The effects of π-spacer on electronic properties,charge transfer,and chemical reactivity in D-A′-π-A configured molecules: Computational approach

Abstract

In this work, a systematic modification of the π-spacer was carried out to evaluate its influence on molecular geometry, electronic structure, charge transport properties, and global chemical reactivity descriptors in a series of D-A′-π-A organic molecules (M1–M4). Density functional theory was employed to analyze key parameters including dihedral angles, highest occupied molecular orbital–lowest unoccupied molecular orbital energies, natural bond orbital interactions, reorganization energies, ionization potential, electron affinity, chemical hardness, chemical potential, electronegativity, and electrophilicity index. The results reveal that M4 demonstrates the most favorable combination of properties, exhibiting the energy gap, reorganization energy, ionization potential, and chemical hardness of 1.4896, 0.4580, 4.8300, and 0.7127 eV, respectively. M4 also shows the highest chemical potential, electronegativity, and electrophilicity index of −4.1174, 4.1174, and 11.8938 eV, respectively. These results demonstrate the critical role of π-spacer engineering in adjusting the electronic behavior of D-A′-π-A systems and suggest that M4 is a promising candidate for high-performance organic semiconducting and optoelectronic uses.

Keywords

DFT D-A′-π-A NBO reorganization energy global reactivity descriptors charge transfer HOMO-LUMO

Introduction

Organic π-conjugated donor-acceptor systems have received considerable attention due to their broad applicability in nonlinear optics, organic electronics, and photovoltaic technologies.^1
–4 In these systems, the π-spacer that connects donor and acceptor units is critical for modulating intramolecular charge transfer (ICT), controlling molecular planarity, and facilitating electronic coupling between subunits.^5
–7 Modifying the π-spacer, especially through the introduction of electron-donating or electron-withdrawing substituents, can significantly influence charge delocalization, reorganization energies, molecular orbital distributions, and chemical reactivity descriptors.^8
–10

Natural bond orbital (NBO) analysis provides an effective method for examining charge distribution, donor-acceptor interactions (via second-order perturbation theory), and electronic delocalization pathways.¹¹ Through evaluation of stabilization energies between donor and acceptor orbitals, NBO analysis enables a quantitative understanding of how substituents and π-bridge modifications influence conjugation and ICT strength. Reorganization energies, for both holes (λ_hole) and electrons (λ_electron), which describe the energetic cost associated with molecular relaxation during charge transfer, are equally important; lower reorganization energies generally correspond to higher charge mobility and improved electronic performance.⁸

In addition, global chemical reactivity descriptors, including ionization potential, electron affinity, chemical hardness, chemical potential, electronegativity, and electrophilicity, provide valuable insight into molecular stability and reactivity patterns. These descriptors, derived from frontier molecular orbital (FMO) energies, help in establishing structure-property relationships in D-A′-π-A chromophores and guide rational molecular design.¹¹

Although several studies have used density functional theory (DFT) and time-dependent DFT (TD-DFT) to investigate the impact of π-bridges on D-π-A dyes (e.g. in dye-sensitized solar cells (DSSCs)),¹² fewer studies have comprehensively examined the combined effects of π-spacer substitution on global descriptors, reorganization energies, and NBO interactions in D-A′-π-A molecular structures. Recent work has shown that incorporating various π-spacers into symmetrical non-fullerene acceptor (A-D-A) systems can widen absorption ranges, lower reorganization energies, and enhance photovoltaic performance.^13,14 Similarly, benzothiadiazole-based π-spacers have been reported to markedly influence band gaps, absorption strength, and charge-transport properties.⁸

In this study, a series of D-A′-π-A molecules that differ only in the π-spacer, with the donor, internal acceptor, and external acceptor held constant are developed. Using DFT at the B3LYP/6-311G level, the reorganization energies, global chemical reactivity descriptors, and NBO characteristics were evaluated. The analysis of π-spacer variations on charge delocalization, charge mobility, and molecular reactivity offers insights to inform the development of advanced π-bridge-modified chromophores for optoelectronic applications. In addition, the photophysical properties and excited state arrangement of these developed molecules, together with TD-DFT calculated absorption maxima and oscillator strength, were established in our previous work.¹⁵ Building on those foundations, the current work focuses on screening-level electronic and transport descriptors to assess their feasibility for DSSC/organic photovoltaic (OPV) uses.

