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ACS Omega
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ACS Omega
2470-1343
American Chemical Society

10.1021/acsomega.4c05150
Article
Synthesis, Crystal Structure, and Theoretical Screening of Solvatochromism and Light-Harvesting Performance of Hexamine V-Substituted Lindqvist-Based Photosensitizer for Photovoltaic Solar Cells
https://orcid.org/0009-0006-5053-8628
Maalaoui Ahlem †
Toumi Baya ‡
https://orcid.org/0000-0002-8008-9572
Agwamba Ernest C. §∥
Okon Gideon A. ⊥#
Rzaigui Mohamed †
https://orcid.org/0000-0002-3401-6399
Akriche Samah *†
† Laboratory of Chemical Materials LR13ES08, Faculty of Sciences of Bizerte, Carthage University, Zarzouna, Bizerte 7021, Tunisia
‡ Laboratoire des Ressources en Eau et Environnement, INRAP Technopole, Sidi Thabet 2020, Ariana-Tunis
§ Computational and Bio-Simulation Research Group, University of Calabar, Calabar 540281, Nigeria
∥ Department of Chemistry, Covenant University Ota, Ota 112104, Nigeria
⊥ Department of Pure and Applied Chemistry, University of Calabar, Calabar 540281, Nigeria
# Department of Chemical Sciences, Clifford University Owerrinta, Umuika 451101, Nigeria
* E-mail: sameh.akriche@fsb.ucar.tn.
28 08 2024
10 09 2024
9 36 3806638079
01 06 2024
19 08 2024
15 08 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by-nc-nd/4.0/ Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).

In this paper, we employ density functional theory (DFT) and time-dependent DFT (TD-DFT) approaches to predict the solvatochromism and light-harvesting properties of a newly synthesized hybrid hexamine (HMTA) vanadium-substituted Lindqvist-type (V2W4) polyoxometalate (POM), (C7H15N4O)2(C6H13N4)2[V2W4O19]·6H2O, (HMTA-V2W4) for application in dye-sensitized solar cells (DSSCs). Single crystal X-ray diffraction (XRD) and noncovalent interaction (NCI) analyses show a 3D-supramolecular packing stabilized by means of hydrogen bonds and van der Waals (vdW) and ionic interactions between highly nucleophilic cage-like HMTA surfactant, lattice water, and electrophilic V2W4 polyanions. Experimental and theoretical UV/vis absorption spectra show large absorption in the visible region, which is strongly solvent polarity dependent. This solvatochromic behavior can be attributed to hydrogen bonding interactions between the V2W4 polyanion and protic solvents. Furthermore, the energy level of semiconductor-like nature of HMTA-V2W4 with high LUMO level matches well with the conduction band (CB) of TiO2, which is beneficial for the photovoltaic device performance. The photovoltaic empirical parameters are theoretically predicted to demonstrate a remarkably high open-circuit voltage (Voc) value (1.805 eV) and a photoelectric conversion efficiency (PCE) value up to 8.7% (FF = 0.88) along with superior light-harvesting efficiency (LHE) (0.7921), and therefore, the studied compound is expected to be a potential candidate as a photosensitizer dye for applications in DSSCs. The aim of this work was to broaden the range of applications of POMs, owing to their low-cost fabrication, leveraging and flourishing optoelectronic properties, and ever-improving efficiency and stability for use in future technology pointed to the development of clean and green renewable energy sources to solve the current energy crisis.

Enseignement SupÃ©rieur et de la Recherche Scientifique 10.13039/100012964 NA University of Carthage 10.13039/100019985 NA document-id-old-9ao4c05150
document-id-new-14ao4c05150
ccc-price
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pmcIntroduction

Dye-sensitized solar cells (DSSCs) have focused extensive attention owing to their easy fabrication process, low price, high power conversion efficacy, and long-term stability. Typically, the semiconductor materials commonly used in solar cells suffer from slow electron mobility, which affects the photoelectric conversion efficiency (PCE).1,2 To solve these problems, many research studies are focused on the development of efficient donor−π–acceptor dyes used for DSSCs. Interestingly, polyoxometalates (POMs), which are mainly constituted by transition metals (W, Mo, Nb, V, ...) in higher oxidation state bridged with oxygen atoms, display great potential in various fields such as optics, catalysis, and electronics.3−5 Indeed, owing to their photoactive properties, strong electron acceptor functions, redox nature, very strong acidity, as well as the diverse and vast chemistry of the transition metals, these compounds have a tremendous potential for applications in single-molecule magnets, photoelectrical devices, sensor design, supramolecular chemistry, and medicinal and biological chemistry.3−10 In addition, due to their photosensitive properties (wide spectral absorption and variable band structure), POMs can be used in photovoltaic devices as sensitizers or cosensitizers. Recently, they have been used as building blocks for third-generation solar cells, including organic solar cells (OSCs), quantum dot-sensitized solar cells (QDSSCs), perovskite solar cells (PSCs), and dye-sensitized solar cells (DSSCs).11−15 These kinds of solar cells have attracted great research interest because of environmental friendliness, low cost, and high theoretical conversion efficiency in addition to their easy preparation. Up to now, numerous studies have investigated the application of Keggin-type, [XM12O40]n−16−20 and Wells–Dawson-type structures, [X2M18O62]n−,21,22 to enhance the photoelectric conversion efficiency of QDSSCs/DSSCs. In addition, El Moll et al.23 have recently reported that the use of Lindqvist-type POMs as additives in p-type DSSCs increases the open-circuit voltage parameter (VOC) by reaching a maximum value of 265 mV. However, the inclusion of V-substituted Lindqvist-type POM, [VxW(6–x)O19]n−, in dye-sensitized solar cells is still scarce. As far as we know, the earlier reported di-V-substituted Lindqvist-type POM [Cu(C12H8N2)2]2[V2W4O19]·4H2O23 was used as a cosensitizer in DSSCs. Compared with pure N719 (PCE = 5.8%), the cosensitized solar cell [Cu(C12H8N2)2]2[V2W4O19]·4H2O/N719 generated a Jsc of 16.71 mA cm–2 and a Voc of 0.691 V with a PCE of 7.05% (FF = 0.609). It may be speculated that these improved results are due to the smaller band gap of [Cu(C12H8N2)2]2[V2W4O19]·4H2O than TiO2, thus giving a cosensitized solar cell with more sunlight absorption.23

