Geometrical Properties
The optimized geometries of the 2D molecular structures (Fig. 1) are presented in Fig. 2. The structures' planarity were observed from benzothiadiazole (BTZ) towards cyanoacrylic acid anchoring group this character is beneficial for intramolecular charge transfer and the remaining part induces non-planarity and is important for the reduction of dye aggregation. The measured bond lengths \({{\delta }}_{\text{N}-\text{X}}\) (2.800 − 2.925 Ǻ) and \({{\delta }}_{\text{H}-\text{X} }\) (2.486 − 3.099 Ǻ) for optimized structures the bonds strengthen as electronegativity of the chalcogen atom increases.
This observation was similar to the findings by Ortiz-Rodríguez and co-workers where it was observed that the bond length decreases with orbital size mismatch between the chalcogen and the H [37]. These substitutions showed minimal effect on the dihedral angle X − C−C − X which remained ∼180° which implies that the substituted chalcogens did not alter the planarity of the investigated sensitizers. For each chalcogen, the bond and angles θ1 and θ2 are equivalent (i.e. Δθ ≈ 0), however, the values decreased with increasing chalcogen size.
Table 1
The calculated dihedral angle Φ (°), the bond angle θi = 1&2 (°) and bond lengths δi (Ǻ)
| Φ | \({}_{1}\) | \({}_{1}\) | \({\delta }_{\text{N}-\text{X}}\) | \({\delta }_{\text{H}-\text{X} }\) | Mulliken charges |
WS − O | 179 | 108 | 108 | 2.800 | 2.486 | −0.321 | −0.268 |
WS − S | 179 | 92 | 92 | 2.896 | 2.799 | −0.095 | −0.175 |
WS − Se | 178 | 87 | 87 | 2.914 | 2.930 | + 0.569 | + 0.641 |
WS − Te | 179 | 82 | 82 | 2.925 | 3.099 | + 0.766 | + 0.852 |
Mulliken charges on the chalcogenides show that O (− 0.294) carries a strongly negative charge followed by S (− 0.135) in the dyes, while the heavier chalcogens have even positive charges Se (0.605) and Te (0.809). The calculated Mulliken charges demonstrate that Se and Te substituted dyes are more stable than the O and S-substituted dyes, this observation is in agreement with the literature [38].
Optical Spectra
The electronic absorption spectra and emission spectra for the dyes containing heteroatoms (O, S, Se and Te) in the π-linkers are presented in Fig. 3. Furthermore, electronic transitions, maxima absorption, oscillator strength, excited-state lifetime, light-harvesting efficiency and corresponding molecular orbital contributions are shown in Table 2. Both absorption and emission spectra are red-shifted with an increase in chalcogenides atomic size. The absorption spectra were characterized by a dual-band absorption profile, the higher energy bands were observed at around 300 nm and the lower energy bands were found within 500 to 600 nm. Contrary to the lower energy bands, the higher energy bands are nearly equivalent in intensities and positions for all dyes. A noticeable trend was observed in the optical gap among the investigated dyes where WS-O (2.37 eV) exhibited the widest gap, followed by WS-S (2.28 eV), WS-Se (2.16 eV), and WS-Te (2.07 eV) which had the narrowest gap, thus these dyes can absorb light up to 523 nm, 545 nm, 575 nm, and 600 nm, respectively. The optical gap energies of the chalcogenides sensitizers decreased systematically as the chalcogenides varied from sulfur (S) through selenium (Se) to tellurium (Te) where a more pronounced red-shift was observed for dyes containing large-size chalcogen atom. The observed hyperchromic response was consistent with the electronegativity of dopant chalcogen atoms. A similar trend was observed for emission \({}_{\text{e}\text{m}}=\) 1.78, 1.67. 1.53 and 1.45 (all in eV); the stoke-shift was found to be 172 (O), 197 (S), 234 (Se), 253 nm (Te). Due to long trailed absorption, red-shifted emission peaks, and larger Stoke’s shift (higher than 100 nm) doping with heavy chalcogen may permit simultaneous excitation of different fluorescence colour through a single excitation source; thus, materials containing these elements may be integrated into the building allowing multi-purpose operation.
