A theoretical investigation on promising acceptor groups for POM-based dyes: from electronic structure to photovoltaic conversion efficiency

Abstract

Theoretical calculations based on the density functional theory (DFT) and time-dependent DFT (TD-DFT) were employed to screen efficient acceptor group candidates for POM-based dyes. Compared to the commonly used cyanoacrylic acid acceptor group in dye 1, the acceptor groups, namely 2-hydroxy-4-(methyleneamino)benzoic acid, 5-methylenepyrimidine-2,4,6(1H,3H,5H)-trione and 5-methyleneimidazolidine-2,4-dione, in dyes 2–4 showed increased adsorption ability onto the TiO₂ surface, which is beneficial for device stability. The reduced density gradient analysis offered a rich visualization of the weak interactions between the two monomers in the dimers of the dyes, indicating that the retarded aggregation in dyes 2–4 resulted from the hydrogen bonds present in the dimers of dyes 2–4, while π–π stacking interactions also existed in the dimer of dye 1. Particularly, dye 3 not only exhibited the broadest absorption spectrum, largest ICT parameters, largest short-circuit photocurrent density governed by electronic coupling and largest open-circuit photovoltage connected with the energy shift of the conduction band among dyes 1–4, but also possessed superior adsorption stability and the lowest interaction energy for the most stable dimer configuration, which can improve the photovoltaic efficiency of DSSCs. Thus, the 5-methylenepyrimidine-2,4,6(1H,3H,5H)-trione acceptor group in dye 3 can be a promising acceptor group candidate for high-performance dyes used in DSSCs.

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1. Introduction

The gradual depletion of fossil fuel sources along with the progressive increase in environmental pollution has stimulated an urgent demand for renewable clean energy sources. Solar energy has the largest potential to satisfy the global need for renewable energy sources, and converting solar energy into electricity presents one of the most challenging technological tasks.¹ Dye-sensitized solar cells (DSSCs) are the most representative examples of the third-generation sunlight-to-electricity devices, which have attracted a great deal of attention due to their low cost and easy fabrication since the seminal work reported by Grätzel in 1991.¹ Even though a record efficiency of 14% has been achieved by the DSSC co-photosensitized with the alkoxysilyl-anchor dye ADEKA-1 and the carboxy-anchor organic dye LEG4, the efficiency still lags behind those of the conventional Si-based solar cells (25%);² thus, further breakthrough is of great significance. Moreover, DSSCs are less stable than Si-based solar cells, which limits their large-scale commercial production.³ A typical DSSC consists of three important components (a dye-sensitized semiconductor photoanode, a counter electrode, and a redox shuttle), which can be individually optimized for higher photovoltaic efficiency. After illumination, the sensitizing dye grafted on the surface of the mesoporous semiconductor substrate (usually TiO₂) injects the photoexcited electrons into the semiconductor conduction band (CB), and the electrons are transferred to the external circuit, while the concomitant holes created in the dye are transferred to the redox mediator, which is in turn regenerated, thus completing the circuit. Considering the important roles of the dyes in DSSCs, massive efforts have been made for seeking potential dyes that match the solar spectrum well as well as have high stability to further improve the efficiency of the light-to-electrical energy conversion.⁴

Polyoxometalates (POMs) are unique anionic metal–oxygen clusters with fascinating structural and photophysical properties, which result in their widespread applications in many fields, such as catalysis, materials science and analytical chemistry.^5–11 POMs can accept many electrons without losing their structural integrity,¹² and recently, POMs have been widely used in DSSCs as photosensitizers due to their electronic versatility.^13,14 POMs have the capability to attach organic molecules onto the surface of their clusters; thus, they can be used as inorganic building blocks for constructing inorganic–organic hybrids, in which POMs act as the electron acceptors and organic segments act as the electron donors. The maximum absorption bands of the hybrids significantly red-shift compared with those of the individual components, resulting from the synergistic effect of the POMs and organic segments,¹⁵ thereby resulting in long-wavelength absorption.

