Theoretical studies of electronic and optical characteristics in donor-π-Acceptor (D-π-A) dyes: DFT and TD-DFT methods

Abstract

This research focused on enhancing D-π-A organic dyes derived from coumarin and its derivatives, collectively referred to as D-CM-A dyes. The study aimed to improve these dyes by introducing various donors and acceptors to the coumarin structure. Six new coumarin dyes were evaluated, primarily for their potential application in dye-sensitized solar cells (DSSCs) to enhance energy efficiency. The analysis involved calculating the geometry, electronic properties, and optoelectronic characteristics of the dye molecules using DFT and TD-DFT methods with the B3LYP functional and the 6-311G basis set in both gas and solvent phases. The primary focus was to understand how modifications to the π-conjugated D-π-A organic dyes influenced their optoelectronic properties, including key factors such as maximum absorption wavelength (λ_max), highest occupied molecular orbital energy (E_HOMO), lowest unoccupied molecular orbital energy (E_LUMO), and energy gap (E_gap). Additionally, the study explored the photovoltaic properties of these dyes. The findings highlighted D4-CM-A4 as a promising candidate with the narrowest energy gap, while D1-CM-A1 and D2-CM-A2 showed superior light-harvesting efficiencies (LHE) compared to other derivatives. In conclusion, this study suggests that D1-CM-A1 and D2-CM-A2 are favourable choices for enhancing the performance of DSSCs due to their promising optoelectronic properties.

Coumarin dye, D-π-A dyes, DFT, TD-DFT methods, HOMO, LUMO energies and optical properties

Introduction

The surge in global energy demand, fueled by population expansion and concurrent developmental activities, has led to a substantial increase in energy prices since the beginning of the 21st century [1]. Presently, the global demand for energy stands at 13 terawatts (TW), with projections indicating a surge to 23 TW by the year 2050 [2]. The predominant contributors to the current energy landscape are fossil fuels, and forecasts suggest the depletion of oil and natural gas fossil resources by 2042 [3]. The excessive utilization of fossil fuels poses a severe threat to the environment. The combustion of these fuels elevates the concentration of greenhouse gases, thereby exerting a significant impact on climatic patterns [4]. Given the potential consequences, there exists a pressing need to accelerate the progress in the development of advanced clean energy technologies, specifically focusing on renewable energy sources. This imperative arises from the global challenges associated with energy security, climate change, and the pursuit of sustainable development.

The recognition of solar energy as a promising future renewable energy source is widespread, but a significant challenge persists in efficiently capturing and converting solar energy into chemical or electrical energy at a cost-effective rate [5]. Diverse technologies have been developed for solar energy harvesting, classified into three generations [6]. The first generation is based on crystalline silicon, the second generation employs thin-film technologies, and the third generation is distinguished by the utilization of organic constituents for processes like light harvesting or charge carrier transport, as seen in technologies like Dye-Sensitized Solar Cells (DSSCs).

In 1991, Michael Grätzel pioneered dye-sensitized solar cells (DSSCs), a subset of thin-film solar cells, attracting significant attention from both academic and commercial research communities [7]. Over the past two decades, DSSCs have emerged as a noteworthy contender for the next generation of solar cells due to their cost-effectiveness, high conversion efficiency, and ease of manufacturing [8–10]. The crucial component of DSSCs is the photosensitizing dye, which plays a pivotal role in determining light absorption range and harvesting efficiency [11–14]. The use of ruthenium polypyridine complexes as photosensitizing dyes has notably facilitated the achievement of conversion efficiencies exceeding 11%, owing to their broad absorption spectra resulting from metal-to-ligand charge transfer (MLCT) and favourable photovoltaic properties [15–17]. However, widespread adoption faces challenges related to the scarcity and high cost of ruthenium, issues associated with isomerization or degradation during purification, and a limited molar extinction coefficient [18, 19].

Conversely, metal-free organic dyes offer several advantages when compared to Ru-complex dyes. These advantages include reduced material costs, higher molar extinction coefficients, and a simplified purification process (Reference: [6]). Additionally, the molecular structure of organic dyes, often constructed with a donor-bridge-acceptor (D-A) configuration, is generally more straightforward to design and modify, especially in terms of adjusting the energy levels of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) [20–25].

Despite these advantages, organic dyes tend to exhibit lower conversion efficiency compared to Ru-complex dyes due to their limited absorption spectra and weaker photovoltaic properties. Furthermore, when used as sensitizers in dye-sensitized solar cells (DSSCs), they may encounter issues such as aggregation and reduced stability [19]. Donor–acceptor (D–A) organic molecules constitute a fundamental class of conjugated organic materials, where electron-donating and electron-accepting groups are interconnected through a π-conjugated bridge. The manipulation of the donor or acceptor components within a D–A molecule enables the adjustment of its physical and chemical characteristics. Molecules structured with D–π–A configurations have gained increasing attention due to their versatile applications as electroactive and photoactive materials in various domains of molecular electronics. These applications span across biochemical fluorescent technology, the development of efficient nonlinear optical (NLO) materials, electrogenerated chemiluminescence, the fabrication of organic light-emitting diodes (OLEDs), and the design of solar cells. The D–π–A molecular structure proves particularly valuable in these areas, underscoring its significance in advancing electronic and optoelectronic technologies [26].

A diverse array of molecular species, including triarylamines, carbazoles, fluorine, thiophenes, and oligothiophenes, primarily function as electron-donating components. In contrast, electron-accepting moieties frequently encompass oxadiazoles, diarylborons, quinolines, quinoxalines, thienopyrazines, and benzothiadiazoles. Within these compounds, the donor moiety supports hole injection and transport, while the acceptor moiety facilitates electron injection and transport. Donors such as carbazole, N, N-dimethylbenzenamine, and phenothiazine are commonly selected for their exceptional thermal and electrochemical stability, along with their effective electron-donating capabilities [27]. The fundamental structure of organic sensitizers comprises donor (D), bridge (π spacer), and acceptor (A) moieties, denoted as D-π-A. This configuration enhances the efficiency of UV/Vis photo-induced intra-molecular charge transfer (ICT). Key factors influencing sensitization include the dye’s ability to effectively harvest light, generating a substantial photocurrent response, strong conjugation across the donor and acceptor groups to establish a pronounced charge transfer character in electronic transitions, and the electronic coupling strength that facilitates efficient electron injection from the dye onto the semiconductor surface (Reference: [28]).

Coumarin-based dyes have proven to be highly effective in dye-sensitized solar cells (DSSCs), demonstrating photovoltaic conversion efficiencies of approximately 8%. These dyes exhibit noteworthy photo responsiveness in the visible region, long-term durability under exposure, and suitable energy level alignment for injection into the conduction band of TiO₂. The coumarin class remains intriguing due to its rapid injection rates onto TiO₂ substrates and the availability of a wide range of chemical derivatives with highly diverse properties. Through careful selection of molecular structure, the performance of coumarin-based DSSCs has been significantly enhanced, addressing aggregation issues while improving both absorption and redox properties [29, 30].

DFT has emerged as a reliable standard tool for theoretically investigating electronic structures and absorption spectra, while TD-DFT provides accurate values for valence excitation energies using standard exchange-correlation functionals. DFT has found extensive application in examining the structures and absorption spectra of sensitizers designed for use in dye-sensitized solar cells (DSSCs) [31–41].

In this research endeavour, a comprehensive examination was undertaken to analyze the electronic structure and optical characteristics of six D-π-A dyes based on coumarin. These dyes are specifically labelled as D1-CM-A1, D2-CM-A2, D3-CM-A3, D4-CM-A4, D5-CM-A5, and D6-CM-A6, as visually represented in Fig. 1 by using the Donors (D1, D2, D3, D4, D5 and D6) at seven position and acceptors (A1, A2, A3, A4, A5 and A6) at four positions in coumarin dye shown in Fig. S1.

Figure 1.

Structures of D-π-A dye. (Donor is seven (7) positions, and acceptor is third (3) positions in coumarin dye).

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Computational methodology

Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TD-DFT) techniques were employed to examine the structural, electronic, and optical characteristics of the D-π-A dyes depicted in Fig. 1. These computations utilized the B3LYP hybrid functional correction with a 6-311G basis set [42, 43]. Geometric configurations, electronic properties, and optical attributes of multiple organic dye molecules were assessed both in a gaseous environment and in chloro-benzene solvent. The neutral molecule structures were optimized, and the HOMO and LUMO energy levels as well as the energy bandgap (E_gap) were determined. For the analysis of electronic transitions, the TD-DFT method was employed, involving a study of the associated wavelengths and oscillator strengths. Additionally, solvent effects, specifically in chlorobenzene, were considered through calculations employing a Polarizable Continuum Model (PCM) [44, 45]. All calculations were performed using the Gaussian program 09 W [46].

Results and discussion

Geometry optimization structures and geometrical parameters

Determining the most stable molecule was the goal of the geometry optimization procedure. Thus, by examining bond length, bond angle, dihedral angle, intramolecular charge transfer (ICT), energy gap, and quadruple moment, this study explored optimal shape. Fig. 2 displays the optimal geometry discovery of the derivatives of coumarin dye in the gas phase (S1 in solvent), whereas Fig. 3 displays it in the solvent phase. The bond lengths of derivatives of coumarin dyes are detailed in Table 1. A reduction in bond length signifies the transfer of intermolecular charge from the donor to the acceptor. Specifically, the bond lengths between the electron donor and linker range from 1.453 to 1.483 angstroms in the gas phase and from 1.452 to 1.488 angstroms in the solvent phase. In the gas phase, the bond lengths between the electron acceptor and linker span from 1.484 to 1.489 angstroms, while in the solvent phase, they range from 1.485 to 1.489 angstroms. Consequently, the computed bond lengths of the model compounds exhibit the following trends: For both the gas and solvent phases, the order is D1-CM-A1 > D2-CM-A2 > D3-CM-A3 > D5-CM-A5 > D4-CM-A4 > D6-CM-A6, with D1-CM-A1 > D2-CM-A2 > D5-CM-A5 > D3-CM-A3 > D4-CM-A4 > D6-CM-A6 in the respective phases.

Figure 2.

