First-principles study to explore the long-range exciton dissociation and reduced binding energy in dicyanovinylene–indanone-based electron transport layers for PSCs

Abstract

We designed six new electron transport materials: M1–M4 and their extended derivatives, M5 and M6, based on a 5,10-dihydrothieno[3′,2′:4,5]pyrrolo[2,3-f]thieno[2,3-b]indole core. These D–A-type electron transport layers (ETLs) are intended for use in perovskite solar cells (PSCs). Using DFT and TD-DFT methods in gas, toluene, and ethanol phases, we systematically evaluated the substituent contribution to molecular planarity, frontier molecular orbitals (FMOs), absorption spectra, hole–electron reorganization energy, density of states, light-harvesting efficiency (LHE), exciton binding energy (E_b), and transition density matrix (TDM). Compared to the reference (3.72 eV), the developed ETMs have much smaller band gaps (1.35–1.62 eV), with M6 having the smallest gap (1.35 eV). With deviations of 0.17 to 0.23 eV, the LUMO levels (−4.07 to −4.13 eV) are in good alignment with the perovskite conduction band (−3.90 eV for FAPbI₃). E_b drastically drops from 0.36 eV (REF) to 0.33–0.20 eV for M1–M6, with M6 exhibiting the lowest E_b value (0.20 eV). All ETMs exhibit outstanding LHE (0.83–0.95), with M5 reaching 0.95. As coulomb energies (E_coul) drop from 5.57 eV (M1) to 1.17 eV (M6), charge transfer distances (D) gradually increase from 0.77 Å (M1) to 16.02 Å (M6), demonstrating an inverse correlation (R² = 0.98). The theoretical V_OC has fill factors of 88.4–89.0% and varies from 1.025 V (M2) to 1.091 V (M6). With an anticipated PCE of 21.5%, the triphenylamine group (M6) offers the greatest V_OC (1.091 V), longest D (16.02 Å), lowest E_b (0.20 eV), and lowest E_coul (1.17 eV). With an anticipated PCE of 20.5%, M5 displays λ_max = 764 nm, LHE = 0.95, and λ_e = 0.36 eV. Excellent planarity (MPP = 0.350–0.445 Å) and balanced properties (expected PCE: 19.8%) are displayed by indole-based M2–M4. As donor tuning maximizes absorption and V_OC, the acceptor-dominated LUMO ensures electron transport. Additionally, the synthetic accessibility score demonstrated the practical viability of the developed chromophores.

Extended charge transfer distances to 16 Å in donor–acceptor thiophene-fused ETMs for perovskite solar cells.

1. Introduction

Solar energy is a great alternative to deal with the environment problems caused by the use of fossil fuels because of its abundance and eco-friendliness. Due to their remarkable potential in solar energy applications, PSCs are considered one of the most promising next-generation technologies.^1–3 They exhibit long photoexcited carrier lifetimes, strong optical absorption over a broad wavelength range, high power conversion efficiencies and can be manufactured via low-cost solution processing.⁴ The PCE of PSCs has exceeded 26.7%. HTMs and ETMs are still required for the enhanced performance of PSCs.⁵ Typically, the conventional configuration of PSCs features a pinch-off structure achieved by sandwiching a perovskite material between HTMs and ETMs. Titanium dioxide (TiO₂) is commonly employed as the ETM due to its excellent performance and cost-effectiveness.⁶ Concurrently, ETMs are pivotal in enabling charge separation and facilitating electron transport within the solar cell and improving the PCE and device stability of PSCs.^7–10

While extensive research has focused on HTMs such as spiro-OMeTAD, the development of efficient, dopant-free ETMs remains critical.¹¹ Most conventional ETMs (TiO₂, SnO₂, and ZnO) require high-temperature processing and suffer from photocatalysis-induced degradation.¹² Organic ETMs offer advantages including low-temperature solution processing, tunable energy levels, and flexible substrate compatibility.^13,14 However, only a limited number of organic ETMs achieve comparable performance to their inorganic counterparts. Thus, considerable research efforts have been dedicated to developing novel ETMs with enhanced electron mobility, suitable energy level alignment, and good stability.^15–18 Recent computational studies have demonstrated that rational molecular engineering is an effective strategy for improving the performance of charge transport materials in perovskite solar cells. DFT and TD-DFT investigations have shown that structural modifications significantly influence frontier molecular orbital alignment,^19,20 optical absorption behavior,²¹ charge transfer characteristics,²² and exciton dissociation efficiency,²³ ultimately affecting intramolecular interaction and photovoltaic performance.^24–26 Moreover, recent studies have emphasized that incorporating strong electron-donating moieties within donor–acceptor architectures can effectively regulate electronic properties, facilitate intramolecular charge transfer, and improve charge carrier mobility.^27,28 Despite these important advances, a systematic understanding of the quantitative relationship between charge transfer distance, coulomb attraction energy, and exciton binding energy in organic electron transport materials remains largely unexplored. Therefore, in the present work, we designed a series of dicyanovinylene–indanone-based ETMs and established direct structure–property correlations governing exciton dissociation and charge separation efficiency through comprehensive DFT and TD-DFT investigations. The working principle and arrangement of ETLs and HTLs in PSCs are given in Fig. 1.

Fig. 1. Cell architecture and operating mechanism of dopant-free PSCs with designed compounds as ETLs and PEDOT:PSS as the hole transport layer.

In this study, we developed a series of organic ETMs based on a rigid, planar 5,10-dihydrothieno[3′,2′:4,5]pyrrolo[2,3-f]thieno[2,3-b]indole core³ functionalized with a strong dicyanovinylene–indanone–dinitroso acceptor. This acceptor unit was selected for its strong electron-withdrawing capability, deep LUMO levels, and ability to promote intermolecular packing. A reference core without the acceptor was used as the baseline. Six derivatives (M1–M6) were designed by varying the substituent at 7-position of the core: 3,5-dimethylphenyl (M1), dihydroindol-2-yl (M2), 3-methyl-dihydroindol-2-yl (M3), 5,6-dimethyl-dihydroindol-2-yl (M4), 3,6-dimethoxyfluoren-9-yl (M5), and triphenylamine (M6). The objective of this research is to uncover the correlation between molecular structures, photovoltaic performance, and photoelectric properties of ETMs, with the aim of offering theoretical insights to optimize the electron transport layer (ETL) and overcome the commercialization challenges faced by PSCs. Additionally, statistical validation using synthetic accessibility analysis was performed to guarantee the robustness and practical viability of the predicted molecules.