The donor–π linker–acceptor (D–π–A) pattern has been extensively exploited in tailoring dyes due to the efficient intramolecular charge transition (ICT) under photo-irradiation. The electron acceptor groups of these dyes anchor to the semiconductor surface directly and play vital roles in light harvesting and electron transfer process. Though a variety of donors and π linker groups have been explored for fabricating efficient dyes, fewer acceptor groups have been studied, and one of the commonly used acceptor group is cyanoacrylic acid. However, it has been observed that dyes with cyanoacrylic acid are vulnerable to dissociation on the semiconductor surface under long-term irradiation, which is undesirable for the stability of the device.^16,17 Thus, it is pivotal to explore the acceptor groups for dyes with increased binding strength. Some heterocyclic groups, such as pyridine,¹⁸ 8-hydroxylquinoline¹⁹ and tropolone,²⁰ have been explored as alternative acceptor groups since the metals in the semiconductors can form strong chelating bonds with the heterocyclic ligands.²¹ Particularly, the metal-free organic dye with the hydantoin acceptor, reported by Dai et al., achieved a higher photovoltaic conversion efficiency of 7.66% compared with the dye containing cyanoacrylic acid as the acceptor group (4.90%).¹⁷ However, it is unclear how the acceptor groups affect the performance of DSSCs, particularly the factors related to short-circuit photocurrent density J_SC and open-circuit photovoltage V_OC. Further, to understand if there are more efficient acceptors than cyanoacrylic acid and the hydantoin acceptor group that can be used in dyes, theoretical calculations have been used as efficient low-cost tools²² to evaluate the performance of dyes in DSSCs.^23–26 Even though a lot of effort has been made to improve the conversion efficiency of DSSCs, few studies have reported on the dye aggregation mechanism that enhances the electron recombination and hence, decreases the overall efficiency of the cell. In this study, a series of POM-based dyes with different acceptor groups were designed and systematically analyzed by the density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations with the aim of qualitatively (or even quantitatively) identifying the properties of these acceptor groups and seeking efficient acceptor group candidates for dyes. Apart from the electronic properties, absorption spectra and ICT characteristics of isolated dyes, J_SC and V_OC, dye aggregation effects as well as the absorption configurations of the acceptor groups onto the TiO₂ surface, which are proven crucial factors affecting the performance of DSSCs, were also taken into consideration. It is expected that this work would give theoretical guidelines to further speed up the designing of high-performance dyes.

2. Methods

2.1. Theoretical background

The power conversion efficiency (η) of DSSCs can be expressed as:²⁷where J_SC is the short-circuit photocurrent density, V_OC is the open-circuit photovoltage, I_S is the intensity of the incident light, and FF is the fill factor of the cell. Accordingly, improving J_SC and V_OC is an effective method to enhance η. J_SC can be defined as follows:where e is the unit charge, IPCE(λ) is the incident photo-to-current conversion efficiency at a fixed wavelength, and ϕ_{ph. AM1.5G}(λ) is the corresponding photo flux of the solar radiation spectrum at a fixed wavelength.

IPCE = LHE(λ)Φ_injη_regη_col (3)

where LHE(λ), the light harvesting efficiency at a specific wavelength, is given by LHE(λ) = 1–10^−f, and f is the oscillator strength of the dye corresponding to the maximum absorption wavelength λ_max. η_col is the charge collection efficiency, which is assumed to be a constant for DSSCs that only differ on the dyes employed. Φ_inj is the electron injection efficiency and is closely connected with k_inj, which can be described as follows:²⁸where V_DA is the coupling between the donor and acceptor states, and χ is the reorganization energy. ΔG_inj can be determined by the following equation:²⁹

ΔG_inj = E_dye* − E_CBM (5)

where E_dye* is the oxidation potential of the dye in the excited state, which is related to the oxidation potential of the dye in the ground state (E_dye) and the vertical transition energy (E_v), i.e., E_dye* = E_dye − E_v.²⁹E_CBM is the conduction band minimum (CBM) of TiO₂, and the experimental value −4.00 eV (vs. vacuum) was used.³⁰η_reg is related to the regeneration driving force ΔG_reg, which is defined as the difference between the redox potential of the electrolyte and E_dye as follows:³¹

ΔG_reg = E_redox − E_dye (6)

