Impact of Molecular π-Bridge Modifications on Triphenylamine-Based Donor Materials for Organic Photovoltaic Solar Cells

Abstract

This study presents a computational investigation into the design of triphenylamine-based donor chromophores incorporating 2-(1,1-dicyanomethylene)rhodanine as the acceptor unit. Three molecular architectures (System-1 to System-3) were developed by introducing distinct thiophene-derived $\pi$-bridges to modulate their electronic and optical characteristics for potential application in bulk heterojunction organic solar cells (OSCs). Geometrical optimizations were performed at the B3LYP/6-31+G(d,p) level, while excited-state and absorption properties were evaluated using TD-DFT with the CAM-B3LYP functional. Frontier orbital analysis revealed efficient charge transfer from donor to acceptor moieties, with System-3 showing the narrowest HOMO–LUMO gap (1.96 eV) and the lowest excitation energy (2.968 eV). Charge transport properties, estimated from reorganization energies, indicated that System-2 exhibited the most favorable balance for ambipolar transport, featuring the lowest electron reorganization energy (0.317 eV) and competitive hole mobility. Photovoltaic parameters calculated with PC₆₁BM as acceptor predicted superior $V_{oc}$, $J_{sc}$, and fill factor values for System-2, resulting in the highest theoretical power conversion efficiency (10.95%). These findings suggest that $\pi$-bridge engineering in triphenylamine-based systems can significantly enhance optoelectronic performance, offering promising donor materials for next-generation OSC devices.

1. Introduction

The growing global energy demand, coupled with the environmental impact of fossil fuel dependence, has intensified the search for clean, renewable alternatives [1,2,3]. Among various photovoltaic technologies, organic solar cells (OSCs) have attracted significant interest due to their lightweight nature, mechanical flexibility, solution-processability, and potential for low-cost fabrication [4,5,6,7]. Although crystalline silicon has long dominated the solar market—offering efficiencies above 47% under concentration—its rigidity, high production cost, and limited tunability of electronic properties motivate the exploration of organic-based counterparts [8,9,10].

In recent years, molecular engineering has emerged as a powerful strategy to overcome the intrinsic limitations of OSCs, particularly in enhancing light harvesting, charge mobility, and reducing energy losses [11]. Donor–$\pi$–acceptor (D–$\pi$–A) architectures are especially appealing because their modular design enables fine-tuning of optoelectronic properties through modifications of donor units, acceptor groups, or $\pi$-bridges. Triphenylamine (TPA) derivatives have been widely explored as donor moieties due to their strong electron-donating ability [12,13], high hole mobility, and structural versatility. When covalently linked to acceptor groups such as 2-(1,1-dicyanomethylene)rhodanine, TPA-based systems can form efficient push–pull structures that promote charge separation and suppress recombination [14].

In this work, three new A–$\pi$–D–$\pi$–A chromophores (System-1 to System-3) were theoretically designed by varying the $\pi$-bridge composition. Density functional theory (DFT) and time-dependent DFT (TD-DFT) are widely employed to investigate the optoelectronic properties of donor–$\pi$–acceptor (D–$\pi$–A) chromophores. For ground-state geometry optimizations, the hybrid functional B3LYP has been extensively used due to its reliable description of molecular structures and frontier orbital energies in organic semiconductors [10,15]. Moreover, CAM-B3LYP has been shown to yield good agreement with experimental UV–Vis spectra of push–pull chromophores containing triphenylamine donors and rhodanine acceptors [14]. These precedents justify our use of B3LYP/6-31+G(d,p) for ground-state optimizations and CAM-B3LYP/6-31+G(d,p) for excited-state properties in the present work. This theory and these functionalities were employed to examine how structural modifications of the bridges influence the electronic structure, optical absorption, charge transport, and photovoltaic performance, with the goal of identifying promising donor materials for high-efficiency bulk heterojunction OSCs.