The optimized structure D-π –A of coumarin dyes (position 4) in gas phase. (Red colour is oxygen atom, Yellow colour is sulfur atom, Dark silver is a carbon atom, Pale silver is a hydrogen atom and Blue colour is a nitrogen atom).

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Figure 3.

The geometry optimized structures of D-π –A of coumarin-based dyes in the solvent phase, calculated by DFT/B3LYP with a 6-311G basis set. The red colour is an oxygen atom; the Yellow colour is a sulfur atom; Dark silver is a carbon atom, Pale silver is a hydrogen atom and the Blue colour is a nitrogen atom.

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Table 1.

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Optimized selected bond lengths of the studied molecules obtained by B3LYP/6-31G level in gas and chlorobenzene solvent phases

Dye	Gas		Chlorobenzene
Dye	(D-π)	(π-A)	(D-π)	(π-A)
OD1	1.45391	1.48970	1.45301	1.48929
OD2	1.45372	1.48861	1.45283	1.48826
OD3	1.48347	1.48722	1.48368	1.48696
OD4	1.45650	1.48595	1.45463	1.48591
OD5	1.48336	1.48666	1.48340	1.48739
OD6	1.45866	1.48433	1.48880	1.48501

Dye	Gas		Chlorobenzene
Dye	(D-π)	(π-A)	(D-π)	(π-A)
OD1	1.45391	1.48970	1.45301	1.48929
OD2	1.45372	1.48861	1.45283	1.48826
OD3	1.48347	1.48722	1.48368	1.48696
OD4	1.45650	1.48595	1.45463	1.48591
OD5	1.48336	1.48666	1.48340	1.48739
OD6	1.45866	1.48433	1.48880	1.48501

Table 1.

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Optimized selected bond lengths of the studied molecules obtained by B3LYP/6-31G level in gas and chlorobenzene solvent phases

Dye	Gas		Chlorobenzene
Dye	(D-π)	(π-A)	(D-π)	(π-A)
OD1	1.45391	1.48970	1.45301	1.48929
OD2	1.45372	1.48861	1.45283	1.48826
OD3	1.48347	1.48722	1.48368	1.48696
OD4	1.45650	1.48595	1.45463	1.48591
OD5	1.48336	1.48666	1.48340	1.48739
OD6	1.45866	1.48433	1.48880	1.48501

Dye	Gas		Chlorobenzene
Dye	(D-π)	(π-A)	(D-π)	(π-A)
OD1	1.45391	1.48970	1.45301	1.48929
OD2	1.45372	1.48861	1.45283	1.48826
OD3	1.48347	1.48722	1.48368	1.48696
OD4	1.45650	1.48595	1.45463	1.48591
OD5	1.48336	1.48666	1.48340	1.48739
OD6	1.45866	1.48433	1.48880	1.48501

In solar cells, the bond length between the donor components and the conjugated linker plays a crucial role in facilitating the transfer of charge between the donor and acceptor groups. Notably, intermolecular charge transfer (ICT) is more likely to occur when the bond length is shorter [47]. Among the dye derivatives, D2-CM-A2 exhibits a notably low bond length, suggesting its favourable potential for charge transfer. Additionally, it’s observed that the bond length between the donor and acceptor tends to decrease as the acceptor’s strength increases [48]. Typically, shorter bond lengths signify stronger bonds, leading to greater molecular stability, while longer bond lengths indicate a less stable molecule [49]. Additionally, the results reveal that in solvent phases, some bond lengths increase while others decrease. This behaviour is attributed to the nature of the bond formed. When a non-polar bond is exposed to a polar solvent, the bond length tends to decrease. Conversely, if the bond is already polar, the addition of a polar solvent tends to increase the bond length.

Dihedral angles are another significant parameter influencing the stability of a molecule. Table 2 provides information on the dihedral angles in both the gas and solvent phases. The average dihedral angles for the donor groups, ranging from D1-CM-A1 to D6-CM-A6, are as follows: −29.570, −25.520, 15.320, −145.220, −133.550, and −150.770 in the gas phase, and −26.440, −22.650, 90.400, −53.440, −134.390, and −151.030 in the solvent phase, respectively. Notably, D2-CM-A2 exhibits a lower dihedral angle value, indicating a less pronounced conjugation effect compared to the other compounds, suggesting a higher degree of coplanarity.

Table 2.

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Optimized selected dihedral angles and Intramolecular charge transfer (ICT) of the studied molecules obtained by B3LYP/6-3IG level in the gas and solvent phases

Dye	dihedral angles in A⁰				Intramolecular charge transfer (ICT)
Dye	Gas		solvent		gas	solvent
OD1	π-A	−169.58	CM-A	116.12	0.00	5.00 × 10⁻⁸
OD1	D-π	116.70	CM-D	−175.26	0.00	5.00 × 10⁻⁸
OD2	π-A	121.18	CM-A	120.22	5.26 × 10⁻⁸	0.00
OD2	D-π	−166.48	CM-D	−171.25	5.26 × 10⁻⁸	0.00
OD3	π-A	35.07	CM-A	−116.49	2.56 × 10⁻⁸	2.62 × 10⁻¹⁸
OD3	D-π	145.74	CM-D	147.12	2.56 × 10⁻⁸	2.62 × 10⁻¹⁸
OD4	π-A	−120.38	CM-A	−119.73	9.91 × 10⁻¹⁹	5.71 × 10⁻⁸
OD4	D-π	13.49	CM-D	−170.71	9.91 × 10⁻¹⁹	5.71 × 10⁻⁸
OD5	π-A	−122.18	CM-A	−120.29	−2.50 × 10⁻⁸	−2.50 × 10⁻⁸
OD5	D-π	146.61	CM-D	−146.81	−2.50 × 10⁻⁸	−2.50 × 10⁻⁸
OD6	π-A	−131.12	CM-A	−124.35	0.00	2.38 × 10⁻⁸
OD6	D-π	−170.95	CM-D	−177.19	0.00	2.38 × 10⁻⁸

Dye	dihedral angles in A⁰				Intramolecular charge transfer (ICT)
Dye	Gas		solvent		gas	solvent
OD1	π-A	−169.58	CM-A	116.12	0.00	5.00 × 10⁻⁸
OD1	D-π	116.70	CM-D	−175.26	0.00	5.00 × 10⁻⁸
OD2	π-A	121.18	CM-A	120.22	5.26 × 10⁻⁸	0.00
OD2	D-π	−166.48	CM-D	−171.25	5.26 × 10⁻⁸	0.00
OD3	π-A	35.07	CM-A	−116.49	2.56 × 10⁻⁸	2.62 × 10⁻¹⁸
OD3	D-π	145.74	CM-D	147.12	2.56 × 10⁻⁸	2.62 × 10⁻¹⁸
OD4	π-A	−120.38	CM-A	−119.73	9.91 × 10⁻¹⁹	5.71 × 10⁻⁸
OD4	D-π	13.49	CM-D	−170.71	9.91 × 10⁻¹⁹	5.71 × 10⁻⁸
OD5	π-A	−122.18	CM-A	−120.29	−2.50 × 10⁻⁸	−2.50 × 10⁻⁸
OD5	D-π	146.61	CM-D	−146.81	−2.50 × 10⁻⁸	−2.50 × 10⁻⁸
OD6	π-A	−131.12	CM-A	−124.35	0.00	2.38 × 10⁻⁸
OD6	D-π	−170.95	CM-D	−177.19	0.00	2.38 × 10⁻⁸

Table 2.

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Optimized selected dihedral angles and Intramolecular charge transfer (ICT) of the studied molecules obtained by B3LYP/6-3IG level in the gas and solvent phases

Dye	dihedral angles in A⁰				Intramolecular charge transfer (ICT)
Dye	Gas		solvent		gas	solvent
OD1	π-A	−169.58	CM-A	116.12	0.00	5.00 × 10⁻⁸
OD1	D-π	116.70	CM-D	−175.26	0.00	5.00 × 10⁻⁸
OD2	π-A	121.18	CM-A	120.22	5.26 × 10⁻⁸	0.00
OD2	D-π	−166.48	CM-D	−171.25	5.26 × 10⁻⁸	0.00
OD3	π-A	35.07	CM-A	−116.49	2.56 × 10⁻⁸	2.62 × 10⁻¹⁸
OD3	D-π	145.74	CM-D	147.12	2.56 × 10⁻⁸	2.62 × 10⁻¹⁸
OD4	π-A	−120.38	CM-A	−119.73	9.91 × 10⁻¹⁹	5.71 × 10⁻⁸
OD4	D-π	13.49	CM-D	−170.71	9.91 × 10⁻¹⁹	5.71 × 10⁻⁸
OD5	π-A	−122.18	CM-A	−120.29	−2.50 × 10⁻⁸	−2.50 × 10⁻⁸
OD5	D-π	146.61	CM-D	−146.81	−2.50 × 10⁻⁸	−2.50 × 10⁻⁸
OD6	π-A	−131.12	CM-A	−124.35	0.00	2.38 × 10⁻⁸
OD6	D-π	−170.95	CM-D	−177.19	0.00	2.38 × 10⁻⁸

Dye	dihedral angles in A⁰				Intramolecular charge transfer (ICT)
Dye	Gas		solvent		gas	solvent
OD1	π-A	−169.58	CM-A	116.12	0.00	5.00 × 10⁻⁸
OD1	D-π	116.70	CM-D	−175.26	0.00	5.00 × 10⁻⁸
OD2	π-A	121.18	CM-A	120.22	5.26 × 10⁻⁸	0.00
OD2	D-π	−166.48	CM-D	−171.25	5.26 × 10⁻⁸	0.00
OD3	π-A	35.07	CM-A	−116.49	2.56 × 10⁻⁸	2.62 × 10⁻¹⁸
OD3	D-π	145.74	CM-D	147.12	2.56 × 10⁻⁸	2.62 × 10⁻¹⁸
OD4	π-A	−120.38	CM-A	−119.73	9.91 × 10⁻¹⁹	5.71 × 10⁻⁸
OD4	D-π	13.49	CM-D	−170.71	9.91 × 10⁻¹⁹	5.71 × 10⁻⁸
OD5	π-A	−122.18	CM-A	−120.29	−2.50 × 10⁻⁸	−2.50 × 10⁻⁸
OD5	D-π	146.61	CM-D	−146.81	−2.50 × 10⁻⁸	−2.50 × 10⁻⁸
OD6	π-A	−131.12	CM-A	−124.35	0.00	2.38 × 10⁻⁸
OD6	D-π	−170.95	CM-D	−177.19	0.00	2.38 × 10⁻⁸

Intramolecular charge transfer (ICT)

The measurement of Intramolecular Charge Transfer (ICT) in dye-sensitized solar cells (DSSCs) is a crucial signal for the transfer of charge from the donor to an anchoring group. A redshift in the organic photovoltaic spectrum may result from ICT’s tendency to stabilize the HOMO and LUMO energy levels and close the energy gap between them. The ICT values for the solvent and gas phases are shown in Table 2. According to the Mulliken charge distribution, the ICT values are arranged as follows: For the gas and solvent phases, respectively, D6-CM-A6 ≈ D1-CM-A1 > D2-CM-A2 > D3-CM-A3 > D4-CM-A4 > D5-CM-A5 and D2-CM-A2 > D4-CM-A4 > D1-CM-A1 > D6-CM-A6 > D3-CM-A3 > D5-CM-A5. Notably, D4-CM-A4 and D5-CM-A5 exhibit lower ICT values, suggesting that electrons can transfer directly from the donor to the anchoring group. When the ICT value is low, charge separation occurs more effectively, and this ICT significantly enhances the delocalization of π-electrons, thereby reducing the bond length of the model compounds [50].

