**3. Results and discussion**

### **3.1 Molecular structure**

Anthocyanidins are based on the flavylium ion or 2-phenylchromenylium (chromenylium may be referred to as benzopyrylium). These natural pigments are derivatives of 2-phenylchromenylium cation or flavylium cation. A relevant feature for this structure is the capability to carry different substituents in the phenyl group at 2-position. Another particularity to note is anthocyanidins differ from other flavonoids because of a positive charge. Molecule substituents and main features are displayed in **Table 1** which includes a molecular scheme in **Figure 1** shown next to the table so the reader may have a good view for a general interpretation of structural differences between anthocyanidin variants. Anthocyanidins have a 15-carbon atoms main structure arranged in two aromatic rings (A and B) as shown in **Figure 1**. A third ring (C) provides the positive charge from an oxygen atom contained in this ring. Two C]C bonds in the C ring differentiate anthocyanidins among the flavonoid family and it is responsible for a positive charge in this molecule, therefore, it is a cation (flavylium) when it is at the stable form at low pH [31].

The phenylbenzopyrylium core of anthocyanins may be modified by the addition of a wide range of chemical groups using hydroxylation, acylation, and methylation.

Geometric parameters are summarized in **Table 2**. The phenylbenzopyrylium is normally combined with a wide range of chemical groups using hydroxylation, acylation, and methylation.

The CdC bond length found within this work has a similar length or nearly enough to 140 pm (CdC bond length average size) which is the typical bond length

**Figure 1.** *General chemical structure of anthocyanidins according to Table 1.*


#### **Table 1.**

*More known anthocyanidins structure and substitution patterns.*


*Excited States of Six Anthocyanidin Variants with Different Solvents as Dye Sensitizers… DOI: http://dx.doi.org/10.5772/intechopen.108158*

#### **Table 2.**

*Selected anthocyanidins geometric parameters summary including bond length and bond angles in Å and °, respectively.*

for benzene. An average of 154.0 pm and 134 pm were found for single and double CdC bonds length, respectively. CdC bond lengths for benzene are customarily accepted around 139 pm in the literature which is near to our findings. The discrepancy is minor near to 0.1 Å in average for CdC bonds of selected pigments considering an average length between 1.346 and 1.444 Å.

Methodologies such as B3LYP/6-31 g(d), B3LYP/6–31 + g(d,p) have been reported in the literature for similar molecules [32–36] and will be included a few selected data from some of these sources to enrich the discussion in this work. At his point, one can say B3LYP reaches accurate results for these molecules' geometries and may be expected good results for similar organic molecules as well. Thus, results in this work for CdC bond lengths comply with the reported data.

The planarity in a structure is related to dihedral angles. For anthocyanidins within this work, the planarity among the three rings forming these molecules skeleton within each anthocyanidin represents an important feature that differentiates one from another. In the literature, the parameter reported is the torsion angle instead of dihedral angles and this value may be in the same way a factor that characterizes an anthocyanidins and influences its electronic structure behavior [32]. Cyanidin is considered a planar molecule because its dihedrals vary by less than 1° from a perfectly planar structure. Delphinidin and petunidin have similar planarity between them but their torsion angle causes the molecules to have the lower planarity level. Peonidin has more dihedrals different than 180° but only a couple of them differ more than 5°. Then, the analysis indicate there are differences in the dihedrals but only a couple cases deviate significantly from a perfect planarity. However, despite the numeric difference is small, it is such differences in planarity that determine most of the molecule character and its chemical properties. Put it in other words, it may be seen that few dihedrals correspond with a nonplanar structure, in such a way that there is a direct relationship with the relative angle or torsion angle between rings, and it represents the main difference observed in the B ring compared with the rest of the structure. All selected structures fall into the torsion angle and planarity concepts mentioned, with exception of cyanidin which has an almost perfectly planar structure confirmed by its dihedral values.

#### **3.2 Electronic structure**

Energy calculations were executed using B3LYP/6311 + g(d,p) method for the gas phase and four solvents (water, ethanol, n-hexane, and methanol). The reader may see HOMO and LUMO molecular orbitals numeric results in **Table 3**. An idea to analyze from these results is how these molecules energy orbitals may overlap with a semiconductor energy orbital for DSSCs and photocatalytic applications.

