Fine structural tuning of diphenylaniline-based dyes for designing semiconductors relevant to dye-sensitized solar cells

Abstract

Motivated by recent study on synthesized N, N-diphenylaniline (DPA)-based dyes [DOI: 10.1016/j.solener.2022.01.062] for use in dye-sensitized solar cells (DSSCs), we theoretically design several dyes and explore their potential for enhancing the efficiency of DSSCs. Our designed dyes are based on the molecular structure of synthesized DPA-azo-A and DPA-azo-N dyes with a donor-π-bridge-acceptor (D-π-A) framework. In this research, we aim to develop the power conversion efficiency (PCE) of DSSCs by fine-tuning the molecular structure of the synthesized dyes. To this end, we focus on designing dyes by replacing the units of DPA-azo-A and DPA-azo-N with a variety of donor, π-bridge, and acceptor. Hence the density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations are done to explore their structure, electronic, optical, charge transport, and photovoltaic properties. Among all newly designed and reference dyes, the D3-azo-N and DPA-π3-N dyes which are designed by substituting the donor (DPA) and π-bridge (azo) units of DPA-azo-N with D3 and π3, respectively exhibit the highest PCE of 45.46% (for D3-azo-N) and 43.20% (for DPA-π3-N) and can be favorable dyes for improving the efficiency of DSSCs. Therefore, the dyes that are designed by substituting the donor and π-bridge units of synthesized dyes have more impact on improving the efficiency of DSSCs than those that involve replacing the acceptor units. Consequently, our theoretical findings will provide valuable insights for the experimentalists to employ these novel effective dyes and boost the performance of DSSCs.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-77953-y.

Introduction

Climate change caused by the common energy resources will require a considerable switch to clean energy technologies. The shortcomings of current fossil fuel energy sources such as oil, natural gas, and coral have motivated researchers worldwide to substitute these energies with renewable and non-polluting ones. Hence, among the most popular renewable energies like wind, hydro, tidal, geothermal, and biomass, solar energy is the most abundant source capable of satisfying global energy consumption demands. The amount of solar energy reaching the earth in an hour exceeds the total energy needed by mankind for an entire year. Some drawbacks of first crystalline silicon solar cells like limited transportability and low photovoltaic performance in low light intensities¹ shifted researchers’ focus from the first generation photovoltaic technologies to third generation like perovskite solar cells (PSCs), organic solar cells (OSCs), and DSSCs. DSSC which is introduced by Grätzel in 1991², is a highly promising type of solar cell which currently undergoing numerous experimental and theoretical research efforts to enhance its efficiency. DSSCs have garnered significant interest in various fields such as medical technology, sports equipment, security devices, wearable electronics, cameras, and wireless sensor networks used in smart buildings, homes, and cities³. DSSCs exhibit good stability and efficiency even in cold temperatures, low-light situations, and moisture environments^4–6 and can generate power consistently throughout the day regardless of the intensity and angle of incidence of the light⁷. Basically, DSSCs consist of four main parts including a working electrode, sensitizer (dye), redox mediator (electrolyte), and counter electrode⁶, so the PCE of DSSCs depends on each component. Accordingly, the dyes play a crucial role in improving light-harvesting efficiencies (LHE) by converting the incident light into an electronic excitation and transferring the charge to the semiconductor. In particular, a suitable dye in DSSCs should possess strong absorption properties in both the visible and near-infrared regions, and be stable in both ground and excited states⁸. Generally, dyes are divided into organic and inorganic dyes. The most widely used inorganic dyes are Ruthenium and Zinc-based organometallic dyes^9–11. However, natural^12,13 and metal-free organic dyes^14,15 are considered alternatives to the rare and expensive inorganic dyes^16,17. Despite the low cost and safety of natural dyes their photo-degradation limited their application in DSSCs¹⁸. Therefore, synthesized metal-free organic dyes with high stability, higher extinction coefficients, tunable spectral responses, high availability, and biodegradability have drawn remarkable attention compared to inorganic and natural dyes^19,20. In this context, over the past two decades, hundreds of metal-free organic dyes have been synthesized. The metal-free organic dyes comprise donors, spacers, and acceptors. The donor (D) consists of electron-donating groups. The spacers link the donor and the acceptor (A) units and usually consist of π-conjugated systems and play a pivotal role in the rate transfer of electrons from donor to acceptor. The acceptor unit facilitates electron transfer from the excited dye to the semiconductor which is essential for converting absorbed light into electrical energy. On the whole, the chemical structure of metal-free organic dyes plays a crucial role in the effectiveness and durability of DSSC devices. The fine-tuning of organic dye structure in DSSCs can reduce the HOMO-LUMO gap and enhance light absorption properties^21–24. To date, numerous metal-free organic dye with D-(π-A)₂, D-π-A, D-D-π-A, D-A-π-A and (D-π-A)₃L₂^25–29 frameworks have been designed and synthesized. The D–π–A structure is particularly popular due to its “push-pull” effect, appropriate intramolecular charge transfer (ICT), efficient electron-hole separation properties, and controllable charge recombination^30–32. There are three significant strategies for enhancing ICT in D–π–A dyes to improve absorption at longer wavelengths. These include increasing the electron-donating ability of the D or π-bridge units by extending π-conjugated structures and incorporating bulky substituents, enhancing the electron-withdrawing features of the A group, and optimizing the structure of the π-bridge(s)^33–36. The D unit of dyes commonly consists of electron-rich moieties such as indoline^37–39, phenothiazine^40–42, coumarin^43,44, phenoxazine^45,46, carbazole^47,48 and triphenylamine derivatives^49,50. The π-spacers can be selected from simple to complex conjugated compounds like thiophene, pyrrole, ethenyl, phenylene, benzotriazole, and quinoxaline⁵¹. Besides the widely-used carboxylic acid, some other groups such as sulphonic acid, salicylic acid, cyanoacrylic acid, and pyridine have also been reported as an A unit⁵². Arslan et al. designed and synthesized a new series of D-π-A organic dyes for DSSCs including dibenzo[b,h] [1,6] naphthyridine unit as the conjugated π-bridge, a cyanoacrylic acid moiety as the acceptor group and three different donor groups such as trimethoxy, methoxy, and dimethylamino and found that the dye with dimethylamino donor showed the highest PCE (5.02%).⁵³ Siddiqui et al. designed and synthesized two organic sensitizers with the D–π–A framework based on an indacenodithiophene core with two different donor units (triphenylamine and phenothiazine) for DSSC applications. The dye with the triphenylamine unit showed a higher short-circuit current density (J_SC) of 23.01 mA cm⁻², and open-circuit voltage (V_OC) of 0.659 V, and more durability than the phenothiazine-based cells, which was because of their band alignment and higher electrical properties⁵⁴. Kacimi et al.. employed the DFT and TD-DFT methods to study six organic dyes with D-π-A framework based on phenothiazine (PTZ) and examined the effect of different π-bridge on structural, photovoltaic, electronic, and optical properties of dyes to compare with the synthesized dyes based PSB-4(R). They observed that the modifications of π-bridge groups affect the performance of designed dye by reducing the energy gap, increasing excited-state lifetime, and enhancing electron mobility compared to reference synthesized dyes⁵⁵. Janjua used DFT and TD-DFT methods to design dyes with different π-bridge units. It was found that the newly designed dyes showed higher red-shift, narrower HOMO − LUMO energy gaps, and superior photovoltaic, and optoelectronic characteristics than synthesized ones¹⁴. Afolabi et al. studied the different dyes with the D-A₂-π-A₁ structure based on phenothiazine donor connected with benzothiadiazole (A₂) linked with furan π-bridge and acceptor unit of cynoacrylic acid (A₁) for DSSCs through the DFT and TD-DFT. They observed that the 2-hexylthiophene considerably lowered the E_g and chemical hardness and produced suitable LHE. So they suggested this dye as the best candidate for DSSCs due to its competing electronic and absorption properties⁵⁶. Recently the dyes with D-π-A framework named DPA-azo-N and DPA-azo-A were designed, synthesized, and applied as metal-free organic dyes in DSSCs⁵⁷. It was recognized that replacing the naphthalene (N) with the anthracene (A) group improved the PCE of the DSSCs. The privilege of the synthesized dyes could be categorized from optical, electrochemical, and energetic aspects. Indeed, due to the higher molar absorption coefficient (ε) of DPA-azo-A compared to the DPA-azo-N dye, it expanded the absorption spectrum and enhanced the LHE. Additionally, the elongated structure of the DPA-azo-A dye with a more hydrophobic unit mitigated undesirable interactions between the dye and the electrolyte by facilitating hole transfer and reduces the recombination rate by increasing the distance between holes and TiO₂. Also, the down-shifted LUMO level of the DPA-azo-A dye promoted more effective electron injection. Herein, to develop these dyes’ performance in DSSC, we designed three sets of dyes by replacing the units of DPA-azo-N and DPA-azo-A dyes⁵⁷ with the variety of commonly used D, π, and A (Fig. 1). We performed DFT and TD-DFT calculations to verify the structure, electronic, optical, charge transport, and photovoltaic properties of newly designed dyes and compared them to the available experimental data of reference DPA-azo-N and DPA-azo-A dyes. We hope our computational findings in adjusting the D, π, and A units of dyes will help to enhance the efficiency of DSSCs.