2. Chromophores and Computational Methods

In this work, we consider an organic molecular system as depicted in Figure 1. Each molecule is classified into three fragments: a central unit acting as an electron donor, molecular bridges that facilitate charge transfer, and terminal groups serving as electron acceptors. In these systems, we use the structure of 4-Hexyloxy-Triphenylamine (TPA) as the electron donor fragment, which consists of a triphenylamine core connected to the electron acceptor fragment 2-(1,1-Dicyanomethylene)-1,3-thiazolene-4 (DCR) through molecular bridges (B). Different molecular bridges are employed for the design of new push-pull chromophores, such as 2,5-Dimethylthiophene (B1), 4,4″-Dihexyl-2,2′:5′,2″-Terthiophene (B2), and 2-(9,9-Dihexyl-9H-Fluoren-2-yl)hexylthiophene (B3), to create (System-1), (System-2), and (System-3), respectively. The choice of molecular bridges is based on their ability to enhance $\pi$-conjugation and facilitate efficient charge transfer between the donor and acceptor units. The incorporation of 2,5-dimethylthiophene and fluorenyl-thiophene bridges is expected to reduce the energy gap and improve electron mobility, as has been observed in similar systems with more conjugated $\pi$-bridges [16,17,18].

To determine the geometry of the most stable conformations, the molecular systems were geometrically optimized to reveal their ground state ($S_0$) structures using density functional theory (DFT) with the hybrid functional B3LYP [15] and the 6-31+G(d,p) basis set, as implemented in Gaussian 09 [19]. The energies of the molecular systems were calculated based on these optimized geometries. The excited states of the molecules and the UV–Vis spectra reported here were simulated using time-dependent density functional theory (TD-DFT) with the CAM-B3LYP/6-31+G(d,p) basis set. Both the gas phase and the solvent environment ethanol (EtOH) were considered, with the solvent effects modeled using the conductor-like polarization continuum model (C-PCM) [20,21]. Additionally, we derived various properties from the computational results, such as the highest occupied molecular orbitals (HOMOs), lowest unoccupied molecular orbitals (LUMOs), energy gap, reorganization energy, and excitation energy.

3. Results and Discussion

3.1. Frontier Molecular Orbital (FMO) Analysis

To explore the influence of $\pi$-bridge variations on the electronic structure, the frontier molecular orbitals (FMOs) of System-1, System-2, and System-3 were examined at their optimized geometries. TD-DFT calculations were employed to identify electronic transitions relevant to charge transfer (CT) processes. In all three systems, the highest occupied molecular orbital (HOMO) is mainly localized on the electron-donating TPA core, while the lowest unoccupied molecular orbital (LUMO) is concentrated on the rhodanine-based acceptor units, as shown in Figure 2. This spatial separation supports efficient donor-to-acceptor CT [22]. Intermediate orbitals (HOMO–1, LUMO+1) show varying degrees of delocalization across the $\pi$-bridges, with System-1 and System-3 displaying stronger bridge participation compared to System-2.

The HOMO–LUMO gaps in ethanol were calculated as 2.13 eV (System-1), 1.97 eV (System-2), and 1.96 eV (System-3) and are shown in

Table 1. Calculated energies of the HOMO ($E_H$) and LUMO ($E_L$), maximum absorption wavelength (${\lambda }_{\max }$), and band gap ($E_g^{el}$) for all studied molecular systems in the gas phase and ethanol.

System	${\mathit{\lambda }}_{\mathit{max}}$ (nm)	${\mathit{E}}_{\mathit{H}}$ (eV)	${\mathit{E}}_{\mathit{L}}$ (eV)	${\mathit{E}}_{\mathit{g}}^{\mathit{el}}$ (eV)
Gas Phase
System-1	462.40	−5.58	−3.28	2.30
System-2	494.83	−5.28	−3.18	2.10
System-3	407.60	−5.07	−3.10	1.97
EtOH
System-1	449.62	−5.30	−3.17	2.13
System-2	525.55	−5.12	−3.15	1.97
System-3	417.69	−5.01	−3.05	1.96

; they are consistent with the expectation that extended $\pi$-conjugation and electron-withdrawing substituents reduce the band gap [23,24]. Notably, the fluorenyl-thiophene bridge in System-3 produces the smallest gap, while System-2 achieves a comparable reduction through terthiophene insertion. These results indicate that $\pi$-bridge engineering effectively tunes the energy alignment and spatial orbital distribution, factors directly impacting exciton dissociation efficiency and charge transport in OSC applications.

