Rational design of new small derivatives of 2,2'-Bithiophene as hole transport material for perovskite solar cells

doi:10.21203/rs.3.rs-3849270/v1

Recently, photovoltaic research has focused on solar cells that use perovskite materials (PSCs). In this class of solar cells, hole-transport materials (HTMs) play a key role in improving the overall performance of PSCs. Due to the ultra-fast charge mobility of HTMs, which significantly enhances both optoelectronic and photovoltaic characteristics. Using Density Functional Theory (DFT) and Time Dependent DFT (TD-DFT) methods, this inquiry theoretically examines seven novel HTMs namely DFBT1, DFBT2, DFBT3, DFBT4, DFBT5, DFBT6, and DFBT7 based on the 2,2’bithiophene core for future use as HTMs for PSCs. The model molecule has been modified through substituting the end groups situated on the diphenylamine moieties with a tow acceptor bridged by thiophene, this modification was performed to test the acceptor’s impact on the electronic, photophysical, and photovoltaic properties of the newly created molecules. DFBT1 – DFBT7 displayed a lower band gap (1.49 eV to 2.69 eV) than the model molecule (3.63 eV). Additionally, the newly engineered molecules presented a greater λ_max ranging from 393.07 nm to 541.02 nm in dimethylformamide solvent, as compared to the model molecule (380.61 nm). The PCEs of all newly designed molecules (22.42–29.21%) were high compared with the reference molecule (19.62%). Thus, this study showed that all seven newly small molecules were excellent candidates for a novel PSC.

hole-transport materials

2

2’bithiophene

DFT

TD-DFT

charge mobility

Most of the energy consumed globally comes from exhaustible sources, such as fossil fuels or natural gas, and the emissions resulting from their combustion are a major environmental problem. To reduce the impact of fossil fuels on the environment, growing interest has been placed on renewable energies, particularly for electricity generation. [1, 2]

Solar energy is one of the most ecological and abundant sources of renewable energy available to mankind. Through photovoltaic technologies, solar energy can be converted into electrical energy [3–5]. Three main generations of photovoltaic technology (PVT) exist, and the absorber materials used in these solar cells can be inorganic, organic, or hybrid semiconductors. The first generation includes cells based on monocrystalline silicon or germanium, while the second generation includes thin-film photovoltaic systems. The third generation PV technology, which is currently making even greater progress, includes dye-sensitized solar cells (DSSCs), organic photovoltaic cells (OPVs), quantum dots and perovskites [6–9].

In recent years, research has focused on developing the efficiency of solar cells based on perovskite materials (PSCs). Over the last 15 years, this efficiency has risen 2.2–25.2%, suggesting interesting prospects for PSC’s commercialization [10–14]. Particularly, perovskite materials composed of metal halide have great potential in terms of prolonged carrier lifetimes, excellent charge mobility, high extinction coefficients, and long carrier diffusion distances. PSCs comprise three main layers: the perovskite material layer, which absorbs light; the hole transport layer (HTL); and the electron transport layer (ETL). Depending on how these layers are organized in a solar cell, there are two main PSC architectures: n-i-p and p-i-n. The HTLs play a significant role, especially in the p-i-n architecture, due to their effect on charge extraction, transportation, and on perovskite crystallization [15–17]. The hole transport materials (HTMs) composing the hole transport layer can be inorganic metal oxides, polymers, or organic small molecules [18]. Nowadays, Spiro-OMeTAD is one of a commonly used HTM in PSCs, due to its molecular properties and PCE of around 23. % [19]. Low-cost HTMs with efficient photovoltaic performance must be designed and synthesized for PSCs, Numerous efforts has been made to remedy the shortcomings of Spiro-OMeTAD [20–27]. Yi Kai Wang and al presented a new strategy for PSCs by synthesizing two new bithiophyne-based HTMs: BT-MTP and DFBT-MTP. Of these two HTMs, DFBT-MTP showed the best performance, with a PCE of 20.15%, a short-circuit current (Jsc) of 23.01, an open-circuit voltage (Voc) of 1.10 V, and fill factors (FF) of 0.797 [28].