Fig. 1.

(a) Molecular structure of the synthesized dye⁵⁷, the examined (b) donors (D1-D4), (c) conjugated bridges (π1-π5), and (d) acceptor units (A1-A5).

Methodological details

Theoretical background

The charge transport properties are important factors in evaluating the performance of dyes in DSSCs. It is expected that the higher charge transport rate of dyes improves the photovoltaic properties and efficiency of DSSCs. The charge transport properties of dyes can be obtained based on the hopping model^58,59. The rate constant (k) for the charge hopping between two adjacent molecules can be obtained by the following Marcus theory⁶⁰

1

where t is the inter-molecular transfer integral, λ is the reorganization energy, ℏ is the Planck constant, k_B is the Boltzmann constant, and T is the temperature (298 K, in this study). The reorganization energy () for the self-exchange hole and electron transfer processes is computed by Nelsen’s four-point method⁶¹

2

here, and are hole and electron reorganization energy, respectively. is the energy of the cation/anion with optimized geometry of the neutral molecule. is the energy of the cation/anion calculated from the optimized cation/anion structure. is the energy of the neutral molecule obtained at the cationic or anionic state, and is the energy of the neutral molecule at the ground state. The transfer integral (t) that indicates the electron coupling strength between the neighbor molecules can be calculated by Koopmans’ theorem⁶². The absolute value of the t for electron [hole] transfer is calculated by

3

where and are the energies of the LUMO+1 and LUMO [HOMO and HOMO−1] in the closed-shell configuration of the neutral state, respectively. Likewise, the charge carrier mobility that is represented as a Brownian motion can be assessed and defined by the particle diffusion process⁶³. The electron mobility () is calculated by the following Einstein Eq. 6⁴

4

is the Boltzmann constant, T is the temperature, e is the electronic charge, and D is the diffusion coefficient obtained from the Einstein-Smoluchowski relation⁶⁵

5

where R is the effective length of the charge transfer approximated by the molecular center-to-center distance of a dimer. Additionally, the efficiency of DSSCs is evaluated using the PCE and can be calculated based on a set of key parameters. The method that is used to compute the PCE is depicted in Scheme 1. The incident photon to current conversion efficiency (IPCE) is another important parameter, which measures the ratio of generated charge carriers to the number of incident photons at a specific wavelength and is determined by the following equation⁶⁶.

6

Scheme 1.

The method used to calculate the efficiency of DSSC involves a series of computational steps.

Typically, the wavelength range for the IPCE in organic dyes used in DSSCs is about 300 nm to 800 nm. This range includes significant absorption in both the ultraviolet (UV) and visible light spectra, with some dyes extending into the near-infrared (NIR)^67–70. The LHE is the light-harvesting efficiencies of dyes and is calculated via the magnitude of the oscillator strength (f) as follows⁷¹

7

is the electron injection efficiency and can be obtained by⁷²

8

where, is the relaxation time for the excited state of dye, obtained experimentally ~ 10 ps⁷³ and is the electron injection lifetime assessed as the reciprocal of the electron injection rate (k) that is derived from the general Marcus theory (Eq. 1). Furthermore, , the charge-collection efficiency is defined as

9

Where, τ_trans is the electron transport time from the conduction band of TiO₂ towards the electrode, and τ_rec is the electron recombination lifetime that is the inverse of the electron recombination rate⁷⁴. In DSSC systems with different dyes, the η_coll is typically considered constant and set to 1 due to the low electron recombination rate. Previous studies revealed that a shorter injection lifetime and longer recombination lifetime can enhance the efficiency of DSSCs^75,76. The short-circuit current density is the current density through a solar cell when the voltage is zero and is defined as⁷⁷

10

here P_inc is incident sunlight and equal to 100 mW.cm^[-2, and λ is the wavelength of the adsorbed photon by the photosensitizer⁷⁸. Moreover, the fill FF that is important for the determination of PCE can be obtained by⁷⁹

11

where, is the normalized form of V_OC computed via . The V_OC is another significant property of DSSCs and can be calculated from the following empirical Eqs. 8^0,81

12

here, e is the elementary charge and 0.3 eV is a key factor arising from the quasi-Fermi energies of electrons and holes within the and ^72,82–84. As a final point, the PCE is defined as the ratio of the electrical power out and the optical power in, which can be estimated as⁸⁵

13

Computational details

The DFT calculation has been done to optimize the geometry of DPA-azo-A via the Gaussian 09⁸⁶ program. To validate our calculations we have reproduced the band gap (E_gap) of DPA-azo-A and compared it to the experimental result. To this end, we have employed the B3PW9 method and different basis sets. As can be observed in Table 1, the 6–31 + g(d) basis set considerably outperforms other basis sets and illustrates less deviation () from the experimental value ()⁵⁷. Therefore, we will use the 6–31 + g(d) basis set for our further calculations.

Table 1.

HOMO, LUMO, and HOMO-LUMO energy gap (E_gap) for the DPA-azo-A with B3PW9 functional and various basis sets. Δ_gap is the deviation from the experimental value. (^aThe experimental data is from the published literature⁵⁷).

Basis set	EHOMO(eV)		ELUMO(eV)	Egap(eV)	(eV)
3–21 g	−5.22	−2.60		−2.62	0.04
6–31 g(d)	−5.12	−2.50		−2.62	0.04
6–31 + g(d)	−5.35	−2.75		−2.60	0.02
6-311 + g(d)	−5.39	−2.77		−2.62	0.04
6-311 + + g(d, p)	−5.40	−2.79		−2.61	0.03
Def2-TZVP	−5.37	−2.73		−2.64	0.06
aExp	−5.98	−3.40		−2.58	-

In the next step, for selecting a DFT functional, a selected basis set (6–31 + g(d)) along with ten diverse methods have been considered for reproducing the E_gap of DPA-azo-A. The classes of GGA and hybrid GGA such as PBE, BP86, B3P86, B3LYP, M062X, HSE06, PBE0, TPSS, CAM-B3LYP, and M11 functional have been used to calculate the E_gap of DPA-azo-A and the results are collected in Table 2. Obviously, the calculated E_gap using the B3P86 and B3LYP functional shows a lower deviation from the experimental value (2.58 eV)⁵⁷. Therefore, the B3LYP and B3P86 functionals with the 6–31 + g(d) basis set are the best for reproducing the experimental E_gap of the DPA-azo-A molecule.

Table 2.

HOMO, LUMO, and HOMO-LUMO energy gap (E_gap) for the DPA-azo-A at the same 6–31 + g(d) basis set and different functional. Δ_gap is the deviation from the experimental value. (^aThe experimental data is from the published literature⁵⁷).

