A DFT and TD-DFT Study of Two Hydralazine Derivatives for Organic Solar Cells and Nonlinear Optical Applications

Tamighang, Remi Nkeih; Ajifack, Dodo Lydie; Tasheh, Stanley Numbonui; Nkungli, Nyiang Kennet; Tsapi, Charly Tedjeuguim; Numbonui Ghogomu, Julius

doi:https://doi.org/10.1155/2023/2162991

Journal of Chemistry

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Abstract Introduction Results and Discussion Conclusion Data Availability Conflicts of Interest Acknowledgments Supplementary Materials References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 2162991 | https://doi.org/10.1155/2023/2162991

A DFT and TD-DFT Study of Two Hydralazine Derivatives for Organic Solar Cells and Nonlinear Optical Applications

Remi Nkeih Tamighang,¹Dodo Lydie Ajifack,¹Stanley Numbonui Tasheh,¹Nyiang Kennet Nkungli,¹Charly Tedjeuguim Tsapi,²and Julius Numbonui Ghogomu^1,2

Academic Editor: J. O. Caceres

Received25 Apr 2023

Revised02 Jun 2023

Accepted25 Nov 2023

Published08 Dec 2023

Abstract

In recent years, organic molecules have been the subject of in-depth research studies using in silico methods for their applications in solar cells and photonic devices. This study reports a theoretical investigation of the organic solar cell (OSC) and nonlinear optical (NLO) properties of (E)-1-(phthalazin-1-yl)-1-[(pyridin-2-yl)ethylidene]hydralazine (PPEH) and 1-[2-(1-(pyridine-3- yl)ethylidene)hydrazinyl]phthalazine (PEHP). The density functional theory (DFT) and its time-dependent extension (TD-DFT) were employed with the B2PLYP, M06-2X, BP86, CAM-B3LYP, and B97-XD functionals, alongside the def2-tzvp and def2-tzvpp basis sets. Geometrical and Frontier molecular orbital (FMO) analyses were performed. Reactivity descriptors, open circuit voltage (V_oc), energy driving force (∆E_L−L), light harvesting efficiencies (LHEs), NLO susceptibilities, and properties were also computed and discussed. The results show that PEPH and PPEH are good electron donor materials for organic solar cells as they possess high FMO energies, V_ocs, ∆E_L−Ls, and LHEs. Moreover, both molecules have static first and second hyperpolarizabilities as well as dynamic NLO responses that are on average 10 times greater than those of para-nitroaniline. PEPH and PPEH also exhibit properties such as second harmonic generation (SHG), electro-optic Pockels effect (EOPE), electric field-induced second harmonic generation (EFISHG), and optical Kerr effect (OKE). Indeed, these molecules are potential candidates for organic solar cells and NLO applications. Findings from this work may further accelerate the synthesis and development of green energy materials for optical solar cells and NLO applications in the future.

1. Introduction

Organic photovoltaic devices such as organic solar cells (OSCs) and organic light-emitting diodes (OLEDs) are state-of-the-art technologies around the world, with research in these areas steadily increasing [1–6]. This is a result of their environmental friendliness, ease of assembly, low cost and physical flexibility [7]. Despite significant advancements in the search for better optoelectronic components, finding high-performance, tiny, and thermally stable organic-based photovoltaic systems are still challenging. This points out how crucial it is to create new organic materials with a variety of functionalities for better optoelectronic device performance. Among the aforementioned photovoltaic devices, OSCs can directly convert sunlight into electrical energy [8, 9]. It constitutes an organic film sandwiched between two electrodes [1, 6, 10]. The materials used to create this film are both donors and acceptors, mounted in a two-layer structural configuration. The fullerene (6,6)-phenyl-C61-butyric acid methyl ester (PCBM) is commonly used as an electron acceptor material in OSCs [11–13], whereas poly(3-hexylthiophene) (P3HT) and its derivatives are widely employed as electron donor materials in OSC devices [11, 14]. Accordingly, P3HT and PCBM were used herein as reference materials for the design of OSCs.