In order to evaluate the CT abilities of the dyes, the CT parameters, including the amount of transferred charges (q^CT), the corresponding effective charge transfer distance (d^CT), and the t index that assesses the degree of separation between ρ⁺(r) and ρ⁻(r) based on the total densities at the ground and excited states, were calculated.³²ρ⁺(r) and ρ⁻(r) are defined as the points in space, where the density increment and depletion upon absorption are produced, respectively. The larger the t, the lesser is the overlap between the electron density depletion and increment regions. The difference in electronic density related to the electronic transition is given by:

Δρ(r) = ρ_ES(r) − ρ_GS(r) (7)

ρ_ES(r) and ρ_GS(r) are proposed to represent the electronic densities of the excited and ground states, respectively. q^CT is given by:The barycenters (r⁺ and r⁻) of the density distributions, defined by ρ⁺(r) and ρ⁻(r), are expressed as the following equations:The difference between r⁺ and r⁻ is defined as d^CT.

To elucidate the interaction energy (ΔE_tot) of the dimers of the dyes, simple energy decomposition was performed. ΔE_tot can be decomposed as follows:³³

ΔE_tot = (ΔE_els + ΔE_ex) + ΔE_orb = ΔE_steric + ΔE_orb (11)

where ΔE_els is electrostatic interaction term, which is normally negative if the two fragments are neutral; ΔE_ex is the exchange repulsion term, which comes from the Pauli repulsion effect and is invariably positive. For convenience, the terms ΔE_els and ΔE_ex are usually combined as the steric term (ΔE_steric). ΔE_orb is the orbital interaction term, which arises from the mix of occupied molecular orbitals (MOs) and virtual MOs. If the combined wavefunction is presumed as the initial equation for the complex, then E_orb can be evaluated by subtracting the first SCF iteration energy from the last SCF iteration energy:

ΔE_orb = E_{SCF, last} − E_SCF,1st (12)

ΔE_steric = ΔE_els + ΔE_ex = ΔE_tot − ΔE_orb (13)

To determine the most stable adsorption mode of the dyes, the adsorption energy (E_ads) was calculated as follows:

E_ads = E_[dye–TiO2] − E_[dye] − E_[TiO2] (14)

where E_[dye–TiO2] is the total energy of the dye–TiO₂ complex, and E_[dye] and E_[TiO2] are the energies of the isolated dye and bare TiO₂, respectively. The larger the E_ads, the greater is the adsorption stability.

V _OC can be defined as:³⁴

where n_c is the number of electrons in CB, and q and kT are the constants, representing the unit charge and thermal energy, respectively. N_CB represents the accessible density of the CB states. A temperature of 300 K and a typical N_CB density of 7 × 10²⁰ cm⁻³ were adopted according to a previous experiment.³⁵ The dye absorbed on the TiO₂ surface can lead to the energy shift of E_CBM (ΔE_CB), and E_CB = E_CBM + ΔE_CB. Apparently, a large ΔE_CB of the dye will induce a significant increase in V_OC.

2.2. Computation details

All the calculations were performed using the Gaussian 09 D01 package,³⁶ unless otherwise stated. The ground-state geometries of all the POM-based dyes were optimized at the B3LYP³⁷ level with LANL2DZ for the Mo atom and 6-31G(d) basis set for other atoms, and the effect of ethyl acetate solvent was taken into account based on the conductor-like polarizable continuum model (CPCM).³⁸ In order to provide insights into the absorption properties of studied dyes, the TD-DFT calculations were performed by computing the lowest 50 singlet–singlet excitation states. The PBE0 hybrid functional³⁹ has been proved to be reliable in predicting the vertical excitation energies of POM-based dyes in our previous study,²⁵ and the two absorption peaks of [Mo₆O₁₈(N-1-C₁₀H₆-2-CH₃)]²⁻ simulated by PBE0 (255 nm and 436 nm) were in agreement with the experimental values (around 235 nm and 400 nm),⁴⁰ which are displayed in Fig. S1 and Table S1 (ESI†), confirming that PBE0 is appropriate for simulating the excitation energy of the studied dyes in this study. Thus, the excitation properties of studied dyes at the PBE0/6-31+G(d)/LANL2DZ level were calculated. The absorption spectra of studied dyes were simulated using Gaussian functions with a full-width at half maximum of 0.15 eV. To identify the most stable dimer structures of dyes 1–4, 60 structure configurations generated by the Molclus program⁴¹ for each dye were adopted as the initial structures for optimization at the B3LYP/3-21G level using the Gaussian 09 D01 package. The lowest energy dimer structures obtained with Na⁺ as the counterion to eliminate the effect of the negative charge were further optimized at the B3LYP level with LANL2DZ for the Mo atom and the 6-31G(d) basis set for other atoms, and D3 dispersion correction was used.⁴² Simultaneously, the interaction energies of the dimers were calculated at the same level of the theory. In addition, the reduced density gradient (RDG) analysis⁴³ and simple energy decomposition were performed by using the Multiwfn software.⁴⁴