Otherwise, the cage polyamine, hexamethylenetetramine (HMTA), attracts interest due to its outstanding structural litheness coupled with chemical, physical, and biological properties.24 Recently, several works reported the successful use of tertiary amine as an additive, providing a new strategy for improving the performance and stability of perovskite solar cells (PSCs).25,26 Tian et al.27 have reported the fabrication of a perovskite solar cell based on the SnO2 electron transport layer modified by adding hexamethylenetetramine (HMTA) with a power conversion efficiency of 22.7%. In addition, Irwan et al.28 have synthesized TiO2 nanoparticles mediated with hexamethylenetetramine surfactant by the hydrolysis method and found that the HMTA surfactant has a great influence on the structural and optical properties of TiO2 particles, especially the reduction of the gap energy and crystal size.28 This higher efficiency successfully confirms the key role of HMTA in the enhancement of the photovoltaic performance and stability of materials used in solar cell devices.

Furthermore, the application of computational methods in molecule design and optimization has become increasingly crucial in recent years.29,30 Our study is a testament to the potential of these performances in optoelectronic devices and development, particularly in the investigation of hybrid complex molecular structures such as POMs, which may be challenging to study experimentally. Computational methods, such as DFT and TD-DFT, offer a powerful and complementary approach to investigate the electronic and photophysical properties of hybrid POMs. Based on the abovementioned research background, herein, we report the synthesis of a new HMTA-di-vanadium–substituted Lindqvist-type POM, (C7H15N4O)2(C6H13N4)2[V2W4O19]·6H2O, (HMTA-V2W4). Its structural, optoelectronic, luminescent, and photovoltaic properties were enhanced by using experiment and theory based on density functional theory (DFT) and time-dependent DFT (TDDFT) quantum calculations.28−30

Here, we aimed at studying the photophysical properties of a synthesized POM-based hexamine-Lindqvist hybrid, understanding the structure–performance relationship, and theoretically searching the efficiency and improvement of TiO2-based solar cell performance when using HMTA-V2W4 as a photosensitizer. The main goal of this work was expected to demonstrate that the POM-based organic–inorganic hybrids are still challenging and may exhibit interesting and tunable photophysical characteristics that can be harnessed for a wide range of innovative technological applications such as photovoltaics.

Results and Discussion

X-ray Diffraction and Noncovalent Interaction Analyses

The crystallinity and purity of the synthesized Lindqvist-based material are confirmed by the go,od correlation between the experimental diffractogram assessed with powder X-ray diffraction (XRD) analysis and the calculated diffractogram obtained from the resulting crystal data (Figure S1). Single-crystal XRD analysis shows that the formula unit of HMTA-V2W4 consists of [V2W4O19]4– Lindqvist-type POM (V2W4), two symmetrical cagelike quaternary organic cations, [(CH2)6N4–CH2OH]+ and [(CH2)6N4–H]+ (HMTA) and six water molecules (Figure 1a). As frequently observed for V-substituted POM,31−33 tungsten and vanadium cations are statistically distributed over the six sites with an occupancy rate of M = (2/3 W + 1/3 V).

Figure 1 (a) Strucutral diagram of HMTA-V2W4. (b) Packing arrangement of HMTA-V2W4 viewed along [001] direction. (c) Hirshfeld surfaces mapped with dnorm of V2W4..

The packing arrangement of HMTA-V2W4 consists of a 3D supramolecular network stabilized by means of various sets of noncovalent interactions (NCIs) including N–H···O, N–H···N, and O–H···O hydrogen bonds, C–H···O van der Waals interactions, and ionic bonding (Figure 1b) occurring between HMTA donors and V2W4 acceptors with donor–acceptor distances ranging from 2.657 (5) Å to 2.994 (8) Å (Table S1). The acceptor centers are indicated by the brightest red spots on the surface of V2W4 generated using the Hirshfeld surface analysis mapped using dnorm,34 as shown in Figure 1c. The 2D fingerprint plots (Figure S2) display the percentage of intercontact contributions with the most prominent being O···H/H···O (58.9%) when compared to H··H (33.5%), N···H/H···N (6.7%), O···N/N···O (0.9%), and other contacts.

Noncovalent interaction (NCI) analysis based on molecular electron density approximation has been applied to confirm the results of X-ray diffraction and Hirshfeld surface analyses.34,35 The RDG versus sign (λ2)ρ(r) and isosurface density plots (Figure 2a,b) are combined to visualize van der Waals (vdW) interactions, hydrogen bonds, and steric repulsion. The 2D-RDG scatter plot and the 3D isosurface map are color coded on a red-green-blue scale based on ρ (r) values, varying from −0.035 to +0.02 a.u. and an isosurface value ranging from −0.05 to 0.05 a.u. The blue spikes appearing between the hydrogen atoms of (N–H) groups and the oxygen atoms OV2W4 with (λ2)ρ ←0.02 a.u. are specifically referred to the strong intermolecular hydrogen bonds between V2W4 and HMTA moieties. Whereas, the green regions figured among the H atoms of (C–H) groups and OV2W4 atoms (sign(λ2)ρ ≈ 0 a.u. in the scatter plot) are due to the extensive C–H···OV2W4 vdW interactions. Also, low-gradient peaks observed on the positive side (+0.01 to +0.02 a.u.) suggest the presence of steric effects. These interactions are particularly evident in the 3D graph, where the steric effects are highlighted by the red color inside V2W4 and HMTA. It should be noted that the blend of colors in some regions indicates the coexistence of mixed interactions.