Method	EHOMO(eV)	ELUMO(eV)	Egap(eV)	(eV)
PBE	−4.73	−3.29	1.44	−1.14
BP86	−4.80	−3.37	1.43	−1.15
B3P86	−5.90	−3.31	2.59	0.01
B3LYP	−5.31	−2.71	2.60	0.02
M062X	−6.42	−1.89	4.53	1.95
HSE06	−5.12	−2.99	2.13	−0.45
PBE0	−5.48	−2.59	2.89	0.31
TPSS	−4.96	−2.90	2.06	−0.52
CAM-B3LYP	−6.51	−1.60	4.91	2.33
M11	−7.41	−1.07	6.34	3.76
aExp	−5.98	−3.40	2.58	-

To ensure the computational accuracy of the selected functional, the reproduction of the maximum absorption wavelength () for the DPA-azo-A in the gas phase and ethanol solvent has also been carried out. We have used the 6–31 + g(d) basis set with different functional to investigate the via TD-DFT calculations. According to the results (Table 3) the that has been obtained by B3LYP and B3P86 functionals in both gas and ethanol phases is in accordance with the experimental value. Thus, both the B3P86 and B3LYP functionals are successful in reproducing the E_gap and λ_max of the DPA-azo-A. Accordingly, both B3P86/6–31 + g(d) and B3LYP/6–31 + g(d) will be used for further calculations, and all the results will be reported at both computational levels.

Table 3.

The maximum absorption wavelength (λ_max) for the DPA-azo-A with different functional at the same 6–31 + g(d) basis set. ∆λ_max is the deviation from the experimental value. (^aThe experimental data is from the published literature⁵⁷).

	Gas phase		Ethanol
Method	λmax (nm)	∆λ max (nm)	λmax (nm)			∆λmax (nm)
B3LYP	531.60	9.40	560.30			19.30
B3P86	533.60	7.40	561.80			20.80
BP86	578.00	37.00	621.60			80.60
CAM-B3LYP	410.60	130.40	258.10			282.90
HSE06	526.40	14.60	261.10			279.90
M11	237.00	304.00	243.80			297.20
M062X	411.10	129.90	240.10			300.90
PBE	576.40	35.40	619.40			78.40
TPSS	587.40	46.40	625.90			84.90
aExp	–	–	541.00			–

Results and discussion

Reference dyes

Structural and Electronic Properties of DPA-azo-A and DPA-azo-N Dyes. First and foremost the structures of two synthesized dyes (DPA-azo-A and DPA-azo-N, Fig. 1, panel (a)) were considered as the starting configurations, and the geometry optimizations were carried out to investigate the structure and electronic properties of these reference dyes. The optimized structure of each molecule is depicted in Fig. 2.

Fig. 2.

Optimized structures and the spatial distribution of HOMO/LUMO of DPA-azo-A and DPA-azo-N dyes.

The calculated geometry parameters including carbon-nitrogen bond length at the donor-π-bridge (C_D-N_π), carbon-nitrogen bond length at the acceptor-π-bridge (C_A-N_π), dihedral angles between the donor and π-bridge (α), and dihedral angle between the acceptor and π-bridge () are reported in Table 4. The α and dihedral angles of DPA-azo-N and DPA-azo-A dyes are displayed in Figure S1, Supplementary material. Actually, the smaller dihedral angle between the donor and π-bridge moieties leads to more planarity of dyes that play an essential role in enhancing the ICT of dye molecules^87–89. Likewise, the smaller dihedral angle between the acceptor and π-bridge increases the planarity of dye molecules which supports the charge transfer from the π-bridge to the acceptor unit and facilitates the electron injection from dyes to the conduction band of the semiconductor. Hence, the α and dihedral angles and planarity of dyes with D–π–A framework are important factors in improving the performance of dyes in DSSCs.

Table 4.

Carbon-nitrogen bond length at the donor-π-bridge (C_D-N_π) and acceptor-π-bridge (C_A-N_π), dihedral angles between donor and π-bridge (α) and the acceptor and π-bridge (), and E_gap of DPA-azo-A and DPA-azo-N dyes in their optimized ground state geometries. Values are reported for the B3LYP and in brackets are for the B3P86 method.

Molecule	d(CD-Nπ)(Å)	d(CA-Nπ ) (Å)	(deg)	(deg)	Egap (eV)
DPA-azo-A	1.40 (1.40)	1.40 (1.40)	0.04 (0.39)	1.42 (1.98)	2.59 (2.58)
DPA-azo-N	1.40 (1.39)	1.41 (1.40)	2.32 (2.85)	1.25 (1.67)	2.78 (2.78)

Evidently, the C_D-N_π and C_A-N_π bond lengths (Table 4) show approximately the same values (about 1.40Å). Moreover, the α and dihedral angles are very small, indicating the high planarity of both DPA-azo-A and DPA-azo-N structures. The results in Table 4 clearly illustrate that in the DPA-azo-A, the is smaller indicating more planarity in the region between DPA-azo that enhances the ICT in DPA-azo-A. On the other hand, the of DPA-azo-N is small representing more planarity in the azo-N region that facilitates the electron injection from dyes to the semiconductor. The E_gap is also reported in Table 4 and is slightly lower (by 0.2 eV) for the DPA-azo-A compared to the DPA-azo-N molecule. Typically, in D-π-A structures, the distribution of HOMO and LUMO on each of the donor and acceptor units will significantly affect the rate of charge transfer in these organic dyes. For a better evaluation of the distribution of HOMO and LUMO on different units of the DPA-azo-A and DPA-azo-N structures, the frontier molecular orbitals (FMO) analysis has been done (Fig. 2) and displays that the distribution of HOMO in both reference dyes is on the donor units (DPA) and the LUMO are predominantly distributed on the naphthalene (N) and anthracene (A) units. To verify the E_gap of the DPA-azo-A and DPA-azo-N the density of state (DOS) plots are shown in Fig. 3. According to the DOS plots, the peaks on both sides of the Fermi energy region in DPA-azo-A confirm the lower E_gap in DPA-azo-A (2.59 eV) than the DPA-azo-N (2.78 eV).

Fig. 3.

The DOS plots of reference DPA-azo-A and DPA-azo-N dyes.

Optical Properties of DPA-azo-A and DPA-azo-N Dyes. The optical properties of DPA-azo-A and DPA-azo-N have been calculated through the TD-DFT approach and are gathered in Table 5. It can be seen that the optical energy gap (E_opt) of DPA-azo-A is lower than DPA-azo-N. Also, the HOMO-LUMO transitions show the highest contribution and the of DPA-azo-N is lower than the DPA-azo-A which is in accordance with the experimental result⁵⁷.

Table 5.

Calculated optical energy gap (E_opt), oscillator strengths (f), maximum absorption wavelength (λ_max), and dominant transition contribution for the DPA-azo-A and DPA-azo-N. Values are reported for the B3LYP and in brackets are for the B3P86 method.

Molecule	Eopt (eV)	f	λ max (nm)	Transition
DPA-azo-A	2.33 (2.32)	0.61 (0.52)	531.6 (533.6)	H → L 65% (61%)
DPA-azo-N	2.53(2.54)	0.96 (0.78)	488.8 (486.3)	H →L 66% (58%)

Charge Transport Properties of DPA-azo-A and DPA-azo-N Dyes. The charge transport properties of the DPA-azo-A and DPA-azo-N such as reorganization energy, intermolecular transfer integral, and rate constant of electrons and holes of both DPA-azo-A and DPA-azo-N are reported in Table 6.

Table 6.

Charge transport parameters for DPA-azo-A and DPA-azo-N. Values are reported for the B3LYP and in brackets are for the B3P86 method.^a.

Molecule	λ+(eV)	t+(eV)	k+(s−1)	λ−(eV)	t−(eV)	k−(s−1)
DPA-azo-A	0.195 (0.193)	0.329 (0.339)	6.19 × 1014(6.71 × 1014)	0.412 (0.408)	0.285 (0.296)	3.87 × 1013 (4.34 × 1013)
DPA-azo-N	0.134 (0.131)	0.542 (0.556)	3.69 × 10 15 (4.02 × 1015)	0.565 (0.559)	0.452 (0.459)	1.87 × 1013 (2.06 × 1013)

^aCalculated properties for hole and electron are shown by “+” and “‒” signs.

These quantities represent the efficiency of a semiconductor in which a dye with a higher electron or hole rate constant will have better performance in a solar cell. The results in Table 6 demonstrate that the of DPA-azo-A is more than DPA-azo-N, which is consistent with experimental results indicating the better performance of DPA-azo-A compared to DPA-azo-N as a dye in DSSCs⁵⁷. It was reported that the DPA-azo-A exhibits better performance with a higher V_OC, LHE, and PCE compared to DPA-azo-N⁵⁷. However, in the DPA-azo-N, higher and lower lead to increasing up to ten times than DPA-azo-A (Table 6).