The (TiO₂)₄₈ cluster obtained by appropriately cutting the anatase (101) surface was used to model the surface effect of bulk TiO₂,⁴⁵ and the dyes adsorbed on (TiO₂)₄₈ were studied using the Dmol³ program.⁴⁶ The dye–TiO₂ systems were optimized using the Perdew–Burke–Ernzerhof (PBE) functional^47,48 of the generalized gradient approximation (GGA)⁴⁹ and the double numerical polarization (DNP) basis set. Based on the optimized geometries of the dye–TiO₂ systems, the adsorption energies were calculated at the B3LYP-D3/3-21G(d) level. The atomic charge distributions were calculated by the Merz-Kollman method^50,51 to obtain the average dye electrostatic potential, and the corresponding computational details are described in ESI.†

3. Results and discussion

3.1. Molecular structures

Naphthylimido-substituted hexamolybdate [Mo₆O₁₈(N-1-C₁₀H₆-2-CH₃)]²⁻ was synthesized as described by Wei et al.⁴⁰ Based on [Mo₆O₁₈(N-1-C₁₀H₆-3-CH₃)]²⁻, a series of POM-based dyes for DSSCs were designed by introducing a thieno[3,2-b]thiophene π linker and different acceptor groups. The acceptor group in dye 1 was the commonly used cyanoacrylic acid group, while dyes 2–4 were designed by replacing cyanoacrylic acid with 2-hydroxy-4-(methyleneamino)benzoic acid, 5-methylenepyrimidine2,4,6 (1H,3H,5H)-trione and 5-methyleneimidazolidine-2,4-dione, respectively. The molecular structures of [Mo₆O₁₈(N-1-C₁₀H₆-2-CH₃)]²⁻ and dyes 1–4 are displayed in Fig. 1.

Fig. 1 The molecular structures of [Mo₆O₁₈(N-1-C₁₀H₆-2-CH₃)]²⁻ and the studied dyes.

3.2. Electronic structures

An ideal dye for DSSCs must match the basic energetic requirement that the lowest unoccupied molecular orbital (LUMO) energy level should be higher than the CB level of TiO₂ (−4.00 eV), ensuring that the electron is injected into TiO₂ from the excited dye, while the highest occupied molecular orbital (HOMO) energy level of the dye should be lower than the redox potential energy I⁻/I₃⁻ (−4.80 eV),⁵² guaranteeing that the dye can be efficiently regenerated. As shown in Fig. 2, the LUMO energy levels of all the studied dyes were more positive than the CB energy of TiO₂, and the HOMO energy levels were more negative than the I⁻/I₃⁻ redox potential, showing that the energy levels of the studied dyes fulfill the requirements for DSSCs.

Fig. 2 Frontier molecular orbital energy levels of the studied dyes.