Motivated by the encouraging results obtained by Yi Kai Wang et al. and to gain a deeper understanding of the influence of modification of the acceptor moiety on the physiochemical properties of HTMs, we have used in this work the previously manufactured compound DFBT-MTP as reference molecule (R) to design seven HTMs (DFBT1 – DFBT7). The reference molecule comprised two diphenylamine as donor fragments (donor 1 and donor 2) and 2,2’bithiophene as core fragments, DFBT1 – DFBT7 molecules were designated into donor 1, core, donor 2, thiophane as bridge, and acceptor moieties. In all the designed molecules, the methanethiol group of donor 2 in the reference molecule was replaced with seven acceptor moieties connected by thiophene namely DFBT1(2-ethylidenemalononitrile), DFBT2 ((z)-2-(2-ethylidene-3-oxo-2,3-dihydro-1H-inden-1-ylidene)malononitrile), DFBT3 (2-(3-methyl-5-methylene-4-oxothiazolidin-2-ylidene) malononitrile), DFBT4 ((z)-5-ethylidene-3-methyl-2-thioxothiazolidin-4-one), DFBT5 ((3S,4R,Z)-5-ethylidene-1,4-dimethyl-2,6-dioxopiperidine-3-carbonitrile), DFBT6 ((Z)-1-(dicyanomethylene)-2-ethylidene-3-oxo-2,3-dihydro-1H-indene-5,6-dicarbonitrile), and DFBT7 (2-(but-2-yn-1-ylidene)malononitrile) as shown in Fig. 1.

Figure 1

In this study, all the calculations were executed by using Gaussian 09 software package [29] under density functional theory (DFT), and results were visualised with GaussView 6.0 interface [30]. The ground state geometry of DFBT reference was obtained by employing three hybrid functionals B3LYP [31], PBE1PBE [32] and MPW1PW91[33] with a 6-31G (d p) and 6-311G (d p) basis set. By comparing the results obtained with those found experimentally [28], which shown that MPW1PW91 with 6-31G (d p) is more appropriate to describe the geometry and the electronic properties of designed HTMs. furthermore, the frequency has been made to confirm that the optimized geometry of the studied molecules has the minimum amount of energy.

The molar absorption coefficient for the reference (R) compound in dimethylformamide solvent was determined through TD-DFT calculations employing four distinct hybrid density functionals, B3LYP, MPW1PW91, CAM-B3LYP [34], WB97XD [35] with 6-31G (d p) basis set, as shown in Table 1. According to these results, we found the CAM-B3LYP with the small absolute error (19,39 nm) compared to other functionals (B3LYP 42,82 nm; MPW1PW91 26,28 nm; CAM-B3LYP 19,39; WB97XD 25,0 nm) is the Favorite to calculate the optical properties for all HTMs candidates. The impact of the solvent has been taken into account through the utilization of the IEFPCM approach [36], a model extensively applied in various studies for assessing the optical properties of analogous molecules. [37, 38]. Furthermore, the electronic density of states (DOS) was pictured via GaussSum package [39]. Moreover, Multiwfn 3.8 software [40] has been used to visualise TDM process and electron-hole reorganisation energies of all proposed molecules

Table 1

Comparative analysis of the functional in TD-DFT prediction of the absolute error (nm) for the reference compound (R) in dimethylformamide solvent.
Fonctionnels	B3LYP	MPW1PW91	CM-B3LYP	WB97XD
Absolute error (nm)	42.82	26.28	19.39	25.9

Table 1

3.1. Geometric optimization, bond length (d) and dihedral angle (θ)

The optimized structures of the reference (R) and newly designed molecules (DFBT1 - DFBT7) using DFT/ MPW1MP91/ 6–31 G (d,p) are shown in Fig. 2. To understand the effects of the different fragments, we calculated the bond lengths (d) and dihedral angles of the newly reported molecules. The results are presented in Table 2 and illustrated schematically in Fig. 3. θ₁ and d₁ represent the dihedral angle and bond length, respectively, between the donor and thiophene bridge, while θ₂ and d₂ denote the dihedral angle and bond length between the thiophene bridge and acceptor. As shown in Table 1, the values of bond length d₁ and d₂ for all the newly designed molecules ranged from 1.453–1.458 and 1.390–1.429 Å, respectively. which correspond to the lengths of C– C and C = C bonds, respectively. This shows that the newly designed molecules have good π-conjugation. According to the findings, the dihedral angel θ₁ range from − 21.02° to -24.98°, so the obtained values of θ₂ are between 0.24° and 2.78° for DFBT1, DFBT2, DFBT3, DFBT4, and DFBT6 while DFBT5 molecule has 5.87° and 12.88° in DFBT7. The low θ₂ value indicating that the spacer-acceptor unit of all newly designed molecules has a coplanar structure.