Computational methodology

Molecular develop

The π-spacer was selectively changed, maintaining the donor (D) unit, internal acceptor (A′), and external acceptor (A) constant across all molecular structures. The donor unit was chosen for its potent donating capacity, whereas benzothiadiazole (BTD) and cyanoacrylic acid were employed as the internal and external acceptors, respectively, to ensure efficient electron withdrawal. A series of four D-A′-π-A molecules (M1–M4), shown in Figure 1, was constructed by systematically varying the π-spacer. The selected π-spacers included thiophene, 4-(thiophene-3-yl)pyridine, 2-(4-(thiophene-2-yl)thiophene, and (E)-5,6-dihydro-6-(4,5-dihydrocyclopenta[b]thiophene-6-ylidene)-4H-cyclopenta[b]thiophene. Any observed variations in electronic or structural properties can be directly attributed to the influence of π-spacer, allowing a clear evaluation of its effect on the D-A′-π-A molecular framework.

Figure 1.

The D-A′-π-A molecules designed using donor, internal acceptor, π-spacer, and external acceptor.

Computational details

The ground-state geometries of the molecules under investigation were taken from our earlier study,¹⁵ where the B3LYP^16,17 functional was used to fully optimize the molecular structures using the Gaussian 09 Rev, D.01 program suite¹⁸ within DFT. To guarantee structural stability, the M1–M4 structures were optimized using strict self-consistency field (SCF) convergence criteria. The geometries match the verified minima discovered in our earlier study,¹⁵ offering a consistent basis for the electronic analysis even though formal frequency analyses were not carried out for this investigation. The optimized geometries described in that work form the structural basis of this study.

This study focuses on a more thorough electronic investigation of the developed sensitizers, building on this established foundation. The Gaussian 09 Rev, D.01 program suite at the B3LYP/6-311G level of theory was employed for all further computations. The B3LYP/6-311G level of theory was chosen in order to reconcile the systematic evaluation of the π-spacers with computing cost. Although it is accepted that the 6-311G basis set lacks polarization functions, which are important for atoms like sulfur, and that B3LYP may underrepresent long-range interactions, this level of theory is suitable for capturing the qualitative-relative trends across the M1–M4 series. Therefore, rather than being predictive-absolute numbers, the data reported here are meant to offer a comparative understanding of the structural influences on electronic properties.

The ionization potential (IP), the electron affinity (EA), the energy of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), and the HOMO-LUMO energy gap are some of the important electronic parameters related to photovoltaic performance that were computed based on the optimized geometries. In addition, the reorganization energies for hole and electron transfer (λ_hole and λ_electron, respectively) were determined, which reveals information about the molecules’ charge-transport properties.

At the same theoretical level, NBO analysis was used to further clarify the ICT behavior inside the developed sensitizers. The FMO distributions were previously reported in our previous work,¹⁵ but in order to provide the electronic context required for interpreting the newly evaluated ICT characteristics as well as charge-transport parameters of those developed molecules.

Ground-state optimization was achieved using DFT/6-311G reliable with the methodology employed for the TD-DFT absorption analysis reported in our previous work.¹⁵ Equations (1)–(4) were employed to determine the energy gap, reorganization energies for the electron (λ_electron), reorganization energies for the hole (λ_hole), as well as total reorganization energy (λ_total)^17,19,20

E_{g} = E_{LUMO} - E_{HOMO}

(1)

λ_{hole} = (E_{0}^{+} - E_{+}^{+}) + (E_{+}^{0} - E_{0}^{0})

(2)

λ_{e l e c t r o n} = (E_{0}^{-} - E_{-}^{-}) + (E_{-}^{0} - E_{0}^{0})

(3)

λ_{t o t a l} = λ_{h o l e} + λ_{e l e c t r o n}

(4)

where E_g indicates the energy band gap, E_HOMO represents the HOMO energy, and E_LUMO indicates the LUMO energy. The neutral, anion, and cation total energies in their respective equilibrium structure are donated by $E_{0}^{0}$ , $E_{-}^{-}$ , and $E_{+}^{+}$ , respectively; the cation/anion total energy in the neutral geometry is $E_{0}^{+}$ / $E_{0}^{-}$ and the neutral in the cation/anion geometry is $E_{+}^{0}$ / $E_{-}^{0}$ .