The FMO distributions of dyes 1–4 are shown in Fig. 3. The HOMO energies of dyes 1–3 were similar due to the similar distributions of HOMOs, which mainly localized on the donor groups and also had some distribution over the π linkers, while the HOMO distribution of dye 4 delocalized over the π linker and the acceptor group, leading to an increased HOMO energy. For dyes 1 and 3, the LUMOs localized on the POMs and spread over the π linkers and acceptor groups, which resulted in similar LUMO energies, while the LUMO energies of dyes 2 and 4 increased compared with those of dyes 1 and 3 as the POM plays a vital role in the distribution of LUMOs. It can be seen that the acceptor groups obviously influenced the HOMO and LUMO energies and eventually the HOMO–LUMO (H–L) gaps. Considering that a smaller H–L gap means lesser energy is needed for dye excitation, the absorption spectra of dyes 3 and 4 might red-shift compared with those of dyes 1 and 2 owing to their smaller H–L gaps. More importantly, the FMO distributions of dyes 1 and 3 showed apparent push–pull characteristics, which are beneficial to the transfer of photoexcited electrons from the donor to the acceptor groups and reduce the recombination of electrons and holes.

Fig. 3 Frontier molecular orbital distributions of the studied dyes.

3.3. Absorption spectra

There is no doubt that insights into the simulated absorption spectra of the dyes will provide a better understanding on the light absorption property. The calculated excitation energies (E_v), maximum absorption wavelengths (λ_max), oscillator strengths (f) and major electronic compositions of the studied dyes are listed in Table 1, and the simulated absorption spectra are illustrated in Fig. 4. The maximum absorption bands of dyes 1–4 were in the following order: 2 (473 nm) < 1 (526 nm) = 4 (526 nm) < 3 (539 nm), confirming that replacing the commonly used cyanoacrylic acid in dye 1 with 5-methylenepyrimidine-2,4,6(1H,3H,5H)-trione in dye 3 contributed in harvesting the sunlight better, which is in good agreement with the results under “Electronic structures” discussed above.

Table 1 The calculated excitation energies E_v (eV), maximum absorption wavelengths λ_max (nm), oscillator strengths f and major electronic compositions of the studied dyes

Dye	E v	λ max	f	Major electronic compositions
1	2.36	526	2.03	H−1 → L(35%), H → L(62%)
	3.01	412	0.32	H → L+5(83%)
	3.65	340	0.04	H−8 → L+19(11%) H−7 → L+1(56%)
2	2.62	473	1.88	H−1 → L+18(20%) H → L+1(73%)
	3.11	399	0.19	H → L+5(16%) H → L+6(58%)
	3.79	327	0.07	H−1 → L+11(13%) H → L+11(65%)
3	2.30	539	2.01	H−1 → L(40%) H → L(53%)
	3.00	414	0.32	H → L+5(71%) H → L+6(12%)
	3.65	340	0.04	H−8 → L+1(12%) H−7 → L+1(54%)
4	2.36	526	2.37	H → L+1(96%)
	3.10	400	0.39	H−1 → L+5(40%) H−1 → L+6(42%)
	3.65	340	0.05	H−8 → L(15%) H−4 → L+1(36%)

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Fig. 4 Simulated absorption spectra of the studied dyes.

3.4. Intramolecular charge transfer analysis

The beneficial ICT process that occurs upon photoexcitation can improve the generation of efficient charge-separated states. To evaluate the extent of ICT, the key parameters of the studied dyes, including q^CT, d^CT and t, are given in Fig. 5. It is apparent that the q^CT values increased as follows: dye 4 < dye 2 < dye 1 < dye 3, while the d^CT and t values followed the order of dye 2 < dye 4 < dye 1 < dye 3. Dye 3 possessed the largest q^CT (1.06 a.u.) and d^CT (3.78 Å) combined with the largest t value (−0.35) among dyes 1–4, confirming that dye 3 acquired not only better light absorption ability, but also an improved CT process. Therefore, it is evident that the ICT properties of dyes can be regulated by appropriate acceptor groups.

Fig. 5 The key ICT parameters of the studied dyes.

3.5. Dye aggregation effects

Dye aggregation is disadvantageous to the electron injection that results from the enhancement of charge recombination, which decreases the overall efficiency of the DSSCs. It is well-known that the effects of dye aggregation are geometry dependent; for example, dimer configurations are responsible for this effect.⁵³ The most stable dimer configurations upon optimization as well as the ΔE_tot values of dyes 1–4 are shown in Fig. 6 and Fig. S2 (ESI†), in which the arrowheads and arrow tails refer to the molecular acceptors and donor groups, respectively.

Fig. 6 The stable dimer configurations as well as the interaction energies ΔE_tot of the studied dyes.