Figure 2 (a) 3D and (b) 2D noncovalent interaction plots, (c) molecular electrostatic potential map, and (d) the optimized structure of HMTA-V2W4 compound.

In addition, the molecular electrostatic potential (MESP) analysis has been employed to elucidate the electrophilic and nucleophilic regions for comprehending the chemical reactivity displayed by the compound.36−38 The examination of the 3D color-coded MESP (Figure 2c) reveals the presence of blue color with positive potential around HMTA cations, especially around the H atoms. These regions are characterized by lower energy level (maximum potential value of 7.353 × 10–2 kcal/mol), making the hydrogen atom electron acceptors, which can simply be attacked by nucleophilic sites. Conversely, the red color around V2W4 and water molecules denotes a negative potential with a minimum value of −7.353 × 10–2 kcal/mol. These red regions are mainly located around the oxygen atoms of V2W4 and water molecules, which are easily attributed to their pairs of electrons, indicating their higher energy levels. As observed in the MESP map, V2W4, which exhibits a red spot acts as a nucleophile due to its electron-rich nature, while the HMTA groups, which display a blue area, are susceptible to electrophilic activity due to their electron-deficient nature.

UV–Vis Spectroscopy, Energy Gap, and Photoluminescence

As depicted in Figure 3, a strong broad band features in the UV–visible spectrum centered around 390 nm and extended to the visible region to 550 nm, mainly attributed to ligand-to-metal charge transfer (LMCT) transitions between oxygen anions (O2–) and the metal cations (V5+/ W6+). Notably, the visible light absorption is primarily due to O → V LMCT transitions. As a result, the incorporation of V5+ in the Lindqvist POM gives rise to an improved visible light absorption spectrum extended up to 550 nm,39 which may enhance the photoelectrocatalytic capacity. Furthermore, the band gap (Eg) value was assessed at 3.08 eV according to the Tauc ((ahv)2 versus hv), as shown in Figure 3. This Eg value is smaller than that of TiO2 (Eg = 3.2 eV), indicating the semiconductor behavior of HMTA-V2W4.35,37

Figure 3 (a) UV–visible spectrum of HMTA-V2W4. (b) Tauc plot use for energy gap determination of HMTA-V2W4.

The photoluminescence emission spectrum upon excitation at 320 nm is shown in Figure 4. A series of emission peaks between 450 and 650 nm are detected, with higher emissions observed at 522 and 572 nm. On the contrary, the solid-state photoluminescence quantum yield (φsdPL) of the synthesized material determined using a calibrated integrating sphere is approximately 51%. This relatively high quantum yields, when compared with the previously reported Lindqvist,40 (C35H29P)2[W6O19], with a φsdPL of 43% may be due to the substitution of tungsten atoms by vanadium atoms.35,37 As well, the strong N–H···O and C–H···O intercontacts created between the highly nucleophilic Lindqvist-POM surface and the organic moieties may have a major role in making HMTA-V2W4 qualified as a strong emitter.40−42

Figure 4 Emission spectrum in solid state of HMTA-V2W4 crystals (λexcitation = 320 nm).

Global Quantum Descriptors

The calculation of quantum descriptors necessitates the determination of the frontier molecular orbital (FMO), which comprises the highest-occupied molecular orbital (HOMO) and the lowest-occupied molecular orbital (LUMO). Additionally, we computed the maximum energy difference between the HOMO and LUMO, referred to as the energy gap (ΔE). These data, along with quantum descriptors based on Koopmans’ approximation,43−45 are summarizedin Table 1 for reference, while the descriptor parameters are computed using mathematical expressions in eqs 1–6.1

Table 1 Quantum Descriptors Calculated on the B3LYP/def2svp Basis Set

parameter	value (eV)	
EHOMO	–6.136	
ELUMO	–3.125	
IP	6.136	
EA	3.125	
ΔE	3.011	
μ	–4.6305	
η	1.5055	
δ	0.3321	
ω	7.121	
EFermi	–4.6305	

The chemical potential (μ) of a system denotes the system’s ability to donate an electron and is mathematically expressed as2

The stability of a chemical system is determined by its chemical hardness (η), and it can be calculated using the formula:3

The global softness (σ) measures the degree of conductivity of the systems and is calculated using the expression:4

The electrophilicity index (ω) of a chemical system is the measure of the stabilization energy when the system gains an electron and imputed using the formula5

The Fermi energy level (EFermi) is described as the gap between the conduction and valence band and is given as6

The FMO analysis of HMTA-V2W4 gives an energy gap of 3.011 eV, very close to the experimental value.46 As displayed in Figure 5, the LUMOs are delocalized over the metal ions with a distinguished contribution from V(V), well agreed with previous theoretical studies.47

Figure 5 HOMO–LUMO isosurface maps of HMTA-V2W4.