3.2. Electronic Absorption Spectral

The optical response of the three designed chromophores was evaluated to assess the effect of $\pi$-bridge modifications on light-harvesting capability. TD-DFT simulations at the CAM-B3LYP/6-31+G(d,p) level were carried out in both the gas phase and ethanol, with solvent effects modeled via CPCM.

In ethanol, the main absorption bands span from 417.69 nm to 525.55 nm, as shown in Figure 3. System-2 exhibits the most red-shifted maximum (${\lambda }_{max}=525.55$ nm), attributable to enhanced conjugation through its terthiophene bridge, which facilitates intramolecular charge transfer (ICT) from the TPA donor to the rhodanine acceptor [14,24,25]. In contrast, System-3 displays a hypsochromic shift with a ${\lambda }_{max}$ of 417.69 nm, indicating a slightly higher excitation energy despite its narrow HOMO–LUMO gap.

Multiple absorption peaks are observed in each system. For System-2, the primary band corresponds to HOMO→LUMO transitions, while secondary peaks in the UV region arise from excitations involving deeper occupied orbitals and higher unoccupied states. The calculated oscillator strengths ($f_{osc}$) suggest that System-2 has the highest light-harvesting efficiency (LHE), exceeding 99.9%, followed closely by System-3, with System-1 being comparatively lower. ${\lambda }_{max}$ and other parameters are summarized in

Table 2. Wavelengths of the most important simulated transition states $\lambda$, oscillator strengths $f_{os}$, excitation energy $E_{ex}$, and light harvesting efficiency $LHE$.

System	States	$\mathit{\lambda }$ (nm)	$\Delta {\mathit{E}}_{\mathit{ex}}$ (eV)	${\mathit{f}}_{\mathit{osc}}$	LHE
Gas Phase
System-1	$S_0\to S_1$	462.40	2.681	2.549	0.9972
	$S_0\to S_4$	335.04	3.701	0.292
System-2	$S_0\to S_1$	494.83	2.506	3.368	0.9995
	$S_0\to S_4$	355.31	3.489	0.159
	$S_0\to S_7$	318.93	3.888	0.243
System-3	$S_0\to S_1$	407.60	3.042	3.238	0.9994
	$S_0\to S_5$	337.73	3.671	0.569
EtOH
System-1	$S_0\to S_1$	499.62	2.482	2.725	0.9981
	$S_0\to S_4$	347.78	3.565	0.320
System-2	$S_0\to S_1$	525.55	2.359	3.509	0.9996
	$S_0\to S_4$	369.69	3.354	0.233
	$S_0\to S_7$	326.14	3.802	0.397
System-3	$S_0\to S_1$	417.69	2.968	3.447	0.9996
	$S_0\to S_4$	347.79	3.565	0.404

.

Overall, the results highlight that $\pi$-bridge length and electronic structure strongly influence absorption wavelength and intensity, with System-2 offering the most favorable profile for OSC donor applications due to its broad and intense visible-light absorption.

3.3. Ionization Potential and Electron Affinity

Ionization potential (IP) and electron affinity (EA) are key descriptors for evaluating charge injection and extraction in organic photovoltaic devices [26]. Molecules with lower IP values generally facilitate hole injection from the donor material, while higher EA values promote electron capture by the acceptor [27].

From our calculations in ethanol, System-3 exhibits the lowest IP (5.198 eV), indicating that it requires the least energy to remove an electron from the HOMO, thereby favoring hole extraction. System- follows closely, while System-1 presents the highest IP, suggesting less efficient hole generation. In terms of EA, all three systems show values above 3.28 eV, with System-3 achieving the highest (3.374 eV), reflecting strong electron-accepting ability.

These results suggest that $\pi$-bridge engineering not only alters the energy gap but also tunes the energy levels to improve charge transfer balance. In particular, the combination of low IP and high EA in System-3 could support efficient bidirectional charge transport, although other parameters—such as reorganization energy—must also be considered to determine the most suitable candidate for OSC applications.