The plots of the electron density ρ(r) multiplied by the sign of the second Hessian eigenvalue λ₂versus RDG of the dimers of dyes 1–4 were created to understand the nature of interactions in the different aggregation modes (Fig. 7), in which the blue, green and red areas represented the hydrogen bonds, van der Waals interactions and steric repulsions, respectively. It was found that the regions of weak interactions on the isosurfaces were around the acceptor groups, indicating that the dye aggregation effects correlate with the acceptor groups. The isosurfaces of the dimers of dyes 2–4 lie between hydrogen and oxygen, which were attributed to the hydrogen bonds, while π–π stacking interactions also existed in the dimer of dye 1, resulting in the largest ΔE_tot value (−28.60 kcal mol⁻¹) among the dyes 1–4. As shown in Table 2, dyes 2–4 possessed smaller ΔE_tot values than that of dye 1 because of their smaller ΔE_orb and ΔE_steric values, which were beneficial for electron injection. In addition, the smallest ΔE_orb value was observed for dye 3 with the 5-methylenepyrimidine-2,4,6(1H,3H,5H)-trione acceptor group, which is responsible for the smallest ΔE_tot value (−13.15 kcal mol⁻¹).

Fig. 7 The plots of the production of electron density ρ(r) and the sign of the second Hessian eigenvalue λ₂versus RDG and the gradient isosurfaces with RDG = 0.5 a.u. for the dimers of studied dyes.

Table 2 The orbital interaction ΔE_orb (kcal mol⁻¹), steric interaction ΔE_steric (kcal mol⁻¹) as well as interaction energy ΔE_tot (kcal mol⁻¹) of studied dyes

Dye	ΔEorb	ΔEsteric	ΔEtot
1	−19.97	−8.63	−28.60
2	−11.36	−2.91	−14.27
3	−10.20	−2.95	−13.15
4	−15.95	−5.32	−21.27

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Considering that one of the important tasks of these dyes is to harvest sunlight,⁵⁴ the simulated absorption spectra of the dimers of dyes 1–4 are illustrated in Fig. 8, and the calculated E_v, λ_max, f and major electronic compositions are listed in Table S2 (ESI†). The maximum absorption bands of the dimers of dyes 1–4 were in the order: 2-dimer (474 nm) < 1-dimer (511 nm) < 3-dimer (534 nm) < 4-dimer (549 nm). The λ_max of the dimers of dyes 1–3 were similar to that of their respective monomers, while the λ_max of the dimer of dye 4 red-shifted compared to the monomer. Moreover, the dimers of dyes 1–4 had increased f values.

Fig. 8 Simulated absorption spectra for the dimers of studied dyes.

3.6. Factors influencing J_SC

It is known that large LHE and V_DA values, negative ΔG_inj and ΔG_reg values combined with a small |ΔG_inj + χ| value can guarantee a high J_SC, according to the discussion in the “Theoretical background” part. The LHE values, the oxidation potential of ground state dye E_dye, the oxidation potential of excited state dye E_dye*, the electron injection driving force ΔG_inj, the regeneration-driving force ΔG_reg and reorganization energies χ of the studied dyes were computed and are summarized in Table 3. Dyes 1–4 showed negative ΔG_inj, implying that they had enough driving force to inject electrons into the TiO₂ surface. The electronic coupling strengths of the dyes were estimated by the delocalization degree of the LUMOs over the anchoring atoms, namely, the fragment contribution of the anchoring atoms for LUMOs.^55–57 The percentage composition of the LUMOs of dyes 1–4 are depicted in Fig. 9. It can be seen that the composition of the anchoring atoms in the LUMOs of dyes 1–4 are in the order of 2 (10%) < 4 (24%) < 1 (29%) < 3 (31%), indicating that dye 3 had the strongest electronic coupling, which is beneficial for injecting electrons into TiO₂. Simultaneously, the ΔG_reg of for dyes 1–4 were in the order: 3 (−10.04) < 1 (−10.03) < 2 (−9.98) < 4 (−9.69), and the values of |ΔG_inj + χ| were in the order: 3 (0.37) < 4 (0.67) < 2 (0.68) = 1 (0.68). Based on the above discussions, the J_SC of dye 3 would be the largest.