Table 2

Calculated bond length and dihedral angle between the fragments of optimized designed molecules (Dfbt1 – Dfbt7).
Molecules	d₁(Å)	d₂(Å)	θ₁(°)	θ₂(°)
DFBT1	1.456	1.424	-24.983	0.839
DFBT2	1.455	1.420	-22.433	2.780
DFBT3	1.456	1.427	-23.192	1.212
DFBT4	1.457	1.429	-24.980	0.243
DFBT5	1.458	1.439	-24.601	12.888
DFBT6	1.453	1.414	-21.027	1.175
DFBT7	1.457	1.390	-24.874	5.872

Table 2

Figure 2

Figure 3

3.2. Frontier molecular orbitals

The energy levels of E_HOMO (Highest-occupied molecular orbital) and E_LUMO (Lowest-unoccupied molecular orbital) in the molecular systems of HTMs play are essential for establishing the charge transport efficiency (CTE) as well as the optical, electronic and absorption properties of the molecules [41]. The distribution patterns of frontier molecular orbitals (FMOs) for both the reference (R) and newly designed molecules (DFBT1 - DFBT7) at the selected DFT/MPW1MP91/6-31G(d,p) level of theory are pictured in Fig. 5. Calculated values for HOMO, LUMO, and Egap are summarized in Table 3. The electronic distribution of these FMOs is correlated with intramolecular charge transfer (ICT). Figure 6 reveals that in the reference molecules (R), the HOMO density is spread over diphenylamine, while LUMO density is localized at the bithiophene with 80% based on the core. Conversely, in DFBT1-DFBT7, the density distribution of HOMOs is primarily localized on the diphenylamine (donor1) and the bithiophene-based core, ranging from 86–92%. Additionally, LUMOs' density is concentrated on the π-bridge and end-capped acceptor fragment, ranging from 85–92%.

The HOMO energies of the reference (R) and DFBT1 - DFBT7 are − 4.969, -5.227, -5.160,

-5.213, -5.093, -5.093, -5.371 and − 5.214 eV, while LUMO energies are − 1.316, -3.014, -3.193, -3.044, -2.730, -2.399, -3.873 and − 3.183 eV. The HOMO energy values of all the newly designed molecules are consistently more negative than those of the reference molecule (R). and lowed negative LUMO energies values than the model molecule. It is important to note that the HOMO level of studied molecules is greater than the valance band of perovskite (MAPbI3: -5.43 eV [42]) and the LUMO level are higher than the conduction band of MAPbI3 (3.93 eV), which ensures the migration of holes to the hole transport layer (HTL) and electrons to the electron transport layer (ETL). The heightened HOMO energy levels of DFBT1 - DFBT7 molecules contribute to the improvement of hole mobility, short-circuit current, fill factor, and power conversion efficiency in PSCs.

Table 2 presents the band gap energies (E_LUMO − E_HOMO) of the examined hole transport materials (HTMs), including the reference molecule (R) and DFBT1 - DFBT7, which are 3.653; 2.213; 1.966; 2.169; 2.362; 2.694; 1.497; and 2.030 eV, respectively. The comparison of the E_gapvalues for these molecules (R, DFBT1 - DFBT7) establishes the order as DFBT6 < DFBT2 < DFBT7 < DFBT3 < DFBT1 < DFBT4 < DFBT5 < DFBTR. These findings affirm that the newly designed molecules exhibit excellent hole transport material properties.

Table 3

Calculated (EHOMO, ELUMO) energy levels, and energy band gap (Eg).
Molecules	E_HOMO(ev)	E_LUMO(ev)	E_gap
R	-4.969	-1.316	3.653
DFBT1	-5.227	-3.014	2.213
DFBT2	-5.160	-3.193	1.966
DFBT3	-5.213	-3.044	2.169
DFBT4	-5.093	-2.730	2.362
DFBT5	-5.093	-2.399	2.694
DFBT6	-5.371	-3.873	1.497
DFBT7	-5.214	-3.183	2.030

Table 3

Figure 4

Figure 5 and Fig. 5 continued

3.3. Photophysical properties

The absorption and capture of light play pivotal roles in influencing photocurrent [43]. Therefore, in order to study the electronic transitions for (DFBT1 - DFBT7), the quantum calculation was performed using TD-DFT/CAMB3LYP/6-31G (d, p) level. The UV-visible spectra of the studied HTMs in gaseous phase and dimethylformamide solvent are shown in Fig. 6 respectively. The calculated absorption wavelengths (λ_max), oscillator strengths (ƒ) and excitation energies (E_x) in gaseous phase and solvent (dimethylformamide) are grouped in Tables 4 and 5 respectively. The absorption profile illustrates that all the newly reported molecules have strong absorption in the visible region (350–700) that can be assigned to intramolecular charge transfer between the donor, π-bridge and acceptor moieties. On the other hand, R and DFBT1 - DFBT7 have maximum absorption (λ_max) at 369.43 ;421.76; 473.98; 446.80; 433.54; 388.41; 517.39 and 436.51nm in the gaseous phase while 380.61; 441.12; 498.57; 457.49; 449.98; 393.07 ;541.02 and 460.55 nm in the dimethylformamide solvent. The order of maximum absorption sequences for the studied molecules in both gaseous and dimethylformamide solvent is as follows: DFBT6 > DFBT2 > DFBT7 > DFBT3 > DFBT4 > DFBT1 > DFBT5 > DFBTR. It is worth to note that DFBT6 compound is accompanied by a higher λ_max value due to the presence of -CN moiety. All newly designed HTMs exhibited higher maximum absorption due to the presence of strong electron-attracting groups compared to the model molecule. Additionally, the λmax value in dimethylformamide solvent strongly correlates with the band gap.