This procedure consists in reproducing a process where an electron is photoinduced in the molecular system by being transferred from the dye-excited state to the semiconductor. The process takes place at HOMO and LUMO energy orbitals. Therefore, a dye sensitizer should have HOMO and LUMO energy levels that mate with electrolyte redox potential and the semiconductor conduction band [25]. Pigments included in this work well with the electrolyte redox level (4.85 eV) and the conduction band edge for TiO2 (4.00 eV), considering values reported in the literature [25–29].

Calculations include molecular orbitals for all variants in the gas phase and with solvents four different solvents. LUMO results are between 6.856 and 6.624 eV for the gas phase, which is relevant because LUMO molecular orbital may be beneficial for the application as dye sensitizers. An expected condition is dye molecular orbitals overlapping semiconductor band gap in some way so it can take place an easier charge transfer process.

There is a shift around 3 eV in HOMO and LUMO for gas phase results if compared to results when added solvents like water and ethanol. This shift is evidenced in


*Excited States of Six Anthocyanidin Variants with Different Solvents as Dye Sensitizers… DOI: http://dx.doi.org/10.5772/intechopen.108158*

#### **Table 3.**

*Energy results for selected molecules: H-L is the HOMO-LUMO gap or energy band. All units in eV.*

HOMO magnitude by around 3 eV. A shift of less than 1.5 eV in HOMO and LUMO is estimated for n-hexane molecular orbitals calculations. The HOMO and LUMO molecular orbitals are shown in **Figures 2** and **3**.

The difference between HOMO-LUMO is generally accepted as a similar value to the band gap. Results for HOMO-LUMO gap were between 2.539 and 2.881 eV in the

**Figure 2.**

*Molecular orbitals for selected anthocyanidins cyanidin [22], delphinidin, malvidin [22], pelargonidin, peonidin [22], and petunidin corresponding to (a) gas phase, (b) water solvent, (c) ethanol solvent, (d) n-hexane solvent and (c) methanol solvent. H-L gap energy units are in eV.*

gas phase with malvidin having the narrower gap and pelargonidin with the wider gap among the six pigments.

Therefore, solvents are responsible for a slight shift of HOMO-LUMO values in all cases. Malvidin in the gas phase has a lower value for the HOMO-LUMO energy. With the addition of solvents, these gaps increase in all cases with n-hexane as the narrower value, followed by petunidin also with n-hexane. Ethanol and methanol solvents have a slighter effect than water. In general, effects in HOMO-LUMO are small, which means there is a similarity in magnitude on the results when used any solvent water, ethanol, n-hexane, or methanol. The HOMO-LUMO gap varies in all cases by less than 10% if compared with the HOMO-LUMO values in the gas phase. The greater shift was 11 and 10% corresponding to malvidin and peonidin, respectively, however, nhexane effect on malvidin shifted only 5%. Then, when water is used a bigger shift in HOMO-LUMO is observed and, in contrast, n-hexane caused the smaller shift. The energy gap had a small variation with 0.3 eV on average considering all variants. Cyanidin and delphinidin have alike energy gap values despite the solvent and despite their differences in geometric parameters and constituents. HOMO-LUMO gap energy seems almost unaffected by planarity and relative angles, which means the effects of the main geometric parameters in gap energy are considered small.

There is an amount of energy needed so a molecule can become ionized, which means if one charge is lost it becomes a cation and if one charge is gained it becomes an anion. Such energy was calculated using intramolecular reorganization energies.

*Excited States of Six Anthocyanidin Variants with Different Solvents as Dye Sensitizers… DOI: http://dx.doi.org/10.5772/intechopen.108158*

#### **Figure 3.**

*Molecular orbitals charge distribution using B3LYP/6–311 + g(d,p), corresponding to: (a) cyanidin [22], (b) delphinidin, (c) malvidin [22], (d) pelargonidin, (e) peonidin [22] and (f) petunidin.*

When the ionized molecule becomes neutral, then these two processes relate to the charge transfer process. The energy needs to be available for charge transfer for that reason reorganization energy (λ) values are low to prevent wasting energy in reorganization processes. Then, the reason why λ is low is to maximize the use of solar energy instead of using sunlight during the energy transfer process. Water, ethanol, and methanol solvent addition cause a decrease in λ. Solvent n-hexane also decreases λ but slightly. The lower electron reorganization energy (λe) was cyanidin with water but with similarities when used ethanol and methanol.