Table 3 The LHE, oxidation potential of ground state dye E_dye (eV), oxidation potential of excited state dye E_dye* (eV), electron injection driving force ΔG_inj (eV), regeneration driving force ΔG_reg (eV) and reorganization energy χ (eV) of studied dyes

Dye	LHE	E dye	E dye*	ΔGinj	ΔGreg	χ	ΔGinj + χ
1	0.991	5.23	2.87	−1.13	−10.03	0.45	−0.68
2	0.987	5.18	2.56	−1.44	−9.98	0.76	−0.68
3	0.990	5.24	2.94	−1.06	−10.04	0.69	−0.37
4	0.996	4.89	2.53	−1.47	−9.69	0.80	−0.67

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Fig. 9 Molecular orbital compositions of the LUMOs of the studied dyes.

3.7. The adsorption of dye on the TiO₂ surface

Dyes with larger E_ads exhibit superior adsorption stability. The adsorption mode between the dyes and TiO₂ is a crucial factor for the electron injection process, which affects the electronic coupling and the surface state energetic activity. For the carboxylic acid group present in dyes 1 and 2, a bidentate bridging mode was extensively investigated.^58,59 However, the adsorption modes of the electron acceptor groups 5-methylenepyrimidine-2,4,6(1H,3H,5H)-trione and 5-methyleneimidazolidine-2,4-dione in dyes 3 and 4 have been rarely studied. Considering that the O and N atoms in the acceptor groups could interact with the unsaturated five-fold coordinated Ti atoms (Ti_5c) on the TiO₂ surface, ten possible adsorption modes for dyes 3 and 4, including dissociative (D) and molecular (M) modes, were considered using 3/4-TiO₂ complexes, as depicted in Fig. S3 (ESI†), and the corresponding details are described in ESI.†

After the optimization of the initial structures of the 3-TiO₂ complex, only four adsorption modes were obtained, and the optimized structures with their E_ads and specific interatomic distances are depicted in Fig. S4 (ESI†). It was found that the structures 3-D1 and 3-D4 were the same upon optimization (expressed as group I). Similarly, the same structures were obtained for the initial configurations 3-D2, 3-D3 and 3-M1 as well as 3-D5, 3-D6, 3-D7 and 3-M2 (expressed as group II and group III, respectively), and 3-D8 was expressed as group IV. We found that E_ads increased in the following order: group IV (15 kcal mol⁻¹) < group II (−63 kcal mol⁻¹) < group I (−67 kcal mol⁻¹) < group III (−93 kcal mol⁻¹), confirming that group III was the most stable due to the largest E_ads. Simultaneously, seven optimized geometrical structures for the 4-TiO₂ complex are shown in Fig. S4 (ESI†); the same structures were obtained on optimizing 4-D2 and 4-M1 as well as 4-D5, 4-D6 and 4-M2 and the most stable adsorption mode was the 4-D4 configuration. The most stable adsorption structures for the dye–TiO₂ complexes with the calculated E_ads values and specific interatomic distances are shown in Fig. 10. The E_ads values were calculated to be −74, −81, −93 and −96 kcal mol⁻¹ for dyes 1–4, respectively, indicating that dyes 1–4 were chemisorbed on the surface of the semiconductor.⁶⁰ The binding strengths between the acceptor groups in dyes 2–4 and TiO₂ were stronger than that of cyanoacrylic acid in dye 1 due to larger E_ads values of dyes 2–4, and particularly, the 5-methylenepyrimidine-2,4,6(1H,3H,5H)-trione acceptor group in dye 3 and 5-methyleneimidazolidine-2,4-dione in dye 4 possessed superior adsorption ability to the TiO₂ surface, which is in favour of device stability.

Fig. 10 Optimized geometrical structures with adsorption energies (E_ads) and specific interatomic distances for dye–TiO₂ complexes.