The design of photovoltaic systems have equally benefited from nonlinear optical (NLO) features brought about by a material’s particles oscillating in response to an external applied electric field [15]. Effective NLO molecules are known to be -conjugated systems and possess electron acceptor (A) and donor (D) groups [16–20]. These molecules are known as push-pull or D--A molecules. The NLO activities of these push-pull molecules are caused by intramolecular charge transfer between D and A [20]. Alterations of the structural as well as functional groups, typically by adding more powerful electron donor/acceptor groups and/or changing the type and length of the spacer, are frequently used to enhance the NLO responses of materials [14]. It is worth mentioning that optical switches and sensors, modulators, optical computing, optical data processing, optical data storage, optical limiting effects, and holography are just a few applications of NLO materials [20–22].

Due to the superior characteristics of organic materials, such as their ultrafast response times, lower dielectric constants, high internal quantum efficiency, high damage threshold, and flexible design [23], more organic materials than their inorganic counterparts have been the subject of electronic quality research in recent years [14, 24–26].

Hydralazine hydrazone-based organic compounds such as (E)-1-(phthalazin-1-yl)-1-[(pyridin-2-yl)ethylidene]hydralazine (PPEH) and 1-[2-(1-(pyridine-3- yl)ethylidene)hydrazinyl]phthalazine (PEHP), synthesized, partially characterized, and screened for their antiplasmodial, antimicrobial, and antioxidant activities by Awantu and collaborators [27] (see Figure 1) are among the organic materials which are likely to have high charge transport capabilities. The structural features of these molecules are donor-π-acceptor-π-donor (D-π-A-π-D) like, which is most likely to enhance intramolecular charge transfer where the donor (D) plays the role of hole transport and the acceptor (A) functions as an electron transporter [14, 17]. Moreover, their extended π-skeleton is a precondition for significant NLO activities. The synthesis, crystal structure, antifungal, and antionchocercal activities of similar compounds have also been reported [28–30].

(a)

(b)

Despite the fascinating structural characteristics of PEHP and PPEH that are amendable to organic solar cell and nonlinear optical applications, there is no comprehensive study of the OSC and NLO properties of these molecules in the literature. Thus, research into these perspectives is necessary. This work sought to theoretically provide insights into the design of PEHP and PPEH as potential materials for applications in optical solar cell and NLO devices, through the prediction of OSC and NLO parameters. To achieve this, geometrical analysis was performed, open circuit voltage (V_oc), the energy driving force (∆E_L−L), electronic adsorption spectra, linear, and nonlinear parameters were computed and discussed. The density functional theory (DFT) and its time-dependent extension (TD-DFT) were chosen for this study because they reflect a reliable alternative for addressing these tasks, as the methodology investigates electronic structure and spectroscopic properties of these types of materials [31]. Again, the theoretical approach is the best tool for overcoming experimental synthesis difficulties and exploring substitutes that reduce material production and processing costs. DFT was also chosen due to its ability to account for electron correlation at a lower computational cost and the balance between computation time and accuracy [16, 21]. The findings from this study will provide insights about the electronic and optical properties of two hydralazine derivatives, contributing to the development of organic solar cells and nonlinear optical applications.

2. Computational Details

Apart from the NLO-related computations, all quantum chemical calculations in this work were done with the ORCA 4.0.1 quantum chemical package [32]. NLO activities were predicted with the Gaussian 16 program package [33]. In all ORCA calculations, the medium-sized numerical quadrature grid 5 and the tight self-consistent field (SCF) convergence criterion were used. Input structures were prepared using the Avogadro 1.1.1 program [34]. Geometry optimization and frequency calculations were performed using the BP86 Generalized Gradient Approximation (GGA) functional [35] and the def2-TZVP Ahlrichs basis set [36, 37]. The resolution-of-the-identity (RI-J) approximation [38] in combination with the chain-of-spheres (COSX) approximation, giving rise to the RIJCOSX approximation, was utilised to speed up the geometry optimization and frequency calculations with negligible accuracy sacrifice. Analysis of vibrational frequencies shows no imaginary frequency, establishing that all optimized geometries were stable structures (minima on the potential energy surface).