Electronic parameters

In determining the charging separation status of dye sensitization, the contribution of Frontier Molecular Orbitals (FMOs) is very significant. There is a well-recognized effect on electronic load transfer characteristics in dyes in the distributed FMOs of the sensitizers. Charging from donor to e-acceptor groups usually shows that the teeth are potent sensitizers [51]. The HOMO orbits are located on the contributor portion, and the LUMO orbitals are found mainly in the acceptor group. HOMO has bonding characters, while LUMO orbitally has an antibody bonding character of all molecules. On the other hand, this creates effective load separation states [28]. ICT from donor to acceptor is one of the most significant features of non-metallic organic dyeing in DSSCs. The electron density contribution of each atom added to the donor and acceptor group determines the dyes’ potential for electron transfer [52].

These findings demonstrate that all HOMO orbits are found on the donor side, whereas LUMO orbits are mostly found in the acceptor (cyanoacrylate) category. While all LUMO orbits have ant-bonds, all HOMO orbits have bonds. However, the HOMOS have all come together. This is done to create proper circumstances for charge separation, as demonstrated in Fig. 4 in the solvent and gas phases of Fig. 5. When evaluating organic solar cells, the energies of the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) are critical factors. Controlling the effectiveness of charge transfer from the donor to the anchoring group is largely dependent on these parameters.

Figure 4.

The contour plots of HOMO and LUMO orbital were calculated by DFT/B3LYP/6-31G of coumarin dyes of D-π-A in the solvent phase.

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Figure 5.

The contour plots of HOMO and LUMO orbital were calculated by DFT/B3LYP/6-311G of coumarin dyes of D-π-Ain the solvent phase.

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The electrochemical characteristics of D-π-A compounds can be greatly influenced by the dye selection in terms of its electron donor capability. Higher HOMO energy levels are typically found in D-π-A dyes with a more robust set of electron donors than in those with weaker electron donors. In a photovoltaic system, the ability for charge transfer between the donor and acceptor to occur depends critically on the HOMO and LUMO energy levels of both the donor and acceptor molecules.

The following energies apply to HOMOs in the gas and solvent phases of D1-CM-A1 to D6-CM-A6: Solvent Phase: −5.365, −5.363, −5.727, −5.594, −6.232, −5.732; Gas Phase: 5.440, −5.412, −5.822, −5.725, −6.328, −5.734. For D1-CM-A1 to D6-CM-A6, the absolute energies of LUMOs in the gas and solvent phases are as follows: −3.520, −3.500, −3.920, −3.898, −4.347, −4.418 for the gas phase; −3.306, −3.365, −3.712, −3.795, −4.084, −4.241 for the solvent phase. Understanding the potential for charge transfer and the general performance of these compounds in the context of organic solar cells depends critically on these energy levels.

In dye-sensitized solar cells (DSSCs), it is crucial to closely match the energy levels of the TiO₂ conductive edge and the electrolyte redox potential with the HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) energy levels of the dye. This alignment is essential for effective charge separation and dye recovery procedures. Specifically, concerning the redox potential (typically around −4.0 eV), the HOMO level must be sufficiently positive to enable effective electron injection from the excited dye to the semiconductor’s conduction band. On the other hand, to ensure that electrons can be injected into the semiconductor’s conduction band, the dye’s LUMO level needs to be more negative than the TiO₂’s conduction band edge, which is typically around −5.0 eV.

The findings show that the energy levels of D1-CM-A1, D2-CM-A2, D3-CM-A3, and D4-CM-A4 are greater than the conduction band edge (−4.0 eV) of the TiO₂ electrode. This suggests that these dyes can efficiently introduce electrons into the conduction band of semiconductors. Nevertheless, as Fig. 6 illustrates, D5-CM-A5 and D6-CM-A6 exhibit LUMO values that are less than TiO₂, indicating that electrons cannot be injected into the semiconductor’s conduction band. The overall efficiency of DSSCs depends on this energy level alignment. One important component in figuring out a dye’s photocurrent is its band gap. When absorbing light energy of the appropriate wavelength, a smaller band gap generally helps to facilitate the passage of electrons from the HOMO (Highest Occupied Molecular Orbital) to the LUMO (Lowest Unoccupied Molecular Orbital).

Figure 6.

HOMO and LUMO energy level of the model compounds by DFT/B3LYP/6-31Gbasis set for the gas phase (left) and solvent phase (right).

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For both the gas and solvent phases, the computed energy gaps of the model compounds under investigation show the following trends: Solvent Phase: D5-CM-A5 > D1-CM-A1 > D3-CM-A3 > D2-CM-A2 > D4-CM-A4 > D6-CM-A6; Gas Phase: D5-CM-A5 > D1-CM-A1 > D3-CM-A3 > D2-CM-A2 > D4-CM-A4 > D6-CM-A6 Among the dye derivatives, D4-CM-A4 and D6-CM-A6 are notable for having the narrowest energy gap values. This implies that in these compounds, the electrons move quickly from the HOMO to the LUMO. Because of their more favourable energy gap characteristics, it is advised that D4-CM-A4 and D6-CM-A6 be used in Dye-Sensitized Solar Cells (DSSCs) rather than the other chemicals.

Absorption properties

The intensity of oscillators associated with the maximum wavelength (topic) absorption and the sheer energy of the dye from the ground-to-excited condition are known as absorption characteristics, and they define the amount of light absorbed by the molecule. The absorption wavelength of the TD-DFT/B3LYP/6-311G techniques for gas and chlorobenzene, as well as the excitation energies and oscillator strengths (f) of the dye molecule, are shown in Table 3 and 4 in the gas and solvent phase respectively. The dye molecules’ vertical excitation energy varied according to the donor group attached to the coumarin tooth. D3-CM-A3 > D4-CM-A4 > D1-CM-A1 > D2-CM-A2 > D6-CM-A6 > D5-CM-A5 and D3-CM-A3 > D4-CM-A4 > D6-CM-A6 > D2-CM-A2 > D1-CM-A1 > D5-CM-A5 are the groups in descending order. The donor community shifts also affected the first vertical enthusiasm impulses. Consequently, the stronger oscillator is the transfer from any transition state’s ground state to its excited state [53].

Table 3.

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The absorption properties of studied dyes derivatives obtained by B3LYP/6-31G level in D-π-A (position 4) gas phase

Dye		λ max(nm)	eV	(f)	MO contribution
OD1	S1	788.47	1.5725	0.0028	H→L (99.24%)
	S2	460.41	2.6929	0.1229	H-1→L (87.88%)
					H→L + 1(10.71%)
	S3	449.91	2.7558	0.7768	H-1→L (10.82%)
					H→L + 1(87.35%)
	S4	400.77	3.0937	0.0038	H-5-L + 1(4.98%)
					H-3→L (20.79%)
					H-2→L (70.38%)
	S5	375.36	3.3031	0.0862	H-4→L (87.60%)
					H-3→L (3.44%)
					H-2→L (4.39%)
	S6	366.29	3.3849	0.0027	H-5→L (28.63%)
					H-4→L (4.82%)
					H-3→L (42.69%)
					H-2→L (23.25%)
OD2	S1	789.66	1.5701	0.0061	H→L (99.33%)
	S2	544.82	2.2757	0.0001	H-1→L (99.83%)
	S3	456.55	2.7157	0.5858	H-2→L (29.00%)
					H→L + 1(69.46%)
	S4	447.17	2.7726	0.2095	H-2→L (69.72%)
					H→L + 1(28.76
	S5	392.15	3.1616	0.0036	H-4→L (13.88%)
					H-3→L (82.33%)
	S6	389.97	3.1793	0.013	H-1-L + 1(98.65%)
OD3	S1	760.69	1.6299	0.0002	H-1→L (4.96%)
					H→L (94.75%)
	S2	749.67	1.6538	0.0007	H-1→L (93.27%)
					H→L (5.13%)
	S3	523.58	2.368	0.0043	H-2→L (98.06%)
	S4	451.56	2.7457	0.0013	H-4→L (46.34%)
					H-3→L (50.15%)
	S5	415.04	2.9873	0	H-4→L (51.84%)
					H-3→L (47.93%)
	S6	404.74	3.0633	0.0065	H→L + 1(97.33%)
OD4	S1	865.45	1.4326	0.0022	H→L (99.38%)
	S2	506.15	2.4495	0.006	H-1→L (99.23%)
	S3	428.72	2.892	0.1603	H-3→L (2.13%)
					H-2→L (73.05%)
					H→L + 1(22.57%)
	S4	418.13	2.9652	0.4087	H-2→L (21.79%)
					H→L + 1(75.02%)
	S5	387.95	3.1959	0.0081	H-6→L (13.46%)
					H-4→L (75.13%)
					H-2→L (8.21%)
	S6	379.29	3.2689	0.0014	H-6→L (6.21%)
					H-4→L (3.91%)
					H-2→L (86.11%)
					H-2→L (3.36%)
OD5	S1	781.44	1.5866	0.0017	H-1→L (2.60%)
					H→L (96.65%)
	S2	570.42	2.1736	0.0061	H-1→L (95.41%)
					H→L (2.34%)
	S3	526.15	2.3564	0	H-7→L (3.35%)
					H-6→L (93.76%)
	S4	494.85	2.5055	0.0011	H-4→L (2.24%)
					H-2→L (26.93%)
					H-2→L (67.85%)
	S5	485.86	2.5516	0.003	H-4→L (4.85%)
					H-2→L (60.36%)
					H-2→L (31.72%)
	S6	433.86	2.8577	0.0004	H-5→L (7.96%)
					H-4→L (84.49%)
					H-2→L (7.30%)
OD6	S1	1224.32	1.0127	0.0009	H→L (98.93%)
	S2	757.83	1.636	0.00i9	H-1→L (97.06%)
	S3	569.68	2.1764	0.0085	H-3→L (6.73%)
					H-2→L (90.77%)
	S4	496.6	2.4966	0.0005	H-8→L (68.86%)
					H-6→L (2.68%)
					H-4→L (10.77%)
					H-3→L (15.09%)
	S5	489.5	2.5329	0.0044	H-8→L (24.36%)
					H-6→L (9.40%)
					H3→L (57.82%)
					H-2→L (5.84%)
	S6	477.04	2.599	0.2857	H→L + 1(95.72%)