Otherwise, the energy gap displayed by HMTA-V2W4 is much smaller than the Eg of isopolytungstate, [W6O19]2– (4.78 eV), and hexatungstovandate, [V2W4O19]4– (3.9 eV).47 This notable decrease can be attributed to the combination of the nucleophilic HMTA surfactant as well as the vanadium substitution of the Lindqvist in the synthesized compound. Moreover, its HOMO level is lower than the electrolyte (I–/I3–) redox potential energy (−4.8 eV), which enhances electron regeneration, whereas its LUMO energy is greater than the conduction band level (ECB) of TiO2 (−4.03 eV), improving the easy electron injection to the TiO2 semiconductor.23 Consequently, with this reduced Eg, HMTA-V2W4 can be a good photosensitizer dye for photovoltaic devices. Nevertheless, additional factors such as ionization potential and electron affinity play a direct role in shaping the donor–acceptor characteristics of chemical compounds.47 Herein, the ionization potential (IP) and electron affinity (EA) values were observed to be 6.136 and 3.125 eV. Hence, compared with other reports, this molecule has great stability with an energy gap relatively smaller than that of TiO2 (3.22 eV), which makes it a good candidate for DSSC application.48 Furthermore, other quantum descriptors for reactivity, such as the electrophilicity index, serve as a quantitative measure that elucidates and characterizes the stabilization energy of molecules. It essentially represents a molecule’s propensity to either accept or resist the exchange of fractional electron charges. This parameter is crucial due to the fact that in addition to achieving an efficient spectral response, molecules employed in DSSCs must possess sufficient stability. This stability is essential in preventing charge recombination and aggregation at the electrode interface, which are factors that could potentially impact the short-circuit voltage (Jsc).48

Density of States Analysis (DOS)

The density of states provides significant insights into the electron contributions and the distribution of electron density among atomic orbitals at distinct energy levels. Using density functional theory at the B3LYP/def2SVP level, we generated plots for the total density of states (TDOS), the partial density of states (PDOS), and the overlap density of states (OPDOS). DOS holds significant importance in comprehending the electronic characteristics of materials, encompassing their electrical conductivity, optical absorption, and thermal behavior. For instance, in semiconductors and insulators, the energy gap between the valence and conduction bands serves as a determining factor for the electrical conductivity of a material.49 Additionally, the density of states (DOS) in proximity to these band edges can serve as an indicator for estimating the mobility of charge carriers within a material.

In essence, the DOS stands as a fundamental parameter in the fields of condensed matter physics and materials science, offering valuable insights into the electronic attributes of materials and furthermore plays a pivotal role in the design and enhancement of electronic and optoelectronic devices.50 Herein, the density of state, as displayed in Figure 6, shows that at the occupied molecular orbital, oxygen (O) and carbon (C) atoms show the most contributions at approximately −10.0 eV and −13.0 eV, respectively, owing to the p-orbital transition. On the virtual orbital, hydrogen (H) was observed to possess the most contribution.

Figure 6 Density of state plot of HMTA-V2W4 showing different fragment contributions.

UV Excitation Energy Analysis and Solvatochromism

To comprehensively elucidate the electronic excitation modes, encompassing vibrational and rotational aspects, within the examined POM compound, we conducted a UV–vis spectroscopic investigation using the TD-DFT method at the CAM-B3LYP/def2SVP level of theory. The calculated absorption spectrum of HMTA-V2W4 (Figure 7) exhibits good similarity with the experimental one (Figure 3a).

Figure 7 Theorical UV–visible spectrum of HMTA-V2W4.

Furthermore, the solvatochromic properties of HMTA-V2W4 were studied using UV–vis spectroscopy in different solvents with varying polarity namely benzene, DMSO, chloroform, and water (Table 2). The insights gathered from UV analysis play a pivotal role in uncovering the complex dynamics of molecular interactions with light, as well as shedding light on the photophysical and photochemical transformations of the molecule.51,52 The observed shifts in λmax across various solvents can be attributed to solvatochromic effects, stemming from alterations in the solvent’s dielectric constant.53 Furthermore, excitation analysis offers the opportunity to investigate how solvation influences the absorption characteristics of compounds.54 The choice of solvents can induce shifts in absorption bands, reflecting alterations in the molecular surroundings and interactions between the solvent and solute. Moreover, in the context of UV analysis, it is crucial to emphasize that the interpretation of parameters adheres to precise principles. An effective system is characterized by attributes such as low energy, extended wavelength, and high oscillator strength.55 In our findings, as summarized in Table 2, in the gas phase, S0 → S1 indicated 2 MO pair excitations, where 326 → 328 had the highest contribution of 68.23%, which accounts for a maximum wavelength of absorption at 405.64 nm with an energy of 3.057 eV. In S0 → S3, 10 MO pair excitations were observed, with 320 → 328 having the highest contribution of 36.25%, which is attributed to 392.17 nm maximum wavelength of absorption with an excitation energy of 3.162 eV. It is obvious that using the Franck–Condon approach, all the electron excitations are higher-energy transitions between O2– 2p and V5+. Considering the different solvent environment for the first excitation state, benzene, which is nonpolar at 326 → 328, had a maximum wavelength of 464.70 nm higher than the gas phase and an energy of 2.668 eV with an oscillator strength of 0.6936. Also, chloroform, a polar solvent at 326 → 328, had a maximum wavelength of 509.53 nm and an energy of 2.433 eV with an oscillator strength of 0.6987. In other polar solvents (DMSO and water) employed in this study, we also noticed that there was a red shift at 327 → 328, the maximum wavelength observed for the first excitation state (S0 → S1) of DMSO was 573.20 nm, with an energy of 2.1630 eV and an oscillator strength of 0.6874. On the contrary, in the water medium, the maximum wavelength observed at 327 → 328 was 578.01 nm with an energy of 2.145 eV and an oscillator strength of 0.7009.

