Optoelectronic Characterization of Natural Dyes in the Quest for Enhanced Performance in Dye-Sensitized Solar Cells: A Density Functional Theory Study

Abstract

This study employs density functional theory (DFT) to evaluate the optoelectronic features of five natural dyes (cyanidin, delphinidin, pelargonidin, peonidin, and petunidin) in gas and ethanol phases for potential dye-sensitized solar cell (DSSC) applications. Calculations cover HOMO and LUMO energy levels, charge transfer potential gaps, and light absorption properties correlated with oscillator strengths. Photovoltaic aspects, including light-harvesting efficiency (LHE), electron injection efficiency (ΔG^inject), regeneration efficiency (ΔG^regen), open-circuit voltage (V_OC), excited-state lifetime (τ), and the electronic coupling constant (|V_RP|), were computed to assess DSSC suitability. DFT analysis reveals that cyanidin, delphinidin, and petunidin exhibit favorable LUMOs for efficient electron injection into the semiconductor’s conduction band. Cyanidin demonstrates a high quantum yield for light absorption. Delphinidin and petunidin act as effective light absorbers with high excitation energies and oscillator strengths, while petunidin and delphinidin display strong LHE, indicating excellent electron-donating capabilities. Peonidin shows promising ΔG^inject despite needing more energy for injection. Pelargonidin excels in ΔG^regen and |V_RP|, enhancing DSSC performance. Petunidin and delphinidin exhibit a high V_OC. Petunidin efficiently transmits energy through a large τ, while pelargonidin’s |V_RP| confirms its potential as a favorable sensitizer. In summary, each dye possesses unique properties, and understanding them aids in selecting the most suitable dye for enhanced DSSC performance.

1. Introduction

The crucial quest for sustainable and renewable energy sources has become increasingly paramount in addressing the world’s escalating energy needs while concurrently mitigating the environmental impacts associated with conventional energy generation methods [1]. Within the domain of solar energy technologies, dye-sensitized solar cells (DSSCs) have attracted significant attention owing to their potential cost-effectiveness and efficiency [2]. The function of DSSCs is based on the principle of converting solar energy into electricity through the utilization of light-absorbing molecules, or dyes, which play a key role in initiating charge separation and transfer processes [3]. The careful selection of these dye molecules is crucial in determining the performance and efficiency of DSSCs.

Several factors contribute to the prominence of DSSCs, including their facile fabrication process, utilization of low-cost materials, and the ability to capture a broad spectrum of light [4]. In light of the increasing emphasis on sustainability and reduced environmental impact, DSSCs emerge as a promising avenue for the future of solar energy [5]. Additionally, the application of eco-friendly natural dyes as sensitizers for DSSCs has garnered growing interest, driven by the aim to enhance the sustainability and environmental friendliness of these photovoltaic devices [6].

To explore the potential of natural dyes in DSSCs, researchers employ density functional theory (DFT), a powerful computational tool widely adopted in the field of materials science [7]. DFT provides a theoretical framework for investigating the optoelectronic properties of materials, allowing researchers to predict and comprehend their behavior with a high degree of accuracy [8]. This approach proves particularly valuable in studying complex systems, such as the interactions between dye molecules and semiconductor surfaces in DSSCs.

Vuai et al. explored the correlation between intramolecular charge transfer (ICT) and the wavelength of light absorbed by a molecule. Their findings documented that increased ICT leads to the absorption of longer wavelengths of light, causing the molecule’s bandgap to narrow with the rise in the wavelength of light absorption. These findings suggest that dyes exhibiting strong ICT and narrower bandgaps are good candidates for applications in DSSCs [9].

Almogati et al. provided insights into the characteristics of a typical dye used in the application of DSSCs. Their study aimed to establish correlations between the electrical structure, spectroscopic features, and the attainment of desirable properties in optoelectronic materials by using computational methodology. The equilibrium geometries and electronic structure of the examined dyes were optimized using a variety of DFT functionals. Natural bond order (NBO) analysis was carried out, and the topological and local features of the charge density distributions were estimated [10].

Roohi et al. investigated the influence of substitutions of donors and electron acceptors incorporated in linkers on the optoelectronic properties of D–A dye-sensitized solar cells in their DFT/TD-DFT study. They employed computational techniques, specifically, time-dependent density functional theory (TD-DFT) and DFT, to design effective sensitizer dyes for DSSCs. The investigation extended to several metal-free organic dyes featuring the D–p–A–A arrangement, examining the impact of donor and acceptor groups on their structural, photochemical, and electrochemical properties. Their findings revealed that the donor group and the electron-accepting substitutions added to p-linkers become a critical factor in the fine-tuning of the optoelectronic characteristics of selected dyes and provide valuable insights into the design of cost-effective sensitizers with high efficiency for DSSCs [11].