3.8. Factors influencing V_OC

The dye adsorbed on the TiO₂ surface affects the ΔE_CB value, and thus further changes the V_OC of DSSCs. The ΔE_CB of the studied dyes were obtained by calculating the DOS profiles of pure TiO₂ and PDOS profiles of TiO₂ in the dye–TiO₂ complexes, as shown in Fig. 11, and the values increased in the following order: dye 2 (0.47 eV) < dye 1 (0.49 eV) < dye 4 (0.56 eV) < dye 3 (0.61 eV), indicating that the acceptor groups significantly affected the ΔE_CB. In order to deeply understand how the molecular structure of the dye affects ΔE_CB, two main effects, including the charge transfer effect attributed to the dye–TiO₂ bond formation and the electrostatic effect owing to the dye dipole moment, were considered. The results demonstrate that the largest ΔE_CB for dye 3 among the dyes 1–4 is caused by the largest n_CT and V_EL, as shown in Table 4, predicting that dye 3 could achieve the largest V_OC. Moreover, V_OC was calculated, and the corresponding values are summarized in Table 5, in which dye 3 possesses the largest V_OC, which is consistent with the discussion above.

Fig. 11 Total and partial density of states (DOS) of the dye–(TiO₂)₄₈ complexes.

Table 4 The CB shift (ΔE_CB, eV), transfer charge (n_CT, e⁻) of the dyes adsorbed onto TiO₂, and the average electrostatic potential (V_EL, eV) of the studied dyes

Dye	ΔECB	n CT	V EL
1	0.49	0.29	−0.26
2	0.47	0.08	−0.23
3	0.61	0.40	−0.28
4	0.56	0.04	−0.25

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Table 5 Estimated E_CB (eV), n_c (cm⁻³) and V_OC (mV) of the studied dyes

Dye	E CB	n c	V OC
1	−3.51	1.87 × 10^22	1375
2	−3.53	6.09 × 10^21	1326
3	−3.39	6.34 × 10^21	1467
4	−3.44	6.07 × 10^21	1416

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4. Conclusions

A theoretical investigation on POM-based dyes with different acceptor groups is presented to screen for efficient acceptor group candidates better than the cyanoacrylic acid group. Besides the electronic properties, absorption spectra and ICT parameters, the key factors that affect J_SC and V_OC, the most stable adsorption modes of the acceptor groups in dyes 1–4 on the TiO₂ surface have been taken into consideration as a major factor affecting the performance of DSSCs. The results indicate that the acceptor groups in dyes 2–4 showed increased binding strength to the TiO₂ surface than that of cyanoacrylic acid in dye 1, contributing to the device stability. Besides, dye 3 with the 5-methylenepyrimidine-2,4,6(1H,3H,5H)-trione acceptor group not only exhibited the broadest absorption spectra, the largest ICT parameters, the lowest interaction energy between two dimers, the largest J_SC and V_OC values resulting from the largest ΔE_CB, but also possessed superior adsorption stability among the dyes 1–4, which can facilitate the improvement of the performance of DSSCs. Thus, 5-methylenepyrimidine-2,4,6(1H,3H,5H)-trione is expected to replace the commonly used cyanoacrylic acid and can be considered a promising acceptor group for high-performance POM-based dyes used in DSSCs. Our results allow us to trace the structure–property relationships required for further development of dyes for DSSCs.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors gratefully acknowledge financial support by NSFC (21403033 and 21571031). We acknowledge Institute of Theoretical Chemistry, Jilin University for providing the computational resources for this work.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Details including the average dye electrostatic potential, dissociative (D) and molecular (M) adsorption modes. Figures displaying experimental and theoretical absorption spectra of [Mo₆O₁₈(N-1-C₁₀H₆-2-CH₃)]²⁻; optimized most stable dimer structures as well as the interaction energies ΔE_tot for studied dyes; possible adsorption configurations for dyes 3 and 4 on the TiO₂ surface; optimized geometrical structures with adsorption energies (E_ads) and specific interatomic distances for dyes 3 and 4 on the TiO₂ surface. Tables compiling experimental and theoretical absorption spectra of [Mo₆O₁₈(N-1-C₁₀H₆-2-CH₃)]²⁻; the calculated excitation energies E_v (eV), maximum absorption wavelengths λ_max (nm), oscillator strengths f and major electronic compositions for dimers of dyes 1–4. See DOI: 10.1039/c9tc04025k

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