Based on the BP86-optimized geometries, single-point (SP) calculations were performed using the double hybrid-GGA functional B2PLYP (with 53% Hartree–Fock and 27% second-order møller plesset perturbation (MP2) [39, 40] and M06-2X (with 54% Hartree–Fock (HF)) [41] along with the Karlsruhe basis set def2-tzvpp [42]. The M06-2X and B2PLYP functionals were employed here due to their effectiveness in energy calculations and their ability to model noncovalent interactions [40, 41]. Long-range dispersion interactions within the studied molecules were accounted for through Grimme’s atom pair-wise dispersion correction with Becke–Johnson’s damping dubbed (D3BJ) [43], except for the M06-2X functional, where the D3zero [41] dispersion correction was used. Absorption spectra and NLO properties of the investigated compounds were computed at CAM-B3LYP/def2-tzvpp and B97-XD/def2-tzvpp levels of theory.

Based on the fact that HOMO and LUMO energy levels of materials are the main determinants of their OSCs quality, some major Frontier molecular orbital (FMO) energy level-based parameters were computed in this study. These include the energy driving force (∆E_L−L), which is the difference between the LUMO energy levels of the donor (the hydralazines studied) and the acceptor (PCBM, a reference material), as well as the open circuit voltage (V_OC) which was calculated according to the following equation:where 0.3 is an empirical factor, is the HOMO energy of the donor molecule, is the LUMO energy of the acceptor material, and is the open circuit voltage.

The dissociation efficiency at the donor/acceptor interface in OSC devices is determined by the energy difference (∆E_L−L) in LUMO energies of donor and acceptor molecules, which were calculated as shown in the following equation:

Within this framework, dissociation is only possible when the values of are less than 0.3 eV [5, 44].

Light harvesting efficiency (LHE) refers to a material’s ability to produce excitons after photon absorption. Thus, it can serve as an important metric in understanding the efficiency optical solar cells [45]. It is worth noting here that, the charge transfer process in solar cells is primarily influenced by LHE values [46]. The LHEs for this study were calculated using the oscillator strengths obtained by TD-DFT calculation according to the following equation:where f is the oscillator strength of the molecule associated to the maximum absorption wavelength.

Components of the static and dynamic electronic linear polarizability (α), the quadratic hyperpolarizability (β), and the cubic hyperpolarizability (γ) tensors were calculated to determine the linear and nonlinear optical properties of PEPH and PPEH. The static dipole polarizabilities [α (0; 0)], first hyperpolarizabilities [β (0; 0, 0)], and second hyperpolarizabilities [γ (0; 0, 0, 0)] were calculated at frequency ω = 0. On the other hand, the dynamic polarizabilities [α (−ω; ω)], first hyperpolarizabilities [(−2ω; ω, ω)], the vector components of the first hyperpolarizabilities projected along the dipole moment [], and the electric field-induced second harmonic generation (EFISHG) [γ (−2ω; ω, ω, 0)] were calculated at ω = 0.04282 a.u.

The induced microscopic polarizability (P), which occurs when a molecule is exposed to an oscillating external electric field produced by strong light, like laser light, can be expressed as a power series in the electric field E as shown in the following equation [47–49]:where α, β, and γ are the linear polarizability, first (quadratic) hyperpolarizability, and second (cubic) hyperpolarizability tensors, respectively.

In this study, equations (5) and (6) were employed to calculate the average linear polarizability and the total static first hyperpolarizability (). Equations (7) and (8) in turn, were used to compute the vector part of the dynamic first hyperpolarizability , and the average (isotropic) second hyperpolarizability (γ), respectively.where , , .

The isotropic values of the second harmonic generation (SHG) [β (−2ω; ω, ω)], electro-optic Pockels effect (EOPE) [β (−ω; ω, 0)], electric field induced second harmonic generation (EFISHG) [γ (−2ω; ω, ω, 0)], and optical Kerr effect (OKE) [γ (0; ω, −ω, 0)] were as well calculated in addition to the aforementioned hyperpolarizabilities. These hyperpolarizabilities are relevant to this study because they can frequently be obtained from experiments and frequently serve as a reference for comparing data obtained from various sources [50].