Equations (5)–(10) were used to study various reactivity parameters, including ionization potential (IP), electron affinity (EA), chemical potential (μ), chemical hardness (η), electronegativity (χ), and electrophilicity index (ω), which provide information about the electrical structure of molecules^21
–24

IP = - E_{H O M O}

(5)

EA = - E_{L U M O}

(6)

μ = - χ

(7)

η = (I P - E A) \frac{1}{2}

(8)

χ = (I P + E A) \frac{1}{2}

(9)

ω = \frac{μ^{2}}{2 η}

(10)

Results and discussion

Geometry optimization and dihedral angle

Although our earlier publication¹⁵ established the structural and FMO characteristics of the M1–M4 series, these parameters are used here as a fundamental baseline to investigate charge-transport dynamics that have not been explored before. By adding NBO analysis and reorganization energy calculations, the current study greatly expands the current photophysical profile and offers deeper mechanistic insights into the electronic coupling and carrier mobility of these developed molecules.

Geometry optimization refers to the techniques used to determine a molecule’s three-dimensional atomic arrangement and reduce its model energy. Specific geometric variables, such as the dihedral angle, were considered in order to assess the conformation of these proposed molecules. Figure 2 shows the optimal arrangement of each examined molecule.

Figure 2.

The optimal structure for all proposed D-A′-π-A molecular systems.

The dihedral angle between the donor, π-spacer, and acceptor units is a crucial factor in determining the degree of planarity within the D-A′-π-A molecular architecture. According to optimized geometries derived from DFT simulations, molecule conformation is significantly influenced by the π-spacer’s nature.

Figure 2 and Table 1 show that the studied D-A′-π-A molecules are planar, with dihedral angles near 180°. This indicates that the chosen π-spacers promote extended conjugation throughout the donor-π-acceptor framework. Such planarity enables effective π-electron delocalization, which improves electrical communication between donor and acceptor units.^25,26 It is anticipated that these structural features likely impact key properties, such as molecular polarizability, charge transport behavior, and FMO alignment.

Table 1.

The selected dihedral angle of the produced D-A′-π-A molecules.

Molecules	D-A′		A′-π		π-A
	ANGLE	DEGREE	ANGLE	DEGREE	ANGLE	DEGREE
M1	C12-C11-C23-C24	–179.971	C26-C28-C43-S42	–179.950	C40-C41-C32-C33	179.992
	C10-C11-C23-C25	–179.972	C27-C28-C43-S39	–179.960
]M2	C12-C11-C23-C24	178.281	C26-C28-C48-S47	175.023	C40-C41-C44-C33	179.646
	C10-C11-C23-C25	177.819	C27-C28-C48-S49	174.821
M3	C12-C11-C23-C24	–176.852	C26-C28-C54-S53	–175.527	C48-C49-C32-C33	179.084
	C10-C11-C23-C25	–176.747	C27-C28-C54-C50	–175.997
M4	C12-C11-C23-C24	–176.203	C26-C28-C45-C44	–175.590	C49-C48-C32-C33	179.985

This pattern aligns with previous computational research where, in twisted donor-acceptor systems, the degree of orbital overlap and charge transfer character were modulated by donor–acceptor dihedral angles.²⁷ DFT analysis of aromatic systems connected to ethylene, disilane, and ethynylene shows that a dihedral angle of 180° indicates ideal conjugation, while twisted geometries increase the HOMO-LUMO gap and decrease conjugative interactions.²⁸