Fahim et al. reported the optoelectronic properties of triphenylamine-based dyes for solar cell applications, focusing on the designing and creation of organic sensitizers for DSSCs. Their investigation explored physicochemical properties of selected dyes based on intended geometries, resulting in favorable electrical and light absorption characteristics. The study achieved stabilization of the lowest unoccupied molecular orbital (LUMO) energy level and a lower energy gap through experiments that introduced electron-withdrawing groups to the bridge. This induced a bathochromic effect, shifting the maximum absorption bands to a lower energy, enabling the modulation of dye absorption properties to convert UV–Vis and near-infrared light into current [12].

The HOMO–LUMO energy gap plays a pivotal role, providing valuable insights into the dyes’ ability to facilitate charge transfer, a fundamental process in the functionality of DSSCs. Consequently, the positioning of the LUMO energy level emerges as a crucial parameter, ensuring that electron transfer is both kinetically fast and thermodynamically feasible. This efficient electron injection from the dye molecules into the semiconductor’s conduction band serves as a strategic approach for achieving high-performance DSSCs.

In addition to energy levels, the absorption properties of these dyes are analyzed, with a specific focus on oscillator strengths. These strengths serve as indicators of a dye’s effectiveness in absorbing light [13]. Strong oscillator strengths suggest the capability of these dyes to absorb light efficiently, leading to the generation of excitons, essential intermediates in the charge separation process within DSSCs.

The comprehensive assessment of the photovoltaic properties of natural dyes is of significant importance, and parameters such as light-harvesting efficiency (LHE), electron injection efficiency (ΔG^inject), electron regeneration energy (ΔG^regen), open-circuit voltage (V_OC), excited-state lifetime (τ), and the electronic coupling constant (|V_RP|) can be computed utilizing data obtained from DFT analysis [14]. These parameters collectively determine the overall performance and efficiency of DSSCs, rendering them indispensable in the selection of suitable sensitizers.

The inspiration for this study stems from the motivation to discern the capability of natural dyes in augmenting the efficiency of DSSCs. By exploring the optoelectronic and photovoltaic properties of cyanidin, delphinidin, pelargonidin, peonidin, and petunidin in both gas (vacuum) and ethanol phases, the aim is to contribute to the broader understanding of how these dyes can be applied in DSSCs [15]. The DFT study for the selected dyes in gas (vacuum) and ethanol phases allowed the calculation of parameters such as highest occupied molecular orbital (HOMO), LUMO, LHE, ΔG^inject, ΔG^regen, V_OC, τ, and |V_RP|. The results have opened new avenues for improving optoelectronic and photovoltaic properties, ensuring the creation of efficient and adaptable DSSCs. These advancements hold practical applications in the realm of renewable energy, aligning with the global commitment to harness solar power for a sustainable and environmentally responsible future.

2. Materials and Methods

Using Gaussian 09W software, the structures of different natural anthocyanin dye molecules were drawn. As indicated in Figure 1, five different anthocyanin dye types were created for this project: cyanidin, delphinidin, peonidin, petunidin, and pelargonidin. These dyes were selected because of their experimental validation, parameterization, and benchmarking, providing insight into structure–property relationships and enabling exploration of new dye candidates.

DFT was used for all optimization computations on the ground state structures in gas and ethanol solvents. The DFT technique, together with the B3LYP exchange correlation function and 6–31 basis set, was used to optimize the geometry of all anthocyanidin dyes in their ground state in the vacuum (gas) and solvent phases, without symmetry constraints. All calculations were completed in the absence of dispersion correction as in the study of Vuai et al. [9].

Along with their electron densities, the energy levels of the LUMO and HOMO were computed, and they were illustrated using Origin software [16,17,18,19]. The geometries’ UV–vis spectra were assessed using TD-DFT at the same level and the gas phase B3LYP technique, using the 6–31 G basis set [20,21,22]. Using the Gaussian 09W program, all calculations were performed in the gas and the ethanol solvent phases. The input and output files were organized using Gauss View 6.0, and the findings were evaluated.

3. Results and Discussions

3.1. Electronic Parameters

The efficiency of DSSCs is notably influenced by a dye’s electrical characteristics, including factors such as bandgap energy and HOMO and LUMO energy levels. Frontier molecular orbitals (FMOs), also known as HOMO and LUMO contributions, must be taken into account in order to determine the dye sensitizers’ charge-separated states. The FMO dispersion of the sensitizers has a major impact on the electrical charge transfer characteristics of dyes [23,24]. As shown in Figure 2 and Figure 3, the contour plots of HOMO and LUMO orbitals were calculated using DFT/B3LYP/6–31G levels for the selected anthocyanin dyes in both gas and ethanol solvent phases.