The maxima absorption band was characterized by HOMO to LUMO as the main electronic transition followed by HOMO − 1 to LUMO, the percentage contributions increase with the increase in the atomic size of the chalcogen atom size where HOMO to LUMO transitions can be found within 55–56% and 32–35% for HOMO − 1 to LUMO transitions.
The intramolecular charge transfer of the studied dyes was assessed through the charge density distribution as depicted in Fig. 4. As can be seen from the figures, the HOMO electron density was mainly delocalized of the donor part extending to benzothiadiazole and only a few traces in one of the modified units. Upon photo-excitation, in the LUMO state, we observe the movement of charge density towards the anchoring group. This phenomenon is evident for intramolecular charge transfer and the investigated sensitizers may efficiently inject charge into the conduction band of the TiO2 semiconductor.
Table 2
Calculated maximum absorption wavelengths (λ, nm), oscillator strength (f), excited-state lifetime (τ, ns), light-harvesting efficiency (ΦLHE, %), and molecular orbital contributions to the first excited state.
Absorption |
Molecule | Transition | λ | f | τ | ΦLHE | Contributions |
WS − O | S0→S1 | 523 | 2.370 | 1.73 | 99.57 | H→L(55%); H−1→L(32%) |
WS − S | S0→S1 | 545 | 2.273 | 1.96 | 99.47 | H→L(55%); H−1→L(34%) |
WS − Se | S0→S1 | 575 | 2.158 | 2.30 | 99.30 | H→L(56%); H−1→L(35%) |
WS − Te | S0→S1 | 600 | 2.067 | 2.61 | 99.14 | H→L(57%); H−1→L(35%) |
Emission |
WS − O | S0←S1 | 695 | 1.968 | 3.68 | 98.92 | H←L(65%); H←L + 1(14%) |
WS − S | S0←S1 | 742 | 2.154 | 3.83 | 99.30 | H←L(66%); H − 1←L + 1(16%) |
WS − Se | S0←S1 | 809 | 2.368 | 4.14 | 99.57 | H←L(66%); H − 1←L(16%) |
WS − Te | S0←S1 | 853 | 2.321 | 4.70 | 99.52 | H←L(66%); H − 1←L(14%) |
Light-harvesting Efficiency
The performance of DSSC is measured through incident photon-to-current conversion efficiency (IPCE) expressed as:
IPCE = ΦLHE⋅Φinj⋅ΦCC
where ΦLHE is the function of light-harvesting efficiency which accounts for electron density movement related to both optical absorption intensity and available electron transition, Φinj is the electron injection efficiency, and ΦCC is the charge collection efficiency. The ΦLHE can be expressed as ΦLHE = 1 − \({10}^{-f}\); where f is the oscillator strength of the sensitizer corresponding to maxima absorption. The obtained f are higher than a unit leading ΦLHE higher than 99% or higher (Table 2), it is worth noting that there was no clear trend in the ΦLHE values.
Excited-state Lifetime
Excited-state lifetimes (τ) for the sensitizers under consideration were evaluated, τ is an important factor that influences the charge transfer. A sensitizer with a longer τ is expected to be more facile for charge transfer and suppresses recombination consequently leading to reduced energy loss. It is a requirement that charge injection time should be shorter than the excited state decay to the ground state for efficient charge injection before radiative or photochemical reactions occur [39–42]. The τ (ns) of a sensitizer can be calculated by using the following relation [43–48]:
$$= \frac{1.499}{f\times {E}^{2}}$$
where ΔE is the transition energy in \({\text{c}\text{m}}^{-1}\) units of measurements; the first excited-state lifetime corresponds to the lowest excitation energies, mostly from \({\text{S}}_{0}\to {\text{S}}_{1}\). Calculated values are found in the range 1.73 − 2.61 ns in the order WS − O < WS − S < WS − Se < WS − Te. One may hypothesize that the inclusion of less electronegative chalcogens (Se and Te) may lead to the stabilization of the excited state possibly supported by the extended valence shell accompanied by the change in hybridization [49].