2. Computational methods

The optimized ground-state geometries of all molecules (REF and M1–M6) and their respective potential energy minimum were achieved by relaxing them using DFT at the D3-B3LYP level,²⁹ coupled with 6-311+G(d,p)basis set, in gas and solvent phases (ethanol and toluene) employing the polarizable continuum model (PCM). Due to computational efficiency and accuracy for conjugated organic systems, the 6-311+G(d,p) basis set was utilized for all calculations.^21–23 The selection of this method was driven by their demonstrated accuracy in energy calculations. Moreover, researchers employed a similar methodology on thiophene-based systems, yielding satisfactory outcomes, and revealed their adaptability in managing a broad spectrum of parameters. To ensure that the stationary points represent genuine energy minima, vibrational frequency analyses were carried out using the same level of theory.^19–21

To understand and predict carrier injection and transport, it is essential to thoroughly examine the frontier molecular orbital (FMO) configuration of ETMs, with particular emphasis on the charge distribution in HOMO and LUMO. The visualization of FMOs was accomplished using an iso-value of 0.02. Quantum chemical parameters including chemical hardness (η),³⁰ chemical potential (µ₀), ionization potential (IP), electron affinity (EA),³¹ light-harvesting efficiency, and reorganization energy (RE) for holes (λ_h) and electrons (λ_e), in addition to geometric factors like binding energy (E_b), dipole moment (µ), charge density difference (CDD), electrostatic potential (ESP), free energy of solvation (ΔG_solv), and total amount of charge transfer (ΔN_max) were evaluated. The performance parameters of PSC devices, such as open-circuit voltage (V_OC) and fill factor (FF), were determined using the density functional theory method. Additionally, absorption spectra (λ_abs), electronic transition energies, oscillator strengths (f), and the radiative lifetime (τ) of all compounds were obtained by employing TD-DFT. All computations were conducted using the Gaussian 16W software,³² while the GaussView 6.0 program³³ and Multiwfn 3.8.8 were employed for drawing, visualization, and analysis of the results. The obtained results were visualized using the VMD 1.9,³⁴ whereas complete theoretical framework is given in Section S1 of the SI.

3. Results and discussion

3.1. Geometric optimization

Dihedral angles and molecular planarity were assessed to evaluate the balance between stiffness and planarity within the molecules under investigation.^35–37 This balance is very important for figuring out how much π-stacking there is between compounds, which in turn affects how well they can carry charge.

Table 1 summarizes the calculated values of bond lengths, bond angles, and molecular planarity for the studied systems. To thoroughly analyze the planarity of the examined molecules, we evaluated the molecular planarity parameter (MPP).³⁸ For a specific collection of N atoms, the MPP is delineated in eqn (1):

1

where represents the distance of the i atom from the fitting plane characterized by A, B, C, and D parameters.

Table 1. Calculated bond length (Å), bond angles (°) and molecular planarity parameters of all studied systems.

Complexes	Atoms	Bond length	Atoms	Bond angle	MPP
M1	C11–C12	1.383	C11–C12–C44	127.598
	C12–C14	1.771	C12–C44–C39	121.318	0.540
	C12–C44	1.468
M2	C11–C12	1.384	C11–C12–C45	127.309
	C12–C14	1.774	C12–C45–N47	121.948	0.350
	C12–C45	1.446
M3	C11–C12	1.384	C11–C12–C45	127.346
	C12–C14	1.774	C12–C45–N47	122.026	0.445
	C12–C45	1.446
M4	C11–C12	1.385	C11–C12–C45	127.378
	C12–C14	1.775	C12–C45–N47	121.989	0.432
	C12–C45	1.445
M5	C11–C12	1.396	C11–C12–C52	122.086
	C12–C14	1.777	C12–C52–C45	136.553	0.611
	C12–C52	1.440
M6	C11–C12	1.385	C11–C12–C43	127.715
	C12–C14	1.773	C12–C43–C44	122.025	0.686
	C12–C43	1.462

It is clear that the MPP shows how far the structure is from being flat overall. A lower MPP value means that the molecule is less likely to deviate from the plane, which means that its structure is more planar. Furthermore, a bigger MPP value means that the surface is not flat. M2 has the most planar structure because it has the lowest MPP value (0.350 Å) compared to the other molecules. A flat structure helps charge transfer and conjugation occur more easily. The highest MPP value for M6 (0.686 Å), however, shows that it is the least planar compared to the other designed compounds, as shown in Fig. 2. This is because the triphenylamine group makes it more difficult for the molecules to fit together.³⁹

Fig. 2. Designed molecules and their optimized structure with MPP values.

To evaluate the suitability of the selected functional, a comparative analysis was performed using D3-B3LYP (Table 2), CAM-B3LYP and ωB97X-D, summarized in Table S8. The D3-B3LYP functional predicted HOMO energy levels in the range of −5.72 to −5.41 eV and band gaps of 1.35–1.62 eV for the designed ETMs, whereas ωB97X-D yielded significantly larger band gaps ranging from 4.02 to 4.88 eV for most derivatives. For instance, the band gap of M6 increased from 1.35 eV at the D3-B3LYP level to 4.62 eV with ωB97X-D, while M5 exhibited a corresponding increase from 1.38 to 4.77 eV. The D3-B3LYP results are more consistent with the expected electronic characteristics of highly π-conjugated thiophene-fused organic semiconductors and provide energy levels that are more suitable for photovoltaic applications.

Table 2. Calculated energies of H–L and E_gap and H_offset and L_offset (in eV) with respect to perovskites of all studied systems.

Molecules	H (eV)	L (eV)	E gap (eV)	H offset	L offset
REF	−5.04	−1.33	3.72	0.36	2.57
M1	−5.72	−4.10	1.62	−0.32	−0.20
M2	−5.66	−4.13	1.52	−0.26	−0.23
M3	−5.61	−4.13	1.48	−0.21	−0.23
M4	−5.54	−4.11	1.44	−0.14	−0.21
M5	−5.49	−4.11	1.38	−0.09	−0.21
M6	−5.41	−4.07	1.35	−0.01	−0.17
FAPbI3	−5.40	−3.90

3.2. Frontier molecular orbitals

Fig. 3 illustrates the distributions of HOMO and LUMO for all examined molecules. For the under-probe molecules, it is seen that HOMO orbitals are spread out over the thieno–pyrrolo–thieno–indole core and the substituent at the terminal position.

Fig. 3. FMOs and fragment contribution towards the HOMO–LUMO distributions of all studied systems.

LUMO orbitals, however, are mostly found on the dicyanovinylene–indanone–dinitroso acceptor. This spatial separation is very helpful for moving charges and breaking up excitons within the same molecule.^40,41 For electrons to be able to move and be extracted, the ETM's LUMO energy level must be lower than the perovskite's conduction band (CB). For holes to be blocked and recombination to be stopped, the ETM's HOMO energy level must be deep enough. This alignment is necessary for high PSC efficiency.⁴⁰ According to Table 2 and Fig. S1, the LUMO values for M1–M6 range from −4.07 eV (M6) to −4.13 eV (M2–M4). All of these values are much lower than the perovskite CB (−3.90 eV) for FAPbI₃, which gives a good LUMO offset of −0.17 to −0.23 eV. This alignment makes sure that electrons can move easily from the perovskite to the ETL.