Optoelectronic properties

The optoelectronic properties of the developed molecules as a function of π–spacer effect are here discussed using FMO energies (HOMO and LUMO energies) and the energy gap. Table 2 and Figure 3 display the HOMO and LUMO energies (E_HOMO and E_LUMO) as well as the HOMO-LUMO energy gap (E_g) for D-A′-π-A proposed molecules (M1, M2, M3, and M4). Since E_HOMO is frequently linked to the molecule of interest’s capacity to donate electrons, larger E_HOMO values signify a greater capacity to contribute electrons to a receptor’s vacant molecular orbital.^15,29 Conversely, a substance with a higher E_HOMO can be regarded as an excellent electron carrier, but the molecule’s capacity to take electrons is correlated with its E_LUMO value. As a result, a material with a lower E_LUMO value is more capable of accepting electrons and acting as a carrier of holes.³⁰

Table 2.

The E_HOMO, E_LUMO, and HOMO-LUMO energies gap for proposed M1–M4.

Molecules	E_HOMO (eV)	E_LUMO (eV)	E_gap (eV)
M1	–5.0540	–3.4621	1.5919
M2	–4.9786	–3.2898	1.6888
M3	–4.9163	–3.3333	1.5830
M4	–4.8469	–3.3573	1.4896

Figure 3.

The electron excitation ability of the proposed M1–M4 molecules.

Smaller HOMO-LUMO gap values indicate increased conductivity and decreased kinetic stability.³¹ M4 has the smallest gap (1.4896 eV) among the series, suggesting a more robust intramolecular charge transfer character and a more efficient orbital coupling through the spacer. Conjugation was not completely suppressed by the increased twist in M4, perhaps as a result of compensatory electrical effects. As observed in Figure 3, M3 is situated between M1 and M2, with a very small gap (1.5830 eV). Larger gaps (1.5919 and 1.6888 eV, respectively) are maintained by M1 and M2, which is consistent with either significantly less conjugation or a more electron-withdrawing character in the spacer. With the exception of steric effects or substituent interactions, the trend of decreasing E_g, in the order M2 > M1 > M3 > M4, qualitatively coincides with increased conjugation and planarity (lower twist). Greater ease of electrical excitation or charge transfer is suggested by the narrower E_g in M4, which is advantageous in organic semiconductor or OPV settings; however, stability and reorganization energy must also be balanced.

The M1–M4 series’ systematic π-spacer engineering is an atomic-scale molecular development technique intended to adjust the degree of planarity and conjugation. This method successfully modifies the charge transfer character and FMO (HOMO/LUMO) levels, which directly affects the reorganization energies and the anticipated charge-transport and optoelectronic performance.³² The study that follows uses these electronic-structure rationales as screening-level descriptors to assess the dyes’ viability for DSSC applications, building upon the excited-state profiles and TD-DFT absorption characteristics developed in our earlier work.¹⁵

Charge population and Molecular linkage

When studying conjugative interactions or charge transfer in molecular systems, NBO analysis is a crucial tool. It offers a helpful paradigm for examining intramolecular and intermolecular linkages as well as bond interactions.³³ Therefore, NBO analysis was carried out here to determine the charge populations for the proposed molecules. Table 3 shows that the donor and π-linker groups of all the proposed molecules (except the π-linker in M2) possess positive NBO charges, confirming their effectiveness as electron-donating groups. Conversely, the negative NBO charges observed for both the internal and external acceptor units (with the exception of the external acceptor in M2) indicate their strong electron-withdrawing ability.

Table 3.

The NBO analysis for all proposed molecules M1–M4.

Molecules	D	A′	π	A	Δq(D-A)
M1	1.11298	−1.2426	1.05896	−1.82755	2.94053
M2	1.12491	−1.24561	−1.06142	1.76896	−0.64405
M3	1.09843	−1.24565	0.94466	−1.70516	2.80359
M4	1.10313	−1.24668	1.08663	−1.82643	2.92956

The negative charge concentrated on the M2 spacer (−1.06142e) in the NBO analysis is a noteworthy finding that contract with positive charges found for the other spacers in this investigation. The M2 framework’s 4-(thiophene-3-yl)pyridine is responsible for this negative character since it serves as an electron-accumulating site. From a kinetic standpoint, this concentrated negative density can be produced on electronic trap between the donor and the anchoring group. In comparison to the other developed molecules, this design is anticipated to hinder the smooth flow of electron density during excitation, which could slow down the injection kinetics and lower overall efficiency of the charge transfer process.

