fragments within the designed molecules. In the heat maps, the x-axis represents hole positions, while the y-axis corresponds to electron positions. As observed in Fig. 13, the TDM plots of all the designed compounds have exhibited prominent off-diagonal features, indicating substantial spatial separation between the holes and electrons upon excitation. This off-diagonal dominance indicates strong intramolecular charge transfer (ICT), where the electron density has been transferred from the donor or π-spacer region to the acceptor moiety. These observations have confirmed the effectiveness of the D–π–A molecular design in facilitating charge separation upon photoexcitation. The pronounced charge transfer character of the S₁ transition has been considered beneficial for exciton dissociation and charge transport, suggesting the potential of these compounds for application in organic photovoltaic devices.

Fig. 13 TDM heat maps for the S₁ transition of the designed compounds.

4.3 D/A blends

The efficiency of organic solar cells depends primarily on the precise molecular arrangement and interactions between donor and acceptor materials. From the observed λ and k_CT values, it is evident that our designed compounds act as acceptor materials. To investigate the properties of donor/acceptor (D/A) blends, we have adopted a standard donor molecule, C4, from a previous work. C4 exhibits a suitable alignment of HOMO and LUMO energy levels with our designed compounds, facilitating efficient charge transfer and compatibility in the blend.⁶⁸ We have arranged the designed acceptor compounds with the adopted donor molecule in a face-to-face arrangement to enable proper intermolecular charge transfer. The initial distance between the center of the donor and acceptor has been fixed at 3.5 Å.⁵ The designed donor/acceptor (D/A) blends have been optimized using the HSEH1PBE functional with the 6-31G(d) basis set, and their absorption parameters have been calculated at the B3LYP-D3/6-31G(d) level of theory. The optimized structure of the C4/3i blend is presented in Fig. S5 of the SI.

4.3.1 Spectral absorption properties of the D/A blends. The absorption parameters of the D/A blends are provided in Table 9 and the respective absorption spectra are presented in Fig. 14. When the adopted donor molecule is blended with the designed acceptor molecules, they tend to aggregate or stack due to intermolecular forces, including π–π stacking interactions. Such aggregation significantly impacts the electronic structure and optical characteristics of the material. In the aggregated state, the effective conjugation length of the molecules is extended, leading to a red shift in the absorption spectra. It has been observed from Tables 7 and 9 that all the designed D/A active blends exhibit a red shift compared to the isolated acceptor molecules. This pronounced red shift in the D/A blends can be attributed to enhanced intermolecular charge transfer. The observed red shift signifies the emergence of charge transfer states, which are crucial for facilitating efficient charge separation. In the D/A blend, the absorption spectrum is primarily influenced by the formation of excitons, which are bound electron–hole pairs generated upon photon absorption. The spectrum represents the energy needed to create these excitons. Charge transfer states arise when an exciton becomes delocalized, resulting in charge separation between the donor and acceptor. These charge transfer states are evident in the absorption spectra.¹⁰⁹ From Table 9, it is observed that the first singlet excitation energies, i.e., the E_g of the blends spans from 1.29 to 1.78 eV, indicating efficient absorption in the visible to near-infrared (NIR) region. Among the studied systems, C4/3j exhibits the lowest excitation energy (1.29 eV), suggesting strong potential for red-shifted absorption. In contrast, blends such as C4/3q, C4/3p, and C4/3l display both intense absorptions (f_OSC > 1.2) and λ_max values above 700 nm, making them especially promising for light-harvesting in organic solar cell applications. Most prominent transitions involve HOMO−2 or HOMO−1 to LUMO or LUMO+1, with significant single-configuration contributions (often >75%), indicating localized and well-defined excitations. Overall, these results highlight that the interaction between donor and acceptor orbitals plays a key role in controlling the light-absorbing properties. All the designed blends demonstrate favorable optoelectronic features, indicating their potential to act as efficient acceptor materials in OSC applications.