HOMO-LUMO Energy Levels
Understanding the energy level of the highest occupied molecular orbital HOMO (EH) or ground state oxidation potential (GSOP) and LUMO (EL) is critical to the successful design of sensitizers with improved PCE. The EH and EL are sensitive to changes in the chemical structures such as nature and placement of the functional group. Charge injection to the CB of the semiconductor proceeds from the unrelaxed excited-state dye species to the CB of the semiconductor [50, 51], the energy level corresponding to this is known as excited-state oxidation potential (ESOP) and can be calculated as: ESOP = GSOP + ΔE, where ΔE corresponds to the vertical excitation energy/ optical gap which can be obtained from the TD-DFT calculations. The ability of the dye to inject charge into the CB of a semiconductor can be quantified through the free energy of charge injection (ΔGinj) calculated as ΔGinj = ECB – ESOP, where ECB is the reduction potential of the CB of the TiO2 semiconductor. The oxidized dye is regenerated by receiving an electron from the \({\text{I}}^{-}/{\text{I}}_{3}^{-}\) electrolyte; dye regeneration is quantified through free energy of dye regeneration (ΔGreg) which can be calculated as: ΔGreg = GSOP − \({E}_{{\text{I}}^{-}/{\text{I}}_{3}^{-}}\). The energy level alignment diagram with conduction band of TiO2 semiconductor − 4.05 eV at pH = 7 [52] and redox potential of iodide/triiodide electrolyte and its value is − 4.8 eV [53]. Table 3 shows the calculated GSOP/EH, vertical transition energies ΔE, energy gap Eg, LUMO, ESOP, ΔGinj and ΔGreg. Generally, we observe nearly similar HOMO energies but the LUMO stabilization (i.e., downward shift) results in the narrowed energy gap.
Table 3
The calculated optical gap ΔE, energy gap Eg, the highest occupied molecular orbital (HOMO) energies, the lowest unoccupied molecular orbital (LUMO) energies, excited-ste oxidation potential (ESOP), free energies of charge injection ΔGinj and free energy of dye regeneration ΔGreg (all values in eV)
Molecule | ΔE | Eg | HOMO/GSOP | LUMO | ESOP | ΔGinj | ΔGreg |
WS − O | 2.37 | 1.97 | −5.11 | −3.14 | −2.74 | −1.31 | −0.31 |
WS − S | 2.28 | 1.87 | −5.11 | −3.25 | −2.83 | −1.22 | −0.31 |
WS − Se | 2.16 | 1.78 | −5.12 | −3.34 | −2.96 | −1.09 | −0.32 |
WS − Te | 2.07 | 1.77 | −5.10 | −3.33 | −3.03 | −1.02 | −0.30 |
Clear trends were observed in the optical (ΔE) and energy (Eg) gaps between dyes. The studied dyes exhibit ΔE values from 2.07 to 2.37 eV and the Eg between 1.77 to 1.97 eV, we observe a positive correlation between the ΔE and Eg defined by the linear equation: ΔE = 1.3576⋅Eg − 0.2882 with R2 = 92%. The decreased energy gaps for dyes containing larger chalcogen atoms is caused by reduced aromaticity in conjugated five-member rings, despite being easier to polarize and having larger atomic radii (O: 0.73 Ǻ; S: 1.02 Ǻ; Se: 1.16 Ǻ; Te: 1.40 Ǻ) [54], exhibit poor orbital overlap with neighboring carbon due to their larger size; aromaticity of the five-member rings decreases in the following order: Te < Se < S < O [55].