The NBO charges on each dye molecule’s donor groups during photoexcitation were sorted as follows, based on Table 3; M2 (1.12491e) > M1 (1.11298e) > M4 (1.10313e) > M3 (1.09843e). M1 and M4 dominate in the donation capacity because M2 has a negative NBO value in its π-linker position that facilitates poor donation of electrons toward the acceptor. M1 and M4 can therefore give electrons more easily than the other molecules, based on these facts.

The NBO charges for the acceptor groups were −1.82755, −1.76896, −1.70516, and −1.82643 for M1–M4, in that order. The electron donor and acceptor’s differential Δq(D-A) is also highlighted in the following order: M1 (2.94053e) > M4 (2.92956e) > M3 (2.80256e) > M2 (-0.64405e). Table 3 demonstrates that M1 and M4 have the largest Δq(D-A) of 2.94053e and 2.92956e. As a result, M1 and M4 have a larger charge separation than other produced molecules. Therefore, it can be concluded that M4 outperforms M1 in charge separation. This is supported by the comparison of their energy gaps and Δq(D-A) values, where M4 exhibits a significantly larger reduction in energy gap (0.1023 eV) and slightly higher Δq(D-A) with difference of 0.01097. So, these NBO metric contribute to the hypothesis that an optimal π-spacer promotes better orbital communication and charge separation, thereby improving charge transfer characteristics.

Although ICT is essentially a dynamic excited-state phenomenon, charge separation potential can be evaluated using ground-state NBO and FMO investigations as crucial benchmarks. The strong spatial decoupling of FMOs in M1 and M4 that were reported to our previous work,¹⁵ where the LUMO moves toward the anchoring group while the HOMO stays localized on the donor, establishes a distinct directional channel for electron migration.³⁴ The nearly complete localization of orbitals on discrete donor-acceptor fragments affords a trustworthy approximation for the ICT mechanism, even if transition density matrix (TDM) analysis offers a more detailed depiction of transition dynamics. This approach is in line with the body of research on push-pull chromophores, confirming that the ground-state electronic topography effectively dictates the primary pathway for charge transfer and injection kinetics in these systems.³⁵

Charge transfer

A key idea in comprehending charge transfer in organic molecules utilized in DSSCs and organic solar cells (OSCs) is reorganization energy. It stands for the energy required to react to an electron transfer event or a shift in the charge distribution within the molecule by rearranging the solvent, counterions, and neighboring molecules.³⁶ Molecules with lower reorganization energies are preferred for DSSCs and OSCs because they enable faster charge transfer rates. Reorganization can be used to estimate the charge transfer characteristics of organic materials, such as the speed at which electrons or holes can flow within organic molecules.³⁷

The overall reorganization energies are calculated by adding the electron-reorganization and hole-reorganization energies. Equations 2−4 were used to compute these energies, and Table 4 displays the findings, where the total reorganization energies for all proposed molecules (M1–M4) are arranged in the order of M2 (0.3834 eV) < M1 (0.4172 eV) < M3 (0.4208 eV) < M4 (0.4580 eV). The results reveal that all developed molecules (M1–M4) exhibit lower reorganization energy. The observation that all the proposed molecules exhibit relatively low reorganization energies is consistent with the findings of Kacimi et al.,³⁸ who reported that dye molecules with total reorganization energies in the range of 0.1–0.5 eV tend to achieve higher charge mobility. In this study, the calculated total reorganization energies fall within 0.3834–0.580 eV, supporting the assertion that these molecules possess favorably low reorganization energies.

Table 4.

The electron, hole, and total reorganization energies (in eV) for all proposed molecules (M1–M4).