Table 2 UV–VIS Excitation Energies, Transitions, Percentage Contribution, and Oscillator Strengths for the Studied HMTA-V2W4 in Different Solvents

transition	MO	MO pair	wavelength (nm)	energy (eV)	f	% contribution	
Gas-Phase	
S0–S1	326 → 328	2	405.64	3.0565	0.6823	68.23	
S0–S2	327 → 328	3	397.96	3.1155	0.6720	67.20	
S0–S3	320 → 328	10	392.17	3.1615	0.3625	36.25	
Benzene	
S0–S1	326 → 328	2	464.70	2.6681	0.6936	96.21	
Chloroform	
S0–S1	326 → 328	2	509.53	2.4333	0.6987	97.63	
DMSO	
S0–S1	327 → 328	2	573.20	2.1630	0.6874	94.50	
Water	
S0–S1	327 → 328	2	578.01	2.1450	0.7009	98.25	

Hole–Electron Analysis

Due to the frequent involvement of LMCT phenomena within photophysical processes, whether occurring within the compound or between molecules, the analysis of holes and electrons plays a pivotal role. Thus, the analytical approach aids in the identification of specific regions within the system that function as electron donors and acceptors, thereby offering valuable insights into the mechanisms governing charge transfer during excited-state processes.

When an electron becomes excited and transits to a higher-energy level, it leaves behind an unoccupied state in the valence band, known as a “hole”. Hole–electron analysis enables us to discern the energy levels and distribution of electron densities, which, in turn, contributes to the determination of the electrical and optical characteristics of the material.

The percentage contributions of the solvents at the first excitation state were 96.21%, 97.63%, 94.50%, and 98.25%, corresponding to benzene, chloroform, DMSO, and water, respectively. This result depicts the fact that solvent affects the photophysical processes of the studied molecule, especially the high red shift observed in water medium when compared to other solvent environments depicting high excitation tendencies, which could be attributed to its high polarity due to its strong hydrogen bonding capabilities and dielectric constant of approximately 78.5, which reflects the degree of polarization that a material experiences in response to an applied electric field.56 This also suggests that HMTA-V2W4 can perform better in polar mediums, as evident from the high absorbance observed herein, which depicts that the compound can perform well for improved dye-sensitized solar cell (DSSC) applications. Moreover, we observed high absorbance wavelength, high oscillator strength, and low energies, which are in line with other studies for a good solar cell material and was observed herein as follows: water > DMSO > chloroform > benzene.

In this investigation, we systematically examined the electron excitation characteristics within the first three sets of excited states (S0 → S1, S2, and S3). To elucidate these excitation processes, we employed fundamental parameters, including D, Sr, H, t, HDI, and EDI. The parameter D, quantified in angstroms (Å), represents the separation between the centroids of the electron and hole in various spatial dimensions, namely X, Y, and Z.57 Utilizing eqs 7–13, we computed the values for various indices, as summarized in Table 3. DX, which signifies the length of charge transfer between the centroid of the electron and hole in the X direction, was determined using eq 7.7

Analogous expressions apply for DY and DZ.

Table 3 Hole–Electron Analysis for First Excited Parameters of HMTA-V2W4a

state	ITD	Sm index (a.u.)	Sr index (a.u.)	D index (Å)	ΔRMSD (H–E) (Å)	H index (Å)	t index (Å)	HDI	EDI	Coulomb attractive energy (eV)	
S0–S1	–0.0026	0.315	0.578	2.716	0.111	5.898	–0.762	2.140	3.070	2.172	
S0–S2	0.0025	0.303	0.551	3.916	2.118	4.895	0.788	5.290	3.110	2.437	
S0–S3	0.0002	0.079	0.228	4.273	3.040	4.434	1.990	18.43	2.98	2.192	
a Integral of transition density: ITD; Sm index: integral of Sm function; Sr index: integral of Sr function; hole delocalization index: HDI; electron delocalization index: EDI; ΔRMSD (H–E): difference between RMSD of hole and electron (delta-sigma).

One possible approach to assess this involves quantifying the separation between the central position of the hole and the central position of the electron, each in its respective directions. This concept is elucidated in eq 8, where the comprehensive measurement of this charge transfer distance is represented as the D index:8

Sr (a.u.), representing the extent of overlap between the hole and electron, which can be visually observed through the isosurfaces of the interacting orbitals, is calculated using eq 9:9

In the equation, r is a vector indicating the position of the hole and electron in the X direction, while ρhole and ρele denote the densities of the hole and electron, respectively.

The H index was employed to elucidate the extent of the spatial distribution of the hole and electron.10

The hole delocalization index (HDI) and electron delocalization index (EDI) serve as critical indicators of the charge distribution within a system. When these indices are smaller, they signify that the charge, either a hole or an electron, is more widely dispersed across the system, resulting in a more even distribution over a larger area.58,59 Both HDI and EDI play a pivotal role in quantifying the spatial extent of charge delocalization, and their mathematical expressions are listed in eqs 11 and 12:11

12

In the context of our investigation, it was observed that the compound exhibited small values for both HDI and EDI. This observation implies that upon excitation from the ground state to the first excitation state, the electrons are broadly delocalized by the compound. Moreover, the t index in our analysis signifies the extent of separation between electrons and holes during the process of charge transfer, as shown in eq 13:6013

To determine this, we computed the disparity between the D and H indices along the direction of charge transfer. Table 3 summarizes the outcomes pertaining to the photophysical characteristics of the investigated HMTA-V2W4, which were obtained through analysis employing the Multiwfn software.61,62

The D value provides insights into the nature of the excitation event that took place and was observed to be 2.716 in S0 → S1, 3.916 in S0 → S2, and 4.273 in S0 → S3 for the first, second, and third excited states, respectively, which indicates ligand–metal charge transfer (LMCT) on excitation. Sr shows relative values with highest of 0.578 (a.u.) in S0 → S1 and 0.551 (a.u.) in S0 → S2, showing characteristics of LMCT charge transfer transitions, while the much lower Sr of 0.228 (a.u) may be joined to π →π* transition between oxygen-centered molecular orbitals.40