3. Results and Discussion

3.1. Structural Analysis

Presented in Figure 2 are the optimized structures of PEPH and PPEH. The optimized Cartesian coordinates of the studied compounds are provided in Tables S1 and S2 of the accompanying electronic supplementary material (ESM).

(a)

(b)

Table 1 displays the selected geometric parameters of the optimized structures.

Geometric parameters obtained theoretically at the BP86-D3(BJ)/def2-TZVP level are found to be consistent with experimental counterparts obtained from the CCDC 1007670 (crystallographic data). The optimized structures are therefore suitable for further analysis. Also presented in Table 1 are some dihedral angles of the studied molecules. Although the dihedral angles deviate slightly from the ideal 0° and 180° values in a perfect square planar geometry, the molecules remain significantly planar. Given that planarity in a molecule is caused by π-conjugation, intramolecular charge transfer between the electron donor and acceptor groups in the studied hydralazine derivatives is likely and may result in a significant OSC.

Linear regression between theoretical and experimental bond lengths was performed to further assess the suitability of the level of theory used and the optimized structures obtained as shown graphically in Figure S1 of the ESM. The regression curves yielded the following equations:

High correlation coefficients () are obtained between theoretical and experimental values in a good linear regression, demonstrating the suitability of the applied theory level and the optimized structures.

3.2. Chemical Stability of the Studied Molecules

Stability is a key quality of ideal materials for photovoltaic cells. Chemical stability is commonly defined by absolute chemical hardness (ƞ), which measures the system’s resistance to exchanging electron density with the surrounding environment [51]. was computed as shown in the following equation:where IP is the ionisation potential and EA is the electron affinity of the system. The values of IP and EA were calculated using equations (11) and (12), respectively, at the B2PLYP-D3(BJ)/def2-tzvpp and M06-2X(D3Zero)/def2-tzvpp levels of theory in the gaseous phase, and the results are provided in Table 2. Listed in Table S3 of the ESM are the energies of the cationic , anionic , and neutral species of the studied molecules in eV. The M06-2X and B2PLYP functionals were chosen here due to their outstanding performance in energy calculation [40, 41].

In these equations, E⁺, E⁻, and E⁰ are single-point energies of the cationic, anionic, and neutral forms of the molecules investigated.

Results from Table 2 indicate that at both levels of theory, a similar trend is observed. The findings also depict that PPEH has a smaller ƞ value (i.e., 3.872 eV for M06-2x and 3.473 eV for B2PLYP) when contrasted with PEPH (i.e., 3.964 eV for M06-2x and 3.562 eV for B2PLYP). This indicates that PPEH is relatively less stable and chemically more reactive than PEPH. Consequently, PPEH is expected to exhibit a higher charge transport rate as required in solar cells. All computed EA values are less than that of experimental oxygen molecule (0.448 eV) [52]. This signifies that the investigated compounds are less stable toward corrosion in the environment [53]. Accordingly, anticorrosive measures are recommended should these molecules be used as organic solar cell materials.

The M06-2X-D3(BJ)/def2-tzvpp level of theory is considered for subsequent discussions thanks to its effectiveness in modelling noncovalent interactions and electronic properties of organic molecules [41].

3.3. Photovoltaic Properties

3.3.1. Frontier Molecular Orbital (FMO) Analysis

The ability of charge to be transferred between the donor and acceptor components of a material is determined by their Frontier molecular orbital (FMO) energy levels [14, 54]. For an efficient charge transfer process, the HOMO and LUMO energies of the materials must be higher than the reference acceptor material, PCBM (HOMO = −6.10 eV and LUMO = −3.75 eV) and lower than that of P3HT (HOMO = −4.65 eV and LUMO = −2.13 eV), a reference donor molecule [14, 24]. To evaluate the ability of the studied molecules to act as charge transfer agents in solar cells, their HOMO and LUMO energies were calculated at M06-2X/def2-tzvpp level of theory in the gaseous phase as presented in Table 3.