HOMO and LUMO energies are crucial factors in solar cell analysis that determine the likelihood of charge transfer. The HOMO energy levels of cyanidin, delphinidin, pelargonidin, peonidin, and petunidin are −6.0238, −6.0360, −6.1068, −5.9536, −6.0216 and −6.0551, −6.1062, −6.1261, −5.9890, −6.1228 eV for vacuum (gas) and ethanol solvent phases, respectively. The absolute energies of LUMOs in the same dyes are −3.7274, −3.2090, −4.3125, −3.6050, −3.1968 and −3.6929, −3.3225, −4.2801, −4.1489, −3.3252 eV for vacuum (gas) and ethanol solvent phases, respectively. The HOMO and LUMO levels are tailored for DSSC use, aligning with the TiO₂ conductive edge energy level and the electrolyte redox potential. This ensures effective charge separation and a reliable dye recovery procedure. The HOMO level of the dye must be sufficiently lower than the redox potential, while the LUMO level must be sufficiently higher than the conduction band edge (E_CB) of TiO₂ for effective electron injection from the excited dye to the conduction band [25].

Upon comparing the LUMOs depicted in Figure 2 and Figure 3, a notable observation emerges, indicating a higher degree of localization in the LUMO compared to the HOMO. Conventionally, optimal orbital overlap is achieved when both the HOMO and LUMO are delocalized, fostering robust interactions and favorable reactions. However, in the context of our DFT DSSC investigation, a localized LUMO presents potential advantages. The localized nature of the LUMO, as revealed in our findings, leads to favorable outcomes regarding the specific locations of reactions and provides insights into charge transfer dynamics. This observation aligns with the findings of Zhang et al. [26] and Yu et al. [27], underscoring the utility of a localized LUMO in DFT DSSC studies. Furthermore, prior research has indicated that similar LUMO behavior can be influenced by factors such as molecular structural symmetry and interactions with solvents [9,28].

The results indicate that the LUMO energies of cyanidin, delphinidin, and petunidin are higher than the conduction band edge of the TiO₂ electrode (−4.0 eV) in both phases. Consequently, these dyes are capable of injecting electrons into the semiconductor’s conduction band. However, pelargonidin has an inability to do so, given its lower LUMO values compared to TiO₂ in each phase, as shown in Figure 4.

In both the gas and solvent phases, the computed energy gaps of the model compounds under study decrease in the following sequence: delphinidin > petunidin > peonidin > cyanidin > pelargonidin and petunidin > delphinidin > cyanidin > pelargonidin > peonidin. The findings emphasize that pelargonidin exhibits lower energy levels in both phases, indicating its inefficiency in electron transition from LUMO to the conduction band. However, as a result, it is suggested that cyanidin, with its optimum energy gap in both phases, is expected to be more stable and stands out as a promising candidate for DSSCs.

3.2. Absorption Properties

Oscillator strengths (f), which dictate the amount of light absorbed by molecules, serve as absorption characteristics connected to the maximum absorption wavelength and the vertical transition energy of the dye from the ground state to an excited state [29].

Table 1. Absorption parameters of the selected anthocyanin dyes in the gas phase.

Dye Molecule	Absorption Wavelength (nm)	Excitation Energy (eV)	Oscillator Strength
Cyanidin	1382.88	0.8966	0.0005
Delphinidin	564.34	2.1970	0.0025
Pelargonidin	879.92	1.4090	0.0014
Peonidin	1401.18	0.8849	0.0005
Petunidin	563.29	2.2011	0.0025

and

Table 2. Absorption parameters of the selected anthocyanin dyes in the ethanol solvent phase.

Dye Molecule	Absorption Wavelength (nm)	Excitation Energy (eV)	Oscillator Strength
Cyanidin	1430.93	0.8665	0.0005
Delphinidin	565.12	2.1940	0.0028
Pelargonidin	857.00	1.4467	0.0023
Peonidin	1447.05	0.8568	0.0005
Petunidin	565.83	2.1912	0.0028

list the oscillator strengths, excitation energies, and absorption wavelengths of the dye molecules in both gas and ethanol solvent phases.

The energy levels and oscillator strengths of the natural dyes in both the gas and solvent phases exhibit significant patterns. In the gas phase, the energy levels decrease in the following order: petunidin > delphinidin > pelargonidin > cyanidin > peonidin. This order demonstrates how the dye molecules’ energy levels are positioned relative to one another, with lower energy levels being more advantageous for electron injection and transfer into a semiconductor’s conduction band in DSSCs. In the solvent phase (ethanol), the decreasing order is delphinidin > petunidin > pelargonidin > cyanidin > peonidin. The oscillator strengths in the gas phase follow the decreasing order of petunidin = delphinidin > pelargonidin > cyanidin = peonidin, reflecting the interplay between electronic transitions and incoming light. Similarly, in the solvent phase, the order is petunidin = delphinidin > pelargonidin > cyanidin = peonidin.