Furthermore, as displayed in Fig. 1 (panels, (b-d)), in the following sections we will design theoretically new dyes and investigate how the replacement of donor, π-bridge, and acceptor units in the reference DPA-azo-A and DPA-azo-N dyes can boost their charge transport properties.

Step I: alter donor

Structural and Electronic Properties of Designed [D1-D4]-azo-A and [D1-D4]-azo-N Dyes. In the first step, we substituted the donor unit (DPA) of the DPA-azo-A and DPA-azo-N with D1-D4 donors (Fig. 1, panel(b)) and optimized the structures as shown in Figure S2, Supplementary material. The C_D-N_π and C_A-N_π bond lengths, α and dihedral angles, and energy gap of designed [D1-D4]-azo-A and [D1-D4]-azo-N dyes are listed in Table 7.

Table 7.

Carbon-nitrogen bond length at the donor- π-bridge (C_D-N_π) and acceptor-π-bridge (C_A-N_π), dihedral angles between donor and π-bridge atom (α) and the acceptor and π-bridge atom (), and energy gap of [D1-D4]-azo-A and [D1-D4]-azo-N dyes in their optimized ground state geometry. Values are reported for the B3LYP and in brackets are for the B3P86 method.

Molecule	d(CD-Nπ) (Å)	d(CA-Nπ )(Å)	α(deg)	(deg)	Egap (eV)
D1-azo-A	1.41 (1.40)	1.40 (1.40)	1.07(1.20)	1.35 (1.48)	2.83 (2.84)
D2-azo-A	1.41 (1.40)	1.40 (1.40)	0.12(0.04)	0.85 (0.94)	2.83 (2.84)
D3-azo-A	1.36 (1.35)	1.39 (1.39)	0.36(0.54)	0.49 (0.64)	2.18 (2.19)
D4-azo-A	1.37 (1.37)	1.40 (1.39)	0.03(0.01)	0.08 (0.01)	2.59 (2.60)
D1-azo-N	1.41 (1.40)	1.41 (1.40)	0.03(0.01)	0.02 (0.00)	3.13 (3.15)
D2-azo-N	1.41 (1.40)	1.41 (1.40)	0.35(0.52)	0.48 (0.61)	3.17 (3.19)
D3-azo-N	1.35 (1.35)	1.40 (1.39)	0.02(0.01)	0.01 (0.01)	2.33 (2.35)
D4-azo-N	1.37 (1.36)	1.40 (1.40)	0.01(0.00)	0.03 (0.00)	2.79 (2.79)

Obviously, both B3LYP and P3P86 functionals show almost the same values and the molecules with D1 and D2 units have similar bond lengths (C_D-N_π and C_A-N_π ) to the reference dyes. However, the molecules with D3 and D4 units show lower C_D-N_π and C_A-N_π bond lengths compared to reference dyes. Comparing the structures of the designed dyes containing [D1-D4] units reveals that molecules containing D3 and D4 and without -CH₃ and -O-CH₃ groups in their structures exhibit a more planarity and aromatic character compared to the D1 and D2 donors, and even the reference dyes. These results are in agreement with the smaller α and dihedral angles of dyes containing D3 and D4 units with shorter bond lengths. Thus, the molecules with shorter bond lengths and smaller dihedral angles are more planer which improves the ICT of dyes and assists the electron injection from dyes to semiconductors. It can be observed (Table 7) that in both systems containing A and N acceptors, the E_gap values are higher in dyes with D1 and D2, but lower or equal in dyes with D3 and D4 compared to the reference dyes. As mentioned earlier, energy levels in organic dyes play an important role in the photovoltaic properties of DSSCs. Therefore, the E_gap values in [D1-D4]-azo-A and [D1-D4]-azo-N affect the charge transport properties that will be discussed in the following sections. Next, to investigate the distribution of HOMO and LUMO in these designed dyes, the FMO analyses have been performed and are displayed in Figure S2. The HOMO and LUMO distribute on donor and acceptor units, respectively that leading to higher charge transfer and dyes performance. Dyes with D3 and D4 donors exhibit aromatic character due to their high degrees of π-conjugation and electron delocalization, while molecules with D1 and D2 units do not possess this characteristic. The partial DOS plots for the designed dyes including D1-D4 donor units are depicted in Figure S3, Supplementary material. Apparently, the new donors that lower the E_gap impact the DOS diagrams in both occupied and unoccupied orbital regions. Clearly, the DOS plots show the new peaks in the forbidden energy region (two sides of Fermi level) of the designed dyes with lower E_gap especially in dyes containing D3.

Optical Properties of Designed [D1-D4]-azo-A and [D1-D4]-azo-N Dyes. The optical properties of [D1-D4]-azo-A and [D1-D4]-azo-N dyes have been calculated via TD-DFT approach and the results are reported in Table 8. From the reported λ_max values (Table 8) a blue shift in D1-azo-A and D2-azo-A and a redshift in D4-azo-A can be observed clearly. Additionally, in the D3-azo-A, the λ_max value is close to the DPA-azo-A dye. Similar results can be observed for [D1-D3]-azo-N, but in this case, a blue shift is observed for D4-azo-N. Thereby, replacing the donor units can alter the λ_max values that affect the performance of these dyes in DSSCs.

Table 8.

Calculated optical energy gap (E_opt), oscillator strengths (f), maximum absorption wavelength (λ_max), and dominant transition contribution for the [D1-D4]-azo-A and [D1-D4]-azo-N. Values are reported for the B3LYP and in brackets are for the B3P86 method.

Molecule	Eopt (eV)	f	λ max(nm)	Transition
D1-azo-A	4.91 (5.01)	0.65 (0.53)	252.5 (247.0)	H →L + 4 43% (32%)
D2-azo-A	4.92 (4.99)	0.78 (0.80)	251.8 (248.3)	H →L + 5 32% (34%)
D3-azo-A	2.06 (2.06)	0.78 (0.74)	601.7 (601.1)	H →L 68% (68%)
D4-azo-A	2.38 (2.38)	0.62 (0.58)	519.9 (519.5)	H →L 68% (68%)
D1-azo-N	2.96 (2.99)	1.44 (1.46)	418.6 (414.5)	H-1→L 70% (70%)
D2-azo-N	2.91 (2.93)	1.32 (1.34)	426.0 (422.4)	H →L 70% (70%)
D3-azo-N	2.25 (2.27)	1.21 (1.14)	548.8 (543.8)	H →L 66% (65%)
D4-azo-N	2.88 (2.91)	1.17 (1.19)	429.3 (425.2)	H-1→L 63% (64%)

Charge Transport Properties of Designed [D1-D4]-azo-A and [D1-D4]-azo-N Dyes. The calculated charge transport properties of [D1-D4]-azo-A and [D1-D4]-azo-N are provided in Table 9. The results demonstrate that replacing the DPA with [D1-D4] in DPA-azo-A alters both and . Noticeably, the D4-azo-A with the most planarity exhibits high due to its higher and lower . The D3-azo-A is the next one with more planarity and high () compared to other designed molecules and DPA-azo-A. Similarly, in [D1-D4]-azo-N dyes, the D3-azo-N and D4-azo-N illustrate higher () than dyes with D1 and D2. These observations can be attributed to better orbital overlap (transfer integral; t) and greater stability of the designed molecules with D3 and D4 donors as a result of their electrons and hole formation (lower reorganization energy; λ). Although the and values of designed dyes with different donor units are almost the same in both functional (P3B86 and B3LYP), the P3B86 function generally shows higher values of and .

Table 9.

Charge transport parameters for [D1-D4]-azo-A and [D1-D4]-azo-N. Values are reported for the B3LYP and in brackets are for the B3P86 method.^a.