The first vertical excitation energies of studies molecules (R and DFBT1 - DFBT7) are classified in decreasing order DFBT6 (2.3964) < DFBT2 (2.6158) < DFBT3 (2.7750) < DFBT7 (2.8404) < DFBT4 (2.8598) < DFBT1 (2.9397) < DFBT5 (3.1921) < R (3.3561) for gaseous state will DFBT6 (2.2917) < DFBT2 (2.4868) < DFBT7 (2.6921) < DFBT3 (2.7101) < DFBT4 (2.7553) < DFBT1 (2.8107) < DFBT5 (3.1543) < R (3.2575) for dimethylformamide solvent. All the newly designed molecules exhibit lower excitation energy compared to the model molecule. Additionally, all studied molecules demonstrate higher excitation energies in the gaseous state than in the solvent.

Table 4

The maximum absorption wavelength (λmax), oscillator strength (f), excitation energy (Ex) and configuration interaction(%) in gaseous phase.
Molecules	λ_max (nm)	ƒ	E_X (ev)	Configuration (%)
R	369.43	1.1897	3.3561	H L 67
DFBT1	421.76	1.2252	2.9397	H L 43
DFBT2	473.98	1.6029	2.6158	H L 36
DFBT3	446.80	2.2995	2.7750	H L 34
DFBT4	433.54	2.2027	2.8598	H L 35
DFBT5	388.41	1.7206	3.1921	H L 37
DFBT6	517.39	1.4598	2.3964	H L 41
DFBT7	436.51	1.8272	2.8404	H L 39

Table 5: The maximum absorption wavelength (λmax), oscillator strength (f), excitation energy (Ex) and configuration interaction(%) in dimethylformamide solvent.

Table 4

Table 5

Figure 6

3.4. Quantum chemical parameter.

To evaluate the chemical reactivity and stability of the investigated molecules, including both the reference molecule (R) and DFBT1 - DFBT7, we have determined several chemical parameters, such as:

$$Chemical potential \left(\mu \right)= \frac{\left({E}_{HOMO}+ {E}_{LUMO}\right)}{2}$$

1

-

$$Chemical hardness \left(ƞ\right)= \frac{\left({E}_{LUMO}+ {E}_{HOMO}\right)}{2}$$

2

-

$$Chemical softness \left(S\right)=\frac{1}{ƞ}$$

3

-

$$Electronegativity \left({\chi }\right)= -\frac{\left({E}_{HOMO}+ {E}_{LUMO}\right)}{2}$$

4

-

$$Electrophilicity index \left({\omega }\right)=\frac{{\left({\chi }\right)}^{2}}{2\left(ƞ\right)}$$

5

-

$$Total amount of charge transfer {(\varDelta \text{N}}_{\text{m}\text{a}\text{x}})=-\frac{\mu }{ƞ}$$

6

-

The quantum chemical parameter values for the investigated molecules are presented in Table 6. The calculation of chemical potential (µ) was performed using Eq. 1 [43]. Molecules with a more negative chemical potential than the reference model suggest increased reactivity and stability, making them less prone to decomposition. The examined HTMs exhibit a higher chemical potential (µ) compared to PC61PM (-4.90 eV [44]), indicating an enhanced capacity for electron donation.

chemical hardness (ƞ) and softness (S) values have been determined using Eqs. 2 and 3 respectively [43]. Among R and DFBT5, all molecules exhibit the lowest hardness and highest softness values, demonstrating their soft nature with the lowest band gaps and highest chemical reactivity.

Electronegativity (χ) and electrophilicity index (ω) were determined using equations 4 and 5, respectively [43]. These parameters are typically interconnected and provide a quantitative description of a molecule's electron-accepting nature [45]. All the molecules under investigation exhibit lower electronegativity (χ) and electrophilicity index (ω) values than PC61BM (χ = 4.90 eV and ω = 10.00 eV [44]). This suggests their reduced ability to attract electrons from PC61BM, positioning them as electron donors.