The reference core (without the acceptor), however, has a much higher LUMO (−1.33 eV) and a larger band gap (3.72 eV), making it not a good ETL (Fig. 4). The designed molecules have energy gaps that are much smaller, ranging from 1.35 eV (M6) to 1.62 eV (M1). This is good for improving intrinsic conductivity and near-IR absorption that works with the perovskite layer.⁴² The HOMO levels of all the ETLs we designed (−5.72 to −5.41 eV) are lower than the perovskite valence band (−5.40 eV), which means they can effectively block holes. The reference core has a HOMO (−5.04 eV) that is too shallow to block holes effectively.

Fig. 4. HOMO and LUMO and band gap values of investigated molecules, together with the perovskite band levels (in eV).

3.3. Global reactivity parameters

To assess the stability of the kinetic behavior and chemical reactivity of the studied ETMs, several global reactivity descriptors were calculated employing Koopmans' theorem (Table 3). Electronegativity (χ),⁴³ chemical hardness (η), chemical potential (µ₀), and electrophilicity index (ω)⁴⁴ were determined through the application of standard equations.

Table 3. Global reactivity descriptors (in eV) of all studied systems.

Compounds	IP	EA	X	η	µ	ω	σ
Ref	5.04	1.13	3.09	1.96	−3.09	2.43	0.26
M1	5.72	4.10	4.91	0.81	−4.91	14.88	0.62
M2	5.66	4.13	4.90	0.77	−4.90	15.66	0.65
M3	5.61	4.13	4.87	0.74	−4.87	16.02	0.68
M4	5.54	4.11	4.83	0.72	−4.83	16.28	0.70
M5	5.49	4.11	4.80	0.69	−4.80	16.70	0.72
M6	5.41	4.07	4.74	0.67	−4.74	16.77	0.75

All molecules have negative chemical potential (µ₀) values, which means they are stable and don't break down easily.⁴⁵ The designed ETMs have a chemical hardness (η) of 0.67 to 0.81 eV, which is much lower than the reference (1.96 eV), as given in Fig. S2. This means that the molecules are softer and more polarizable, which makes it easier for them to transfer charge. Although the reduced chemical hardness values suggest enhanced charge transfer capability and improved electronic softness, excessively low hardness may increase chemical reactivity. Nevertheless, the hardness values of the designed ETMs remain within a moderate range, indicating a suitable balance between efficient charge transport and acceptable chemical stability. The favorable hydrophobicity and robust conjugated frameworks of these molecules further support their potential structural stability; however, experimental studies are required to evaluate their long-term device durability. The electrophilicity index (ω) rises significantly from 2.43 eV (REF) to 14.88–16.77 eV (M1–M6), validating the remarkably potent electron-accepting nature of the dicyanovinylene–indanone–dinitroso group.

3.4. Density of states

DOS calculations were employed to get easier look at FMOs, and we used their maps to show how FMOs are involved in electronic excitation (Fig. S3). The density of state gives us useful information about different levels of energy.⁴⁶ A higher DOS means a bigger contribution. Table 4 shows the contributions of the fragments to HOMO and LUMO for all the systems. D stands for the donor substituent at the terminal position, linker stands for the thieno–pyrrolo–thieno–indole backbone, and A stands for the dicyanovinylene–indanone–dinitroso acceptor.

Table 4. Fragment contribution for the DOS (in %) of all investigated systems.

Molecules		D	Linker	A
M1	H	11.08	0.74	0.14
	L	0.04	0.01	0.99
M2	H	34.68	0.55	0.10
	L	0.07	0.02	0.98
M3	H	39.12	0.51	0.09
	L	0.07	0.01	0.98
M4	H	41.60	0.50	0.09
	L	0.07	0.01	0.98
M5	H	43.86	0.48	0.08
	L	0.13	0.02	0.98
M6	H	58.85	0.35	0.06
	L	0.06	0.01	0.99

The DOS analysis shows a very interesting pattern: the HOMO is mostly localized on the donor substituent (D), with only a small amount coming from the core. The LUMO, however, is almost completely (≥98%) localized on the acceptor (A) fragment. This almost complete separation of HOMO and LUMO in space is very good for intramolecular charge transfer (ICT) because charges move from the donor/linker regions to the acceptor when they are excited by light.⁴⁷ This attribute boosts the material's charge mobility, leading to increased overall efficiency of PSCs. Among the molecules investigated, M5 and M6 show the highest donor contributions to HOMO (43.86% and 58.85%, respectively), suggesting enhanced ICT character.

3.5. Vertical absorption, light-harvesting efficiency, and radiative lifetimes

The characteristics of ideal ETMs encompass proper electronic energy levels, suitable light-absorbing and emissive properties, and optical transparency in the visible region where the perovskite absorbs strongly. More crucial attributes indicating structural flexibility and deformation from ground to excited states, such as appropriate absorption behavior and larger Stokes shift (Δλ_St) values, serve as indicators of the pore-filling characteristics of the ETL layer.³ The Δλ_St value was calculated using eqn (2):

Δλ_St = λ^max_em − λ^max_abs 2

Table 5 presents the simulated photophysical properties in the gas phase, ethanol, and toluene. For all designed ETMs (M1–M6), the λ_max values range from 553 to 764 nm in the gas phase and extend into the near-IR (up to 888 nm) in ethanol. The perovskite material absorbs strongly in the range of 300–830 nm, with insignificant absorption above 800 nm.

Table 5. Maximum absorption (λ^max_abs in nm), emission (λ^max_em in nm), Stokes shift (Δλ_St in nm), excitation energy (E_ex in eV), oscillator strength (f), light-harvesting efficiency (LHE), radiative lifetime (τ in ns), major transitions, and CI coefficients of investigated molecules in gas, ethanol, toluene and chloroform phase.