The findings from the table indicate that the computed HOMO and LUMO energies of the studied molecules are lower than those of P3HT, but greater than those of PCBM. This indicates efficient injection of electrons into the lowest-lying unoccupied molecular orbital of the acceptor material. Resultantly, the studied molecules may serve as electron donor agents in organic solar cells. Moreover, this ability of photo-excited electron transfer from the investigated molecules to PCBM is of significant importance to both organic solar cells and most photovoltaic devices.

Also presented in Table 3 are the energy gap (E_gap) values of the compounds under investigation. The E_gap value of PPEH is slightly lower than that of PEPH. This indicates that PPEH is more reactive and less stable than PEPH. Consequently, PPEH is expected to be a better electron donor material in organic solar cells. The FMO iso-surfaces of the molecules studied as visualised with Avogadro 1.1.1 [34] are displayed in Figure 3.

3.3.2. Open Circuit Voltage ()

The open circuit voltage () is an important factor that determines the efficiency of an organic solar cell. As initially defined is a function of the HOMO energy of the donor material and LUMO energy of the acceptor material, from which the rate of charge transfer is effectively determined [55, 56]. The computed at the M06-2X/def2-tzvpp level of theory and those of the reference donor (P3HT) and acceptor materials (PCBM), along with the ∆E_L−L values are listed in Table 4.

The outcomes indicate that all the calculated values are greater than those of the prototypical materials: P3HT and PCBM. This demonstrates the ability of the molecules under study to introduce electrons into the open orbitals of the acceptor material PCBM. All of the investigated molecules can therefore be used as donor materials in organic solar cells. It is also clear from the table that the differences between the LUMO energy of the studied molecules and the LUMO of the reference acceptor material are far greater than 0.3 eV. This raises the possibility of a significant transfer of photo-excited electrons from the molecules under study to the acceptor material (PCBM), further confirming the ability of these molecules to be used in the fabrication of photovoltaic devices. The ∆E_L−L trend of the studied compounds varies as follows: PPEH < PPEH. Notably, this finding concurs with the chemical stability, E_gap, and FMO analysis, indicating the likelihood that PPEH will function well as charge transporters in photovoltaic devices.

3.4. Nonlinear Optical (NLO) Properties and Susceptibilities

Presented in Tables S4–S9 of the ESM are the tensor components of the nonlinear properties and susceptibilities used for this study.

3.4.1. Average Static Linear Polarizability Isotropies

To predict the linear optical activities of the investigated compounds, their average linear polarizability isotropy , which determines charge distribution and plays a key role in the intramolecular charge transfer (ICT) rate for linear optical response in materials, was computed [48, 49]. Here, the origin of Cartesian coordinate system was used as the centre of mass in each molecule. Presented in Table 5 are the average linear polarizability isotropies and its x, y, and z components computed at CAM-B3LYP/def2-tzvpp and wB97-XD/def2-tzvpp levels of theory. The range-separated functionals CAM-B3LYP and ωB97-XD were used here owing to their effectiveness to model the orbital energy of -conjugated molecules that involve charge transfer in excited states [57, 58]. Also presented in this table are the values of para-nitroaniline, a prototypical push-pull chromophore for nonlinear optics, which was used as a reference. The following conversion factors were used in this work: for linear polarizability, for first hyperpolarizability and second hyperpolarizability.

The results show that the values for the compounds examined at both levels are all higher (i.e., by about 2 × esu times) and very similar to those of PNA for each level used. On this basis, PEPH and PPEH possess higher linear optical properties than PNA. The results also show that is dominant in the x-direction (see values for component in the table) for all compounds under investigation, suggesting that ICT occurs primarily in the x-direction, along which lies a bulk of the π-conjugated system of the molecules. In addition, PEPH has the highest values, which results in significant ICT required for linear optical applications.

3.4.2. Static First and Second Hyperpolarizabilities

To determine the susceptibilities of the investigated molecules to NLO activities in response to an applied static electric field, their static first () and second hyperpolarizabilities were computed at ω = 0. The static first and second hyperpolarizabilities are denoted β (0; 0, 0) and γ (0; 0, 0, 0), respectively. Tables 6 and 7 present the computed values of β (0; 0, 0) and γ (0; 0, 0, 0), respectively, at different levels of theory alongside their molecular tensor components along the , , and cartesian coordinate axes.