Figure 5 shows a minimal shift in the EH energies among the investigated dyes ranging between − 5.12 to − 5.10 eV, this observation was consistent with the findings by Planells and co-workers [55]; implying that the dyes have comparable ΔGreg within the range − 0.30 and − 0.32 eV. A strong π* character with electron density fully delocalized over the modified units containing the heteroatom resulted in a deeper shift in the LUMO energy level with an increase in heteroatom size which consequently led resulted in a reduced energy gap. It is interesting to note the monotonic decrease in the ESOP energy level from oxygen to tellurium, this observation is consistent with atomic orbital energies for group VI where the p orbital valence energies increase moving down group VI (from O 2p, S 3p, Se 4p, Te 5p) [56].
Adsorption on the TiO2 surface
For the purpose of understanding the adsorption capability of the four dyes on TiO2 anatase (1 0 1), geometrical parameters and adsorption energies of adsorbed systems were studied using PBE + U level. It is possible for carboxylic acid groups to be anchored to TiO2 surface through three modes; mono-dentate, bidentate-chelating, and bi-dentate bridging [59]. In previous theoretical studies, the adsorption of carboxylic acid on TiO2 by bi-dentate was found to be the more stable mode than the other two modes[60, 61]. The reason for this is the binding distance of bidentate is short, resulting in an increase in electron injection rates. Hence, this study considered the bi-dentate bridging mode. Figure 11 presents the optimized geometries of four dyes adsorbed systems.
Using Eq. 1, the adsorption energy (\({E}_{\text{a}\text{d}\text{s}})\)can be determined for the four adsorbed systems and they are tabulated in Table 4 along with geometrical parameters (bond lengths and dihedral angles) using PBE + U functional. Each of the four dyes is adsorbed on TiO2 by bonded between oxygen atoms of the anchoring group and surface atoms and the bond lengths fall in the range of 2.031–2.122 Å. Based on the literature [62], those values indicated strong interactions between the investigated dyes and the surface.
Table 4
Ti–O bond lengths (Å) dihedral angles (o), adsorption energies \({{E}}_{{a}{d}{s}}\), and enegy fermi \({E}_{f}\) (eV) for the adsorption systems.
System | (Ti − O)1 | (Ti − O)2 | a\(\phi\)1 | a\(\phi\)2 | \({E}_{\text{a}\text{d}\text{s}}\) | \({E}_{f}\) | |
WS − O@TiO2 | 2.122 | 2.084 | 172.832 | 175.555 | −0.08 | −2.60 | |
WS − S@TiO2 | 2.044 | 2.073 | 171.617 | 174.275 | −0.59 | −2.57 | |
WS − Se@TiO2 | 2.040 | 2.075 | 171.251 | 173.972 | −0.41 | −2.49 | |
WS − Te@TiO2 | 2.059 | 2.031 | 170.866 | 172.688 | −0.77 | −2.47 | |
a \(\phi\)1 (Ti − O−C − C)1; \(\phi\)2 (Ti − O−C − C)2. |
The four investigated adsorption systems are stable based on their negative adsorption energies which indicated the exothermic processes occurred. It can be noted also the adsorption energies are relatively small and ranged from − 0.08 to − 0.77 eV. This means it is possible that dyes will be physically absorbed onto TiO2 surface. Among the four adsorbed systems, WS − Te@TiO2 has the strongest interaction with the TiO2 surface due to its higher adsorption energy (the most negative value) leading to faster charge transfer rates and enhanced DSSC performances [62, 63]. The opposite note has been observed for WS − O@TiO2. On the other hand, the Fermi energies are negative and they increase with increased electronegative of chalcogenides (i.e. from Te to O atoms) in the order WS − Te@TiO2 < WS − Se@TiO2 < WS − S@TiO2 < WS − O@TiO2. Generally, these results indicated that the dyes were tightly adsorbed on the semiconductor surface, which might result in improved photovoltaic performance.