Phase	Complex	λ max	λ max	ΔλSt	E ex	f	LHE	τ	Major transition	CI (%)
Gas	REF	336.07	—	—	3.36	0.58	0.74	0.23	H − 1 → L	86
	M1	669.03	847.34	178.31	1.85	0.77	0.83	1.17	H → L + 1	74
	M2	703.74	846.33	142.59	1.76	1.17	0.93	0.78	H → L + 1	96
	M3	716.88	845.08	128.20	1.73	1.16	0.93	0.82	H → L + 1	98
	M4	732.51	848.70	116.19	1.69	1.20	0.94	0.85	H → L + 1	98
	M5	763.64	883.92	120.28	1.62	1.35	0.95	0.82	H → L + 1	99
	M6	553.23	606.34	53.11	2.24	1.03	0.91	1.10	H − 4 → L	86
Ethanol	REF	341.47	—	—	3.63	0.74	0.82	0.15	H − 1 → L	92
	M1	673.09	736.36	63.27	1.84	0.91	0.88	0.49	H → L + 1	89
	M2	810.50	828.24	17.74	1.53	1.18	0.93	0.54	H → L + 1	95
	M3	822.07	840.36	18.29	1.51	1.22	0.94	0.54	H → L + 1	95
	M4	840.08	855.07	14.99	1.48	1.28	0.95	0.54	H → L + 1	96
	M5	853.80	866.13	12.33	1.45	1.47	0.97	0.48	H → L + 1	98
	M6	888.29	890.34	2.05	1.40	0.99	0.90	0.78	H → L + 1	87
Toluene	REF	343.82	—	—	3.61	0.74	0.82	0.16	H − 1 → L	93
	M1	748.74	809.06	60.32	1.66	1.07	0.92	0.51	H→L + 1	93
	M2	781.81	800.80	18.99	1.59	1.44	0.96	0.41	H → L + 1	98
	M3	795.73	813.18	17.45	1.56	1.44	0.96	0.43	H → L + 1	98
	M4	815.33	831.54	16.21	1.52	1.47	0.97	0.44	H → L + 1	99
	M5	842.29	854.05	11.76	1.47	1.63	0.98	0.42	H → L + 1	99
	M6	859.81	862.55	2.74	1.44	1.21	0.94	0.60	H → L + 1	98
Chloroform	REF	342.97	—	—	3.62	0.75	0.82	0.15	H − 1 → L	93
	M1	769.56	836.8	67.2	1.61	0.91	0.88	0.63	H → L + 1	91
	M2	797.94	815.1	17.2	1.55	1.34	0.95	0.46	H → L + 1	97
	M3	811.10	828.2	17.1	1.53	1.36	0.96	0.47	H → L + 1	98
	M4	830.55	845.5	15.0	1.49	1.41	0.96	0.48	H → L + 1	98
	M5	851.48	862.5	11.0	1.46	1.58	0.97	0.45	H → L + 1	99
	M6	878.14	880.1	2.0	1.41	1.17	0.93	0.64	H → L + 1	98

To elucidate the significant bathochromic shift observed for M6, it is important to note that the molecule exhibits pronounced ICT characteristics, resulting in an excited state with higher polarity than the ground state. In the polar ethanol environment, this charge-separated excited state undergoes preferential stabilization, leading to a substantial reduction in the excitation energy gap, and consequently, causing a remarkable red shift in the absorption maximum from 553 nm to 878 and 888 nm in a polar medium. This pronounced solvatochromic behavior indicates the strong sensitivity of M6 toward the surrounding dielectric medium and is consistent with the behavior commonly observed for donor–acceptor systems with significant ICT character.

Our ETMs complement perovskite absorption by absorbing in the near-IR region, making them excellent candidates for tandem or semi-transparent devices.⁴⁸ All designed ETMs show significantly larger Stokes shifts than typical HTMs, signifying high structural deformation between ground and excited states, suggesting molecular flexibility beneficial for film formation. Fig. 5 shows the simulated absorption spectra.

Fig. 5. UV-vis absorption spectra of all designed compounds in gas, toluene and ethanol phases.

We used the oscillator strength (f) in eqn (3) to figure out the light-harvesting efficiency (LHE):

LHE = 1 − 10^−f 3

All of the designed molecules have good LHE efficiency (0.83–0.95) in the gas phase (Fig. 6), and hence, they work very well as materials for making photocurrent when used in inverted or bilayer device architectures. The radiative lifetimes (τ) of M1–M6 are between 0.78 and 1.17 ns, which is longer than the reference value of 0.23 ns. Longer lifetimes are very important for slowing down the charge recombination process. This raises the V_OC value, which makes ETMs in PSCs more efficient.

Fig. 6. Calculated light-harvesting efficiency and radiative lifetime of all systems (M1–M6).

To further evaluate solvent effects, chloroform was additionally included alongside ethanol and toluene. As presented in Table 5, the optical and charge-transfer properties of the designed ETMs exhibit a pronounced dependence on the solvent environment. For instance, M5 shows a significant bathochromic shift from 763.64 nm (gas) to 853.80 nm (ethanol), 842.29 nm (toluene) and 851.48 (chloroform), corresponding to wavelength increases of approximately 12%. Similarly, the excitation energy of M5 decreases from 1.62 eV in the gas phase to 1.45–1.47 eV in solvents, indicating enhanced electronic delocalization in these solvents. Moreover, the light-harvesting efficiency (LHE) increases from 0.95 in the gas phase to 0.97 in ethanol and chloroform and 0.98 in toluene, corresponding to improvements of approximately 2.1% and 3.2%, respectively. The excited-state lifetime (τ) also decreases from 0.82 ns in the gas phase to 0.42–0.48 ns in the solvent phase, reflecting faster charge-transfer dynamics (Fig. S4). These findings demonstrate that solvent polarity and solute–solvent interactions significantly influence the absorption behavior, ICT, and photovoltaic performance of the investigated ETMs, emphasizing the importance of solvent selection when evaluating materials for practical photovoltaic applications.

3.6. Exciton binding energy, quantitative charge transfer analysis, and fragment contributions

Table 6 shows that the exciton binding energy (E_b) values of the designed systems (M1–M6) range from 0.20 eV (M6) to 0.33 eV (M1), following the order: M6 (0.20 eV) < M5 (0.21 eV) < M3 (0.22 eV) < M4 (0.23 eV) < M2 (0.24 eV) < M1 (0.33 eV). This represents a substantial reduction from the reference value of 0.36 eV, with M6 showing the lowest E_b, corresponding to an improvement of approximately 44% relative to REF. Low E_b values indicate how easily electron–hole pairs can break up into independent charge carriers, which increases short-circuit current density and accelerates electron transit.⁴³ The trend in E_b directly correlates with the electron-donating strength of the substituent at the terminal position. M1, bearing a 3,5-dimethylphenyl group, shows the highest E_b (0.33 eV) among designed ETMs because the two methyl groups at the 3- and 5-positions create steric hindrance that twists the phenyl ring relative to the core, limiting conjugation and reducing ICT.

Table 6. Exciton binding energies and reorganization energies of holes and electrons of all systems.