Molecule			(s−1)			(s−1)
D1-azo-A	0.330 (0.354)	0.337 (0.556)	1.22 × 10 14 (1.10 × 1014)	0.270 (0.265)	0.080 (0.080)	1.52 × 1013 (1.59 × 1013)
D2-azo-A	0.332 (0.355)	0.348 (0.359)	1.39 × 1014 (1.15 × 1014)	0.283 (0.277)	0.303 (0.298)	1.86 × 1013 (1.92 × 1013)
D3-azo-A	0.201 (0.188)	0.317 (0.326)	5.31 × 1014 (6.63 × 1014)	0.223 (0.221)	0.288 (0.281)	3.38 × 1014 (3.29 × 1014)
D4-azo-A	0.199 (0.191)	0.380 (0.391)	7.89 × 1014 (9.15 × 1014)	0.275 (0.268)	0.191 (0.190)	8.12 × 1013 (8.63 × 1013)
D1-azo-N	0.250 (0.244)	0.547 (0.561)	8.87 × 1014 (1.00 × 1015)	0.395 (0.386)	0.035 (0.038)	7.23 × 1011 (9.18 × 1011)
D2-azo-N	0.264 (0.260	0.567 (0.582)	8.05 × 1014 (8.85 × 1014)	0.389 (0.380)	0.267 (0.251)	4.35 × 1013 (4.29 × 1013)
D3-azo-N	0.181 (0.178)	0.562 (0.572)	2.15 × 1015 (2.32 × 1015)	0.310 (0.303)	0.255 (0.252)	9.64 × 1013 (1.02 × 1014)
D4-azo-N	0.214 (0.205)	0.630 (0.644)	1.79 × 1015 (2.10 × 1015)	0.375 (0.366)	0.227 (0.234)	3.68 × 1013 (4.34 × 1013)

^aCalculated properties for hole and electron are shown by “+” and “‒” signs.

Accordingly, replacing the donor units in DPA-azo-A and DPA-azo-N with the D3 and D4 can improve the electron and hole transfer rates and will enhance the photovoltaic properties and performance of these dyes in DSSCs.

Step II: alter π-bridge

Structural and Electronic Properties of Designed DPA-[π1-π5]-A and DPA-[π1-π5]-N Dyes. In the second step, the π-bridge unit in the DPA-azo-A and DPA-azo-N is replaced by five π-bridges (Fig. 1, panel (c)), and their optimized structures are illustrated in Figure S4, Supplementary material. As shown in Fig. 1, panel (c), the π1 and π4 units contain a single thiophene ring and connected thiophene rings, respectively; while in other π-bridge units, the thiophene or thiazole rings are connected with a single bond. According to Table 10, the bond lengths between the C_D-N_π and C_A-N_π in DPA-[π1-π5]-A and DPA-[π1-π5]-N are longer than the reference dyes. Additionally, the substitution of π1-π5 in the DPA-azo-A increases both and dihedral angles.

Table 10.

Carbon-nitrogen bond length at the donor-π-bridge (C_D-N_π) and acceptor-π-bridge (C_A-N_π), dihedral angles between donor and π-bridge (α) and the acceptor and π-bridge (), and E_gap of DPA-[π1-π5]-A and DPA-[π1-π5]-N dyes in their optimized ground state geometry. Values are reported for the B3LYP and in brackets are for the B3P86 method.

Molecule	d(CD-Nπ) (Å)	d(CA-Nπ )(Å)	α(deg)		β(deg)	Egap (eV)
DPA-π1-A	1.46 (1.46)	1.47 (1.46)	25.22 (34.38)		56.01 (52.48)	2.77 (2.76)
DPA-π2-A	1.46 (1.45)	1.47 (1.46)	25.16 (24.76)		53.14 (50.18)	2.67 (2.66)
DPA-π3-A	1.46 (1.45)	1.47 (1.46)	4.82 (3.67)		57.27 (54.93)	2.75 (2.74)
DPA-π4-A	1.46 (1.45)	1.47 (1.46)	28.98 (27.07)		48.22 (46.56)	2.70 (2.70)
DPA-π5-A	1.46	1.47	26.09		48.96	2.60
DPA-π1-N	1.46 (1.45)	1.46 (1.45)	27.00 (26.66)		25.17 (23.80)	2.98 (2.99)
DPA-π2-N	1.46 (1.45)	1.46 (1.45)	24.04 (24.48)		22.51 (21.86)	2.77 (2.79)
DPA-π3-N	1.46 (1.45)	1.46 (1.45)	2.27 (1.40)		0.96 (1.92)	2.74 (2.81)
DPA-π4-N	1.46 (1.45)	1.46 (1.45)	27.70 (27.98)		28.06 (27.34)	2.91 (2.92)
DPA-π5-N	1.46	1.46	27.12		21.94	2.73

Therefore, it can be generally concluded that the DPA-[π1-π5]-A exhibits lower planarity than the DPA-azo-A. Also, an enhancement of bond lengths, dihedral angles, and energy gaps is observed in the DPA-[π1,π2,π4,π5]-N dyes. However, the lower values of and dihedral angles of DPA-π3-N than DPA-azo-N results in higher planarity of this dye that improves the ICT in DPA-π3-N and facilitates electron injection from this dye to the semiconductor. Also, the substitution of the π1-π5 can mostly increase the E_gap (Table 10) compared to the reference dyes, and the dyes with π1 show the highest E_gap. However, the calculated E_gap with the B3LYP method (Table 10) is lower in the DPA-π3-N compared to the DPA-azo-N. Generally, the non-planar structures have higher E_gap, which leads to lower ICT between the D,π, and A units. The HOMO/LUMO distribution on different parts of the designed DPA-[π1-π5]-A and DPA-[π1-π5]-N is shown through the FMO analyses (Figure S4). Obviously, for all these ten designed dyes, the LUMOs are distributed on acceptor units. However, the HOMOs are distributed on donor and π-bridge units in dyes with π1-π3 and on π-bridge units in dyes containing the π4 and π5. The partial DOS diagrams for these ten designed dyes are demonstrated in Figure S5, Supplementary material. Furthermore, the DOS plots indicate that in the DPA-[π1-π5]-A and DPA-[π1-π5]-N, the HOMO and LUMO peaks are shifted to lower (more negative) and higher (more positive) energy values, respectively that results in an enhancement of the E_gap. The appearance of peaks related to the new π-bridge units on both sides of the Fermi energy (green peaks) highlights the impact of the π-bridge units on increasing the E_gap in these designed dyes.

Optical Properties of Designed DPA-[π1-π5]-A and DPA-[π1-π5]-NDyes. The optical properties of designed DPA-[π1-π5]-A and DPA-[π1- π5]-N dyes have been obtained via TD-DFT calculations and are shown in Table 11.

Table 11.

Calculated optical energy gap (E_opt), oscillator strengths (f), maximum absorption wavelength (λ_max), and dominant transition contribution for the DPA-[π1-π5]-A and DPA-[π1- π5]-N. Values are reported for the B3LYP method and in brackets are for the B3P86 method.

Molecule	Eopt(eV)	f	λ max(nm)	Transition
DPA-π1-A	3.18 (3.20)	0.68 (0.69)	389.8 (386.9)	H → L + 1 68% (68%)
DPA-π2-A	2.84 (2.87)	1.10 (1.09)	435.2 (431.5)	H → L + 1 66% (63%)
DPA-π3-A	2.78 (2.80)	1.04 (1.07)	444.6 (441.2)	H → L + 1 69% (69%)
DPA-π4-A	3.06 (3.08)	1.02 (1.02)	444.2 (401.7)	H → L + 1 68% (69%)
DPA-π5-A	2.75 (2.76)	1.61 (1.59)	450.3 (447.7)	H → L + 1 66% (64%)
DPA-π1-N	2.68 (2.69)	0.80 (0.79)	461.4 (459.4)	H → L 70% (70%)
DPA-π2-N	2.48 (2.50)	1.16 (1.15)	499.1 (495.8)	H → L 70% (70%)
DPA-π3-N	2.44 (2.46)	1.29 (1.29)	506.5 (503.2)	H → L 70% (70%)
DPA-π4-N	2.63 (2.64)	0.98 (0.97)	470.5 (468.7)	H → L 70% (70%)
DPA-π5-N	2.46 (2.47)	1.49 (1.47)	502.6 (500.1)	H → L 69% (69%)

It can be observed that the substitution of the azo in the DPA-azo-A with π1-π5 leads to a blue shift in the designed dyes with the maximum in DPA-π1-A. Furthermore, in all DPA-[π1-π5]-A, the , corresponds to transitions from the HOMO to LUMO + 1. In contrast, in the case of the DPA-[π1-π5]-N dyes, there is a noticeable red shift in some dyes in the order of DPA-π3-N DPA-π5-N DPA-π2-N and a blue shift in DPA-π1-N and DPA-π4-N. Importantly, in all DPA-[π1-π5]-N dyes the is the result of transitions from HOMO to LUMO.