Dye		λ max(nm)	eV	(f)	MO contribution
OD1	S1	788.47	1.5725	0.0028	H→L (99.24%)
	S2	460.41	2.6929	0.1229	H-1→L (87.88%)
					H→L + 1(10.71%)
	S3	449.91	2.7558	0.7768	H-1→L (10.82%)
					H→L + 1(87.35%)
	S4	400.77	3.0937	0.0038	H-5-L + 1(4.98%)
					H-3→L (20.79%)
					H-2→L (70.38%)
	S5	375.36	3.3031	0.0862	H-4→L (87.60%)
					H-3→L (3.44%)
					H-2→L (4.39%)
	S6	366.29	3.3849	0.0027	H-5→L (28.63%)
					H-4→L (4.82%)
					H-3→L (42.69%)
					H-2→L (23.25%)
OD2	S1	789.66	1.5701	0.0061	H→L (99.33%)
	S2	544.82	2.2757	0.0001	H-1→L (99.83%)
	S3	456.55	2.7157	0.5858	H-2→L (29.00%)
					H→L + 1(69.46%)
	S4	447.17	2.7726	0.2095	H-2→L (69.72%)
					H→L + 1(28.76
	S5	392.15	3.1616	0.0036	H-4→L (13.88%)
					H-3→L (82.33%)
	S6	389.97	3.1793	0.013	H-1-L + 1(98.65%)
OD3	S1	760.69	1.6299	0.0002	H-1→L (4.96%)
					H→L (94.75%)
	S2	749.67	1.6538	0.0007	H-1→L (93.27%)
					H→L (5.13%)
	S3	523.58	2.368	0.0043	H-2→L (98.06%)
	S4	451.56	2.7457	0.0013	H-4→L (46.34%)
					H-3→L (50.15%)
	S5	415.04	2.9873	0	H-4→L (51.84%)
					H-3→L (47.93%)
	S6	404.74	3.0633	0.0065	H→L + 1(97.33%)
OD4	S1	865.45	1.4326	0.0022	H→L (99.38%)
	S2	506.15	2.4495	0.006	H-1→L (99.23%)
	S3	428.72	2.892	0.1603	H-3→L (2.13%)
					H-2→L (73.05%)
					H→L + 1(22.57%)
	S4	418.13	2.9652	0.4087	H-2→L (21.79%)
					H→L + 1(75.02%)
	S5	387.95	3.1959	0.0081	H-6→L (13.46%)
					H-4→L (75.13%)
					H-2→L (8.21%)
	S6	379.29	3.2689	0.0014	H-6→L (6.21%)
					H-4→L (3.91%)
					H-2→L (86.11%)
					H-2→L (3.36%)
OD5	S1	781.44	1.5866	0.0017	H-1→L (2.60%)
					H→L (96.65%)
	S2	570.42	2.1736	0.0061	H-1→L (95.41%)
					H→L (2.34%)
	S3	526.15	2.3564	0	H-7→L (3.35%)
					H-6→L (93.76%)
	S4	494.85	2.5055	0.0011	H-4→L (2.24%)
					H-2→L (26.93%)
					H-2→L (67.85%)
	S5	485.86	2.5516	0.003	H-4→L (4.85%)
					H-2→L (60.36%)
					H-2→L (31.72%)
	S6	433.86	2.8577	0.0004	H-5→L (7.96%)
					H-4→L (84.49%)
					H-2→L (7.30%)
OD6	S1	1224.32	1.0127	0.0009	H→L (98.93%)
	S2	757.83	1.636	0.00i9	H-1→L (97.06%)
	S3	569.68	2.1764	0.0085	H-3→L (6.73%)
					H-2→L (90.77%)
	S4	496.6	2.4966	0.0005	H-8→L (68.86%)
					H-6→L (2.68%)
					H-4→L (10.77%)
					H-3→L (15.09%)
	S5	489.5	2.5329	0.0044	H-8→L (24.36%)
					H-6→L (9.40%)
					H3→L (57.82%)
					H-2→L (5.84%)
	S6	477.04	2.599	0.2857	H→L + 1(95.72%)

Table 3.

Open in new tab

The absorption properties of studied dyes derivatives obtained by B3LYP/6-31G level in D-π-A (position 4) gas phase

Dye		λ max(nm)	eV	(f)	MO contribution
OD1	S1	788.47	1.5725	0.0028	H→L (99.24%)
	S2	460.41	2.6929	0.1229	H-1→L (87.88%)
					H→L + 1(10.71%)
	S3	449.91	2.7558	0.7768	H-1→L (10.82%)
					H→L + 1(87.35%)
	S4	400.77	3.0937	0.0038	H-5-L + 1(4.98%)
					H-3→L (20.79%)
					H-2→L (70.38%)
	S5	375.36	3.3031	0.0862	H-4→L (87.60%)
					H-3→L (3.44%)
					H-2→L (4.39%)
	S6	366.29	3.3849	0.0027	H-5→L (28.63%)
					H-4→L (4.82%)
					H-3→L (42.69%)
					H-2→L (23.25%)
OD2	S1	789.66	1.5701	0.0061	H→L (99.33%)
	S2	544.82	2.2757	0.0001	H-1→L (99.83%)
	S3	456.55	2.7157	0.5858	H-2→L (29.00%)
					H→L + 1(69.46%)
	S4	447.17	2.7726	0.2095	H-2→L (69.72%)
					H→L + 1(28.76
	S5	392.15	3.1616	0.0036	H-4→L (13.88%)
					H-3→L (82.33%)
	S6	389.97	3.1793	0.013	H-1-L + 1(98.65%)
OD3	S1	760.69	1.6299	0.0002	H-1→L (4.96%)
					H→L (94.75%)
	S2	749.67	1.6538	0.0007	H-1→L (93.27%)
					H→L (5.13%)
	S3	523.58	2.368	0.0043	H-2→L (98.06%)
	S4	451.56	2.7457	0.0013	H-4→L (46.34%)
					H-3→L (50.15%)
	S5	415.04	2.9873	0	H-4→L (51.84%)
					H-3→L (47.93%)
	S6	404.74	3.0633	0.0065	H→L + 1(97.33%)
OD4	S1	865.45	1.4326	0.0022	H→L (99.38%)
	S2	506.15	2.4495	0.006	H-1→L (99.23%)
	S3	428.72	2.892	0.1603	H-3→L (2.13%)
					H-2→L (73.05%)
					H→L + 1(22.57%)
	S4	418.13	2.9652	0.4087	H-2→L (21.79%)
					H→L + 1(75.02%)
	S5	387.95	3.1959	0.0081	H-6→L (13.46%)
					H-4→L (75.13%)
					H-2→L (8.21%)
	S6	379.29	3.2689	0.0014	H-6→L (6.21%)
					H-4→L (3.91%)
					H-2→L (86.11%)
					H-2→L (3.36%)
OD5	S1	781.44	1.5866	0.0017	H-1→L (2.60%)
					H→L (96.65%)
	S2	570.42	2.1736	0.0061	H-1→L (95.41%)
					H→L (2.34%)
	S3	526.15	2.3564	0	H-7→L (3.35%)
					H-6→L (93.76%)
	S4	494.85	2.5055	0.0011	H-4→L (2.24%)
					H-2→L (26.93%)
					H-2→L (67.85%)
	S5	485.86	2.5516	0.003	H-4→L (4.85%)
					H-2→L (60.36%)
					H-2→L (31.72%)
	S6	433.86	2.8577	0.0004	H-5→L (7.96%)
					H-4→L (84.49%)
					H-2→L (7.30%)
OD6	S1	1224.32	1.0127	0.0009	H→L (98.93%)
	S2	757.83	1.636	0.00i9	H-1→L (97.06%)
	S3	569.68	2.1764	0.0085	H-3→L (6.73%)
					H-2→L (90.77%)
	S4	496.6	2.4966	0.0005	H-8→L (68.86%)
					H-6→L (2.68%)
					H-4→L (10.77%)
					H-3→L (15.09%)
	S5	489.5	2.5329	0.0044	H-8→L (24.36%)
					H-6→L (9.40%)
					H3→L (57.82%)
					H-2→L (5.84%)
	S6	477.04	2.599	0.2857	H→L + 1(95.72%)