The datasets depict that the computed values of β (0; 0, 0) and γ (0; 0, 0, 0) of the studied molecules are approximately 3.5 times greater than those of PNA at all levels of theory under investigation, indicating their likelihood of significant NLO activities. Consequently, they are promising NLO chromophores for use in optoelectronic devices. PPEH exhibits the largest β (0; 0, 0) and γ (0; 0, 0, 0) values at all study levels and is predicted to demonstrate more significant NLO activities.

3.4.3. Dynamic First Hyperpolarizability ()

To determine the capability of the studied hydralazine molecules undergoing NLO activities in response to an applied dynamic (frequency dependent) electric field, the vector components of the dynamic first hyperpolarizability () were calculated at the Nd: YAG laser wavelength (λ) of 1064 nm (i.e., at frequency, ω = 0.04282 a.u.) and the results are listed in Table 8.

Table 8 demonstrates that the computed values of are significantly higher than those of PNA, demonstrating their potential for quadratic dynamic NLO effects at the specified light wavelength. It isIt’s interesting to note that all computed values of at wavelength 1064 nm are positive and, as a result, parallel to the dipole moment vector. It is also obvious that PPEH has the largest computed values of across all levels of theory. This suggests that PPEH may exhibit a relatively more significant dynamic second-order NLO activity necessary for the design of optoelectronics and photonics devices. It is worth mentioning that the results are in line with those suggested by chemical stability, open circuit voltage , , β (0; 0, 0) and γ (0; 0, 0, 0). PPEH and PEPH are therefore promising materials for OSC and NLO devices.

3.4.4. NLO Properties (SHG, EOPE, EFISHG, and OKE)

The NLO response of the investigated molecules was predicted through the second harmonic generation (SHG) [β (−2ω; ω, ω)], electro-optic Pockels effect (EOPE) [β (−ω; ω, 0)], electric field-induced second harmonic generation (EFISHG) [γ (−2ω; ω, ω, 0)], and optical Kerr effect (OKE) [γ (0; ω, −ω, 0)]. These results are listed in Table 9. The calculations were all carried out at the popular laser frequency of 0.08242 a.u. using the range-separated functionals CAM-B3LYP and ωB97-XD in conjunction with the def2-tzvpp Ahlrich basis set.

The findings indicate that the range-separated functionals CAM-B3LYP and B97-XD yield similar results, although those obtained with CAM-B3LYP are slightly higher. It can be inferred from Table 9 that the computed values of the dynamic first hyperpolarizabilities: SHG [β (−2ω; ω, ω)] and EOPE [β (−ω; ω, 0)] of the studied molecules are greater than those of PNA. This suggests that they are potential candidates for Second Harmonic Generation and Electro-Optic Pockel’s effect applications. The results also show that PPEH has the highest SHG and EOPE values at both levels of theory, and is expected to have significant SHG and EOPE activities, which are necessary for optoelectronic applications.

Moreover, the predicted values of EFISHG and OKE of the investigated molecules are higher than those of PNA, suggesting their applicability in optoelectronic and photonic devices. As expected, the calculated EFISHG and OKE values of PPEH are relatively larger than those of PEPH at both levels of theory. This confirms PPEH as a better NLO chromophore.

3.5. TD-DFT Study

The absorption wavelength of a suitable NLO material must satisfy certain absorption property requirements; otherwise, the undesirable optical transparency effect may occur. Due to strong electromagnetic (EM) absorption in the visible region (400–800 nm), optical transparency significantly reduces the properties of a material. Strong visible-range light absorption can result in high optical transparencies, limiting the NLO applications of materials [59, 60]. Moreover, materials which show intense absorption of light (characterized by high oscillator strength) are likely to undergo electronic transitions with charge transfer character that can enhance their nonlinear response [59, 60].