Complexes	E b (eV)	λ e (eV)	λ h (eV)	λ (eff)
REF	0.36	0.15	0.17	0.32
M1	0.33	0.37	0.18	0.55
M2	0.24	0.37	0.19	0.56
M3	0.22	0.37	0.19	0.56
M4	0.23	0.37	0.20	0.57
M5	0.21	0.36	0.20	0.56
M6	0.20	0.39	0.19	0.57

The exciton binding energy, which represents the energy required to dissociate a bound electron–hole pair into free charge carriers, was estimated using the following expression:

E_b = E_g − E_x 4

where E_g is the electronic energy gap determined from the HOMO–LUMO energy difference obtained through DFT calculations, and E_x is the lowest singlet excitation energy calculated using TD-DFT. Since the optical gap can be approximated by the first excitation energy, this approach provides a practical estimate of exciton binding energies in organic semiconducting materials. Similar definitions have been widely employed in previous studies of organic electronic materials.^49,50

In contrast, M2 with an indol-2-yl group shows improved E_b (0.24 eV) due to the electron-rich nature of the indole ring and its better conjugation with the core through the NH group. M3 (3-methyl-indol-2-yl) and M4 (5,6-dimethyl-indol-2-yl) show further reduced E_b values of 0.22 and 0.23 eV, respectively, as the methyl substituents on the indole ring increase electron density and enhance donor strength. M5 (3,6-dimethoxyfluoren-9-yl) exhibits a very low E_b value of 0.21 eV because the two methoxy groups provide strong resonance electron donation through oxygen lone pairs, while the planar fluorenyl core maintains good conjugation (Fig. S5). Significantly, M6 with the triphenylamine group exhibits the lowest E_b of 0.20 eV, as the triphenylamine moiety is the strongest electron donor among all substituents, with the nitrogen lone pair delocalizing across three phenyl rings to create a powerful push–pull system with the acceptor.

To quantitatively assess the intramolecular charge transfer character, we calculated the hole–electron distance (D), exciton size (H), and coulomb attraction energy (E_coul) for the S₀ → S₁ transition. Table 7 reveals that REF and M1 exhibit very small D values of 0.00 and 0.77 Å, respectively, indicating predominantly local excitation character. For M1, the 3,5-dimethylphenyl group's steric hindrance limits conjugation, resulting in minimal charge separation. In contrast, M2–M6 show substantially larger D values ranging from 5.90 Å (M2) to 16.02 Å (M6). The progressive increase in charge transfer distance correlates directly with the increasing electron-donating ability of the substituent. M2 (indol-2-yl) achieves D = 5.90 Å due to the planar indole ring allowing better conjugation.

Table 7. Quantitative charge transfer parameters for S₀ → S₁ transition: hole–electron distance (D), RMS distribution of holes (S_r) and electrons (S_m), exciton size (H), directional charge transfer length (t), coulomb energy (E_coul), hole delocalization index (HDI), and electron delocalization index (EDI).

System	Transition	D (Å)	S r	S m	H (Å)	t (Å)	E coul (eV)	HDI	EDI
Ref	S0 → S1	0.00	0.80	0.52	3.54	−1.07	4.71	7.31	5.74
M1	S0 → S1	0.77	0.62	0.34	2.67	−1.05	5.57	15.55	11.26
M2	S0 → S1	5.90	0.52	0.27	5.86	0.63	2.69	8.64	9.82
M3	S0 → S1	12.70	0.32	0.12	5.16	8.15	1.62	4.69	8.57
M4	S0 → S1	13.87	0.26	0.08	4.83	9.67	1.38	4.87	8.45
M5	S0 → S1	14.37	0.25	0.08	4.83	10.27	1.27	4.68	8.54
M6	S0 → S1	16.02	0.23	0.07	5.05	11.61	1.17	5.29	8.51

M3 (3-methyl-indol-2-yl) and M4 (5,6-dimethyl-indol-2-yl) show increased D values of 12.70 Å and 13.87 Å, respectively, because the methyl groups enhance electron density on the indole ring without introducing significant steric hindrance. M5 (3,6-dimethoxyfluoren-9-yl) achieves D = 14.37 Å, as the methoxy groups provide strong resonance donation and the fluorenyl core maintains planarity. Remarkably, M6 with the triphenylamine group exhibits the longest charge transfer distance of 16.02 Å, as the triphenylamine moiety is the strongest electron donor, creating the most pronounced push–pull effect with the dicyanovinylene–indanone–dinitroso acceptor.

The coulomb attraction energy (E_coul) decreases systematically from 5.57 eV (M1) to 1.17 eV (M6). Fig. 7d demonstrates an inverse exponential correlation between D and E_coul (R² = 0.98), confirming that longer charge transfer distances directly reduce hole–electron binding, consistent with the E_b analysis. Specifically, M1's high E_coul (5.57 eV) reflects its weak donor character and limited ICT, while M6's exceptionally low E_coul (1.17 eV) confirms that the triphenylamine group creates the weakest hole–electron attraction, facilitating exciton dissociation. Exciton size (H) ranges from 2.67 Å (M1) to 5.86 Å (M2), with M2 showing the largest exciton delocalization. The small exciton size of M1 (2.67 Å) indicates tightly bound excitons localized on the core, consistent with its local excitation character. The quantitative relationship of electron excitation analysis is given in Fig. 7a–d.

Fig. 7. Quantitative charge transfer studies in the S₀ → S₁ transition of REF and tailored ETMs (M1–M6): (a) exciton size (H), expressed as the RMSD of the entire exciton; (b) relation between charge transfer distance (D) and directional charge transfer length (t); (c) exponential trendline (R² = 0.98) representing the correlation between D and E_coul (stronger intramolecular charge transfer character and simpler exciton dissociation are indicated by lower E_coul and higher D values); and (d) E_coul between holes and electrons.

M6's greater charge separation ability is confirmed by the fact that it has the longest charge transfer distance (16.02 Å) and the lowest coulomb energy (1.17 eV) of all the derivatives. Fig. 8 presents the transition density matrix (TDM) maps for M1–M6, while Fig. 9 shows the fragment percentage for hole–electron distribution analysis. These visualizations, together with the fragment contribution data in Fig. 9, confirm that holes are predominantly delocalized over the donor units and central core, while electrons are mainly localized on acceptor fragments. For M3–M6, the spatial separation between hole and electron densities is more pronounced, consistent with the increasing donor strength of the substituents from indole to methoxy fluorene to triphenylamine.

Fig. 8. Transition density matrix representation of M1–M6 in the gas phase.

Fig. 9. Fragment contribution of hole and electron distribution pattern for all studied systems.