The total charge transfer (∆Nmax), representing the molecules' transport capability, was computed using Eq. 6 [46]. As depicted in Table 6, all compounds demonstrate a greater charge transfer capacity than the reference (R). Consequently, it is anticipated that all examined hole-transporting materials (HTMs) will exhibit superior photovoltaic performance.

Table 6: Calculated quantum chemical parameter.

Molecules	μ	ƞ (ev)	S(ev)	χ	ω	∆N_max
R	-3.142	1.82	0.54	3.142	2.713	1.726
DFBT1	-4.120	1.10	0.90	4.120	7.719	3.746
DFBT2	-4.176	0.98	1.02	4.176	8.901	4.262
DFBT3	-4.128	1.08	0.92	4.128	7.892	3.823
DFBT4	-3.912	1.18	0.84	3.912	6.485	3.315
DFBT5	-3.746	1.34	0.74	3.746	5.237	2.795
DFBT6	-4.622	0.74	1.35	4.622	14.439	6.246
DFBT7	-4.198	1.01	0.99	4.198	8.727	4.157

Table 6

3.5. Dipole moment

The solubility of HTMs in an organic solvent correlate directly with their dipole moment, with a larger dipole moment indicating higher solubility [47–48]. The dipole moment (µ) of the stuadied molecules was theoretically assessed using the chosen "CAM-B3LYP/6-311G (d,p)" level of theory in the gaseous state (µg) and in dimethylformamide solvent (µe). The outcomes are succinctly presented in Table 7 and visually depicted in Fig. 7. The dipole moment in gaseous state is 0.000424; 14.434749; 14.199408; 16.917832; 10.178780;11.694892; 20.761649; and 9.534254 wile 0.002229, 17.376093, 16.917041; 19.406650;12.393430; 12.836779; 24.373151; and 10.292502 in the solvent. All newly reported molecule showed a higher dipole moment as compared to model molecule. Our outcomes shows that all designed molecules (R and DFBT1 – DFBT7) display greater µ_e than µ_g, which show that they have a high solubility in dimethylformamide solvent.

Table 7

Evaluated dipole moment of (R and DFBT1 – DFBT7) in gaseous phase (µg), excited phase (µe) and difference between two phases (Δµ).
Molecules	µ	ƞ (ev)	S(ev)	χ	ω	∆N_max
R	-3.142	1.82	0.54	3.142	2.713	1.726
DFBT1	-4.120	1.10	0.90	4.120	7.719	3.746
DFBT2	-4.176	0.98	1.02	4.176	8.901	4.262
DFBT3	-4.128	1.08	0.92	4.128	7.892	3.823
DFBT4	-3.912	1.18	0.84	3.912	6.485	3.315
DFBT5	-3.746	1.34	0.74	3.746	5.237	2.795
DFBT6	-4.622	0.74	1.35	4.622	14.439	6.246
DFBT7	-4.198	1.01	0.99	4.198	8.727	4.157

Table 7

Figure 7

3.6. Density of state analysis (DOS)

The Density of States (DOS) analysis is conducted to ascertain the contribution of electronic states that retain electrons within a specific energy state across the entire molecular system [49–50]. The DOS study, performed at the DFT level, involves manipulating the charge distribution using the GaussSum package. For the DOS investigation, the reference molecule R is divided into donor 1 (depicted in black), core (in red), and donor 2 (in blue) regions. Conversely, all other molecules, DFBT1 – BFBT2, are partitioned into five segments: donor 1 (black), core (red), donor 2 (blue), bridge (green), and acceptor (purple), as illustrated in the Fig. 8.

Table 8 presents the orbital contribution from molecular fragments to Fragment Molecular Orbitals (FMOs). In the reference molecule R, the HOMO is composed predominantly of contributions from donor 1 and donor 2 (52%), while the LUMO is primarily shaped by the core (80%). The contributions of various moieties to HOMO and LUMO formation in DFBT1 - DFBT7 are comparable, with HOMO particularity formed by donor 1 and the core (86–92%), designated as the donor, while LUMO is mainly formed by the bridge and the acceptor (85–92%) and partly by donor 2 (8–14%). The results indicate an increased contribution of LUMOs through end-capped acceptors and HOMOs through bithiophene. This suggests that charge transfer will occur from the bithiophene-based core to the acceptor's portion due to the extended conjugation of the designed molecules.