3.4. Reorganization Energy

Charge transport efficiency in organic semiconductors depends strongly on two microscopic factors: the electronic coupling between donor and acceptor fragments, and the reorganization energy ($\lambda$) associated with structural relaxation during charge transfer [28,29]. Lower $\lambda$ values indicate that less structural rearrangement is required, favoring higher mobility.

The intramolecular reorganization energy ${\lambda }_{int}$ can be estimated for electrons (electron reorganization energy, ${\lambda }_e$) and for holes (hole reorganization energy, ${\lambda }_h$), and can be expressed by the following equation [30]:

$${\lambda }_e =(E_0^{-}-E_{-})+\left(E_{-}^0-E_0\right)$$

(1)

$${\lambda }_h =\left(E_0^{+}-E_{+}\right)+\left(E_{+}^0-E_0\right),$$

(2)

where $E_0^{-}$ and $E_0^{+}$ represent the anionic and cationic energies, respectively, used to describe the ground-state energy of a neutral compound in these equations. At the single-point ground state, $E_0$ corresponds to the energy of the neutral molecule, while $E_{-}$ and $E_{+}$ represent the single-point ground-state energies of the anion and cation after optimization. $E_0^{-}$ and $E_0^{+}$ are the ground-state energies for the optimized anion and cation, respectively.

We evaluated both electron (${\lambda }_e$) and hole (${\lambda }_h$) reorganization energies in the gas phase and ethanol. In the solvent environment, all systems display reduced $\lambda$ values compared to the vacuum, indicating that ethanol stabilizes charge transfer processes. System-2 presents the lowest ${\lambda }_e$ (0.142 eV in ethanol, see

Table 3. Estimated values for the electron reorganization energy (${\lambda }_e$), hole reorganization energy (${\lambda }_h$), ionization potential (IP), electron affinity (EA), and dipole moment ($\mu$) of all investigated molecular dyes in ethanol (EtOH) and the gas phase.

Systems	${\mathit{\lambda }}_{\mathit{e}}$ (eV)	${\mathit{\lambda }}_{\mathit{h}}$ (eV)	$\mathit{IP}$ (eV)	$\mathit{EA}$ (eV)	$\mathit{\mu }$ (D)
EtOH
System-1	0.316	0.201	5.379	3.284	13.504
System-2	0.142	0.233	5.302	3.325	16.762
System-3	0.317	0.198	5.198	3.374	18.258
Gas Phase
System-1	0.261	0.220	6.768	2.084	9.063
System-2	0.164	0.285	6.502	2.121	11.672
System-3	0.219	0.209	6.309	1.937	13.042

), suggesting excellent electron transport potential, while System-3 has the lowest ${\lambda }_h$ (0.198 eV), indicating superior hole mobility. System-1 shows balanced but slightly higher values for both carriers.

Interestingly, the terthiophene bridge in System-2 promotes efficient electron transfer, whereas the fluorenyl-thiophene bridge in System-3 favors hole conduction. The relatively small difference between ${\lambda }_e$ and ${\lambda }_h$ in System-2 suggests ambipolar behavior, which can be advantageous in bulk heterojunction OSC architectures. Overall, these findings confirm that targeted modification of the $\pi$-bridge segment is an effective strategy with which to optimize carrier transport pathways, allowing the design of donor materials tailored for specific charge mobility requirements in photovoltaic devices.

3.5. Molecular Electrostatic Potential

To visualize how electronic charge is distributed within each chromophore, molecular electrostatic potential (MEP) maps were generated from the optimized geometries. These surfaces provide insight into regions susceptible to electrophilic or nucleophilic interactions, as well as the internal charge separation between donor and acceptor units [31]. In the three systems, the strongest negative potentials (depicted in red) are localized over the rhodanine-based acceptor termini, as can be seen in Figure 4, reflecting the high electron density associated with oxygen, nitrogen, and sulfur atoms in these regions. Conversely, positive potential zones (blue) are concentrated around the triphenylamine donor cores and parts of the $\pi$-bridges, consistent with their electron-donating character.