The UV-Vis absorption spectra of the investigated molecules were calculated using the TD-DFT method to ascertain whether the transparency-efficiency trade-off mentioned above might apply to them. The predicted absorption wavelength (λ_abs), excitation energy (E_abs), oscillator strength, orbital coefficients, dominant electronic transitions, and light harvesting efficiencies (LHEs) are listed in Table 10. The parameters in this table correspond to the absorption bands with the highest oscillator strengths, which represent the most intense band in the UV-Vis spectrum.

The findings reveal that both levels of theory employed here yield similar trends. However, discussion is based on that obtained by the CAM-B3LYP/def2-tzvpp level. The outcomes also show that PEPH and PPEH have oscillator strengths of 0.3617 and 0.3923, respectively. Interestingly, the computed values of at the specified levels of theory fall within the UV region of the EM spectrum (100–400 nm), indicating that the molecules strongly absorb in this region. The molecules are therefore likely to experience only minor optical losses, leading to a favourable nonlinear efficiency-accuracy trade-off. The electronic absorption energies are 3.971 and 3.941 eV for PEPH and PPEH, respectively. It can also be seen from Table 10 that the highest electronic absorption is due to the electronic transition involving the S₀ and S₁ states.

The computed LHEs for PEPH and PPEH are 0.5652 and 0.5947, respectively, as shown in Table 10. As a result, the values of LHE are similar; hence, the studied molecules are expected to produce almost equal amount of photocurrent in OSCs. However, PPEH is slightly more effective than PEPH at producing a higher photocurrent, owing to its highest oscillator strength. This observation is in accordance with a similar study [45], where the LHE is proportional to the oscillator strength.

The simulated absorption spectra of PEPH and PPEH in the gaseous phase are shown in Figure 4.

The spectra indicate the most prominent and more intense secondary absorption peak for each molecule.

4. Conclusion

A theoretical study of the geometries, chemical stability, photovoltaic properties, absorption spectra, and nonlinear optic properties of PEPH and PPEH was carried out using the DFT method and its time-dependent extension (TD-DFT). These molecules have been studied for their potential use in NLO response and as organic solar cell (OSC) components. NLO and OSC property predictions in this work were preceded by structural analysis on the optimized geometries. Due to their higher HOMO and LUMO energy values relative to those of PCBM, along with their higher energy gaps and higher open circuit voltage (V_oc), the results suggest that PEPH and PPEH may function as electron donor materials in OSCs. Also, the ∆E_L−L values are greater than 0.3 eV, which predicts the possibility of photo-excited electron transfer from the studied molecules to PCBM, a common requirement in photovoltaic devices. From the results obtained, the static first and second hyperpolarizabilities of PEPH ( and , respectively), PPEH ( and , respectively), and the dynamic NLO response are on average 10 times greater than those of the prototypical NLO molecule, para-nitroaniline. The absorption wavelengths of the investigated molecules fall within the ultraviolet (UV) region (100–400 nm) of the electromagnetic (EM) spectrum, indicating that the hydralazine molecules studied may undergo only minimal transparency-nonlinearity trade-off, making them promising lead molecules in the design of NLO and optoelectronic devices.

Data Availability

The data that support the findings of this study are included in the article and in the supplementary data file.

Conflicts of Interest

The authors declare that they have no conflicts of interest regarding the publication of this paper.

Acknowledgments

We gratefully acknowledge the support of the Ministry of Higher Education of Cameroon through its Research Modernization allowance for this project.

Supplementary Materials

The supplementary material contains a figure and tables as a part of this work. Figure S1: linear regression of PEPH and PPEH at B86/Def2-TZVP level of theory. Tables S1 and S2, respectively, contain the DFT/BP86-D3(BJ)/def2-TZVP optimized geometrical Cartesian coordinates of PEPH and PPEH. Table S3 contains computed cationic , anionic , and neutral energies in eV at B2PLYP-D3(BJ)/def2-tzvpp and M06-2X(D3zero)/def2-tzvpp levels of theory in gas phase. Tables S4–S9 contain the tensor components of the nonlinear properties and susceptibilities. (Supplementary Materials)

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