Cyanidin lower hole reorganization energy (λh) was obtained when used solvent methanol followed by water with similar values but not as close as in the case of λe.

The results for hole extraction potential (HEP) and electron extraction potential (EEP) present higher values for the gas phase, and a decrease is observed when any of the solvents is used.

Water, ethanol, and methanol have a similar effect in HEP and EEP, and it is bigger than n-hexane in all cases. Higher values for HEP were observed in pelargonidin in the gas phase, in general, for gas-phase HEP results are around 10 eV.

With solvent n-hexane, HEP goes around 8 eV and with solvents such as water, ethanol, and methanol its value is nearly 6 eV. EEP values are near 1 eV for solvents water, ethanol, and methanol and go down to 0.5 eV with n-hexane. Higher EEP was observed in delphinidin in the gas phase as expected because of the OH radical present in its molecular structure, but the rest of the selected anthocyanidins had similar values in the gas phase with 0.1 eV variation. Reorganization energies show malvidin is the best choice followed by petunidin.

Cyanidin with methanol produces the best electron reorganization energy λ<sup>e</sup> followed by water and ethanol. Cyanidin is more suitable for hole energy λ<sup>h</sup> with the same solvents. Petunidin is the next more suitable but with a modest advantage by 0.05 eV over cyanidin. It is possible that λ values performance relates with molecule planarity. The effect of solvents in EEP and HEP is unclear in contrast with λ. Malvidin with water is the best choice from EEP and HEP viewpoint but the variation is minor considering the same solvent is used in other molecules.

#### **3.3 Chemical reactivity properties**

Chemical reactivity properties were calculated with conceptual DFT. These properties are shown in **Table 4**.

Ionization potential (IP) is associated with the electronic cloud stiffness. In terms of reactivity, the cloud is wary to become a participant in electron transfer. Therefore, a lower ionization potential is enticing to have a larger molecular potential so electron donation boosts. Malvidin presents the lower IP in its gas phase and decreases further with solvent addition. A similar effect in IP magnitude was caused by water, ethanol, and methanol but the lower IP value was when water is used as a solvent in cyanidin among all variants.

In the gas phase, IP was near 11 eV and when used water, ethanol, and methanol IP decreased to values near 6 eV. IP values also had a reducing trend with solvent nhexane with results around 8 eV. The lower IP was observed in cyanidin with water and methanol meanwhile for malvidin and petunidin their lower values were observed with these two solvents.

For molecules in its gas phase, EA results were around 5 eV and with solvents water, ethanol, and methanol a reducing trend was observed with results around 3 eV, and n-hexane effect on EA also was a reducing trend to values around 4 eV. Delphinidin in n-hexane has the higher EA but its EA values are only slightly higher than those for pelargonidin, petunidin, peonidin, and malvidin, all with n-hexane.

Attracting electron pairs may be measured with electronegativity (χ). For a better suitability to act as a charge acceptor, a high electronegativity (χ) is desirable. Pelargonidin displayed the highest χ value in the gas phase, in general χ results are near 8 eV and have a decreasing trend with values near 5 eV when solvents such as water, ethanol, and methanol are used. For n-hexane solvent, results are near 6 eV. Pelargonidin with n-hexane presents the higher value but it is slightly over the rest of the molecules using n-hexane as well.


*Excited States of Six Anthocyanidin Variants with Different Solvents as Dye Sensitizers… DOI: http://dx.doi.org/10.5772/intechopen.108158*

**Table 4.**

*Chemical reactivity of selected anthocyanidins. Properties displayed are ionization potential (IP), electron affinity (EA), electronegativity (χ), chemical hardness (η), electrophilicity index (ω), and chemical softness (Ѕ), units are eV.*

Therefore, chemical properties show similarity among resulting values which may be induced by the molecular resemblances including the torsion angle, and the small structural differences may be responsible for the main differences as well as their molecule constituents.

## **3.4 Excited states with TDDFT**

TDDFT excited states were computed with B3LYP/6311 + g(d,p) methodology in Gaussian16. The literature supports that B3LYP is a suitable hybrid functional [25– 29, 36] for this kind of computations and has been successful in similar molecules.