Dye		λ max(nm)	eV	(f)	MO contribution
OD1	S1	788.47	1.5725	0.0028	H→L (99.24%)
	S2	460.41	2.6929	0.1229	H-1→L (87.88%)
					H→L + 1(10.71%)
	S3	449.91	2.7558	0.7768	H-1→L (10.82%)
					H→L + 1(87.35%)
	S4	400.77	3.0937	0.0038	H-5-L + 1(4.98%)
					H-3→L (20.79%)
					H-2→L (70.38%)
	S5	375.36	3.3031	0.0862	H-4→L (87.60%)
					H-3→L (3.44%)
					H-2→L (4.39%)
	S6	366.29	3.3849	0.0027	H-5→L (28.63%)
					H-4→L (4.82%)
					H-3→L (42.69%)
					H-2→L (23.25%)
OD2	S1	789.66	1.5701	0.0061	H→L (99.33%)
	S2	544.82	2.2757	0.0001	H-1→L (99.83%)
	S3	456.55	2.7157	0.5858	H-2→L (29.00%)
					H→L + 1(69.46%)
	S4	447.17	2.7726	0.2095	H-2→L (69.72%)
					H→L + 1(28.76
	S5	392.15	3.1616	0.0036	H-4→L (13.88%)
					H-3→L (82.33%)
	S6	389.97	3.1793	0.013	H-1-L + 1(98.65%)
OD3	S1	760.69	1.6299	0.0002	H-1→L (4.96%)
					H→L (94.75%)
	S2	749.67	1.6538	0.0007	H-1→L (93.27%)
					H→L (5.13%)
	S3	523.58	2.368	0.0043	H-2→L (98.06%)
	S4	451.56	2.7457	0.0013	H-4→L (46.34%)
					H-3→L (50.15%)
	S5	415.04	2.9873	0	H-4→L (51.84%)
					H-3→L (47.93%)
	S6	404.74	3.0633	0.0065	H→L + 1(97.33%)
OD4	S1	865.45	1.4326	0.0022	H→L (99.38%)
	S2	506.15	2.4495	0.006	H-1→L (99.23%)
	S3	428.72	2.892	0.1603	H-3→L (2.13%)
					H-2→L (73.05%)
					H→L + 1(22.57%)
	S4	418.13	2.9652	0.4087	H-2→L (21.79%)
					H→L + 1(75.02%)
	S5	387.95	3.1959	0.0081	H-6→L (13.46%)
					H-4→L (75.13%)
					H-2→L (8.21%)
	S6	379.29	3.2689	0.0014	H-6→L (6.21%)
					H-4→L (3.91%)
					H-2→L (86.11%)
					H-2→L (3.36%)
OD5	S1	781.44	1.5866	0.0017	H-1→L (2.60%)
					H→L (96.65%)
	S2	570.42	2.1736	0.0061	H-1→L (95.41%)
					H→L (2.34%)
	S3	526.15	2.3564	0	H-7→L (3.35%)
					H-6→L (93.76%)
	S4	494.85	2.5055	0.0011	H-4→L (2.24%)
					H-2→L (26.93%)
					H-2→L (67.85%)
	S5	485.86	2.5516	0.003	H-4→L (4.85%)
					H-2→L (60.36%)
					H-2→L (31.72%)
	S6	433.86	2.8577	0.0004	H-5→L (7.96%)
					H-4→L (84.49%)
					H-2→L (7.30%)
OD6	S1	1224.32	1.0127	0.0009	H→L (98.93%)
	S2	757.83	1.636	0.00i9	H-1→L (97.06%)
	S3	569.68	2.1764	0.0085	H-3→L (6.73%)
					H-2→L (90.77%)
	S4	496.6	2.4966	0.0005	H-8→L (68.86%)
					H-6→L (2.68%)
					H-4→L (10.77%)
					H-3→L (15.09%)
	S5	489.5	2.5329	0.0044	H-8→L (24.36%)
					H-6→L (9.40%)
					H3→L (57.82%)
					H-2→L (5.84%)
	S6	477.04	2.599	0.2857	H→L + 1(95.72%)

Table 4.

Open in new tab

The absorption properties of studied dyes derivatives obtained by B3LYP/6-31G level in D-π-A (position 4) solvent phase

Dye	state	λ_max(nm)	eV	(f)	MO Contribution
OD1	S1	724.53	1.7112	0.0082	H→L (99.35%)
	S2	479.7	2.5846	1.0734	H→L + 1(98.84%)
	S3	421.25	2.9433	0.0106	H-5→L (97.98%)
	S4	380.35	3.2597	0.0278	H-4→L (6.65%)
					H-3→L (13.68%)
					H-2→L (39.25%)
					H→L (37.91%)
	S5	372.37	3.3296	0.1139	H-4→L (21.34%)
					H-3→L (54.05%)
					H-2→L (18.19%)
	S6	359.61	3.4478	0.255	H-1-L + 1(3.89%)
					H→L + 2(93.06%)
OD2	S1	749.2	1.6549	0.0131	H→L (99.41%)
	S2	525.25	2.3605	0.0002	H-1→L (99.82%)
	S3	478.84	2.5892	0.9934	H→L + 1(98.66%)
	S4	422.37	2.9354	0.0133	H-2→L (98.00%)
	S5	398.35	3.1125	0.0184	H-2-L + 1(98.97%)
	S6	379.17	3.2699	0.0087	H-4→L (14.40%)
					H-3→L (82.78%)
OD3	S1	711.26	1.7432	0.0002	H→L (99.25%)
	S2	683.95	1.8128	0.0024	H-1→L (97.95%)
	S3	474.18	2.6147	0.0064	H-3→L (97.99%)
	S4	425.12	2.9164	0.0036	H-4→L (88.13%)
					H-3→L (7.64%)
	S5	419.2	2.9576	0.0127	H→L + 1(98.86%)
	S6	401.05	3.0915	0.6698	H-1→L + 1(96.89%)
OD4	S1	879.43	1.4098	0.0045	H→L (99.52%)
	S2	478.34	2.592	0.015	H-1→L (99.52%)
	S3	449.56	2.7579	0.6612	H→L + 1(96.32%)
	S4	420.94	2.9454	0.0195	H-3→L (27.23%)
					H-2→L (68.48%)
	S5	391.03	3.1707	0.0012	H-3→L (70.59%)
					H-2→L (29.09%)
	S6	372.57	3.3278	0.0081	H-7→L (3.16%)
					H-6→L (71.82%)
					H-5→L (2.07%)
					H-4→L (19.62%)
OD5	S1	701.73	1.7668	0.0033	H-1→L (2.09%)
					H→L (97.22%)
	S2	512.2	2.4206	0.0069	H-1→L (95.49%)
	S3	478.58	2.5907	0.0001	H-6→L (97.38%)
	S4	528.55	2.3458	0.0049	H-6→L (3.79%)
					H-3→L (79.81%)
					H-2→L (11.77%)
	S5	488.85	2.5363	0.0007	H→L + 1 (12.48%)
					H→L + 2 (87.35%)
	S6	481.49	2.5363	0.2975	H→L + 1 (86.01%)
					H→L + 2 (10.82%)
OD6	S1	1048.67	1.1823	0.0026	H→L (98.75%)
	S2	692.78	1.7897	0.0022	H-1→L (97.01%)
	S3	526.32	2.3557	0.0099	H-3→L (9.43%)
					H-2→L (88.29%)
	S4	478.17	2.5929	0.4709	H→L + 1(97.75%)
	S5	469.25	2.6422	0.0012	H-7→L (57.89%)
					H-4→L (14.17%)
					H-3→L (22.84%)
					H-2→L (2.54%)
	S6	463.93	2.6725	0.0037	H-7→L (38.68%)
					H-4→L (10.22%)
					H-3→L (42.16%)
					H-2→L (6.44%)

Dye	state	λ_max(nm)	eV	(f)	MO Contribution
OD1	S1	724.53	1.7112	0.0082	H→L (99.35%)
	S2	479.7	2.5846	1.0734	H→L + 1(98.84%)
	S3	421.25	2.9433	0.0106	H-5→L (97.98%)
	S4	380.35	3.2597	0.0278	H-4→L (6.65%)
					H-3→L (13.68%)
					H-2→L (39.25%)
					H→L (37.91%)
	S5	372.37	3.3296	0.1139	H-4→L (21.34%)
					H-3→L (54.05%)
					H-2→L (18.19%)
	S6	359.61	3.4478	0.255	H-1-L + 1(3.89%)
					H→L + 2(93.06%)
OD2	S1	749.2	1.6549	0.0131	H→L (99.41%)
	S2	525.25	2.3605	0.0002	H-1→L (99.82%)
	S3	478.84	2.5892	0.9934	H→L + 1(98.66%)
	S4	422.37	2.9354	0.0133	H-2→L (98.00%)
	S5	398.35	3.1125	0.0184	H-2-L + 1(98.97%)
	S6	379.17	3.2699	0.0087	H-4→L (14.40%)
					H-3→L (82.78%)
OD3	S1	711.26	1.7432	0.0002	H→L (99.25%)
	S2	683.95	1.8128	0.0024	H-1→L (97.95%)
	S3	474.18	2.6147	0.0064	H-3→L (97.99%)
	S4	425.12	2.9164	0.0036	H-4→L (88.13%)
					H-3→L (7.64%)
	S5	419.2	2.9576	0.0127	H→L + 1(98.86%)
	S6	401.05	3.0915	0.6698	H-1→L + 1(96.89%)
OD4	S1	879.43	1.4098	0.0045	H→L (99.52%)
	S2	478.34	2.592	0.015	H-1→L (99.52%)
	S3	449.56	2.7579	0.6612	H→L + 1(96.32%)
	S4	420.94	2.9454	0.0195	H-3→L (27.23%)
					H-2→L (68.48%)
	S5	391.03	3.1707	0.0012	H-3→L (70.59%)
					H-2→L (29.09%)
	S6	372.57	3.3278	0.0081	H-7→L (3.16%)
					H-6→L (71.82%)
					H-5→L (2.07%)
					H-4→L (19.62%)
OD5	S1	701.73	1.7668	0.0033	H-1→L (2.09%)
					H→L (97.22%)
	S2	512.2	2.4206	0.0069	H-1→L (95.49%)
	S3	478.58	2.5907	0.0001	H-6→L (97.38%)
	S4	528.55	2.3458	0.0049	H-6→L (3.79%)
					H-3→L (79.81%)
					H-2→L (11.77%)
	S5	488.85	2.5363	0.0007	H→L + 1 (12.48%)
					H→L + 2 (87.35%)
	S6	481.49	2.5363	0.2975	H→L + 1 (86.01%)
					H→L + 2 (10.82%)
OD6	S1	1048.67	1.1823	0.0026	H→L (98.75%)
	S2	692.78	1.7897	0.0022	H-1→L (97.01%)
	S3	526.32	2.3557	0.0099	H-3→L (9.43%)
					H-2→L (88.29%)
	S4	478.17	2.5929	0.4709	H→L + 1(97.75%)
	S5	469.25	2.6422	0.0012	H-7→L (57.89%)
					H-4→L (14.17%)
					H-3→L (22.84%)
					H-2→L (2.54%)
	S6	463.93	2.6725	0.0037	H-7→L (38.68%)
					H-4→L (10.22%)
					H-3→L (42.16%)
					H-2→L (6.44%)

Table 4.