Charge Transport Properties of Designed DPA-[π1-π5]-A and DPA-[π1-π5]-N Dyes. The computed values of transport properties of electrons and holes in ten dyes based on different π-bridge units (π1-π5) are demonstrated in Table 12.

Table 12.

Charge transport parameters for DPA-[π1-π5]-A an DPA-[π1-π5]-N. Values are reported for the B3LYP method and in brackets are for the B3P86 method. ^a.

Molecule			(s−1)			(s−1)
DPA-π1-A	0.311 (0.289)	0.415 (0.417)	2.53 × 1014 (3.28 × 1014)	0.356 (0.351)	0.268 (0.276)	6.29 × 1013 (7.08 × 1013)
DPA-π2-A	0.330 (0.305)	0.274 (0.280)	8.87 × 1013 (1.23 × 1014)	0.339 (0.335)	0.263 (0.267)	7.41 × 1013 (7.99 × 1013)
DPA-π3-A	0.265 (0.248)	0.197 (0.208)	9.64 × 1013 (1.31 × 1014)	0.317 (0.314)	0.248 (0.253)	8.38 × 1013 (9.05 × 1013)
DPA-π4-A	0.291 (0.270)	0.376 (0.381)	2.60 × 1014 (3.38 × 1014)	0.341 (0.334)	0.254 (0.263)	6.70 × 1013 (7.77 × 1013)
DPA-π5-A	0.338	0.245	6.50 × 1013	0.320	0.231	7.10 × 1013
DPA-π1-N	0.270 (0.251)	0.404 (0.409)	3.84 × 1014 (4.85 × 1014)	0.448 (0.437)	0.386 (0.397)	4.80 × 1013 (5.72 × 1013)
DPA-π2-N	0.286 (0.273)	0.330 (0.338)	2.13 × 1014 (2.59 × 1014)	0.394 (0.389)	0.292 (0.300)	4.97 × 1013 (5.48 × 1013)
DPA-π3-N	0.209 (0.212)	0.331 (0.302)	5.26 × 1014 (4.24 × 1014)	0.313 (0.356)	0.288 (0.308)	1.19 × 1014 (8.41 × 1013)
DPA-π4-N	0.286 (0.267)	0.373 (0.379)	2.70 × 1014 (3.46 × 1014)	0.440 (0.434)	0.335 (0.346)	3.91 × 1013 (4.45 × 1013)
DPA-π5-N	0.342	0.288	8.51 × 1013	0.406	0.243	2.99 × 1013

aCalculated properties for hole and electron are shown by “+” and “‒” signs.

The results reveal that the decreases in all these designed dyes compared to the reference ones. In both DPA-[π1-π5]-A and DPA-[π1-π5]-N the higher and lower , leads to reducing the . The charge transport parameters of the designed dyes, particularly DPA-π3-A and DPA-π3-N, exhibit a significant enhancement in that is due to the lower values of . The of DPA-π3-N (calculated via the B3LYP method) is approximately 10 times more than in DPA-azo-N, which is in accordance with its higher planarity structure compared to other designed and DPA-azo-N dyes. Consequently, the results of designed dyes based on different π-bridge units illustrate that the transfer rate of electrons in dyes including two connected thiophene rings (π4) and one thiophene ring (π1) are almost equal. However, the π-bridge units with thiophene rings connected by a bond (π3) and longer double-chained bridge units (π5), are more successful in ICT.

Step III. alter acceptor

Structural and Electronic Properties of Designed DPA-azo-[A1-A5] Dyes. In the final step, the replacement of the acceptors with A1-A5 (Fig. 1, panel(d)) is done and the newly designed dyes have been optimized (Figure S6, Supplementary material). The structural properties including bond lengths, dihedral angles, and energy gaps of the DPA-azo-[A1-A5] are collected in Table 13. The results (considering the B3LYP method) show that the C_D-N_π and C_A-N_π bond lengths in the DPA-azo-A1 and DPA-azo-A4 are equal to the reference dyes. In the DPA-azo-A2 dye, the C_A-N_π bond length decreases compared to reference dyes. Moreover, in the DPA-azo-A3 and DPA-azo-A5, the carbon-nitrogen bond lengths are shorter than in the reference dyes. According to the data (Table 13), the α dihedral angles in the DPA-azo-[A1-A5] are more than in DPA-azo-A indicating the lower planarity of these designed dyes than the DPA-azo-A.

Table 13.

Carbon-nitrogen bond length at the donor- π-bridge (C_D-N_π) and acceptor-π-bridge (C_A-N_π), dihedral angles between donor and π-bridge (α) and the acceptor and π-bridge (), and E_gap of DPA-π-[A1-A5] dyes in their optimized ground state geometry. Values are reported for the B3LYP and in brackets are for the B3P86 method.

Molecule	d(CD-Nπ) (Å)	d(CA-Nπ ) (Å)	(deg)	(deg)	Egap (eV)
DPA-azo-A1	1.40 (1.39)	1.40 (1.39)	2.03 (1.90)	2.45 (2.61)	2.51 (2.51)
DPA-azo-A2	1.40 (1.39)	1.39 (1.38)	0.91 (0.89)	31.10 (29.46)	2.05 (2.06)
DPA-azo-A3	1.39 (1.39)	1.38 (1.37)	3.44 (3.48)	29.45 (18.20)	1.71 (1.74)
DPA-azo-A4	1.40 (1.39)	1.40 (1.40)	1.51 (1.63)	5.76 (4.33)	2.28 (2.30)
DPA-azo-A5	1.39 (1.39)	1.36 (1.35)	1.19 (1.53)	0.21 (0.33)	2.26 (2.27)

However, among all designed DPA-azo-[A1-A5], the DPA-azo-A3 shows higher α compared to the DPA-azo-N. Considering the lower α dihedral angles in designed dyes with A1, A2, A4, and A5 acceptors, these dyes have a greater planarity than DPA-azo-N in the connection region of the DPA-azo which increases the ICT in these designed dyes. Accordingly, the dihedral angle in DPA-azo-A5 is lower than both reference dyes representing the greater planarity of DPA-azo-A5 in the connection region of the azo-A5 that facilitates the injection of electron from this dye to the semiconductor. Furthermore, the E_gap in these five designed dyes is lower than the reference dyes, and the DPA-azo-A3 shows the lowest value. Additionally, to evaluate the distribution of the HOMO and LUMO in these designed dyes, the FMO analyses are shown in Figure S6 indicating that except for the DPA-azo-A4 the HOMO of other designed dyes are uniformly distributed on different units (along the molecular chain) and represents the aromatic character. However, in the DPA-azo-A4, the HOMO is primarily distributed on the acceptor unit. Moreover, in all designed DPA-azo-[A1-A5], the distribution of LUMO is the same and located on the azo unit and predominantly on acceptor units that represent the quinoid characteristic created by non-bonding electrons of heteroatoms such as nitrogen and sulfur⁹⁰. The partial DOS diagrams of DPA-azo-[A1-A5] are shown in Figure S7, Supplementary material. It can be observed that replacing acceptor units particularly A3 (with the lowest E_gap) causes the appearance of new peaks on both sides of the Fermi energy (green peaks) that reduce the E_gap of these designed dyes.

Optical Properties of Designed DPA-azo-[A1-A5] Dyes. The optical properties of DPA-azo-[A1-A5] dyes are provided in Table 14. The values of DPA-azo-[A1-A5] are more than the reference dyes that represent the red shift in these newly designed dyes.

Table 14.

Calculated optical energy gap (E_opt), oscillator strengths (f), maximum absorption wavelength (λ_max), and dominant transition contribution for the DPA-π-[A1-A5]. Values are reported for the B3LYP and in brackets are for the B3P86 method.