Table 9 λ _max, oscillator strength (f_OSC), configuration, %contribution of electronic transitions and excitation energy for the first excited state (E_g) values of D/A blends

D/A blends	λ max	f OSC	Configuration	%Contribution	E g
C4/3i	799.05	0.051	H−1 → L+1	77.01	1.36
	777.70	1.014	H−2 → L+1	75.37
	775.84	0.026	H−1 → L+2	83.34
C4/3j	786.20	0.027	H−1 → L+1	96.54	1.29
	769.49	0.006	H−1 → L+2	87.88
	733.40	1.215	H−2 → L+2	75.04
C4/3k	763.25	0.702	H−2 → L	96.61	1.64
	752.96	0.152	H−1 → L+1	72.91
	729.44	0.672	H−3 → L	89.10
C4/3l	732.30	1.281	H−2 → L+1	93.32	1.69
	708.15	0.489	H → L+2	67.19
	651.02	0.069	H−4 → L+3	62.69
C4/3n	696.11	1.413	H−2 → L+1	79.43	1.78
	682.73	0.395	H−1 → L+1	63.39
	648.84	0.078	H−1 → L+3	79.27
C4/3o	696.11	1.413	H−2 → L	79.43	1.65
	682.73	0.395	H−1 → L+1	64.35
	622.99	0.119	H−2 → L+2	75.70
C4/3p	777.56	0.121	H−2 → L	76.53	1.59
	748.45	1.588	H−2 → L+1	63.49
	747.76	0.806	H−1 → L+1	59.78
C4/3q	713.28	1.770	H−2 → L+1	92.62	1.73
	703.69	0.655	H → L+1	51.80
	666.48	0.059	H → L+3	47.55

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Fig. 14 UV-vis spectra of D/A blends.

4.4 Photovoltaic properties

To explore the practical potential of the D/A blends in OSCs, we have evaluated their photovoltaic performance using the spectroscopic limited maximum efficiency (SLME) method. This approach, originally proposed by Yu and Zunger,⁸⁰ goes beyond traditional models by considering not just the energy levels but also the actual absorption spectra, the nature of the band gaps, and radiative recombination losses. Compared to the widely used Scharber model, SLME provides a more realistic estimate of the upper limit of power conversion efficiency (PCE) by incorporating material-specific optical data.¹¹⁰ We have implemented the SLME method through a Python-based script that processes TDDFT-calculated absorption data along with the standard AM1.5G solar spectrum. The script interpolates the absorption spectrum, calculates the short-circuit current density (J_sc) and radiative dark current (J₀), and solves the diode equation to determine the optimal output voltage. All calculations have been carried out at room temperature (293.15 K), assuming an active layer thickness of 50 μm.

Key parameters such as J_sc, eV_oc, v_oc, FF, and PCE are summarized in Table 10. Among all the studied complexes, C4/3p has shown the highest theoretical PCE of 21.18%, which can be attributed to its optimal balance of high J_sc, V_oc, and FF. While this value reflects an ideal scenario based on SLME calculations, it is important to note that experimental efficiencies are typically lower due to practical factors such as morphology, interface losses, and fabrication constraints. However, similar theoretical PCEs have been reported in the literature using SLME and other first-principles-based models,¹¹¹ and certified experimental efficiencies for organic solar cells have already reached 20.82% for optimized non-fullerene systems.¹¹² These precedents suggest that achieving an efficiency close to that predicted for C4/3p is attainable under optimized experimental conditions, reinforcing its potential as a promising candidate for future development.

Table 10 Calculated photovoltaic parameters of D/A blends

D/A blends	J sc (mA cm^−2)	eV oc (eV)	v oc	FF (%)	PCE (%)
C4/3i	27.15	1.96	75.82	93.05	19.14
C4/3j	31.47	1.58	61.16	91.75	17.66
C4/3k	23.74	1.96	75.66	93.04	16.71
C4/3l	33.26	1.71	66.22	93.65	20.63
C4/3n	24.31	2.01	77.73	94.39	17.85
C4/3o	32.37	1.58	61.23	93.26	18.48
C4/3p	29.08	1.99	77.19	94.36	21.18
C4/3q	29.93	1.72	66.74	93.68	18.17

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To provide context, we compared these theoretical results with the experimental performance of truxene-based donor 6a, which is taken as the reference molecule for this work. In those experiments, 6a paired with PC₇₁BM and Y6 acceptors exhibited PCEs of 7.33% and 8.82%, with J_sc values of 11.8–16.2 mA cm⁻², V_oc values of 0.98–1.10 V, and FFs around 60–68%. While the experimental performance was influenced by factors such as photon harvesting, charge transfer efficiency, and active layer morphology, our SLME-based predictions for the designed D/A blends (C4 paired with 3i–3q) suggest somewhat higher ideal PCEs, ranging from 16.71 to 21.18%. Although these values are calculated under idealized conditions and do not include practical fabrication or morphological effects, they indicate that the designed molecules could serve as promising candidates for experimental validation.