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The absorption properties of studied dyes derivatives obtained by B3LYP/6-31G level in D-π-A (position 4) solvent phase

Dye	state	λ_max(nm)	eV	(f)	MO Contribution
OD1	S1	724.53	1.7112	0.0082	H→L (99.35%)
	S2	479.7	2.5846	1.0734	H→L + 1(98.84%)
	S3	421.25	2.9433	0.0106	H-5→L (97.98%)
	S4	380.35	3.2597	0.0278	H-4→L (6.65%)
					H-3→L (13.68%)
					H-2→L (39.25%)
					H→L (37.91%)
	S5	372.37	3.3296	0.1139	H-4→L (21.34%)
					H-3→L (54.05%)
					H-2→L (18.19%)
	S6	359.61	3.4478	0.255	H-1-L + 1(3.89%)
					H→L + 2(93.06%)
OD2	S1	749.2	1.6549	0.0131	H→L (99.41%)
	S2	525.25	2.3605	0.0002	H-1→L (99.82%)
	S3	478.84	2.5892	0.9934	H→L + 1(98.66%)
	S4	422.37	2.9354	0.0133	H-2→L (98.00%)
	S5	398.35	3.1125	0.0184	H-2-L + 1(98.97%)
	S6	379.17	3.2699	0.0087	H-4→L (14.40%)
					H-3→L (82.78%)
OD3	S1	711.26	1.7432	0.0002	H→L (99.25%)
	S2	683.95	1.8128	0.0024	H-1→L (97.95%)
	S3	474.18	2.6147	0.0064	H-3→L (97.99%)
	S4	425.12	2.9164	0.0036	H-4→L (88.13%)
					H-3→L (7.64%)
	S5	419.2	2.9576	0.0127	H→L + 1(98.86%)
	S6	401.05	3.0915	0.6698	H-1→L + 1(96.89%)
OD4	S1	879.43	1.4098	0.0045	H→L (99.52%)
	S2	478.34	2.592	0.015	H-1→L (99.52%)
	S3	449.56	2.7579	0.6612	H→L + 1(96.32%)
	S4	420.94	2.9454	0.0195	H-3→L (27.23%)
					H-2→L (68.48%)
	S5	391.03	3.1707	0.0012	H-3→L (70.59%)
					H-2→L (29.09%)
	S6	372.57	3.3278	0.0081	H-7→L (3.16%)
					H-6→L (71.82%)
					H-5→L (2.07%)
					H-4→L (19.62%)
OD5	S1	701.73	1.7668	0.0033	H-1→L (2.09%)
					H→L (97.22%)
	S2	512.2	2.4206	0.0069	H-1→L (95.49%)
	S3	478.58	2.5907	0.0001	H-6→L (97.38%)
	S4	528.55	2.3458	0.0049	H-6→L (3.79%)
					H-3→L (79.81%)
					H-2→L (11.77%)
	S5	488.85	2.5363	0.0007	H→L + 1 (12.48%)
					H→L + 2 (87.35%)
	S6	481.49	2.5363	0.2975	H→L + 1 (86.01%)
					H→L + 2 (10.82%)
OD6	S1	1048.67	1.1823	0.0026	H→L (98.75%)
	S2	692.78	1.7897	0.0022	H-1→L (97.01%)
	S3	526.32	2.3557	0.0099	H-3→L (9.43%)
					H-2→L (88.29%)
	S4	478.17	2.5929	0.4709	H→L + 1(97.75%)
	S5	469.25	2.6422	0.0012	H-7→L (57.89%)
					H-4→L (14.17%)
					H-3→L (22.84%)
					H-2→L (2.54%)
	S6	463.93	2.6725	0.0037	H-7→L (38.68%)
					H-4→L (10.22%)
					H-3→L (42.16%)
					H-2→L (6.44%)

Dye	state	λ_max(nm)	eV	(f)	MO Contribution
OD1	S1	724.53	1.7112	0.0082	H→L (99.35%)
	S2	479.7	2.5846	1.0734	H→L + 1(98.84%)
	S3	421.25	2.9433	0.0106	H-5→L (97.98%)
	S4	380.35	3.2597	0.0278	H-4→L (6.65%)
					H-3→L (13.68%)
					H-2→L (39.25%)
					H→L (37.91%)
	S5	372.37	3.3296	0.1139	H-4→L (21.34%)
					H-3→L (54.05%)
					H-2→L (18.19%)
	S6	359.61	3.4478	0.255	H-1-L + 1(3.89%)
					H→L + 2(93.06%)
OD2	S1	749.2	1.6549	0.0131	H→L (99.41%)
	S2	525.25	2.3605	0.0002	H-1→L (99.82%)
	S3	478.84	2.5892	0.9934	H→L + 1(98.66%)
	S4	422.37	2.9354	0.0133	H-2→L (98.00%)
	S5	398.35	3.1125	0.0184	H-2-L + 1(98.97%)
	S6	379.17	3.2699	0.0087	H-4→L (14.40%)
					H-3→L (82.78%)
OD3	S1	711.26	1.7432	0.0002	H→L (99.25%)
	S2	683.95	1.8128	0.0024	H-1→L (97.95%)
	S3	474.18	2.6147	0.0064	H-3→L (97.99%)
	S4	425.12	2.9164	0.0036	H-4→L (88.13%)
					H-3→L (7.64%)
	S5	419.2	2.9576	0.0127	H→L + 1(98.86%)
	S6	401.05	3.0915	0.6698	H-1→L + 1(96.89%)
OD4	S1	879.43	1.4098	0.0045	H→L (99.52%)
	S2	478.34	2.592	0.015	H-1→L (99.52%)
	S3	449.56	2.7579	0.6612	H→L + 1(96.32%)
	S4	420.94	2.9454	0.0195	H-3→L (27.23%)
					H-2→L (68.48%)
	S5	391.03	3.1707	0.0012	H-3→L (70.59%)
					H-2→L (29.09%)
	S6	372.57	3.3278	0.0081	H-7→L (3.16%)
					H-6→L (71.82%)
					H-5→L (2.07%)
					H-4→L (19.62%)
OD5	S1	701.73	1.7668	0.0033	H-1→L (2.09%)
					H→L (97.22%)
	S2	512.2	2.4206	0.0069	H-1→L (95.49%)
	S3	478.58	2.5907	0.0001	H-6→L (97.38%)
	S4	528.55	2.3458	0.0049	H-6→L (3.79%)
					H-3→L (79.81%)
					H-2→L (11.77%)
	S5	488.85	2.5363	0.0007	H→L + 1 (12.48%)
					H→L + 2 (87.35%)
	S6	481.49	2.5363	0.2975	H→L + 1 (86.01%)
					H→L + 2 (10.82%)
OD6	S1	1048.67	1.1823	0.0026	H→L (98.75%)
	S2	692.78	1.7897	0.0022	H-1→L (97.01%)
	S3	526.32	2.3557	0.0099	H-3→L (9.43%)
					H-2→L (88.29%)
	S4	478.17	2.5929	0.4709	H→L + 1(97.75%)
	S5	469.25	2.6422	0.0012	H-7→L (57.89%)
					H-4→L (14.17%)
					H-3→L (22.84%)
					H-2→L (2.54%)
	S6	463.93	2.6725	0.0037	H-7→L (38.68%)
					H-4→L (10.22%)
					H-3→L (42.16%)
					H-2→L (6.44%)

The oscillator intensity values have been arranged in order of decrease. D1-CM-A1 > D2-CM-A2 > D4-CM-A4 > D6-CM-A6 > D3-CM-A3 > D5-CM-A5 and D1-CM-A1 > D2-CM-A2 > D3-CM-A3 > D4-CM-A4 > D5-CM-A5 > D6-CM-A6respectively for gas and solvent. The results demonstrate that chlorobenzene solution is added to the dye molecules because of the difference between the value of gas and solvent level oscillator strengths. Hence the strength of oscillators is higher than other molecules in D1-CM-A1 and D2-CM-A2. The D‐CM-A1 to D6-CM-A6 optical absorption spectra in D-π-A are 449.91, 456.55, 404.74, 418.3, 477.04, 570.42 and 479.7, 478.84, 401.05, 449.56, 478.17 and 481.49 respectively.

The photo’s existing DSSC conversion efficiency will be impacted by the longer wavelength molecules, which will exhibit a redshift. The findings demonstrate that the D6-CM-A6 and D5-CM-A5 dyes have longer wavelengths than other compounds because of the impacts of aromatics and the conjugating system. However, because of the low energy value of LUMO, these dyes are unable to pump electrons into a semiconductor’s conduction band; instead, as Figs 7 and 8 demonstrate, D1-CM-A1 and D2-CM-A2 have more excellent wavelength absorption.

Figure 7.

Simulated UV-Visible optical absorption spectra of the studied coumarins dye (D-π-A) calculated by TD/DFT/B3LYP/6-31G level in gas phase.

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Figure 8.

Simulated UV-Visible optical absorption spectra of the studied coumarins dye (D-π-A) calculated by TD/DFT/B3LYP/6-31G level in solvent phase.