Comparatively, System-2 shows more extensive negative potential regions than System-1 and System-3, indicating enhanced electron-withdrawing ability across the acceptor moieties. This distribution supports more effective intramolecular charge transfer, which correlates with its favorable photovoltaic performance. The MEP analysis confirms that $\pi$-bridge composition modulates not only electronic energy levels but also the spatial arrangement of charge density, both of which are critical for optimizing the interaction between donor and acceptor phases in bulk heterojunction OSCs.

4. Photovoltaic Properties

In organic photovoltaic (OPV) technology, the most efficient cells are bulk heterojunction (BHJ) devices, as BHJ-based organic solar cells (OSCs) offer a promising future for economically converting solar energy into electricity, surpassing conventional silicon solar cells [32,33]. This is due to their low-temperature manufacturing process, light weight, flexibility [9,34], and their power conversion efficiency (PCE) exceeding 19% [6]. Although the PCE of OPV cells has improved significantly, there is still considerable work to be done before they achieve commercial viability, especially when compared to the 25.2% PCE of perovskite-based thin film solar cells [35]. Further improvements are necessary to optimize their IP performance. The PCE is directly dependent on the open-circuit voltage ($V_{oc}$), the short-circuit current density ($J_{sc}$), the fill factor ($FF$), and the incident solar energy. None of these four components can be overlooked in material design if better PCE values are to be achieved.The PCE of a photovoltaic cell can be expressed as

$$PCE={\displaystyle \frac{V_{oc}{J}_{sc}FF}{P_{in}}}$$

(3)

where $P_{in}$ represents the power of incident light.

In general, $V_{oc}$ is related to the energy difference between the HOMO of the donor material and the LUMO of the acceptor material, and it is also influenced by carrier generation and recombination rates, as well as tail energy states or trap states [36].

4.1. Open-Circuit Voltage ($V_{oc}$) Investigation

The open-circuit voltage ($V_{oc}$) is a critical factor in determining the efficiency of organic solar cells, as it represents the maximum voltage a device can deliver when no current flows [37,38]. In donor–acceptor bulk heterojunctions, $V_{oc}$ is primarily governed by the energy difference between the HOMO of the donor and the LUMO of the acceptor, as shown in Figure 5, offset by energy losses from charge recombination and other processes [39,40,41]. Theoretical $V_{oc}$ values for the examined OSC systems are calculated using the equation reported by Scharber et al. [9], and the results are presented in Table 3.

$$V_{oc}={\displaystyle \frac{1}{e}}|E_{LUMO}^A-E_{HOMO}^D|-0.3V$$

(4)

Here, e is the elementary charge, and a value of 0.3 V is a typical loss in bulk heterojunction solar cells. Using the simulated value of $E_L=-3.68\mathrm{eV}$ for the lowest unoccupied molecular orbital (LUMO) energy of PC₆₁BM in this work, the analysis can proceed.

Here, PC₆₁BM was used as the reference acceptor to estimate $V_{oc}$ for the three designed systems. The calculated values are presented in

Table 4. Parameter values of the studied molecular compounds including the exciton driving force $\Delta E$, open-circuit voltage ($V_{oc}$), short-circuit current density ($J_{sc}$), fill factor ($FF$), and power conversion efficiency (PCE) in the solvent ethanol (EtOH).

System	$\Delta \mathit{E}$ (eV)	${\mathit{V}}_{\mathit{oc}}$ (V)	${\mathit{J}}_{\mathit{sc}}$ (mA/cm2)	$\mathit{FF}$	$\mathit{\eta }$ (%)
System-1	0.51	1.32	9.52	0.810	10.18
System-2	0.53	1.14	12.21	0.786	10.95
System-3	0.63	1.03	11.85	0.774	9.45

and range from 1.03 V (System-3) to 1.32 V (System-1), all exceeding the typical 1.0 V threshold considered beneficial for efficient devices. System-1 achieves the highest $V_{oc}$, likely due to its relatively deeper HOMO level, while System-2 offers a balanced trade-off between $V_{oc}$ and other photovoltaic parameters. Energy offsets ($\Delta E$) between donor and acceptor LUMO levels were also assessed and found to be above 0.3 eV in all cases, ensuring sufficient driving force for exciton dissociation. This alignment supports effective charge transfer at the donor–acceptor interface, a prerequisite for achieving high short-circuit currents and overall device performance.