This spatial separation confirms that charge transfer excitation processes dominate over local excitation, leading to reduced charge loss and enhanced charge mobility. As given in Fig. 9, M1 has the 3,5-dimethylphenyl donor, and the donor contributes 13.97% to hole density and 25.41% to electron density, indicating that this substituent is a relatively weak donor. The linker dominates both hole (85.47%) and electron (73.84%) densities, confirming that M1 exhibits predominantly local excitation within the core with minimal ICT. The acceptor contributes negligibly (0.56% hole and 0.75% electron), consistent with the limited charge separation observed for this derivative. The two methyl groups at the 3- and 5-positions create steric hindrance that twists the donor ring relative to the core, limiting conjugation and electron donation.

For M2 with the indol-2-yl donor, the donor contribution increases significantly to 35.15% for holes and 28.62% for electrons. The linker still dominates both densities (63.28% hole and 70.69% electron), but the increased donor contribution indicates the beginning of ICT character. The electron-rich indole ring with its NH group allows better conjugation with the core, enhancing the donor strength. The acceptor remains minimal (1.58% hole and 0.69% electron).

For M3 with the 3-methyl-indol-2-yl donor, the donor becomes dominant for holes (53.37%) while contributing 31.19% to electrons. The linker shows 43.47% hole density and 68.18% electron density, confirming efficient charge transfer from the donor to the linker.

The methyl group at the 3-position increases electron density on the indole ring without steric hindrance, enhancing the donor strength compared to M2. The acceptor contribution remains small (2.79% hole and 0.63% electron). For M4 with the 5,6-dimethyl-indol-2-yl donor, the donor dominates hole density (51.73%) with 31.30% electron contribution. The linker shows 28.40% hole density and 68.04% electron density, while the acceptor contribution increases substantially to 19.87% for holes, though electron density on the acceptor remains minimal (0.65%).

The two methyl groups at the 5- and 6-positions further enhance donor strength, causing the acceptor to begin participating in hole delocalization. For M5 with the 3,6-dimethoxyfluoren-9-yl donor, the donor dominates holes (53.88%) with 31.40% electron contribution. The linker contributes 42.20% to holes and 67.97% to electrons. The methoxy groups provide strong resonance electron donation through oxygen lone pairs, while the planar fluorenyl core maintains good conjugation. The acceptor contribution is moderate for holes (3.92%) but minimal for electrons (0.62%), confirming effective spatial separation.

For M6 with the triphenylamine donor, the donor contributes 43.49% to holes and 31.35% to electrons. The linker contributes 38.88% to holes and 68.01% to electrons, while the acceptor shows substantial hole contribution (17.63%) but minimal electron contribution (0.64%). The triphenylamine group is the strongest electron donor among all substituents, as the nitrogen lone pair delocalizes across three phenyl rings, creating the most powerful push–pull system. This results in the acceptor participating significantly in hole delocalization while electrons remain primarily on the linker, achieving the best spatial separation of charges.

In summary, as the donor strength increases progressively from M1 through M6, the hole density gradually shifts from the linker to the donor and acceptor fragments, while electron density remains predominantly localized on the linker. The increasing acceptor hole contribution from M1 (0.56%) to M6 (17.63%) demonstrates that stronger donors enable the acceptor to participate in hole delocalization, further enhancing charge separation. The best spatial separation is observed for M6, consistent with its longest charge transfer distance (16.02 Å) and lowest exciton binding energy (0.20 eV).

Hole and electron reorganization energies (λ_h and λ_e) were calculated using eqn (5) and (6):

λ_h = [E₀⁺E₊] + [E₊⁰E₀] 5

λ_e = [E₀⁻E₋] + [E₋⁰E₀] 6

Important information about the charge transport properties of the suggested ETMs is provided by the reorganization energies shown in Table 6 and Fig. S6. The studied molecules have λ_h between 0.18 and 0.20 eV, which are slightly higher than reference 0.17 eV. The electron reorganization energies (λ_e) are much higher than the reference (0.15 eV), ranging from 0.36 to 0.39 eV. Since band transport would be characterized by vanishingly small or zero reorganization energy, the limited reorganization energies reported for the proposed molecules demonstrate that charge transport follows a hopping process instead of band transport.

M5 has the lowest exciton binding energy (0.21 eV) and electron reorganization energy (0.36 eV) among the developed series, suggesting better exciton dissociation and charge transport properties. These ETMs may also display ambipolar transport behavior, which is advantageous for charge balance in perovskite solar cells, based on the very low hole reorganization energies (≤0.20 eV).

Fig. 10 represents the charge density difference between ground and excited states for all studied molecules. Upon excitation, electron density shifts from the donor and core/linker regions to the acceptor fragment. For M1, the shift is minimal due to the weak donor character of the 3,5-dimethylphenyl group. For M2–M4, progressively larger charge density shifts are observed as the indole-based donors become stronger. For M5 and M6, the most pronounced charge density shifts are observed, confirming that the methoxy fluorene and triphenylamine groups create the strongest push–pull systems. The CDD analysis further demonstrates that these ETL compounds exhibit negligible charge dissociation barriers due to the effective spatial separation of excited charges, making them highly suitable for use in perovskite solar cells.⁴⁴

Fig. 10. Visualization of the charge density difference between the ground and excited states of all the studied molecules.

3.7. Solubility, stability, and electrostatic potential

The solubility of ETMs is essential in film fabrication, ensuring ease of processing and cost-effectiveness. ETMs are commonly found in the form of non-crystalline films, and the incorporation of polar functional groups enhances their surface wetting properties. This characteristic proves beneficial in achieving a sleek morphology, ultimately enhancing the electron transport and FF. To address humidity sensitivity issues, the development of hydrophobic ETMs has emerged as a highly effective solution.^51,52

Table 8 summarizes the dipole moments, solvation free energy, and partition coefficients. It should be mentioned that the type of solvent and the specific solute–solvent interactions involved have a significant impact on the link between dipole moment and solubility. Higher dipole moments typically increase solubility through preferential dipole–dipole interactions in extremely polar solvents like ethanol (dielectric constant ε = 24.85), although this trend is not always present in solvents with lower or moderate polarity. For example, chloroform (ε = 4.81) and chlorobenzene (ε = 5.62), which are frequently employed in organic semiconductor manufacturing, are moderately polar rather than nonpolar, while toluene (ε = 2.38) is a low-polarity solvent.

Table 8. Dipole moment in the gas phase (µ_g) and in ethanol solvent (µ_s), solvation free energy (ΔG_solv), and partition coefficient (log P) of investigated molecules.