Table 8

Orbital contribution of donor1, core, donor2, bridge, and acceptor of the HOMO and LUMO of (R, DFBT1-DFBT7).
Molecules	µ_g (D)	µ_e (D)	∆µ (D)
R	0.0004	0.002	0.0018
DFBT1	14.434	17.376	2.941
DFBT2	14.199	16.917	2.717
DFBT3	16.917	19.406	2.488
DFBT4	10.178	12.393	2.214
DFBT5	11.694	12.836	1.141
DFBT6	20.761	24.373	3.611
DFBT7	9.534	10.292	0.758

Table 8

Figure 8

3.7. Transition density Matrix, binding energy, and molecular electronic potential

The transition density matrix (TDM) is an essential means of viewing and examining electronic excitation, diffusion, recombination and the separation process within the examined molecules. Its primary objective is to elucidate the connection from the donor and acceptor groups in the course of the excitation process [51–52].

TDM analysis of the investigated molecules (R, DFBT1 – DFBT7) was conducted using the selected hybrid DFT functional. The Fig. 9 illustrates a visual representation comparing the reference molecule (R) with the designed molecules (DFBT1 – DFBT7). The reference molecule (R) is segmented into three components: donor1 (D1), core (C), and donor2 (D2), while the designed molecules (DFBT1-DFBT7) are divided into five fractions: donor1 (D1), core (C), donor2 (D2), bridge (B), and acceptor (A).

The assessment of charge transmission potential can be extended to include the evaluation of excitation binding energy (Eb). In this investigation, the excitation binding energy of the investigated molecules in the gaseous state and in dimethylformamide solvent was determined using the Eq. 7, and the outcomes are detailed in Table 9.

E _b = E_g - E_x (7)

E_g indicates the energy band gap, E_x is the first excitation energy, and E_b represents the binding energy. As shown in Table 9, the binding energy value phase are increased in the following order R > DFBT1 > DFBT4 = DFBT5 > DFBT3 > DFBT2 > DFBT7 > DFBT6 in gaseous phase, while R > DFBT4 > DFBT5 > DFBT2 > DFBT3 > DFBT1 > DFBT7 > DFBT6 in solvent phase. In both the gas phase and dimethylformamide, our newly designed molecules consistently display lower binding energy values compared to the model molecule. This indicates a greater likelihood of exciton dissociation into holes and electrons, resulting in higher charge density and enhanced performance in PSCs.

The Molecular Electrostatic Potential (MEP) provides a visual representation that facilitates the understanding of reactive zones susceptible to electrophilic and nucleophilic attacks within the analyzed molecules. The electrostatic potential mapped surfaces of both R and DFBT1 – DFBT7 are illustrated in Fig. 10. The red color on the mapped molecule surface denotes the negative region, primarily concentrated around oxygen and nitrogen atoms of the acceptor groups in all newly designed molecules. In contrast, the blue color indicates the positive region distributed across the core and donor 1 fragments.

Table 9

Computed exciton binding energy (Eb) in gaseous and solvent phase of investigated molecules.
Molecules	Orbitals	Donor 1 (eV)	Core (eV)	Donor 2 (eV)	Bridge (eV)	Acceptor (eV)
R	HOMO	26	49	26	-	-
R	LUMO	10	80	10	-	-
DFBT1	HOMO	49	43	6	1	1
DFBT1	LUMO	0	0	14	37	48
DFBT2	HOMO	47	43	7	1	1
DFBT2	LUMO	0	0	8	24	68
DFBT3	HOMO	47	43	7	1	1
DFBT3	LUMO	0	0	11	28	61
DFBT4	HOMO	43	43	10	2	2
DFBT4	LUMO	0	0	11	28	61
DFBT5	HOMO	45	43	9	2	1
DFBT5	LUMO	0	0	16	34	49
DFBT6	HOMO	47	43	7	1	1
DFBT6	LUMO	0	0	8	24	68
DFBT7	HOMO	49	43	6	1	1
DFBT7	LUMO	0	0	9	25	66

Table 9

Figure 9

Figure 10

3.8. Reorganisation energies

According to Marcus’ theory, the reorganisation energy (RE) and charge transfer integral have an impact on the mobility of charge carriers. RE is a quantitative parameter used to measure the extent of electron and hole mobility, serving as a critical factor in evaluating the performance of photovoltaic cells. [53]. The internal reorganisation energy has been assessed at designed MPW1PW91/ 6–31 G (d, p) functional. Electron – hole reorganisation values of reported molecules (R and DFBT1 – DFBT7) for the hole (λ_h) and electron (λ_e) are evaluated by using Eq. 8 and Eq. 9 and the outcomes are listed in Table 10 and illustrated in Fig. 11.