Transition Density Matrix (TDM) and Charge Density Distribution (CDD) Analysis

The transition density matrix in real-space representation, concerning the excited state and ground state of an N-electron system with spinlessness and one electron, is defined by eq 14,63,64 where we have assumed that the wave functions are of the real type and thus have omitted the complex conjugation sign:14

where Φ0 represents the Slater determinant of the wave function of the ground state. The variable X denotes the coordinate in spin space, while σ represents the spin coordinate. The matrix T is named this way because it possesses two continuous indices. In the case of an excited-state wave function produced by single-reference methods, when expanding ψexc and employing the Slater–Condon rule, it becomes apparent that T can be expressed in a clear and explicit manner in eq 15:15

If we focus solely on the diagonal elements of the transition density matrix, we can derive the transition density, as depicted in eq 16:16

The transition density, or T(r), can be examined as a conventional function in real space. It can be visualized through an isosurface map, for instance. When considering a single dominant orbital transition, such as the HOMO to LUMO transition, the transition density is simply the product of the HOMO and LUMO orbital densities, denoted as φHOMO(r)φLUMO(r). Consequently, one can easily grasp that regions with a high magnitude of transition density indicate a strong coupling between the hole and the electron in that area. Conversely, regions with a low distribution of T(r) suggest minimal overlap between the hole and electron. Clearly, T(r) serves as a valuable tool for understanding the nature of electron excitation, and its key distribution characteristics are closely connected to the Sr(r) function.63,64 Based on the expansion coefficients of molecular orbitals and configuration coefficients, the transition density matrix (TDM) can be constructed in terms of basis functions. By considering the TDM between the ground state and an excited state (excluding de-excitation transitions for simplicity), we can calculate its value using eq 17:6317

The expansion coefficients of basis functions (Cμi) in molecular orbitals (MOs) are used to construct the TDM in terms of basis functions. It is important to mention that the TDM in real-space representation can be easily generated using the TDM in basis function representation, where χ represents the basis function, as shown in eq 18:6318

The off-diagonal elements of the TDM essentially represent the coupling between various basis functions during electron excitation.

In this study, TDM and CDD were employed to study the S0–S1, S0–S2, and S0–S3 excited states of HMTA-V2W4, which are depicted in Figures 8–10a,b. For S0–S1 excitation, represented in Figure 8a for TDM and Figure 8b for CDD, the contribution to hole and electron distribution is mainly attributed to O atoms and C atoms on the outer section of HMTA-V2W4. This indicates that during excitation between these states, there is a transfer of charge from O atoms, leading to hole formation, to the C atoms having localized electron density. This also indicates that there is no coherence between the inner region and outer region of the molecules, i.e., the V- and W-metal clusters did not make any contribution to the distribution of hole and electron during S0–S1 excitation.

Figure 8 (a) TDM heatmap for S0–S1 excitation and (b) CDD isosurface plot for S0–S1.

During S0–S2 excitation (Figure 9), holes are created on the C atoms when electrons are transferred to N and O atoms. It can be said that during excitation, the C, N, and O atoms make the major contribution to the distribution of holes and electrons in HMTA-V2W4, which are on the outer region and have no coherence to the inner region.

Figure 9 (a) TDM heatmap for S0–S2 excitation and (b) CDD isosurface plot for S0–S2 excitation.

For S0–S3 excitation, as depicted in Figure 10, it shows the contribution of hole and electron distribution by V-metals and O, C, and N atoms. The charge transfer is observed from V-metals and O atoms in the inner section of the molecules, leading to hole formation, to C and N atoms in the outer region of the molecules to create electron cloud density. This excitation indicates that there is high coherence between HMTA and V2W4. H atoms did not participate, as reported for S0–S1.

Figure 10 (a) TDM heatmap for the S0–S3 excitation and (b) CDD isosurface plot for S0–S3 excitation.

In conclusion, the transition density matrix (TDM) and charge density distribution (CDD) analyses provide valuable insights into the nature of electron excitation and the coupling between different basis functions. The TDM, represented by off-diagonal elements, quantifies the interaction or coupling between different basis functions during electron excitation. It can be visualized as a transition density function in real space, which indicates the magnitude of coupling between the holes and electrons in different regions. Regions with high transition density values show strong coupling, while a low distribution suggests a minimal overlap between the holes and electrons. The TDM can also be constructed in terms of basis functions by using the expansion coefficients of molecular orbitals and configuration coefficients. This allows for a more detailed analysis of the coupling between different basis functions during electron excitation.63

In the case of the HMTA-V2W4 system, TDM and CDD analyses revealed interesting insights into the excited states. For the S0–S1 excitation, the contribution to hole and electron distributions was mainly attributed to the presence of the O atoms and C atoms on the outer section of the molecule. This indicates a transfer of charge from the O atoms to C atoms during excitation. During S0–S2 excitation, holes were created on the C atoms, while electrons were transferred to N and O atoms. This suggests that C, N, and O atoms make the major contribution to the distribution of holes and electrons in the outer region of the molecule. For S0–S3 excitation, the hole and electron distributions were contributed by V-metals and O, C, and N atoms. Charge transfer was observed from V-metals and O atoms, in the inner section of the molecule, to C and N atoms, in the outer region, indicating high coherence between HMTA and V2W4.

The TDM and CDD analyses provide valuable information about the electronic structure and coupling between different basis functions during electron excitation, shedding light on the nature of excited states in HMTA-V2W4 systems.

Photovoltaic Properties of HMTA-V2W4

This study primarily focuses on investigating the potential of HMTA-V2W4 as a photosensitizer dye for enhanced DSSC applications, specifically looking at the processes that occur when light interacts with this material. This includes understanding how the materials respond and relax after being exposed to light. In fact, as previously mentioned, the semiconductor-like nature of HMTA-V2W4 with high LUMO energy level (ELUMO = −3.125 eV) than the conduction band (CB) of TiO2 (ECB = −4.030 eV), can generate photoinduced electrons that then migrate via TiO2 to reach the external circuit (Figure 11).65 To assess these interactions, the study examines various photovoltaic characteristics, such as factors related to energy levels and efficiencies, which are essential for applications such as solar cells.