Molecule	Eopt (eV)	f	λ max (nm)	Transition
DPA-azo-A1	2.26(2.27)	0.52(0.53)	546.9(544.2)	H → L 70% (70%)
DPA-azo-A2	1.79(1.79)	0.38(0.37)	691.4(690.6)	H → L 67% (66%)
DPA-azo-A3	1.57(1.58)	0.44(0.44)	789.1(784.3)	H → L 70% (69%)
DPA-azo-A4	2.05(2.05)	0.61(0.61)	604.7(602.7)	H → L 70% (70%)
DPA-azo-A5	2.08(2.10)	0.62(0.62)	593.7(590.0)	H → L 70% (70%)

Charge Transport Properties of Designed DPA-azo-[A1-A5] Dyes. The charge transport properties of designed DPA-azo-[A1-A5] dyes are reported in Table 15.

Table 15.

Charge transport parameters for DPA-azo-[A1-A5]. Values are reported for the B3LYP and in brackets are for the B3P86 method. ^a.

Molecule			(s−1)			(s−1)
DPA-azo-A1	0.167 (0.168)	0.502 (0.510)	2.05 × 10 15 (2.07 × 1015)	0.436 (0.419)	0.392 (0.384)	5.60 × 1013 (6.47 × 1013)
DPA-azo-A2	0.398 (0.395)	0.619 (0.625)	2.12 × 1014 (2.23 × 1014)	0.506 (0.493)	0.275 (0.277)	1.30 × 1013 (1.52 × 1013)
DPA-azo-A3	0.473 (0.452)	0.772 (0.770)	1.46 × 1014 (1.82 × 1014)	0.426 (0.413)	0.312 (0.316)	3.98 × 1013 (4.69 × 1013)
DPA-azo-A4	0.138 (0.130)	0.408 (0.413)	1.95 × 1015 (2.24 × 1015)	0.364 (0.354)	0.446 (0.452)	1.60 × 1014 (1.84 × 1014)
DPA-azo-A5	0.214 (0.201)	0.571 (0.574)	1.47 × 1015 (1.75 × 1015)	0.471 (0.464)	0.486 (0.498)	5.91 × 1013 (6.71 × 1013)

^aCalculated properties for hole and electron are shown by “+” and “‒” signs.

Our results show that the in all DPA-azo-[A1-A5] dyes are lower than in DPA-azo-N. Nevertheless, the in DPA-azo-A1, DPA-azo-A4, and DPA-azo-A5 is higher than DPA-azo-A. The higher values of in the two dyes with A1 and A4 can be attributed to lower and higher values of and , respectively than in DPA-azo-A. It can be observed (Table 15) that except for DPA-azo-A2 in DPA-azo-[A1-A5] dyes, other dyes illustrate higher than reference dyes. Therefore, considering the B3LYP method the DPA-azo-A1 and DPA-azo-A4 demonstrate higher and , respectively. Strong HOMO overlap indicates that the designed DPA-azo-[A1-A5] dyes can be identified as p-type semiconductors because HOMO wave functions play a more effective role in hole transport⁹¹. As indicated, the higher intermolecular overlap of electronic wave function leads to a wider band gap and impacts the charge mobility in dyes^92,93. Additionally, from the Hopping theory, the influence of orbital overlap on the rate of charge hopping leads to an increase in the charge transport of dyes⁹⁴. Thus, these explanations can be attributed to the higher values of than in DPA-azo-[A1-A5] dyes.

Hole and electron mobility of dimer of dyes with π-stacking pattern

Carrier mobility is another important factor that affects charge transport. From the above analyses, we focus on the most efficient designed dyes in steps I-III (D3-azo-A, D3-azo-N, DPA- π3-A, DPA-π3-N, and DPA-azo-A4) and reference ones (DPA-azo-A and DPA-azo-N) to investigate the hole and electron mobility of their dimers. In organic semiconductors, charge carriers transfer through the molecular π-orbitals, so the overlap between molecular orbitals is significant in determining charge mobility. Packing configurations that promote strong intermolecular overlaps help to increase the charge carrier mobility under field-effect conditions. X-ray diffraction analysis shows a herringbone packing arrangement in which molecules are packed in an edge-to-face orientation between layers. This orientation hinders efficient charge transport due to the reduction of π-π overlap between adjacent segments^95–97. According to hopping theory, having a face-to-face stacking geometry is ideal for achieving higher mobility^98–100. Experimental evidence suggests that a π-stacking configuration can enhance charge carrier transport properties. Hence, we focus on evaluating carrier mobility using only face-to-face π-stacking geometry. Since the B3LYP method is not precise in describing weak interactions in dimer stacking patterns, we have used a DFT + D3 (D stands for dispersion) approach with Grimme’s van der Waals correction to estimate the carrier mobility¹⁰¹.

Optical Properties of Dyes Dimer. The optical properties of the dye dimers are collected in Table 16. The values of DPA-azo-A, DPA-azo-N, DPA-π3-A, and DPA-π3-N dimers are almost the same as in monomer. However, the is lower (with a blueshift) in the dimer of dyes with D3 donors and A4 acceptor compared to their monomer.

Table 16.

Calculated optical energy gap (E_opt), oscillator strengths (f), maximum absorption wavelength (λ_max), and dominant transition contribution for the dimer of dyes.

Type	Eopt (eV)	f	(nm)	Transitions
DPA-azo-A-dimer	2.33	0.65	530.8	H-1 → L (69%)
DPA-azo-N-dimer	2.51	1.53	493.8	H → L + 1(56%)
D3-azo-A-dimer	2.17	0.92	568.9	H-1 → L (66%)
D3-azo-N-dimer	2.44	1.92	506.5	H-2 → L (38%)
DPA-π3-A-dimer	2.79	1.40	444.2	H-1 → L + 2 (63%)
DPA-π3-N-dimer	2.58	1.64	479.7	H-1 → L (55%)
DPA-azo-A4-dimer	2.10	1.00	590.1	H-1 → L + 1 (44%)

The FMO analyses that represent the distribution of HOMO-1, HOMO, LUMO, and LUMO + 1 for the studied dimers in the face-to-face configurations are illustrated in Figure S8, Supplementary material. It can be observed that the structure of some optimized dimers changes from the initial face-to-face structures. The enhancement in torsion angles of molecules in a bilayer compared to a monolayer is mainly because of the repulsion of π-electrons and chalcogen interactions between sulfur atoms of the molecules in each layer¹⁰². Furthermore, according to the FMO analysis, the LUMOs indicate the diffused electron distribution. The delocalization of the LUMO throughout the entire structure of the bilayer system reduces the recombination phenomenon and facilitates electron mobility.

Charge Transport Properties of Dyes Dimer. The charge transport parameters (Table 17) show that the designed dyes containing D3 moiety (D3-azo-A-dimer and D3-azo-N-dimer) exhibit the highest values of and compared to the reference dyes and other designed ones. The results in Table 17 clearly show that, besides the electron and hole rate constant, the dyes with D3 unit have higher electron and hole mobility (and ) between layers and exhibit the best performance among all the efficient and reference dyes.

Table 17.

Charge transport parameters of the dimer of dyes.^a.

Molecule	(eV)	(eV)	(s−1)	(cm2/Vs)			(s−1)	(eV)	(s−1)	(cm2/Vs)
DPA-azo-A-dimer	0.183	0.061	2.52 × 1013		0.0009		0.335	0.060	4.04 × 1012	0.0001
DPA-azo-N-dimer	0.120	0.033	1.69 × 1013		0.0005	0.512		0.028	1.26 × 1011	0.0000
D3-azo-A-dimer	0.139	0.084	8.20 × 1013		0.0011	0.140		0.174	3.47 × 1014	0.0044
D3-azo-N-dimer	0.283	0.179	6.42 × 1013		0.0027	0.197		0.252	3.54 × 1014	0.0148
DPA-π3-A-dimer	0.011	0.001	4.38 × 1011		0.0000	0.360		0.041	1.45 × 1012	0.0000
DPA-π3-N-dimer	0.202	0.022	2.65 × 1012		0.0000	0.237		0.027	2.55 × 1012	0.0001
DPA-azo-A4-dimer	0.089	0.018	8.06 × 1012		0.0002	0.292		0.037	2.49 × 1012	0.0001

^aCalculated properties for hole and electron are shown by “+” and “‒” signs.