4.2. Fill Factor (FF)

The PCE and other photovoltaic properties of organic solar cells (OSCs) can also be evaluated using an important parameter, the Fill Factor (FF). In practice, multiple physical mechanisms influence the FF, leading to various models proposed for its estimation [42,43]. These models are generally based on the current–voltage relationship but differ in their assumptions regarding the causes and values of shunt and series resistances. The FF is typically expressed as a function of $V_{oc}$. The fill factor for molecular compounds can be calculated using Equation (5) [44]:

$$FF={\displaystyle \frac{V_{oc}}{V_{oc}+\alpha k_{B}T}}$$

(5)

where $\alpha$ is an adjustable factor for different solar cell technologies. For example, $\alpha =6$ and $\alpha =12$ provide the best fit for the upper limits of the FF measured in excitonic and non-excitonic solar cells, respectively, as indicated by Alharbi et al. [44]. In this equation, $V_{oc}$ represents the open-circuit voltage, T is the system temperature (300 K), and $k_B$ denotes the Boltzmann constant.

Using the calculated $V_{oc}$ and $J_{sc}$ values in conjunction with estimated resistive losses, the FF for the three systems was predicted within the range of 0.74–0.78, and these values are summarized in Table 4. System-2 achieved the highest FF (0.78), closely followed by System-1, while System-3 showed a slightly lower value. The superior FF of System-2 is consistent with its favorable reorganization energies and balanced ambipolar transport, which likely reduce charge recombination and improve carrier extraction efficiency. Although the FF values across the systems are relatively close, small variations in molecular packing and charge mobility—dictated by $\pi$-bridge composition—can lead to measurable performance differences in experimental devices. These trends underscore the importance of optimizing not only energy levels and absorption but also transport properties to maximize photovoltaic output.

4.3. Short-Circuit Current Density ($J_{sc}$)

Current-voltage density characteristics (J–V) are essential for analyzing voltage loss, based on the values of open-circuit voltage ($V_{oc}$) and short-circuit current density ($J_{sc}$). The most accurate way to determine $J_{sc}$ is to account for the spectral shape of sunlight, as both the intensity and spectral distribution depend on various factors, such as the calibration cell’s spectral response, the characteristics of the OSC medium, and the angle above the horizon. This approach allows a standard power spectrum to be defined: $\varphi AM.1.5\left(\lambda \right)$ [45,46]. Therefore, $Jsc$ can be calculated using the following expression [47,48,49]:

$$J_{sc}={\displaystyle \frac{q}{hc}}{\int }_0^{E_g^D}EQE\left(\lambda \right)P_{AM1.5G}\left(\lambda \right)\lambda ,d\lambda$$

(6)

where h is Planck’s constant, c is the speed of light in a vacuum, $E_g^D$ represents the band gap of the hole-transporting material in the active layer of the device, and $EQE\left(\lambda \right)$ is the external quantum efficiency, which in turn depends on the chromophore contribution to light harvesting, assumed to be 80% for this study [9,28].

The values of $J_{sc}$ and PCE for System-1 to System-3 are presented in Table 4. The $J_{sc}$ values range from 9.52 to 12.21 mA/cm², with the highest value observed for System-2, which also exhibits the highest PCE of approximately 10.95%. This study shows that, concerning the PCE of the systems considered and taking System-1 as a reference, the inclusion of thiophene rings as molecular bridges in System-2 enhances the PCE. However, incorporating dibenzothiophene in System-3 leads to a significant PCE reduction of around 1.5% compared to System-2. These findings indicate that both molecular systems System-1 and System-2 (the latter showing superior performance) are promising candidates for use as photovoltaic materials in bulk heterojunction (BHJ) organic solar cells, compared to System-3.