Additionally, the oscillator strength values in the gas phase undergo alterations when an ethanol solution is introduced to the dye molecules. This implies that the polarity of the solvent, ethanol in this case, can influence the electronic transitions and optical characteristics of the dyes. According to the data, petunidin and delphinidin exhibit stronger oscillators than the other dyes. This indicates that petunidin and delphinidin interact more strongly with light and are more likely to effectively absorb light in the studied system.

A higher absorption wavelength in DSSCs implies that the dyes may absorb light with longer wavelengths, which equates to lower energy photons. This is crucial because the typical operation of a DSSC involves absorbing light from the visible and near-infrared range, utilizing the absorbed energy to create electron–hole pairs in the dye molecule. Achieving a higher total light-to-energy conversion efficiency in the DSSC may result from using a larger fraction of the solar spectrum due to a higher absorption wavelength [30].

The optical absorption spectra of five naturally occurring dyes: cyanidin, delphinidin, pelargonidin, peonidin, and petunidin are provided for both the gas and solvent phases. These absorption spectra values reflect the wavelengths at which the dyes exhibit the highest light absorption. In the gas phase, the wavelengths of cyanidin, delphinidin, pelargonidin, peonidin, and petunidin are given as 1382.88, 564.34, 879.92, 1401.18, and 563.29 nm, respectively. The wavelengths for the same dyes in the solvent phase are 1430.93, 565.12, 857.00, 1447.05, and 565.83 nm. That redshift, or a shift towards longer wavelengths, is a phenomenon exhibited by molecules when their absorption spectra show a displacement towards longer wavelengths.

A redshift in the absorption spectra can have an impact on the DSSC’s photo-to-current conversion efficiency. According to the results of Table 1 and Table 2, cyanidin and peonidin exhibit greater absorption wavelengths compared to other dyes. Despite their longer wavelengths, these dye derivatives face limitations in electron injection into the semiconductor’s conduction band due to their lower LUMO energy levels. The energy level of the LUMO is a critical factor for effective electron injection in DSSCs.

In contrast, petunidin and delphinidin exhibit longer absorption wavelengths. This implies that, in comparison to the other dyes, they are capable of absorbing light at substantially higher levels of energy.

3.3. Photovoltaic Properties

It is possible to calculate the efficiency of the DSSC system by factoring in photovoltaic properties such as light-harvesting efficiency (LHE), electron injection efficiency (ΔG^inject), electron regeneration energy (ΔG^regen), open-circuit voltage (V_OC), excited-state lifetime (τ), and the electronic coupling constant (|V_RP|) [31]. The following Table 3 indicates the photovoltaic properties of the studied selected dyes in both the gas and ethanol solvent phases.

3.3.1. LHE

LHE in a DSSC represents the proportion of photons in the incident light that is absorbed by the dye, contributing to the formation of electron–hole pairs. The calculation of LHE involves the total of the dye’s optical density, light absorption coefficient, and quantum yield from electron injection into the semiconductor [32]. LHE is a crucial metric, reflecting the dye’s ability to capture incoming light and transform it into an excited state. In DSSCs, effective energy conversion relies on the dye’s capacity to absorb light and generate excited states, with a higher LHE indicating improved power conversion efficiency.

LHE in a DSSC can be influenced by various factors, including the choice of the dye and electrolyte, the thickness of the dye layer, and the shape and quality of the semiconductor layer. To enhance the photocurrent response, a high LHE is essential. The LHE values are calculated by using the below Equation (1) [33].

LHE = 1 − 10^−f

(1)

where:

• LHE = Light harvesting efficiency
• f = Oscillator strength.

Table 3 displays the values of LHE for the natural dyes in both the gas and solvent phases based on the information given. In the gas phase, the increasing order of LHE values is petunidin = delphinidin > pelargonidin > cyanidin = peonidin, and this order is maintained in the solvent phase. Among the dyes examined, petunidin and delphinidin exhibit the highest LHE values in both the gas and solvent phases. This suggests that petunidin and delphinidin have substantial electron-donating capabilities, allowing them to effectively absorb and change incoming light into excited states.

Table 3. Photovoltaic properties of studied molecules in the gas and ethanol solvent phases.