Molecules	µ g (D)	µ s (D)	Δµ (D)	ΔGsolv (kcal mol−1)	log P
REF	2.45	3.12	0.67	−12.30	3.85
M1	4.82	6.94	2.12	−18.20	4.65
M2	5.63	8.41	2.78	−19.45	4.92
M3	5.41	8.12	2.71	−19.10	4.88
M4	5.85	8.93	3.08	−19.80	5.01
M5	6.21	9.54	3.33	−20.15	5.18
M6	7.03	10.87	3.84	−21.05	5.42

Instead of relying solely on the dipole moment, solubility in such solvents is controlled by a complicated interplay of intermolecular forces, such as dispersion interactions, hydrogen bonding, and particular solute–solvent interactions. Therefore, rather than being treated as a universal predictor of improved solubility across all organic solvents, dipole moment should be regarded as one of several contributing factors influencing solubility, and its effect must be evaluated in the context of the solvent's polarity and the solute's molecular structure. The solvent-phase dipole moments (µ_s) are greater than the ones calculated in the gas phase (µ_g) for M1–M6. This increase in solvent-based µ_s corresponds to improved polarizability and enhanced intermolecular electrostatic interactions. In the solution-based film formation process, electrostatic interactions organize molecular self-assembly and favored orientation. Hence, they lead to better molecular ordering and uniform film morphology. These properly ordered structures with lower energy disorder accelerate charge transport and reduce electron–hole recombination. Therefore, the enhanced µ_s trend is associated with the formation of densely packed, properly ordered thin films, to boost the overall PV performance of PSCs.

The calculated ΔG_solv values for M1–M6 are in the appropriate range, indicating that the D–A groups promote better solubility of the molecule. The partition coefficients (log P) indicate good hydrophobic characteristics, affirming superior hydrophobicity and reduced surface pinholes in comparison to many studied materials.

Electrostatic potential maps (Fig. 11) provide insights into a molecule's polarity and reactivity. The negative zone, represented by red color, is mainly concentrated around the oxygen and nitrogen atoms present in the acceptor and bridge groups, suggesting that these regions are favorable for electron accepting. The positive zone (blue color) is mainly distributed on the donor substituents and on hydrogen atoms.^53,54 ESP analysis reveals the remarkable electron density distribution in the newly proposed molecules as it traverses from the donor through the core to the acceptor.

Fig. 11. 3D ESP map visualization of all the designed molecules.

3.8. Photovoltaic parameters

The open-circuit voltage, fill factor, and theoretical power conversion efficiency were estimated using standard relations, and are shown in Table 9. For ETLs, V_OC is influenced by the alignment between the ETL LUMO and the perovskite CB.

Table 9. Calculated fill factor and its percentage and open-circuit voltages of all molecules.

Compounds	V OC (V)	Normalized VOC	FF	% FF
REF	3.830	148.158	0.960	95.975
M1	1.060	41.015	0.887	88.739
M2	1.025	39.668	0.884	88.447
M3	1.034	40.015	0.885	88.524
M4	1.055	40.805	0.887	88.694
M5	1.051	40.647	0.887	88.661
M6	1.091	42.194	0.890	88.982

The designed ETMs exhibit theoretical V_OC values around 1.0–1.1 V and FF values around 88–89%, which are highly promising for practical applications. As given in Table 9, REF exhibits an anomalously high V_OC of 3.83 V, attributed to its large E_gap. The LUMO of the REF lies at −1.33 eV with a larger E_gap of 3.72 eV, not suitable as the ETL. The designed molecules have E_gap much smaller, ranging from 1.35 eV for M6 to 1.62 eV for M1. However, such a high V_OC for REF does not correspond to realistic device performance, which comes at the expense of poor energy-level alignment and lower current density. The LUMO offsets of our designed M1–M6 are in the range of −0.17 to −0.23 eV, making them suitable for the perovskite layer. These favorable offsets lead to efficient electron injection as well as CT, while decreasing interfacial energy losses. Therefore, our designed molecules are more balanced and provide a practical approach to boost the PV performance through improving charge extraction and minimizing recombination losses. The PCE of solar cells is influenced directly by J_sc, fill factor, and V_oc, while being inversely linked to the incoming radiation impacting the cell surfaces.¹⁹ The relationship is defined as follows:

7

where J_SC denotes the short-circuit current density, V_OC is the open-circuit voltage, FF is the fill factor, and P_in represents the incident solar power density under standard illumination conditions (100 mW cm⁻²).

V _oc of the solar cell was determined using the difference in energy between the acceptor LUMO and donor HOMO, normalized to the excited-state binding energy.⁵⁵ The calculation was done using the following equation:

8

where E^A_LUMO is the energy of the lowest unoccupied molecular orbital (LUMO) of the acceptor material, E^D_HOMO represents the energy of the highest occupied molecular orbital (HOMO) of the donor material, e is the elementary charge, and 0.3 V is an empirical factor accounting for energy losses during charge separation and charge transport processes in the photovoltaic device.

FF is defined and modeled by the partitioning production of realizable power to the product of V_oc and J_SC. It can be computed theoretically using the following formula:

9

where is the normalized open-circuit voltage, e is the elementary charge, V_OC is the open-circuit voltage, k_B is the Boltzmann constant (1.381 × 10⁻²³ J K⁻¹), and T is the absolute temperature, which was taken as 300 K.

Additionally, the J_sc can be expressed as follows:

10

where LHE(λ) is the light-harvesting efficiency at wavelength λ, ∅_inject is the electron injection efficiency, η_collect is the charge collection efficiency, and dλ represents the differential wavelength interval. The light-harvesting efficiency was calculated as LHE = 1 – 10^−f, where f is the oscillator strength obtained from TD-DFT calculations. In accordance with previous theoretical studies, ∅_inject and η_collect were assumed to be unity.

3.9. Substituent effect on electro-optical properties

The impact of substituent modification on the electro-optical characteristics of M1–M6 is summarized in Table 10. The LUMO energy level (about −4.10 eV) is dominated by the dicyanovinylene–indanone–dinitroso acceptor, which guarantees uniform electron injection in all derivatives.

Table 10. Summary of substituent effects on the electro-optical properties of M1–M6.

Property	M1	M2	M3	M4	M5	M6
Substituent	3,5-Dimethylphenyl	Indol-2-yl	3-Methyl-indol-2-yl	5,6-Dimethyl-indol-2-yl	3,6-Dimethoxy fluoren-9-yl	Triphenylamine
MPP (Å)	0.540	0.350	0.445	0.432	0.611	0.686
HOMO (eV)	−5.72	−5.66	−5.61	−5.54	−5.49	−5.41
LUMO (eV)	−4.10	−4.13	−4.13	−4.11	−4.11	−4.07
E gap (eV)	1.62	1.52	1.48	1.44	1.38	1.35
λ max (nm) (gas phase)	669	704	717	733	764	553
LHE	0.83	0.93	0.93	0.94	0.95	0.91
τ (ns)	1.17	0.78	0.82	0.85	0.82	1.10
λ e (eV)	0.37	0.37	0.37	0.37	0.36	0.39
K h (×1015 s−1)	2.25	2.48	2.50	2.73	2.74	2.65
E b (eV)	0.33	0.24	0.22	0.23	0.21	0.20
V OC (V)	1.060	1.025	1.034	1.055	1.051	1.091
FF (%)	88.74	88.45	88.52	88.69	88.66	88.98
Expected PCE (%)	19.5	18.5	19	19.8	20.5	21.5

The HOMO level, on the other hand, fluctuates considerably with the donor strength in the following order: M1 (−5.72 eV) < M2 (−5.66 eV) < M3 (−5.61 eV) < M4 (−5.54 eV) < M5 (−5.49 eV) < M6 (−5.41 eV). As a result, intrinsic conductivity is increased as the band gap shrinks from 1.62 eV (M1) to 1.35 eV (M6).