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Photovoltaic properties

Table 5 incorporates all optoelectronic features. The parameter used to characterize any compound’s performance, power conversion efficiency (PCE), can be utilized to calculate the dye-sensitized solar cell devices’ efficiency. In addition, the following expression is used to determine the fill factor (FF), incoming photon to current efficiency (P_inc), short circuit current density (Jsc), open-circuit photovoltage (Voc), and fill factor (FF). Every optoelectronic property is included in Table 5. The most popular metric for characterizing compound output, power conversion efficiency (PCE), can be used to determine the efficiency of the dye-sensitive solar cell system. Additionally, the incidence photons to current efficiency (P_inc) and fill factor (FF) were calculated using the following formula, and the open circuit picture voltage (V_OC) and short circuit current (J_SC) were utilized by other paediatricians to gauge this performance.

η = FF \frac{J_{SC} V_{OC}}{P_{inc}}

(1)

Table 5.

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Estimated Photovoltaic properties of studied molecules at B3LYP/6-3IG level in gas and solvent phases

Gas
Dye	LHE	$E_{o x}^{dye *}$ (eV)	${Δ G}_{inject}$ (eV)	${Δ G}_{dye}^{regen}$ (eV)	Voc $(e V)$	\|V_RP\| $(V)$	ԏ(ns)
OD1	0.832	−7.076	−11.013	0.59042	0.4796	−3.4404	3.92
OD2	0.740	−6.983	−10.983	0.56293	0.4995	−3.4129	8.64
OD3	0.014	−7.453	−11.452	0.97247	0.0796	−3.8224	378.80
OD4	0.609	−7.158	−11.158	0.87559	0.1016	−3.7255	18.35
OD5	0.013	−7.915	−11.915	1.4786	−0.3478	−4.3286	80.17
OD6	0.482	−6.747	−10.742	0.88457	−0.4186	−3.7345	11.97

Gas
Dye	LHE	$E_{o x}^{dye *}$ (eV)	${Δ G}_{inject}$ (eV)	${Δ G}_{dye}^{regen}$ (eV)	Voc $(e V)$	\|V_RP\| $(V)$	ԏ(ns)
OD1	0.832	−7.076	−11.013	0.59042	0.4796	−3.4404	3.92
OD2	0.740	−6.983	−10.983	0.56293	0.4995	−3.4129	8.64
OD3	0.014	−7.453	−11.452	0.97247	0.0796	−3.8224	378.80
OD4	0.609	−7.158	−11.158	0.87559	0.1016	−3.7255	18.35
OD5	0.013	−7.915	−11.915	1.4786	−0.3478	−4.3286	80.17
OD6	0.482	−6.747	−10.742	0.88457	−0.4186	−3.7345	11.97

Solvent
Dye	LHE	$E_{o x}^{dye *}$ (eV)	${Δ G}_{inject}$ (eV)	${Δ G}_{dye}^{regen}$ (eV)	Voc $(e V)$	\|V_RP\| $(e V)$	ԏ(ns)
OD1	0.915	−7.076	−11.077	0.51531	0.69314	−3.36531	3.22
OD2	0.898	−7.018	−11.019	0.51368	0.63447	−3.36368	13.32
OD3	0.786	−7.471	−11.471	0.87749	0.28753	−3.72749	3.61
OD4	0.781	−7.005	−11.005	0.7447	0.20453	−3.5947	4.59
OD5	0.495	−7.998	−11.999	1.382	−0.08419	−4.232	11.71
OD6	0.661	−6.914	−10.914	0.88212	−0.24147	−3.73212	7.29

Solvent
Dye	LHE	$E_{o x}^{dye *}$ (eV)	${Δ G}_{inject}$ (eV)	${Δ G}_{dye}^{regen}$ (eV)	Voc $(e V)$	\|V_RP\| $(e V)$	ԏ(ns)
OD1	0.915	−7.076	−11.077	0.51531	0.69314	−3.36531	3.22
OD2	0.898	−7.018	−11.019	0.51368	0.63447	−3.36368	13.32
OD3	0.786	−7.471	−11.471	0.87749	0.28753	−3.72749	3.61
OD4	0.781	−7.005	−11.005	0.7447	0.20453	−3.5947	4.59
OD5	0.495	−7.998	−11.999	1.382	−0.08419	−4.232	11.71
OD6	0.661	−6.914	−10.914	0.88212	−0.24147	−3.73212	7.29

Table 5.

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Estimated Photovoltaic properties of studied molecules at B3LYP/6-3IG level in gas and solvent phases

Gas
Dye	LHE	$E_{o x}^{dye *}$ (eV)	${Δ G}_{inject}$ (eV)	${Δ G}_{dye}^{regen}$ (eV)	Voc $(e V)$	\|V_RP\| $(V)$	ԏ(ns)
OD1	0.832	−7.076	−11.013	0.59042	0.4796	−3.4404	3.92
OD2	0.740	−6.983	−10.983	0.56293	0.4995	−3.4129	8.64
OD3	0.014	−7.453	−11.452	0.97247	0.0796	−3.8224	378.80
OD4	0.609	−7.158	−11.158	0.87559	0.1016	−3.7255	18.35
OD5	0.013	−7.915	−11.915	1.4786	−0.3478	−4.3286	80.17
OD6	0.482	−6.747	−10.742	0.88457	−0.4186	−3.7345	11.97

Gas
Dye	LHE	$E_{o x}^{dye *}$ (eV)	${Δ G}_{inject}$ (eV)	${Δ G}_{dye}^{regen}$ (eV)	Voc $(e V)$	\|V_RP\| $(V)$	ԏ(ns)
OD1	0.832	−7.076	−11.013	0.59042	0.4796	−3.4404	3.92
OD2	0.740	−6.983	−10.983	0.56293	0.4995	−3.4129	8.64
OD3	0.014	−7.453	−11.452	0.97247	0.0796	−3.8224	378.80
OD4	0.609	−7.158	−11.158	0.87559	0.1016	−3.7255	18.35
OD5	0.013	−7.915	−11.915	1.4786	−0.3478	−4.3286	80.17
OD6	0.482	−6.747	−10.742	0.88457	−0.4186	−3.7345	11.97

Solvent
Dye	LHE	$E_{o x}^{dye *}$ (eV)	${Δ G}_{inject}$ (eV)	${Δ G}_{dye}^{regen}$ (eV)	Voc $(e V)$	\|V_RP\| $(e V)$	ԏ(ns)
OD1	0.915	−7.076	−11.077	0.51531	0.69314	−3.36531	3.22
OD2	0.898	−7.018	−11.019	0.51368	0.63447	−3.36368	13.32
OD3	0.786	−7.471	−11.471	0.87749	0.28753	−3.72749	3.61
OD4	0.781	−7.005	−11.005	0.7447	0.20453	−3.5947	4.59
OD5	0.495	−7.998	−11.999	1.382	−0.08419	−4.232	11.71
OD6	0.661	−6.914	−10.914	0.88212	−0.24147	−3.73212	7.29

Solvent
Dye	LHE	$E_{o x}^{dye *}$ (eV)	${Δ G}_{inject}$ (eV)	${Δ G}_{dye}^{regen}$ (eV)	Voc $(e V)$	\|V_RP\| $(e V)$	ԏ(ns)
OD1	0.915	−7.076	−11.077	0.51531	0.69314	−3.36531	3.22
OD2	0.898	−7.018	−11.019	0.51368	0.63447	−3.36368	13.32
OD3	0.786	−7.471	−11.471	0.87749	0.28753	−3.72749	3.61
OD4	0.781	−7.005	−11.005	0.7447	0.20453	−3.5947	4.59
OD5	0.495	−7.998	−11.999	1.382	−0.08419	−4.232	11.71
OD6	0.661	−6.914	−10.914	0.88212	−0.24147	−3.73212	7.29

The difference between the donor’s and acceptor’s HOMO and LUMO the energy lost during photo charge generation was used to calculate the volatile organic compound (VOC). The conduction band energy of the titanium oxide (TiO₂) semiconductor was −4.0 eV (E_CB = −4.0 eV) [54]. V_OC in DSSC can be computed as

V_{OC} = E_{LUMO} - E_{CB}

(2)

The lowest unoccupied molecular orbital of the dye is called E_LUMO, and the energy of the semiconductor’s conduction band is referred to as E_CB. The definition of the J_sc takes into consideration the conduction band, the sensitizer, and the sensitizer’s absorption coefficient. The J_sc in the DSSC can be written as,

J_{s c} = \int LHE Φ_{inject} η_{collect} (d λ)

(3)

The light-harvesting efficiency (LHE) at a specific wavelength, the electron injection efficiency (Φ_inject), and the charge collection efficiency (β_collect) are represented in this formula. With distinct sensitizers and the same electrode, the dye-sensitized solar cell η_collect can be viewed as constant. The oscillator strength (f), which is chosen using the following equation [55], typically determines the LHE.

LHE = 1 - 10^{- f}

(4)

The oscillator strength of the absorbed dye molecule is denoted by f. Two important elements that affect the J_sc factor are LHE and ΔG^inject. If the LHE is large, the largest short circuit current density can be achieved. The following expression can be used to compute the injection driving force in DSSC [56].

Δ G^{inject} = E^{dye *} + E_{00}

(5)

E^dye* represents the oxidation potential energy in an excited state and E_CB in reducing the semiconductor’s potential, whose value is −4.0 eV. The oxidation potential energy of the dye in an exciting form was explained by [57] as follows;

E^{dye *} = E^{dye} - E_{00}

(6)

The vertical electronic transition energy E₀₀ corresponds to the wavelength maximum (λ_max), while E^dye is the oxidation potential energy of the dye in its ground state [58] outlined the two schemes—the relaxed and unrelaxed paths—through which ΔG^inject can be evaluated. The molecule is immediately injected by the electron from its ground state into the excited state of the semiconductor’s conduction band through a relaxed route. When an electron is injected from the dye’s excited state into the semiconductor conduction band, it determines the unrelaxed path, but this path is truly deserving.

The LHE and electron injection efficiency must be higher to determine the short circuit current density of the dye molecule. The oscillator strength is associated with LHE, and the oscillator force should be higher to achieve greater LHE. The electron injection efficiency values have been negative, which implies that the excited dye molecule lies above the conductance band of the semiconductor. Therefore, the electron more rapidly injects the molecule with higher efficiency. Another critical factor affecting the J_SC of DSSCs is electron regeneration capacity. The lower energy of regeneration of the electron makes the transmission of electrons more effective.