Molecules	λ_electron (eV)	λ_hole (eV)	λ_total (eV)
M1	0.2209	0.1963	0.4172
M2	0.1595	0.2239	0.3834
M3	0.2061	0.2147	0.4208
M4	0.2305	0.2275	0.4580

The reduced reorganization energies observed in M1, M2, M3, and M4 can be attributed to the incorporation of π-spacer units, which promote structural flexibility and efficient intramolecular charge delocalization. Consequently, the low reorganization energies suggest that these dyes are capable of achieving higher electron-transfer efficiency. This property is expected to enhance electron mobility and, ultimately, improve the overall electrical performance of the proposed molecular systems.

When reorganization energies are compared, M2 has the lowest numerical value, suggesting an inherent kinetic advantage for charge transport. In material science, a trade-off between transport efficiency and light-harvest capability determines a chromophore’s overall performance, even if lower reorganization energy is essentially advantageous for transport kinetics. M4 is still a very competitive option due to its more optimized energy gap and higher maximum absorption as reported to our previous paper,¹⁵ even though M2 has better kinetic potential. Therefore, rather than being distinguished by absolute kinetic superiority over M2, M4 is classifies as a balanced architecture when advantageous charge mobility maintained within the 0.1-0.5 eV range complements its enhanced light-harvesting capabilities.

Chemical reactivity and electronic behavior

The electronic behavior and chemical reactivity of the considered molecules as a function of π-spacer is discussed through its Global reactivity descriptors. The global reactivity descriptors provide complementary insights into the chemical reactivity and electronic behavior of the proposed molecules. These parameters, derived from FMO energies, help evaluate properties such as stability, charge transfer propensity, and electrophilic/nucleophilic behavior. A high energy bandgap indicates that the chemical system is more stable and less reactive.³⁹ Using HOMO and LUMO energies, we computed the ionization potential (IP), electron affinity (EA), chemical potential (μ), electronegativity (χ), chemical hardness (η), and electrophilicity index (ω). Table 5 and Figure 4 show the results of global chemical descriptors for proposed molecules M1–M4.

Table 5.

The global reactivity descriptors in (eV) for all proposed molecules (M1–M4).

Molecules	IP	EA	χ	η	µ	Ω
M1	5.0009	3.5293	4.2651	0.7358	−4.2651	12.3615
M2	4.8948	3.2398	4.0673	0.8275	−4.0673	9.9957
M3	4.8646	3.3541	4.1093	0.7553	−4.1093	11.1794
M4	4.8300	3.4047	4.1174	0.7127	−4.1174	11.8938

Figure 4.

The predicted reactivity of designed molecules using global reactivity descriptors.

Electron affinity depicts the energy shift of a neutral molecule with the addition of an electron, whereas ionization energy illustrates the energy change that results from the removal of an electron from the molecule’s neutral state.⁴⁰ Understanding the ionization potential and electron affinity is necessary to solve fundamental issues in organic chemistry, such as whether the molecules are more or less reactive. For many organic substances, as well as the molecules under study, experimental measurements of ionization energy and electron affinity are few. The energy barrier for the injection of holes and electrons is directly related to the ionization potential and electron affinity. Higher electron affinity values and a smaller ionization potential are desirable because they facilitate hole and electron injection.^41,42 Table 5 and Figure 4 show the computed global reactivity descriptors for the studied molecules. The following is a ranking of the compounds according to their ionization potential: M4 < M3 < M2 < M1. The findings indicate that M4 has the lowest ionization potential of all the developed molecules, measuring 4.8300 eV. The molecules are arranged according to electron affinity as follows: M1 > M4 > M3 > M2, with M1 showing the highest values at 3.5293 eV. Due to its larger ionization potential difference (0.1709 eV) compared to the relatively small difference in electron affinity (0.1246 eV), M4 demonstrates superior hole- and electron-injection capability relative to M1.

In the ground state, the chemical hardness parameter describes the dye’s resistance to charge transfer and the tendency of charge to escape from the system. This quality is essential to understanding the behavior of the chemical system. The molecules are sorted as follows: M4 < M1 < M3 < M2. The calculated chemical hardness values are shown in Table 5 and Figure 4. The results showed that the M4 molecule had the lowest chemical hardness values. We get to the conclusion that M4 is more likely than the other molecules to release electrons and lower the barrier to ICT because of the lower chemical hardness values.