Vacuum (Gas) Phase
Dye Molecule	LHE	Edyeox (eV)	ΔGinject (eV)	ΔGregen (eV)	VOC (eV)	|VRP| (eV)	τ (ns)	η * (%)
Cyanidin	0.001	−6.572	−10.572	1.1738	0.2726	−4.0238	70.400	-
Delphinidin	0.006	−7.820	−11.820	1.1860	0.7910	−4.0360	43.860	-
Pelargonidin	0.003	−7.132	−11.132	1.2568	−0.3125	−4.1068	39.040	-
Peonidin	0.001	−6.496	−10.496	1.1036	0.3950	−3.9536	7.078	-
Petunidin	0.006	−7.806	−11.806	1.1716	0.8032	−4.0216	17.170	-
Ethanol Solvent Phase
Cyanidin	0.001	−6.609	−10.609	1.2051	0.3071	−4.0551	86.720	0.56 [34]
Delphinidin	0.006	−7.891	−11.891	1.2562	0.6775	−4.1062	19.140	0.61 [35]
Pelargonidin	0.005	−7.174	−11.174	1.2761	−0.2801	−4.1261	29.820	0.60–0.68 [36]
Peonidin	0.001	−6.538	−10.538	1.1390	−0.1489	−3.9890	17.590	0.87 [37]
Petunidin	0.006	−7.910	−11.910	1.2728	0.6748	−4.1228	17.190	0.69 [38]

* The symbol η represents the experimental efficiency of DSSCs sensitized with these dyes in ethanol for comparison.

Table 3. Photovoltaic properties of studied molecules in the gas and ethanol solvent phases.

Vacuum (Gas) Phase
Dye Molecule	LHE	Edyeox (eV)	ΔGinject (eV)	ΔGregen (eV)	VOC (eV)	|VRP| (eV)	τ (ns)	η * (%)
Cyanidin	0.001	−6.572	−10.572	1.1738	0.2726	−4.0238	70.400	-
Delphinidin	0.006	−7.820	−11.820	1.1860	0.7910	−4.0360	43.860	-
Pelargonidin	0.003	−7.132	−11.132	1.2568	−0.3125	−4.1068	39.040	-
Peonidin	0.001	−6.496	−10.496	1.1036	0.3950	−3.9536	7.078	-
Petunidin	0.006	−7.806	−11.806	1.1716	0.8032	−4.0216	17.170	-
Ethanol Solvent Phase
Cyanidin	0.001	−6.609	−10.609	1.2051	0.3071	−4.0551	86.720	0.56 [34]
Delphinidin	0.006	−7.891	−11.891	1.2562	0.6775	−4.1062	19.140	0.61 [35]
Pelargonidin	0.005	−7.174	−11.174	1.2761	−0.2801	−4.1261	29.820	0.60–0.68 [36]
Peonidin	0.001	−6.538	−10.538	1.1390	−0.1489	−3.9890	17.590	0.87 [37]
Petunidin	0.006	−7.910	−11.910	1.2728	0.6748	−4.1228	17.190	0.69 [38]

* The symbol η represents the experimental efficiency of DSSCs sensitized with these dyes in ethanol for comparison.

Petunidin and delphinidin have powerful electron-donating characteristics, which contribute to their higher LHE values and suggest their potential as good candidates for DSSC applications. Petunidin and delphinidin are advantageous sensitizers for improving the overall performance of DSSCs due to their capacity to efficiently capture light energy and produce excited states. Regarding the abnormality observed in the sign change of peonidin V_OC from the gas phase to the solvent phase, it may be attributed to interactions between peonidin and ethanol molecules when applying the solvent model. However, for further clarification, additional DFT studies and/or experimental investigations may be necessary.

3.3.2. Electron Injection Efficiency (ΔG^inject)

Electron injection efficiency in a DSSC is the proportion of photoexcited electrons in the dye that are successfully transported to the semiconductor’s conduction band. When light is absorbed by the dye in the DSSC, a photoexcited electron is generated in the molecule’s HOMO. This photoexcited electron needs to be moved to the semiconductor’s conduction band so it may take part in charge transport, allowing the DSSC to generate an electrical current. This phenomenon is referred to as electron injection [39].

The efficiency of electron injection depends on the electrical coupling between the dye and the semiconductor, the energy levels of the dye’s HOMO and LUMO, the conduction and valence bands of the semiconductor, and the kinetics of the electron transfer process. Experimentally, the short-circuit current density of a DSSC in both light and dark settings is often compared to assess electron injection efficiency. The ratio of the photocurrent to the intensity of the incident light acts as a barometer for the efficiency of the electron injection process. The photocurrent is represented by the difference in current density between these two states.

Two methods may be employed to examine the ΔG^inject: the relaxed and unrelaxed routes. A relaxed route is used by an electron to inject the molecule from its ground state into the semiconductor’s conduction band. The unrelaxed route is employed when an electron is introduced from the excited state of the dye into the semiconductor conduction band. Equations (2) and (3) are used to compute ΔG^inject.