Although complexes like C4/3l and C4/3o have exhibited higher J_sc values, their overall PCEs have remained slightly lower, reaffirming that maximizing a single parameter alone is not sufficient but a balanced optimization is key. All the complexes have shown impressively high FF values, indicating efficient charge extraction and minimal recombination under the simulated ideal conditions.

Looking at the photovoltaic performance of these D/A blends, we can observe clear trends linked to the molecular structure. In the thiophene-spacer series (C4/3i–C4/3l), C4/3l stands out with the highest short-circuit current (J_sc) and PCE, suggesting that its specific BODIPY substituent promotes better light absorption and charge separation. For the benzene-spacer series (C4/3n–C4/3q), C4/3p achieves the best efficiency, highlighting how even with a less conjugated spacer the right substituent can optimize energy level alignment and enhance charge extraction. These observations show that both the choice of π-spacer and the functionalization of the acceptor unit play a key role in determining device performance. Thiophene tends to boost current generation, while benzene can help to achieve higher open-circuit voltages and fill factors when paired with favorable substituents.

Overall, the present findings underscore the strong potential of the designed molecules as non-fullerene small molecular acceptors in organic photovoltaics and reinforce the critical role of molecular-level design in achieving next-generation high-efficiency OSCs. The conclusions of this work can be viewed as predictive guidelines based on first-principles calculations, for the detection of absolute performance values in experimental work. The trends observed here are intended to guide experimental efforts and inspire further design of truxene–BODIPY systems for next-generation OSCs.

5 Conclusion

This work presents a rational and structure-guided approach to designing eight novel truxene–BODIPY-based small molecule acceptors for use in organic solar cells (OSCs). Using a combination of DFT and TDDFT methods, we have systematically explored how changes in π-spacer and acceptor moieties influence the electronic structure and optical performance of these molecules. All the designed compounds exhibited strong intramolecular charge transfer characteristics, low reorganization energies, and broad absorption ranging from the visible to the near-infrared region both in their isolated forms and when blended with a standard donor.

Our findings emphasize the power of molecular engineering at the truxene core to develop efficient NFSMAs. Among the series, compound 3i exhibits the highest electron transfer rate, while compounds 3j, 3l, 3p, and 3q exhibit narrow energy gaps and spatial separation of frontier orbitals, making them excellent candidates for effective light harvesting and charge transport. Notably, the donor–acceptor blend C4/3p achieves the highest power conversion efficiency (PCE) of 21.18%, underlining the importance of D/A compatibility in overall device performance.

Altogether, this study highlights the significance of thoughtful structural modifications in tuning photovoltaic properties. These results not only point to truxene–BODIPY systems as promising alternatives to fullerene-based acceptors, but also offer meaningful design strategies for the development of next-generation, high-performance organic photovoltaic materials. Looking ahead, experimental synthesis and device integration of these molecules, together with advanced theoretical studies on morphology and interfacial dynamics, will validate and extend the promising performance trends observed in this work.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: optimized structures of the designed acceptor molecules, coordinates of the optimized structures of the designed compounds in angstrom units, optimized structure of the test compound, representation of dihedral angles in 3i, spectral data of the designed compounds obtained from PDOS spectra, representative structures of two stacked 3i monomers along with distance l, optimized structure of the adopted donor molecule, and representative optimized structure of the C4/3i blend. See DOI: https://doi.org/10.1039/d5nj03508b.

Acknowledgements

The authors would like to acknowledge the Department of Science and Technology (SB/FT/CS-077/2013 and CRG/2022/001313), India for the financial support. The authors would also like to acknowledge the University Grants Commission for the UGC-BSR Research start-up-grant (No. F.30.-122/2015(BSR)), Gauhati University for providing the research facilities and financial support.

Notes and references

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