λ_h = [E⁰(M⁺) - E(M)] + [E⁺(M) - E(M⁺)] (8)

λ_e = [E⁰(M⁻) - E(M)] + [E⁻(M) - E(M⁻)] (9)

where E(M) reflects the energy of the neutral molecule, E^±(M) represents the energy of the cation or anion estimated with the optimized structure of the neutral molecule, E(M^±) the calculated energy of the cation or anion with the optimized structure of the cation or anion and E⁰(M^±) the estimated energy of the neutral molecule in the cationic or anionic state.

As indicated in Table 10, the hole RE (λ_h) of all researched molecules are increased in the following order DFBT5 < DFBT4 < DFBT7 < DFBT3 < DFBT1 < DFBT6 < DFBT2 < R and DFBT6 < DFBT2 < DFBT7 < DFBT3 < DFBT4 < DFBT1 < DFBT5 < R for the electron RE (λ_e). all our newly molecules display a lower RE value of electron (λ_e) than model molecule, which shows that they have a greater mobilities of an electron between donor and acceptor fragments. The hole reorganisation energies of designed HTMs (R and DFBT1 – DFBT7) range from 0,0116 eV to 0,031 eV. All the developed molecules exhibit lower λ_h values compared to the reference R. This can be attributed to the presence of acceptor groups, which facilitate hole transport. On the other hand, a comparison of the λ_h and λ_e values of all reported molecule indicates that the λ_h higher than λ_e. this suggests that the mobility of hole carriers in these compounds is greater than that of electrons carriers. The efficiency of charge transfer, a crucial factor affecting the charge rate, is influenced by the transfer integrals of electrons (t_e) and holes (t_h) [54]. These parameters are computed using equations 10 and 11. The outcomes are summarized in Table 10 and illustrated in Fig. 11.

$${t}_{h}= \frac{\left({E}_{HOMO}- {E}_{HOMO-1}\right)}{2}$$

10

$${t}_{e}= \frac{\left({E}_{LUMO+1}- {E}_{LOMO}\right)}{2}$$

11

Among all designed molecules, DFBT1, DFBT2, DFBT3, DFBT6, and DFBT7 have displayed higher hole transfer integral values. The charge transfer integral study demonstrates that all investigated molecules are better candidates as HTMs for PSCs.

Table 10

Reorganization Energy of Hole (λh)and Electron (λe), and Transfer Integral of Hole (th) and Electrons (te) of R and DFBT1 – DFBT7.
Molecules	E_b(eV) gaseous	E_b(eV) solvent
R	0.29	0.39
DFBT1	− 0.01	− 0.59
DFBT2	− 0.64	− 0.52
DFBT3	− 0.60	− 0.54
DFBT4	− 0.49	− 0.39
DFBT5	− 0.49	− 0.45
DFBT6	− 0.89	− 0.79
DFBT7	− 0.80	-0.66

Table 10

Figure 11

3.9. Photovoltaic parameters.

The assessment of efficiency and performance in PSCs is significantly reliant on the open-circuit voltage (Voc). This crucial parameter is ascertained by examining the disparity between the HOMO of the donor and the LUMO of the acceptor, while considering the energy lost during photo-charge generation [55]. In this investigation, Eq. 12 is employed to compute the theoretical Voc values for the mentioned molecules (R and DFBT1 - DFBT7) [56].

$${V}_{oc}= \frac{1}{e} \left(\left|{{E}^{D}}_{HOMO}- {{E}^{A}}_{HOMO}\right|\right)-\text{0,3}$$

12

Here, "e" represents the elementary charge on the molecule, and 0.3 is the photovoltaic constant. The widely recognized standard PC61BM (E_HOMO = -6.10 and E_LUMO = -3.70) was employed as an acceptor. The alignment of the LUMO energy level of PC61BM was with the HOMO energy level of the designed molecules (R and DFBT1 – DFBT7). The calculated Voc values for these molecules, ranging from 1.03 V to 1.37 V, are provided in the table and illustrated in the figure. The reported molecules exhibit Voc values in the following order: DFBT6 > DFBT1 > DFBT3 = DFBT7 > DFBT2 > DFBT5 = DFBT4 > R.

The fill factor (FF) is an additional parameter used to assess the power conversion efficiency of solar devices. It can be theoretically computed using the Eq. 13. [55].

$$FF=\frac{ \frac{e{V}_{oc}}{{K}_{B}T}-\text{l}\text{n}(\frac{e{V}_{oc}}{{K}_{B}T}+\text{0,72})}{\frac{e{V}_{oc}}{{K}_{B}T} +1}$$

13

Whereas V_oc is the open-circuit voltage, $\frac{e{V}_{oc}}{{K}_{B}T}$ is the normalized open-circuit voltage, e is the fundamental constant charge, T is the temperature at 298 K and K_B is the Boltzmann constant. The compiled outcomes of the computed fill factor (FF) can be found in Table 11. the order of FF values of studied molecules is DFBT6 > DFBT1 > DFBT3 = DFBT7 > DFBT2 > DFBT5 = DFBT4 > R. By modifying the acceptor moieties at the end, all recently developed molecules have demonstrated a superior (FF) compared to the reference molecules (R).