Figure 11 Predicted electron transport mechanism of HMTA-V2W4.

The key parameters analyzed in this research include the negative free energy for electron injection (ΔGinject), light-harvesting efficiency (LHE), and energy levels of the compounds in both their ground and excited states (EPOM). Additionally, open-circuit voltage (Voc), which helps to evaluate the effectiveness of solar cells, is investigated alongside other photovoltaic properties, as depicted in Table 4.

Table 4 Photophysical Properties of HMTA-V2W4

parameter	value	
E (eV)	6.136	
ELUMO (eV)	–3.125	
ECB (eV)	–4.030	
EVB (eV)	–7.250	
Eele (eV)	–4.800	
f	0.6823	
ΔGinject (eV)	0.905	
ΔGreg (eV)	1.675	
LHE	0.7921	
Jsc (mA/cm2)	5.69	
Voc (eV)	1.805	
FF	0.854	
PCE (%)	8.77	

The open-circuit photovoltage plays a crucial role in evaluating the power conversion efficiency (PCE) of solar cells (DSSCs).66 In DSSCs, the process of electron transfer typically occurs from the LUMO of the adsorbed molecule to the conduction band of the semiconductor.

Consequently, when the ELUMO is raised, it results in a higher Voc. This increase in Voc leads to a stronger driving force for the regeneration process, thereby enhancing the efficiency of regeneration (ηreg) in DSSCs.67

In the context of solar cell analysis, Voc is crucial as it relates to the difference in energy levels between the semiconductor (TiO2) and the electrolyte redox couple (I–/I3–) in the cell. This voltage is determined by various factors, including the properties of the materials used, as expressed in eq 19:19

where ECB represents the conduction band edge of TiO2, q stands for the elementary charge unit, T denotes the absolute temperature, k represents the Boltzmann constant, nC corresponds to the number of electrons in the conduction band, and NCB signifies the density of available states within the conduction band. Additionally, Eredox designates the redox potential of the electrolyte. The parameter ΔCB signifies the shift of the conduction band when the materials are adsorbed. This relationship is mathematically expressed as20

In this context, μnormal represents the dipole moment of an individual molecule, oriented perpendicular to the surface of TiO2. The variable γ signifies the concentration of the molecule on the surface. Additionally, the constants ε0 and ε correspond to the vacuum and dielectric permittivity, respectively.

The study also delves into mathematical expressions and calculations that help quantify these parameters, with a focus on the interaction of light-absorbing molecules with the semiconductor material titanium dioxide (TiO2).23 Meanwhile, the estimation of Voc can also be approximated by calculating the energy-level difference between the lowest-unoccupied molecular orbital (ELUMO) and the energy level of the conduction band (ECB). This particular approach is selected because the materials under investigation do not exist in an adsorbed state on the surface of TiO2. Therefore, calculations involving the number of charge carriers (nC) and the number of charge carriers in the conduction band (NCB) serve the purpose of estimating Voc. Meanwhile, Jsc, the short-circuit current density, can be mathematically described as21

where LHE(λ) signifies the light-harvesting efficiency at the wavelength of maximum absorption, Φinject represents the efficiency of electron injection, and ηcollect stands for the efficiency of charge collection. Achieving a higher Jsc requires maximizing both LHE and Φinject, which should be high.68 The mathematical representation of LHE is as follows:22

where f represents the oscillator strength of the material corresponding to the maximum absorption wavelength λmax. The efficiency of electron injection (Φinject) is closely related to the thermodynamic driving force (ΔGinject) for electron injection from the excited states of the adsorbed material to the conductive band of TiO2. ΔGinject can be mathematically represented as follows:23

Herein, E* denotes the redox potential of the oxidized molecule in the excited state, E is the redox potential of the oxidized molecule in the ground state, and ΔE is the lowest vertical excitation energy and signifies the quasi-Fermi energy level of TiO2 conduction band. Furthermore, ΔGreg (driving force energy for molecule regeneration) is mathematically represented as24

The power conversion efficiency (PCE) is the final key parameter used to study the performance of solar cells in the conversion of sunlight into electricity. It can be predicted as shown in eq 20:6925

where ϕinc is the incident photon to current efficiency (100 mW·cm–2) and FF is the fill factor, which can be determined as follows:26

According to previously reported articles,70,71 an oxidized molecule with a ΔGinject value exceeding 0.20 eV indicates efficient electron injection. These calculations are essential for determining Jsc, which represents the maximum current that flows through a solar cell when its terminals are short circuited (i.e., the voltage across the terminals is zero), and for assessing the overall conversion efficiency (μ).

From the computed results, the studied compound can be a potential candidate for photosensitizer of TiO2 solar cells. In fact, the ΔGinject value observed with POM molecule was 0.905 eV, which shows that HMTA-V2W4 molecule has a high penetration efficacy. With an energy gap of 3.012 eV observed herein, the open-circuit photovoltage (Voc) was 1.805 eV, depicting a high driving force for regeneration of the adsorbed molecule. Notably, in line with observations by other authors, an ECB experimental value of approximately −4 eV is applied to the TiO2 semiconductor, and hence, considering the ΔGreg, which signifies the ability of the material to get reduced by the electrolyte to be used in the DSSC, we observed a value of 1.675 eV.