A good match between the absorption spectrum and the solar irradiation spectrum in DSSCs benefits its performance. An indicator of the light-harvesting effectiveness may be data related to the dye's absorption and such data become relevant for the performance of the DSSCs [37–41] as a whole. Our results are in acceptable accord with experimental values and the differences may be caused by solvent effects and variation added by measuring methodologies [36, 42–44]. For ΔE, a low value is desirable so the first excited state may need as low energy as possible. In the gas phase, malvidin presents the lower value for ΔE and, with solvent addition, the lower value was malvidin with n-hexane closely followed by petunidin with n-hexane. The literature reports two main regions in anthocyanidins UV–Vis spectra. The first one at 260– 280 nm and the second one at the visible region between 490 and 550 nm. There is a third peak at 310–360 nm [43], but we will focus on the main peak located in the visible region.

This group of anthocyanidins in the gas phase had absorption wavelengths between 479.1 and 536.4 nm. These molecules work in the visible with both cyanidin and pelargonidin working in the blue region. Pelargonidin and malvidin are the lower and higher values while cyanidin presents a similar value with pelargonidin results which may be related to the fact that both have a small relative angle at the B ring and, they are the simplest molecules regarding their constituents. Addition of solvent shifts absorption spectra by increasing its wavelength by less than 5 nm in the case of water, ethanol, and methanol. When used n-hexane, absorption spectra shift by nearly 10 nm. TDDFT excited states absorption data are shown in **Table 5** and absorption spectra are shown in **Figure 4**. Photon-to-current conversion relies on the visible and near UV regions results and based on these results one can attain microscopic information related to electronic transitions and MO properties.

A goal of TDDFT excited states was to calculate absorption data and our numeric results are shown in **Table 5** and absorption spectra are shown in **Figure 4**.

Light harvesting energy (LHE) index was calculated due to its importance in electronic transfer.

The light-harvesting energy (LHE) index was calculated due to its importance in electronic transfer. In a dye sensitizer, a high LHE maximizes photo-current response, and it can be calculated with equation (1):

$$\text{LHE} = \mathbf{1} - \mathbf{10}^{-\text{f}} \tag{1}$$

where f is the oscillator strength of the dye associated with the wavelength corresponding to the peak absorbance through intramolecular charge transfer [45, 46]. Singlet-to-singlet transitions of the absorption bands with maximum wavelength and oscillator strength were obtained for all selected anthocyanidins. In the gas-phase cyanidin had a higher LHE followed by petunidin and on the other hand, malvidin had a lower LHE value. After the addition of solvents, there is an increase in LHE in all cases but with malvidin, the effect of the solvent is more noticeable especially when methanol is used. Cyanidin, petunidin, and malvidin have higher LHE values after solvent addition. The lowest energy absorption in these molecules is due


*Excited States of Six Anthocyanidin Variants with Different Solvents as Dye Sensitizers… DOI: http://dx.doi.org/10.5772/intechopen.108158*


*Cyanidin, malvidin, and peonidin data has been regenerated for this work with very similar results, considering there is a set of our own results obtained with different methodology that were published previously elsewhere [22]. \*Experimental data from the literature [43].*

#### **Table 5.**

*TD-DFT excited states absorption data for selected molecules.*

#### **Figure 4.**

*Absorption spectra using TD-DFT for gas phase and solvents water, ethane, n-hexane, and methane for: (a) cyanidin [22], (b) delphinidin, (c) malvidin [22], (d) pelargonidin, (e) peonidin [22], and (f) petunidin.*

to the transition from HOMO to LUMO with the largest oscillator strength resulting in an enhanced LHE, this approach emphasizes the parameters recommended in the literature to identify the best choice [41, 47, 48].

*Excited States of Six Anthocyanidin Variants with Different Solvents as Dye Sensitizers… DOI: http://dx.doi.org/10.5772/intechopen.108158*

To obtain an effect where the absorption spectrum overlaps with the solar spectrum, the energy gap will have to reduce. Such action could be possible with the inclusion of a co-absorber of appropriate properties. Among the dyes studied, anthocyanidins with the higher LHE may work well with solar energy and may be recommended as the better suited for use as a potential sensitizer for DSSC.