Chemical potential is sometimes known as the electronic chemical potential or the Fermi level. The energy required to add or remove an electron from the system at a constant particle number and volume is a measure of the system’s ability to donate or receive electrons. Chemical potential has a major impact on both the electronic charge transfer mechanism and the spontaneity of reactions. According to Ayers, Anderson, and Bartolotti (2005), molecules with a high electronic potential are good electron donors, whereas those with a small electronic potential are good electron acceptors.⁴³ Table 5 and Figure 4 display the computed chemical potential of the molecules in the following order: M2 > M3 > M4 > M1. The results show that M2 has higher chemical potential values, implying that it is effective electron donor. This makes it easier for M2 to give electrons to the semiconductor, which acts as an electron acceptor. However, we make conclusion on that due to its significant difference between M2 and M4 on energy gap of 0.1992 eV while slight difference on chemical potential of -0.0501 eV so it makes M4 to be more favorable candidate to release electrons to the semiconductor rather than M2 based on these facts.

The electronegativity of an atom in a molecule is a measure of its capacity to attract electron density to itself. Among the numerous chemical characteristics that are impacted by electronegativity are bond polarity, acidity, and basicity. Molecules that have a greater electronegative value are more readily able to receive electrons. Table 5 and Figure 4 rank the electronegativity values of the molecules as follows: M1 > M4 > M3 > M2. Based on the data presented in Table 5 and Figure 4, M1 and M4 exhibit the highest electronegativity values among all the molecules. This indicates that these two systems have a stronger tendency to attract and accept electrons compared to the others.

The electrophilic index is a helpful metric for assessing the electrophilic character of a molecule or a reaction site within a molecule.²¹ It provides details on a species’ electron-taking propensity, which is crucial for understanding reaction mechanisms, determining reactivity, and developing new chemical processes. It was discovered that compounds with superior electrophilic groups have lower chemical potential and decreased chemical hardness.⁴⁴ Through the acquisition of electrons from the surrounding environment, a molecule with a higher electrophilicity index (ω) was shown to be more efficient and to have higher energy stability. Table 5 and Figure 4 display the electrophilicity index values, which are arranged as follows: M1 > M4 > M3 > M2. The results indicate that M1 and M4 have higher electronegativity indices than the other molecules. Thus, it may be concluded that M1 and M4 possess higher photoelectric properties.

Actually, the global reactivity descriptors were computed at the B3LYP/6-311G theoretical level using Koopmans’ theorem. This functional is a well-known benchmark for organic photovoltaic materials, offering a balanced representation of the FMO, despite being sensitive to the 20% Hartree–Fock exchange present in B3LYP. The relative trends in all descriptors are thought to be reliable for forecasting the comparative performance of these solar cell sensitizers because the current work concentrates on the methodical comparison of structurally similar series (M1–M4).

Conclusion

Our computational analysis shows that the π-spacer’s type has a major impact on the D-A′-π-A systems’ electrical characteristics, charge transfer features, and chemical reactivity. With the lowest energy gap, reorganization energy, ionization potential, and chemical hardness of 1.4896, 0.4580, 4.8300, and 0.7127 eV, respectively, among the molecules (M1–M4) under study, M4 stood out as the most viable candidate. These characteristics reflect enhanced charge transport capabilities and structural adaptability. In addition, M4 demonstrates the highest chemical potential, electronegativity, and electrophilicity index values of −4.1174, 4.1174, and 11.8938 eV, respectively, indicating a strong tendency to accept electrons and participate in favorable intermolecular interactions. The combined performance metrics highlight M4 as a candidate for applications in organic electronic and optoelectronic materials. These insights may serve as a useful foundation for the rational design of advanced chromophores and semiconducting systems in future studies.

Footnotes

Acknowledgements

The authors acknowledge the support of the Muslim University of Morogoro and the University of Dodoma.

ORCID iD

Michael Kennedy Sanama

Ethical consideration

In this article, there is no study employing animal or human subjects.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Author contributions

Ismail Abubakari (Conceptualization), Michael Kennedy Sanama (Writing original draft), and Melkizedeck Hiiti Tsere (Formal analysis).

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

Data supported by the article itself.

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