ΔG^inject = E^dye* + E_CB

(2)

where:

• ΔG^inject = Electron injection efficiency
• E^dye* = Oxidation potential energy in the excited state
• E_CB = the semiconductor’s reduction potential (4.0 eV).

E^dye* = E^dye − E₀₀

(3)

where:

• E^dye = Oxidation potential energy in the ground state
• E₀₀ = Vertical electronic transition energy.

The findings, as shown in Table 3, reveal the sequence of decreasing ΔG^inject values for the natural dyes in both the gas and solvent phases. In the gas phase, it was observed that ΔG^inject decreased in the following order: peonidin > cyanidin > pelargonidin > petunidin > delphinidin, while for the solvent phase, the order is peonidin > cyanidin > pelargonidin > delphinidin > petunidin. In a DSSC, the term “ΔG^inject” describes the energy difference necessary for the injection of electrons from the excited dye molecule into the semiconductor’s conduction band [40]. A higher ΔG^inject value indicate an improved performance of the device, denoting a more favorable energy environment for electron injection.

Peonidin exhibits the highest value of ΔG^inject among the studied dyes in both the gas phase and the ethanol solvent phase. This indicates that, compared to other dyes, peonidin requires a greater energy difference for electron injection. In addition, the higher ΔG^inject value of peonidin suggests its suitability for use in DSSCs, as it may facilitate effective electron injection and charge transfer processes within the DSSC system.

The LHE and ΔG^inject figures are useful for determining the short-circuit current density (J_SC) in DSSCs. LHE illustrates how well the dye is able to absorb incoming light and convert it into an excited state, whereas ΔG^inject indicates the energy required for electron injection. To achieve the maximum J_SC, a high LHE and a substantial ΔG^inject are preferable. Peonidin is recommended as a promising candidate dye for DSSC applications due to its higher ΔG^inject value [41], and it has a potential to improve overall charge transfer efficiency and increase J_SC in DSSCs.

3.3.3. Electron Regeneration Energy (ΔG^regen)

The energy required in a DSSC to convey an electron from a reduced dye molecule to an oxidized electrolyte molecule is crucial for renewing the dye and completing the electron transport cycle. In a DSSC, a dye molecule is converted into a cation (positively charged ion), leading to the injection of the dye molecule’s photoexcited electrons into the semiconductor’s conduction band. The resulting electron-deficient dye can be recovered by accepting an electron from a reduced electrolyte molecule, typically a redox pair dissolved in the electrolyte solution. Electron regeneration involves the moment of electrons at the DSSC’s counter electrode [42].

The efficiency of electron regeneration depends on a number of factors, including the electrical properties of the dye and electrolyte molecules, the redox potentials of the redox pair, and the kinetics of the electron transfer procedure. When evaluating the DSSC’s performance, electron regeneration energy is a critical component to consider as it impacts the overall efficacy of the system. Electron regeneration energy (ΔG^regen) may be calculated using the energy difference between the reduced state of the dye and the oxidized state of the redox pair. This energy can also be measured experimentally using techniques such as cyclic voltammetry. The calculation of ΔG^regen is performed using Equation (4) [43].

ΔG^regen_dye = E^electrolyte_redox + E^dye_ox

(4)

where:

• ΔG^regent_dye = Electron regeneration energy
• E^electrolyte_redox = the redox potential
• E^dye_ox = Dye’s ground state oxidation potential energy.

As shown in Table 3, the findings indicate that pelargonidin dye derivatives exhibited the highest values of electron regeneration efficiency among the investigated dyes, in both the gas and ethanol solvent phases. In the gas phase, the decreasing order of the electron regeneration efficiency is pelargonidin > petunidin > delphinidin > cyanidin > peonidin, but in the solvent phase, the order is pelargonidin > petunidin > delphinidin > cyanidin > peonidin. Effective electron regeneration is crucial for the device to function at its peak and keep a steady current flow.

Among the examined dyes, pelargonidin demonstrated the highest electron regeneration efficiency. This suggests that pelargonidin has a larger capacity to regenerate electrons effectively, allowing a faster rate of electron transfer back from the semiconductor to the dye molecule. Further supporting evidence that pelargonidin supports effective dye regeneration comes from the high ΔG^regen (energy difference for electron regeneration) reported in this compound. The increased ΔG^regen in pelargonidin suggests a more favorable energy environment for the regeneration process, which may lead to an enhanced electron transfer back to the dye and, as a result, an improvement in the short-circuit current (J_SC) of the DSSC.