Comparing the performance of solar cells is crucial, and one significant parameter for this comparison is the power conversion efficiency (PCE), which is calculated using Eq. 14 [58–59]. The obtained results are presented in Table 11.

$$PCE= \frac{\left({V}_{oc}\right) \left(FF\right) \left({J}_{sc}\right)}{\left({P}_{in}\right)}$$

14

In this context, Jsc represents the experimentally measured short-circuit current density, established at 23.01 mA cm-2 for the model molecule and assumed for all molecules [28]. P_in denotes the incident light intensity on the solar cell device, typically set at AM 1.5 G, 100 mW cm-2. The newly formulated molecules exhibit a higher power conversion efficiency (PCE) ranging from 22.42–29.21%, surpassing the PCE of the model molecule at 19.62%. These findings collectively indicate that the newly explored hole transport materials (HTMs) stand out as the top contenders for achieving high-efficiency perovskite solar cells (PSCs).

Table 11: calculated Photovoltaic parameters of the reference molecule (R) and designed HTMs (DFBT1 – DFBT7).

Molecules	V_OC (v)	FF	PCE (%)
Molecules	V_OC (v)	FF	Calculated	Experimental
R	1.03	0 .8863	19.62	20.15
DFBT1	1.22	0.8999	25.42	-
DFBT2	1.16	0.8962	23.93	-
DFBT3	1.21	0.8997	25.12	-
DFBT4	1.09	0.8913	22.42	-
DFBT5	1.09	0.8913	22.43	-
DFBT6	1.37	0.9257	29.21	-
DFBT7	1.21	0.8997	23.13	-

Table 11

Figure 12

In this article, seven new hole transport materials (HTMs) based on bithiophene derivatives (DFBT1 - DFBT7) have been designed by extending the thiophene-bridge, and end-capped acceptor groups on the basis of effective HTM model molecule reported using DFT and TD-DFT methods. The verification and the validation of our findings is demonstrated by comparing our data with the experimental data available for the reference molecule DFBT-MTP. The results demonstrate that the newly reported molecules have yielded remarkable outcomes. indeed, DFBT1 – DFBT7 displayed a lower band gap (1.49 eV to 2.69 eV) compared to the model molecule (3.63 eV). The newly engineered molecules exhibited a greater λmax, ranging from 393.07 nm to 541.02 nm in dimethylformamide solvent, compared to the reference molecule (380.61 nm). These molecules (DFBT1 – DFBT7) exhibit a higher dipole moment (10.29 D to 24.37 D), indicating improved solubility and reduced charge recombination. The reorganization energy further confirms that all newly formulated molecules possess greater charge mobility compared to the model molecule. Notably, the planned molecules (DFBT1 – DFBT7) consistently exhibit higher hole transfer integral values, ranging from 0.25 to 0.37, affirming their enhanced hole mobility and suggesting their potential as hole transport materials (HTMs) for perovskite solar cells (PSCs). Conversely, when evaluated with the PC61BM acceptor, all newly designed molecules exhibit higher Voc values (ranging from 1.09 V to 1.37 V) compared to the model molecule (1.03 V), indicating their pivotal role in achieving increased operational efficiency. The power conversion efficiencies (PCEs) of the newly designed molecules (22.42–29.21%) significantly surpass those of the reference molecule (19.62%). All seven designed HTMs emerge as excellent candidates for innovative PSC applications.

Funding:

The authors have no relevant financial or non-financial interests to disclose.

Author Contribution

Mohamed ADADI: Writing – original draft, Writing – review & editing, Visualization, Investigation, Methodology, Formal analysis, Conceptualization. Mohamed HACHI: Writing—review & editing, Visualization, Validation. Khalid SAID, Anouar AMZIANE EL HASSANI, Jihane ZNAKI, Fatima Zahra ZNAKI, Adil TOUIMI BENJELLOUN, Samir CHTITA: Writing—review & editing, Validation. Souad ELKHATTABI: Writing—review & editing, Visualization, Validation, Supervision, Project administration, Software.

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No competing interests reported.

Rational design of new small derivatives of 2,2'-Bithiophene as hole transport material for perovskite solar cells

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Computational details

3. Results and discussion