The photovoltaic parameters listed in Table 4 clearly indicate a potential performance of HMTA-V2W4 as a photosensitizer dye with relatively enhanced power conversion efficiency of 8.77% (FF = 0.88) when compared to the DSSC device with N719 dye (PCE = 7.8%, FF = 0.61). Likewise, the high value of Voc (1.805 eV > 0.65 eV (N719)) allows an increase in the conversion efficiency of the DSSCs.65

Conclusion

A vanadium-substituted Lindquist polyoxometalate, HMTA-V2W4, was successfully prepared and characterized. Multiple noncovalent interactions are enriched through cage-like amine donors and V-substituted polyanion acceptors, giving rise to a stable 3D-supramolecular self-assembly. DFT and TD-DFT calculations were performed to investigate the photoelectric and solvatochromic properties of HMTA-V2W4. The introduction of the cage-like HMTA surfactant as well as the vanadium substitution of Lindqvist in the reported compound had a remarkable effect on the absorption properties, which is strongly solvent dependent. This, in turn, had a high effect on the light-harvesting response determined using empirical parameters, resulting in remarkable high values of open-circuit voltage (Voc = 1.805 eV), photoelectric conversion efficiency (PCE = 8.77%, FF = 0.88), and light-harvesting efficiency (LHE = 0.7921) compared to those observed in N719-based DSCC. These findings make HMTA-V2W4 a promising candidate for DSSCs, suggesting further experimental investigations for potential use as photosensitizers in photovoltaic applications.

Methods and Materials

Synthesis of HMTA-V2W4

A mixture of vanadium pentoxide, V2O5 (0.18 g, 1 mmol), sodium tungstate dihydrate, Na2WO4.2H2O (1.18 g, 4 mmol), and hexamethylenetetramine, C6H12N4 (0.28 g, 2 mmol) was dissolved in 60 mL of distilled water. pH of the solution was adjusted to 5 by HCl (0.3 mL, 8.0 mmol), and the resulting solution was kept at room temperature (25 °C) for crystallization. After 10 days, yellow crystals were filtered off from the solution, washed with distilled water, and dried in air (yield: 65% based on W). Elemental analysis: for HMTA-V2W4: W, 39.05, V, 5.24 C, 16.57; H, 3.56; N, 2.3% (obsd); W, 39.27, V, 5.44 C, 16.65; H, 3.63; N, 11.95% (cald). (IR, KBr, cm–1): 3390 (m), 2588 (w), 1674 (s), 1464 (w), 1382 (w), 1300 (w), 1255 (w),1145 (w), 1010 (w), 980 (vs), 970 (vs), 935 (vs), 816 (s), 788 (vs),588 (m), 506 (m), 441 (m) (Figure S4).

Materials and Physical Measurements

All reagents (vanadium pentoxide, sodium tungstate dihydrate, hexamethylenetetramine, and hydrochloric acid) were purchased from Sigma-Aldrich Chimie (S.a.r. St. Quentin Fallavier Cedex 38 297 France) and used without further purification. The CHN analysis of the synthesized material were obtained by using a PerkinElmer 2400 CHN elemental analyzer, V and W were analyzed on ICP-AES inductively coupled plasma spectrometer. The IR spectrum was recorded with PerkinElmer Spectrum BXII spectrometer through a sample dispersed in a spectroscopically pure KBr pellet in the 400–4000 cm–1 region. The UV–vis spectrum was obtained on a PerkinElmer Lambda 19 spectrophotometer in the 200–800 nm range. The photoluminescence analysis including quantum yield (PLQY) was performed in the solid state by using a FP-6000 fluorescence spectrophotometer at room temperature. The powder diffraction pattern was determined through a D8 Advance Bruker powder diffractometer with Cu Kα (λ = 1.5418 Å) radiation. The crystal structure was determined from the single-crystal X-ray diffraction data obtained with a Bruker APEX-II CCD diffractometer (Mo Kα, λ = 0.71073 Å). Additional details of structural refinement and crystallographic data of HMTA-V2W4 are listed in Table S2. Moreover, complete crystallographic details for the structural analysis (CCDC 2144096) can be found in www.ccdc.cam.ac.uk/conts/retrieving.html.

Computational Details

In this study, the structure of HMTA-V2W4 derived from XRD analysis was optimized on Gaussian 16 and visualized on GaussView 6.0.16 software.72,73 To find the ground-state quantum electronic properties, which include the global reactivity index, HOMO–LUMO isosurface plot, natural bond order (NBO), noncovalent interaction (NCI), molecular electrostatic potential (MESP), and density of state (DOS), the CAM-B3LYP/def2svp level of theory, coupled with empirical dispersion correction (gd3), was used. Here, Multiwfn package/VMD74,75 was also applied for postprocessing of the wave function files. UV–vis spectroscopic investigation using the TD-DFT method at the CAM-B3LYP/def2SVP level of theory based on a single-point energy calculation was performed in order to understand the excited dynamics, which was performed in different solvents. In addition to this, the hole–electron analysis was also performed and the photovoltaic properties were evaluated, as summarized in tables and depicted in figures highlighted in this work.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.4c05150.The XRD patterns of HMTA-V2W4; table of hydrogen bond geometry; Hirshfeld surface of HMTA-V2W4 mapped with dnorm and the contribution of various intercontacts determined with 2D finger plots; UV–visible spectrum of HMTA-V2W4; the FT-IR analysis of HMTA-V2W4; table of crystallographic parameters (PDF)

Crystallographic data for HMTA-V2W4 (CIF)

Supplementary Material

ao4c05150_si_001.pdf

ao4c05150_si_002.cif

Author Contributions

All authors contributed to the study conception and design. A.M., B.T., M.R., and S.A. contributed to material preparation, XRD and spectroscopic measurements, and data collection. A.M., E.C.A., and G.A.O. contributed to DFT calculations and computational analyses. The manuscript was written by A.M. and all authors. All authors read and approved the final manuscript.

The authors declare no competing financial interest.

Acknowledgments

The authors are thankful to the Department of Chemistry, University of Carthage, Faculty of Sciences of Bizerte for providing necessary facilities. All authors acknowledge the financial support through Carthage University, Ministry of Higher Education and Scientific Research, Tunisia.
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