Overall, pelargonidin exhibited superior greater electron regeneration efficiency compared to other dyes, suggesting its potential as a promising sensitizer for DSSCs. By enhancing current flow and boosting overall power conversion efficiency, the effective electron regeneration made possible by pelargonidin can help a device function better.

3.3.4. Open-Circuit Voltage (V_OC)

The open-circuit voltage (V_OC) in a DSSC represents the maximum voltage generated by the cell when there is no external load or current flowing through the cell, reflecting the voltage across the DSSC terminals in the absence of electrical current. V_OC is closely tied to the energy gap between the redox potential of the electrolyte and the conduction band of the semiconductor, playing a crucial role in DSSC performance. As the energy difference widens, the V_OC of the DSSC increases. V_OC is also linked to the cell’s maximum theoretical efficiency, as determined by the Shockley–Queisser limit [44].

Several factors, including the choice of dye and semiconductor, the thickness and quality of the semiconductor layer, and the composition and redox potential of the electrolyte, can affect the V_OC in a DSSC. The power conversion efficiency in DSSCs can be calculated by using the V_OC. Typically, the dye molecules transfer electrons from their LUMO to the semiconductor conduction band. This also means that if the E_LUMO is high, the V_OC will also be high. The following Equation (5) has been used to compute the theoretical values of open-circuit voltage (V_OC).

V_OC = E_LUMO − E_CB

(5)

where:

• V_OC = Open-circuit voltage
• E_LUMO = the energy of the LUMO
• E_CB = the energy of the semiconductor’s conduction band.

Table 3 shows the V_OC values for natural dyes in both the gas and solvent phases. In the solvent phase, the order of the V_OC values is delphinidin > petunidin > cyanidin > peonidin > pelargonidin, while for the gas phase is petunidin > delphinidin > peonidin > pelargonidin. In both the gas and solvent phase, petunidin and delphinidin exhibited the highest V_OC levels among all the dyes. This suggests that petunidin and delphinidin have a better chance than the other dyes of generating greater voltage outputs in DSSCs. Due to their higher V_OC values, petunidin and delphinidin are recommended as viable choices for DSSC applications. By permitting the formation of greater electrical potentials, which is necessary for effective power conversion, these dyes can help increase device performance.

3.3.5. Excited-State Lifetime (τ)

The excited-state lifespan in a DSSC is the duration during which a dye molecule remains in an excited state before returning to its ground state. The transition to ground state can be through various mechanisms such as fluorescence, non-radiative decay, or electron injection into the semiconductor. The excited-state lifespan regulates the likelihood of electron injection into the semiconductor and also the competition between electron injection and alternative decay modes [45]. The excited-state lifetime can be calculated using the following Equation (6).

τ = (h × c)/(ΔE × φ)

(6)

where:

• τ = Excited-state lifetime
• h = Planck’s constant (6.626 × 10⁻³⁴ J·s)
• c = Velocity of light in vacuum
• ΔE = Excitation energy (in joules)
• φ = Oscillator strength.

Table 3 shows the excited-state lifetimes of the natural dyes in both the gas and ethanol solvent phases. The order of excited-state lifetimes in the gas phase is cyanidin (70.4 ns) > delphinidin (43.86 ns) > pelargonidin (39.04 ns) > petunidin (17.17 ns) > peonidin (7.078 ns), while in the ethanol solvent phase, the order shifts to cyanidin (86.72 ns) > pelargonidin (29.82 ns) > delphinidin (19.14 ns) > peonidin (17.59 ns) > petunidin (17.19 ns).

The length of time it takes for an excited dye molecule to return to its ground state is known as the excited-state lifetime. The claim emphasizes that petunidin, both in the gas phase and the ethanol solvent phase, has the lowest excited-state lifetime among the dyes under study. This is explained by the oscillator strength’s maximum value, which denotes a more powerful interaction between the dye’s electronic transitions and the incident light.

Additionally, petunidin is anticipated to have a better energy injection procedure and a greater light harvesting efficiency without affecting the DSSC’s short-circuit current (J_SC). This suggests that petunidin has a greater potential for effectively absorbing light and injecting electrons into the semiconductor material’s conduction band. Moreover, solvents with higher polarities have longer exciting lifetimes. This implies that the dyes’ excited-state lifetime is extended in more polar solvents like ethanol. Since polar liquids have a longer lifespan than nonpolar ones, more energy can be transferred, and electrons may be injected for longer periods of time, potentially improving device performance.

3.3.6. Electronic Coupling Constant (|V_RP|)

In a DSSC, the electronic coupling constant measures how strongly the dye molecule interacts with the semiconductor surface. It calculates the amount of electron transfer between the electronic states of the dye and the semiconductor, which is an important step in the conversion of light energy into electrical energy. The electronic coupling constant, which is expressed in electron volts (eV), may be calculated using the DFT, a popular quantum mechanical method. A larger coupling constant, which indicates a stronger bond between the dye and the semiconductor and a faster rate of electron transfer, may lead to improved DSSC performance [46].