#### **3.5 Excited states using CIS-TDDFT**

Cis-TDDFT methodology was used to calculate excited states with the scheme implemented in Gaussian16 [23]. Emission wavelength values increase after solvents are included in most cases if compared with results obtained for emission in anthocyanidins gas phase, respectively, for each variant. Emission spectra for each selected anthocyanidin are shown in **Figure 5**. According to experimental data, DFT calculations underestimate wavelength values by approximately 8%. Cyanidin, delphinidin, malvidin, and pelargonidin have similar effects with each solvent presenting slightly increased emission wavelength values for water, ethanol, and methanol and a slight decrease in wavelength value for n-hexane solvent. Peonidin and petunidin have similar effects when water and ethanol are used with a slight increase in wavelength value and are similar to the effect when used solvent n-hexane with a slight decrease but there is a different effect on these two anthocyanidins when methanol is used since, in these two variants, wavelength presents a slight decrease.

Overall, the effects of solvents in these six anthocyanidins are similar, maybe petunidin presents stronger effects in the wavelength with solvents than the others but the effects can be considered small even for this case.

Oscillator strength for the selected anthocyanidins has a particular effect for each variant that may be related to the solvent. In all cases, the gas phase displayed the lower oscillator strength value except for malvidin which presents the lower oscillator

#### **Figure 5.**

*Emission spectra data using TD-DFT excited states for gas phase and solvents water, ethane, n-hexane, and methane applied in the next molecules: (a) cyanidin, (b) delphinidin, (c) malvidin, (d) pelargonidin, (e) peonidin, and (f) petunidin.*

strength value for the solvent methanol. In all cases, the higher oscillator strength value was observed when used solvent ethanol except for petunidin since it was with solvent water where the higher value was observed. Oscillator strength and data obtained for excited states calculations are shown in **Table 6**.

Cyanidin presented the higher oscillator strength values if compared with each anthocyanidin variant, and this behavior is maintained when the solvent is included. For cyanidin, when solvents are added the oscillator strength values increase if


*Excited States of Six Anthocyanidin Variants with Different Solvents as Dye Sensitizers… DOI: http://dx.doi.org/10.5772/intechopen.108158*


#### **Table 6.**

*Excited states emission results for selected anthocyanidins using CIS-TD-DFT.*

compared with its gas phase value and the higher oscillator strength values were observed with ethanol and n-hexane.

Malvidin resembles cyanidin with slightly smaller values for oscillator strength but a similar trend and in all cases when added a solvent oscillator strength, values increase aside from methanol which can be considered the only exception. Delphinidin, pelargonidin, and peonidin resemble cyanidin as well but with smaller values than malvidin so the difference with cyanidin is bigger in these cases.

Cyanidin presented the higher oscillator strength values if compared with each anthocyanidin variant and this behavior is maintained when solvent is included. For cyanidin addition of solvents cause an increase in the oscillator strength values from the gas phase value with ethanol and n-hexane having the higher oscillator strength values.

Malvidin resembles cyanidin but with smaller values for oscillator strength with a similar trend and in all cases when added solvent oscillator strength values increase with the only exception of methanol. Delphinidin, pelargonidin, and peonidin resemble cyanidin as well but with smaller values than malvidin so the difference with cyanidin is bigger in these cases. Also, in these cases, all values obtained for oscillator strength when added solvents were smaller than gas-phase oscillator strengths. For petunidin, oscillator strength changes after solvent addition are moderate, the bigger change was with the addition of water solvent.

The transition energy for the selected anthocyanidins has a similar trend among all selected after the addition of the different solvents. For cyanidin, delphinidin, malvidin, and pelargonidin transition energy for gas-phase decreases for all solvents except for n-hexane which is the only solvent where transition energy increases. For petunidin and peonidin, all the prior effects occur with the only difference that using methanol also presents an increase in the transition energy values if compared with the gas phase with similar values to those observed in n-hexane.

Also, in these cases all values obtained for oscillator strength when added solvents were smaller than gas phase oscillator strengths.

For petunidin, oscillator strength changes after solvent addition are moderate, the bigger change was with the addition of water solvent.

Transition energy for the selected anthocyanidins has a similar trend among all selected after the addition of the different solvents. For cyanidin, delphinidin, malvidin, and pelargonidin transition energy for the gas phase decreases for all solvents except for n-hexane which is the only solvent where transition energy increases. For petunidin and peonidin, all prior effects occur with the only difference that methanol also presents an increase in the transition energy values if compared with gas phase with similar values to those observed in n-hexane.