As shown in Table 10, M2 is more planar with a lower E_b value of 0.24, hence it shows a lower expected PCE of 18.5% than M1. The power conversion efficiency always depends upon the interconnected multiple factors including V_OC. The anomalous behavior of M2 corresponds to trade-offs between multiple parameters such as LUMO at −4.13 eV as compared to M1's LUMO at 4.10 and reduced V_OC of M2 at 1.025 V, whereas V_OC of M1 at 1.060 V. These parameters offset the morphological advantages of MPP and the exciton dissociation capability of M2. The most promising option for high-voltage PSCs is the triphenylamine-substituted M6, which has the greatest V_OC (1.091 V), lowest exciton binding energy (0.20 eV), and outstanding FF (88.98%). For near-IR absorption and thick-film devices, M5 (fluorenyl-methoxy) exhibits the longest λ_max (764 nm), highest LHE (0.95), and lowest electron reorganization energy (0.36 eV). The enhanced LHE of M5 originates from the synergistic effect of the strong electron-donating methoxy groups and the rigid fluorene backbone, which together improve π-electron delocalization and facilitate efficient intramolecular charge transfer. Consequently, M5 exhibits the highest oscillator strength (f = 1.35 in ethanol and f = 158 in chloroform), leading to superior light-harvesting capability.

Methyl substitution (M3 and M4) enhances the performance of indole-based derivatives M2–M4, which exhibit higher molecular planarity (MPP = 0.350–0.445 Å), encouraging π-stacking and charge transport. A reference with intermediate performance is the 3,5-dimethylphenyl derivative M1. Overall, donor adjustment enables the optimization of absorption, solubility, and open-circuit voltage for PSC topologies, whereas acceptor-dominated LUMO guarantees dependable electron transport.

3.10. Synthetic accessibility analysis

Synthetic accessibility analysis was carried out to evaluate how feasible it would be to prepare the designed electron transport materials under normal laboratory conditions. The SA score serves as a helpful computational guide that estimates the ease of synthesis based on several factors, including overall molecular complexity, contributions from different molecular fragments, and specific structural features such as ring systems, stereochemistry, and the presence of unusual functional groups.^43,44 SA scores are reported on a scale from 1 to 10. Lower values, typically between 1 and 3, point toward molecules that can be made relatively easily using established synthetic routes. Higher scores, however, indicate greater difficulty in synthesis, often due to complicated structures or the need for many reaction steps. For the reference compound and the six designed ETMs, the calculated SA scores fall within a range of approximately 2.45 to 3.25. These values suggest that all seven molecules may possess favorable synthetic accessibility with low to moderate structural complexity, although experimental validation is required to confirm their practical synthetic feasibility. The reference core without the acceptor attachment shows the lowest score, meaning that it is the most straightforward to prepare among the series. Among the designed derivatives, M1 and M2 display the most accessible synthetic routes, while M5 and M6 show slightly higher scores due to the presence of the bulkier fluorenyl and triphenylamine substituents, which introduce additional aromatic rings and require more advanced coupling steps.

The increasing order of synthetic accessibility scores is as follows: REF (2.45) < M1 (2.68) < M2 (2.72) < M3 (2.81) < M4 (2.85) < M5 (3.12) < M6 (3.24). The slightly higher scores for M5 and M6 reflect the added complexity of incorporating the 3,6-dimethoxyfluoren-9-yl and triphenylamine groups, both of which may require palladium-catalyzed cross-coupling reactions such as Suzuki or Buchwald–Hartwig coupling. Nevertheless, these synthetic methodologies are well documented in the literature for structurally related compounds. However, the actual synthesis of the proposed molecules may require further optimization and experimental verification.

Overall, the synthetic accessibility analysis provides preliminary computational evidence supporting the potential synthetic feasibility of the designed ETMs. However, these predictions should be interpreted with caution, as actual synthetic accessibility depends on factors beyond the scope of the SA model, including the reaction yields, purification challenges, and experimental optimization. Therefore, experimental synthesis studies are required to validate the practical feasibility of these proposed molecules.

4. Conclusion

In this work, six novel organic compounds with a thiophene-fused core structure were created as electron transport materials for perovskite solar cells. Donor–acceptor type systems M1 through M6 were designed by combining a strong dicyanovinylene–indanone–dinitroso acceptor with the core framework, 5,10-dihydrothieno[3′,2′:4,5]pyrrolo[2,3-f]thieno[2,3-b]indole. Our DFT and TD-DFT studies yielded several important conclusions. When compared to the reference, all six derivatives exhibit better charge transfer between molecular segments. Better charge mobility and overall device performance are indicated by the computed ionization potentials and electron affinities, as well as the distinct separation of frontier molecular orbitals and the concentration of LUMO density on the acceptor part. Throughout the series, more advantageous characteristics were noted. These materials have the potential to be useful electron transport layers due to their low reorganization energies, long radiative decay times, elevated light-harvesting efficiency, and strong solubility in commonly used organic solvents. Exciton binding energies between 0.33 and 0.20 eV show that electron–hole couples can split rather easily, which should facilitate electron mobility and possibly increase the short-circuit current. M1 through M6 absorb light that supports the absorption range of conventional perovskite layers since their absorption spectra span the visible and near-infrared regions. All proposed molecules exhibit strong intramolecular charge transfer, however M5 and M6 have the longest conjugated paths and the strongest acceptor impact. M4 and M5 are notable for their radiative lifetimes and M5 and M6 seem to be the most promising of the series. Their spatial distribution of electrons and holes exhibits little overlap, which facilitates effective charge separation upon activation. When combined, the findings offer solid theoretical justification for experimental synthesis. Therefore, we advise future research to prepare and test these high-performing electron transport materials in actual perovskite solar cell devices.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

All data generated or analysed during this study are included in the supplementary information (SI) and are available from the corresponding author upon reasonable request. Supplementary information is available. See DOI: https://doi.org/10.1039/d6ra07055h.