The packing and orientation of the dye molecule and the semiconductor surface, as well as the properties of the electrolyte in the vicinity, all have an effect on the electronic coupling constant. Enhancing the electronic coupling between the dye and the semiconductor is a current area of research that aims to improve the performance of DSSCs. The generalized Mulliken–Hush (GMH) model presupposed the following method for calculating coupling constants from Equations (7) and (8).

|V_RP| = ΔE_RP/2

(7)

ΔE_RP = [E^dye_LUMO + 2 E^dye_HOMO] − [E^dye_LUMO + E^dye_HOMO + E_CB]

(8)

where:

• |V_RP| = Electronic coupling constant.

As shown in Table 3, the order of the energy gaps of the natural dyes in the gas phase is pelargonidin > delphinidin > cyanidin > petunidin > peonidin. However, in the solvent phase, the sequence changes to pelargonidin > petunidin > delphinidin > cyanidin > peonidin. The energy gap plays a significant role in a dye’s ability to absorb light and participate in electronic transitions. Pelargonidin reportedly possesses the smallest energy gap among other studied dyes for both the gas and solvent phases [47]. For successful light harvesting in optoelectronic devices like DSSCs, a lower energy gap is preferred, since it enhances the likelihood of collecting light in the visible spectrum. This also indicates that pelargonidin has a stronger inclination for coupling, referring to the electrical coupling between an excited dye molecule and a semiconductor’s conduction band. This indicates that pelargonidin is more likely to facilitate the fast transfer of electrons from the dye molecule to the semiconductor’s conduction band. Effective electron transport is crucial for DSSCs because it enables the conversion of absorbed light energy into electrical energy. The final column in Table 3 presents the reported experimental efficiencies of DSSCs sensitized with dyes extracted in ethanol solvent, providing a comprehensive overview of their performance.

These findings support the notion that pelargonidin, among the studied natural dyes, is the most favorable sensitizer due to its small energy gap and strong electron coupling. These characteristics suggest that pelargonidin is likely to have increased light absorption and quick electron injection into the semiconductor material’s conduction band, enhancing the overall effectiveness of the DSSCs.

It is imperative to recognize several inherent limitations to this study. Firstly, the adoption of a 6–31 G basis set, while conventionally considered large, may be perceived as outdated in the current computational landscape. Additionally, the omission of dispersion correction introduces the possibility of results deviating more significantly from actual outcomes. Nevertheless, this decision aligns with the methodology employed in a prior investigation conducted by Vuai et al. [9].

In future studies related to this research, we aim to address these limitations by exploring the adoption of a more advanced basis set and incorporating dispersion correction. This strategic enhancement will not only enable more accurate comparisons with the current study but also has the potential to broaden the scope of our investigation.

4. Conclusions

The analysis of electronic parameters revealed that cyanidin, delphinidin, and petunidin have LUMO energies lower than the conduction band edge of the TiO₂ electrode, making them suitable candidates for electron injection into the semiconductor’s conduction band. In terms of absorption properties, delphinidin and petunidin exhibited the highest excitation energies and oscillator strengths in both gas and ethanol phases, suggesting their potential for efficient light absorption.

The photovoltaic properties results demonstrated that petunidin and delphinidin possess superior attributes. They exhibited the highest LHE values, indicating their ability to efficiently capture and convert incoming light into excited states. Peonidin showed a higher ΔG^inject value, making it suitable for improving electron injection and charge transfer processes, thereby enhancing the short-circuit current (J_SC) in DSSCs. Pelargonidin displayed excellent electron regeneration efficiency, indicating its capability to effectively regenerate electrons and support a steady current flow.

In terms of open-circuit voltage (V_OC), petunidin and delphinidin exhibited the highest values, suggesting their potential to generate greater voltage outputs in DSSCs. Additionally, petunidin demonstrated a shorter excited-state lifetime, indicating a more stable excited state and efficient energy transmission. Furthermore, pelargonidin displayed the smallest energy gap and strong electron coupling, making it a favorable sensitizer for enhanced light absorption and rapid electron injection into the semiconductor’s conduction band.

In summary, these findings indicate that anthocyanin dyes, specifically petunidin, delphinidin, and pelargonidin, show potential as promising candidates for enhancing DSSC applications. Each dye exhibits a unique property that surpasses the others when evaluated individually. Consequently, a comprehensive understanding of these subtle properties, as explored in this study, can aid in selecting the most suitable dye for fabricating DSSCs, thereby contributing to enhanced device performance and energy conversion efficiency.