Photovoltaic parameters

Our analyses demonstrated that the designed dyes satisfy the essential energy alignment criteria and possess the potential to be used as sensitizers in DSSCs. Taking these factors into account, the photovoltaic properties of both the references and the efficiently designed dyes were evaluated (Table 18). Generally, the efficient dyes in DSSCs should have strong anchoring groups to attach to the semiconductor surface and the LUMO energy level of the dyes should be higher than the conduction band minimum (CBM) of TiO₂ semiconductor (-4.05 eV)¹⁰³ to inject electron from dyes to semiconductor. Also, the HOMO energy levels of dyes should be lower than the redox potential of the electrolyte (-4.85 eV)¹⁰⁴ to allow efficient regeneration. The HOMO and LUMO energies for the designed and reference dyes, as well as the CBM of TiO₂ semiconductor and redox potential of the electrolyte in a DSSC, are depicted in Fig. 4. Evidently, the energy levels of the LUMO in all dyes are higher than the CBM level of TiO₂ (-4.05 eV) which affirms the possibility of electron injection from the excited states of dyes to the TiO₂ semiconductor. However, except D3-azo-A with the highest HOMO energy level (-4.78 eV), all efficient dyes illustrate a lower HOMO energy level than the redox potential of the electrolyte that guarantees efficient dye regeneration (Fig. 4)¹⁰⁵.

Table 18.

Computed photovoltaic parameters for the reference and designed dyes.

system	LHE	injφ	IPCE	Jsc(mA/cm2)	Voc(V)	FF	PCE%
D3-azo-A	0.83	1.000	0.834	40.41	1.16	0.895	41.98
D3-azo-N	0.94	0.999	0.937	41.42	1.22	0.899	45.46
DPA-π3-A	0.91	0.999	0.908	32.50	1.27	0.903	37.26
DPA-π3-N	0.95	0.999	0.948	38.68	1.24	0.901	43.20
DPA-azo-A4	0.75	0.999	0.754	36.73	0.56	0.820	16.86
DPA-azo-A	0.75	0.997	0.753	29.62	1.03	0.885	27.01
DPA-azo-N	0.89	0.995	0.886	34.85	1.09	0.890	33.82

Fig. 4.

The energy level diagrams of studied dyes relative to the CBM of semiconductor (TiO₂) and the redox potential of the electrolyte ().

Based on the stated equations (Eqs. 6 and 7), it is evident that greater values of LHE lead to higher IPCE. As can be seen in Table 18, the LHE and IPCE values of D3-azo-N, DPA-π3-A, and DPA-π3-N are higher than other designed and reference dyes. Additionally, of all selected designed dyes falls in the visible region indicating that these dyes are proper candidates for utilizing in DSSCs. The Jsc (Eq. 10) is directly proportional to IPCE and λ and mostly shows higher values in all designed dyes compared to reference ones and the D3-azo-A and D3-azo-N exhibit the highest values. The Voc values (Table 18) are another important parameter that directly impacts the PCE. Among all the designed dyes, only DPA-azo-A4 displays a very low Voc, which can be attributed to the lowest LUMO energy level of this dye relative to the TiO₂ CBM. Basically, the dyes with large V_OC and suitable J_SC can be the better sensitizer in DSSCs. From Table 18 it can be concluded that except for DPA-azo-A4, the other designed dyes with higher values of Voc, and FF demonstrate higher PCE compared to the DPA-azo-A and DPA-azo-N dyes and the D3-azo-N, and DPA-π3-N dyes with the highest PCE (45.46% and 43.20%, respectively) can be the effective dyes for enhancing the DSSCs’ performance.

Adsorption of dye on the TiO2 surface

Interfacial electron transfer between dye and semiconductor is crucial for the stability and energy alignment, impacting the overall efficiency of DSSCs. So, examining the adsorption of designed dyes on the TiO₂ semiconductor is also worthwhile. Due to the high computational cost, we investigated the adsorption of DPA-azo-A4 on the TiO₂ surface with different acceptor unit (A4) compared to the reference dyes. The adsorption energy (E_ads) of the dye/TiO₂ complex is computed by:

14

where E_dye/TiO2 is the total energy of the dye/TiO₂ system, and E_dye and E_TiO2 are the energies of dye and TiO₂ anatase unit cell, respectively. The optimized structure of DPA-azo-A4/TiO₂ is represented in Fig. 5.

Fig. 5.

Adsorption geometry for DPA-azo-A4/TiO₂.

The interaction between the C₂N₂S ring and Ti atoms, as well as the H atom of dye and the O atom on the TiO₂ surface, gives rise to the stable adsorption geometry. A negative Eads of -1.18 eV reveals that DPA-azo-A4 can be stably adsorbed on the TiO₂. Interestingly, the C₂N₂S unit serves as an anchoring group for dye adsorption on the semiconductor surface. Conversely, the absence of such an anchoring group is advantageous for DPA-azo-A and DPA-azo-N reference dyes.

Conclusions

To sum up, this research focused on the development of new dyes for DSSC by altering the donor, π-bridge, and acceptor units of two synthesized dyes with D-π-A framework. In this regard, we considered the DPA-azo-A and DPA-azo-N dyes and designed [D1-D4]-azo-A/[D1-D4]-azo-N, DPA-[π1-π5]-A/DPA-[π1-π5]-N, and DPA-azo-[A1-A5] dyes. The structure, electronic, optical, charge transport, and photovoltaic properties of these dyes were evaluated theoretically and compared to the reference dyes (DPA-azo-A and DPA-azo-N). Among all [D1-D4]-azo-A/[D1-D4]-azo-N dyes, the dyes with D3 donor demonstrated more aromatic character and planarity resulting in high degrees of π-conjugation and electron delocalization. So the D3-azo-A and D3-azo-N showed the lowest E_gap and higher charge transfer rate constant which are capable of enhancing the ICT and electron injection to the semiconductors. Moreover, in the DPA-[π1-π5]-A/DPA-[π1-π5]-N dyes, the DPA-π3-N exhibited lower E_gap and more planarity than DPA-azo-N that enhance the ICT and eases the electron injection from this dye to semiconductor. Furthermore, in the DPA-π3-A and DPA-π3-N dyes the π3 is the thiophene rings that are connected by a bond revealing the more electron rate constant. In the case of DPA-azo-[A1-A5] dyes, the dyes with A1, A2, A4, and A5 acceptors showed greater planarity in the connection region of the DPA-azo indicating the higher ICT in these designed dyes. The DPA-azo-A3 had the lowest E_gap and the DPA-azo-A1 and DPA-azo-A4 showed the higher hole and electron rate constant, respectively. Additionally, the charge transport properties of the face-to-face π-stacking pattern of effective dyes demonstrated that the D3-azo-A and D3-azo-N had the highest values of electron/hole rate constant and mobility between layers. Lastly, the calculated photovoltaic parameters of the efficient dyes exhibited that the designed dyes including the D3 and π3 had higher values of IPCE, LHE, J_SC, V_OC, FF, and PCE compared to the reference dyes and the D3-azo-A, D3-azo-N, and DPA-π3-N showed the higher PCE values. Although these three designed dyes showed a higher value of PCE, the higher HOMO energy level of D3-azo-A than the redox potential of electrolyte may reduce its efficiency in DSSCs. Conclusively, our theoretical findings propose that substituting the donor (DPA) and π–bridge (azo) units in DPA-azo-N dyes with D3 and π3 to design the new D3-azo-N, and DPA-π3-N dyes can improve the PCE values and boost the efficiency of DSSCs.

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

Author contributions

Akbar Omidvar: Supervision; Conceptualization; Investigation; Writing & editing; Software; Reviewed the manuscriptFateme Fazeli: Software; Formal analyses; Visualization; Prepared all figuresTahereh Ghaed-Sharaf: Investigation; Writing & editing; Reviewed the manuscriptReza Keshavarzi: Reviewed the manuscript.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Data availability

Availability of Data and Materials: The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Conflict of interest

The authors declare no competing financial interest.

Supplementary Information

Supplementary material available: The Dihedral angles, most stable structures, FMO analyses, DOS analyses, and the cartesian coordinates for the reference dyes.

Ethics approval

Not Applicable.