Light harvesting efficiency (LHE)

The percentage of light intensity absorbed by dye molecules is known as the light-harvesting (LHE) performance. For organic dyes in DSSCs, one of the most crucial parameters is performance in light harvest. The LHE needs to be robust to promote the photocurrent response. In equation 3, the higher the oscillator frequency, the higher the LHE, the greater the power injection efficiency, and the higher the JSC. In accordance, the LHE values (Table 5) rise; In D1-CM-A1 > D2-CM-A2 > D4-CM-A4 > D6-CM-A6 > D3-CM-A3 > D5-CM-A5 and D1-CM-A1 > D2-CM-A2 > D3-CM-A3 > D4-CM-A4 > D6-CM-A6 > D5-CM-A5, the solvent and gas phases, respectively, are considered. The findings indicate that D2-CM-A2 and D1-CM-A1 have the highest amounts of LHE because they can double-bond the electrodes to the lone couples. As a result, the DSSC application suggests successful applicants.

Electron injection efficiency (ΔG^inject)

Electron injection efficiency is known as the capacity of dye molecules to inject the electron from the low unoccupied molecular orbital (LUMO). Equation 5 is used to measure this. The more efficient the electron injection, the density of short circuit power (J_SC) that results in the increased efficiency of solar cells’ power conversion. Table 5 shows the findings. This is a declining pattern (ΔG^inject). D6-CM-A6 > D2-CM-A2 > D1-CM-A1 > D4-CM-A4 > D3-CM-A3 > D5-CM-A5 and D6-CM-A6 > D4-CM-A4 > D2-CM-A2 > D1-CM-A1 > D3-CM-A3 > D5-CM-A5. The findings reveal that D2-CM-A2 has a greater omnibus meaning. It is also recommended that DSSCs be used correctly.

Electron regeneration energy ΔG^regen

The term Electron Regeneration Efficiency (ΔG^regen) refers to a dye’s capacity to recover electrons from the electrolyte following photoexcitation. One important aspect influencing the efficiency of photoelectric conversion is the energy of dye renewal [59]. The following equation represents its expression; efficiency [59]. Its expression is represented through the following equation;

{Δ G}_{dye}^{regent} = E_{redox}^{electrolyte} + E_{o x}^{dye}

(7)

One important aspect influencing the efficiency of photoelectric conversion is dye regeneration-free energy, tri iodide-iodide’s redox potential, which is −4.85 eV [60], is the dye’s ground state oxidation potential energy.

In the results, Table 5, it was indicated the highest electron recovery efficiency values of dye derivatives in the gas and solvent phases compared with other dye molecules. The significant (along with ΔG^regen) dye regeneration can be promoted, the JSC will increase, and D5-CM-A5 will perform better. This is the trend towards decreasing the regeneration efficiency of an electron; D5-CM-A5 > D3-CM-A3 > D6-CM-A6 > D4-CM-A4 > D1-CM-A1 > D2-CM-A2 and D5-CM-A5 > D6-CM-A6 > D3-CM-A3 > D4-CM-A4 > D1-CM-A1 > D2-CM-A2 respectively in gas and solvent phases. The results show that the regeneration values for D5-CM-A5 and D6-CM-A6 are higher but cannot regenerate because of a higher LUMO energy level. Instead, the value D3-CM-A3 > D4-CM-A4 is higher since the energy value of D5-CM-A3 is higher than that of the semiconduction (−4.0 eV).

Open circuit photo voltage (V_OC)

The unplugged In DSSCs, photovoltaic voltage is utilized to calculate the power conversion efficiency (η). Since electrons often migrate from dye molecules’ LUMO to the semiconductor conduction band, a high E_LUMO will also result in a high V_OC. The greater the driving force regeneration, the better the φreg. The V_OC values were shown as follows in Table 5: The third position is occupied by D2-CM-A2 > D1-CM-A1 > D4-CM-A4 > D3-CM-A3 > D5-CM-A5 > D6-CM-A6, and for gas and solvent, respectively, D1-CM-A1 > D2-CM-A2 > D3-CM-A3 > D4-CM-A4 > D5-CM-A5 > D6-CM-A6. The findings indicate that the V_OC levels are greater in D2-CM-A2 and D1-CM-A1. They are therefore recommended as a strong contender for the DSSCs application.

Excited-State lifetime

The efficiency of charging transfer can be influenced by the lifetime of the first exciting countries. The longer the molecule’s life is spent transferring too much and remains longer in cat-ionic, the more conducive it is to transfer a charge. Awakened public life increases the delay of the recombination of charges and increases the productivity of photovoltaic cells. The prolonged radioactive lifetime increases electron movement due to the highest light-emitting efficiency from the LUMO electron donor to the LUMO electron receiver. The following formula gives the exciting lifetime (τ)

τ = \frac{c^{3}}{2 {(E)}^{2} f}

(8)

where f is the oscillator intensity, E is the excitation energy, and c is the speed of light [61, 62]. The excited-state lifespan (τ) in Table 5 has the following order: In the gas and solvent phases, respectively, D5-CM-A5 > D3-CM-A3 > D5-CM-A5 > D4-CM-A4 > D6-CM-A6 > D1-CM-A and D2-CM-A2 > D5-CM-A5 > D6-CM-A6 > D4-CM-A4 > D3-CM-A3 > D1-CM-A1. Because D1-CM-A1 has the strongest oscillator, they have the lowest lifetime value. As a result, D1-CM-A1 and D2-CM-A2 will have uninterrupted ΔG^inject and improved light harvesting efficiency on the Jsc.

Electronic coupling constant

The classic theory of Marcus explains the injection of the electron by coupling constant [63–65].

k_{inject} = | V_{R P} | {[\frac{2}{h} (\frac{Π}{λ k_{B}} T))}_{2}^{1} exp [- {(Δ G_{inject} + λ)}_{4}^{2} λ k_{B} T]

(9)

K_injects are the rate constant (in s⁻¹) when the electron is injected from the dye molecule to the semiconductor.

The Generalized Milliken–hush (GMH) assumed the coupling constant formula. The injection-free energy is denoted by KB, and the coupling constant between the reaction and product potential curves is known as VRP. This equation states that the best dye (sensitizer) is ultimately produced by a higher coupling constant value, which also implies a larger rate constant. This results in rapid electron mobility and the strongest possible electron connection between the two states. The coupling constant formula was assumed using the Generalized Milliken-Hush (GMH).

| V_{R P} | = \frac{Δ ERP}{2}

(10)

Δ ERP = [E_{LUMO}^{dye} + 2 E_{HOMO}^{dye}] - [E_{LUMO}^{dye} + E_{HOMO}^{dye} + E_{C B}]

(11)

In this case, the conduction band of the semiconductor obtained through experimentation is called E_CB [66]. E_CBTiO₂ = −4.0 eV. The matching values are displayed in Table 5. In both the gas and solvent phases, respectively, the results in D-π-A are as follows: D5-CM-A5 > D3-CM-A3 > D6-CM-A6 > D4-CM-A4 > D1-CM-A1 > D2-CM-A2 and D5-CM-A5 > D6-CM-A6 > D3-CM-A3 > D4-CM-A4 > D1-CM-A1 > D2-CM-A2.D5-CM-A5 is the best sensitizer compared to all other dye derivatives because it exhibits a higher propensity of coupling, which allows the electron to pass from the dye molecule to the conduction band of a semiconductor extremely quickly.

Conclusion

Changes were carried out in the molecular structures designed for 12 coumarin dye derivatives to find their optoelectronic features in different positions to find a suitable role to find other new compounds based on coumarin dyes. The geometry, electronics and optoelectronic properties of dyes were analyzed at the level of DTF andTD-DFT/B3LYP/6-31G in this analysis. D5-CM-A5 and D6-CM-A6 have shown that band gap derivatives are higher in D5-CM-A5 and D6-CM-A6 than other teeth’ existence of highly-negative (nitrogen) elements within the molecules that result in these tinting derivatives having a low LUMO content compared to the LUMO conduction strip (−4.0 eV). Instead, these dyes cannot inject electrons into the semiconductor conduction band. The dye derivates of D1-CM-D1 and D2-CM-A2 are more capable of taking up spectra due to the LUMO value being higher (3.31 eV and 3.26 eV), respectively than the semicircular conduction band (-4.0 eV). In addition, the light harvest efficiency (LHE), photovoltaic open circuit (V_OC) and energy gap value (E_g) in all gas phases, as well as in solvent phases, are more significant in D1-CM- A1 and D2-CM-A2. Thus, the study shows that compared with other coumarin dye derivatives, D1-CM-A1 and D2-CM-A2 are acceptable in the DSSC.

Data availability

No new data were generated or analysed in support of this research.

Authors’ contributions

Surendra Babu Numbury (Conceptualization [equal], Project administration [equal]); Mwanahadia Khalfan (Data curation [equal], Investigation [equal] Said A.H. Vuai (Formal analysis [equal]).

Conflict of interest statement: The authors declare that none of the work reported in this study could have been influenced by any known competing financial interests or personal relationships and no funding available for this research work.

References

Orebiyi

Eng

Barnes

et al. Dye-sensitized solar cells, Innovation in Education and Inclusion. In: Proceedings of the 16th LACCEI International Multi-Conference for Engineering, Education and Technology,

2018

Kalyanasundaram

Dye-Sensitized Solar Cells

Lausanne, Switzerland

EPFL press

2010

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Article Contents

Theoretical studies of electronic and optical characteristics in donor-π-Acceptor (D-π-A) dyes: DFT and TD-DFT methods

Abstract

Introduction

Computational methodology

Results and discussion

Geometry optimization structures and geometrical parameters

Intramolecular charge transfer (ICT)

Electronic parameters

Absorption properties

Photovoltaic properties

Light harvesting efficiency (LHE)

Electron injection efficiency (ΔGinject)

Electron regeneration energy ΔGregen

Open circuit photo voltage (VOC)

Excited-State lifetime

Electronic coupling constant

Conclusion

Data availability

Authors’ contributions

References

Supplementary data

Citations

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Electron injection efficiency (ΔG^inject)

Electron regeneration energy ΔG^regen

Open circuit photo voltage (V_OC)