**3.1 Solvent dependence of TPP**

It has been reported in literature that the measured absorption spectra of the TPP considerably depend on the dielectric constant of the solvent. For instance, the experimentally measured absorption spectrum the TPP exhibited the Soret-band at 398 nm in a pulsed supersonic expansion of helium [50], which is considerably shifted to 420 nm in toluene (ε = 2.374) [51], 419 nm in benzene (ε = 2.271) [52], 417 nm in *tetrahydrofuran* (ε = 7.426) and 415 nm in acetone (ε = 20.493) [51]. The Q(0-0) bands have been measured at 529 and 640 nm in a pulsed supersonic expansion of helium [50], which are also significantly shifted to 548 and 647 nm in benzene [52]. Furthermore, the lowest triplet state (T1) of TPP at 77 K in methylcyclohexane [53] and diethyl ether/petroleum ether/isopropyl alcohol (in the ratio of 5/5/2) [54] was observed at 865 nm and 859 nm, respectively. The triplet-triplet absorption transitions of TPP in toluene were experimentally observed at 780, 690, 430, 405 and 390 nm [55].

It is worthy to note that the geometric structures of the TPP molecule both in the ground state and the lowest triplet state belong to the C2v symmetry point group. The calculated solvent effect on the electronic spectrum of the TPP are summarized below.

*Density Functional Theory Study of the Solvent Effects on Electronic Transition Energies… DOI: http://dx.doi.org/10.5772/intechopen.99613*

**Singlet TPP: Figure 1A** provides the calculated absorption spectra of FBP in the different solutions used. The shifts in spectral positions of the Q, B (Soret) and L bands caused by the solvent are given in **Figure 1B** as functions of the dielectric constant of the solvent (ε).

The calculations indicate that the solvent effect on the Q1 and Q2 bands of the TPP are inconsequential. For instance, the Q1 band at 17398 cm−1 (574.8 nm) and Q2-band at 18566 cm−1 (538.6 nm) in gas-phase spectrum are 40 and 90 cm−1 red shifted to 17358 (576 nm) and 18473 cm−1 (541.4 nm), respectively, with increase in ε from 1.00 to 5.32; which then increased and become almost constant at around 17384 and 18506 cm−1 for ε > 20.493. However, the dependence of the calculated Soret bands (B1 and B2-bands) of the TPP significantly depend on solvent polarity. For example the B1 band at 25405 cm−1 (393.6 nm) and B2 band 26271 cm−1 (380.6 nm) in the gas phase spectrum initially decreased to 23890 (418.6 nm) and 24160 cm−1 (414.4 nm), respectively, with increase of ε from 1 to 5.32, and then blue-shifted to 23890 cm−1 (418.6 nm) and 24131 cm−1 (414.4 nm), respectively, for ε = 20.493 (acetone). With further increase in the dielectric constant (ε > 20.493), these bands positions become nearly stable at around 24574 (406.9, B1) and 24919 cm−1 (401.3 nm, B2) within 120 cm−1 fluctuations.

Similar to the modification in the positions of the B-bands, the spectral position of the L-band at 28862 cm−1 (346.5 nm) in the gas-phase (ε = 1.00) is first red-shifted to 28212 cm−1 (354.5 nm) in region of ε = 1 to 5.324, then blue-shifted to 29067 cm−1 (334 nm) for ε = 20.493, and then remains unchanged at 28334 cm−1 (352.9 nm) within ±20 cm−1 variation with the further increase in ε (**Figure 1**).

**Triplet TPP:** The lowest triplet state T1 of the TPP in both gas-phase and solvent phase was estimated from calculated global energy difference between the singlet ground state and the lowest triplet state, i.e., E(T1) = E(the global energy of the lowest triplet state)- E(the global energy of the ground state). The energy level of the T1 state of the TPP in the gas phase lies about 11406 cm−1 (876.8 nm) above the ground state energy (S0). The estimated solvent effect on the energy gap between S0-T1 states is inconsequential, only about 20 cm−1 red-shifted with increasing solvent polarity (see **Figure 2B**).

The calculated triplet-triplet electronic transitions up to 25000 cm−1 (400 nm) are given in **Figure 2(A** and **B)**. The calculations indicate that the triplet states

#### **Figure 1.**

*(A) The calculated solvent-dependence of the singlet-singlet electronic absorption spectrum of the TPP in the thirty-nine different environments, where the dielectric constant of the molecular environment increases from bottom (*ε *= 1.00) to top (*ε *= 181.560); (B): The shift in the positions of the Q1, Q2, B1, B2 and L1 bands reference to their corresponding values in gas-phase spectrum as function of dielectric constant of the solvent (*ε*).*

**Figure 2.**

*(A) The calculated solvent-dependence of the triplet-triplet electronic absorption spectrum of the TPP in the thirty-nine different environments, where the dielectric constant of the molecular environment increases from bottom (*ε *= 1.00) to top (*ε *= 181.560); (B): The shift in the energy level of the Tn state reference to their corresponding value in gas-phase spectrum as function of dielectric constant of the solvent (*ε*). The shift in the energy level of the T1 state:* Δ*E(T1,*ε*) = E(T1,*ε*)-E(S0,*ε*).*

at 18805 cm−1 (531.8 nm; labeled as T10) and 20722 cm−1 (482.6 nm, T13) in the gas-phase spectrum of the TPP are gradually red-shifted to 18232 and 20041 cm−1 (or 548.5 and 499.0 nm) as a function of ε up to 28.29), respectively, and become stable within a few wavenumbers variation with the further increment in solvent dielectric constant (ε). On contrary to red-shifts in the energy level of the T10 and T13 states, the T21 (at 22130 cm−1/451.9 nm) and T25 (22926 cm−1/436.2 nm) in the gas-phase are blue-shift to 22666 cm−1 (441.2 nm) and 23849 cm−1 (419.3 nm), respectively, as function of ε up to 28.29. Additionally, the solvent leads to blue shifts (around 400 cm−1) and red shifts (about 200 cm−1) in the calculated energy levels of other triplet states as seen in see **Figure 2B**.

The İntersystem crossing (ISC) between singlet and triplet excited states of a molecular system is very important for many purposes in photochemistry. Therefore, we also investigated solvent effect on the energy barrier between singlet and triplet state, ΔE(ISC) = E(triplet)-E(singlet), where the ISC may take place.

The results from calculations show that the energy gap between Q2-band and T3 triplet state regularly decreases to −4 cm−1 (ε = 10.125) from −330 cm−1 (in gas-phase) with increasing solvent polarity and then slowly increases up to 60 cm−1 with the increase solvent polarity up to ε = 78.355. The gap between B2 band and T4 triplet state rapidly decreases from −972 cm−1 in the gas phase to −84 cm−1 in Xenon (ε = 1.706), increases from 132 cm−1 (ε = 1.911) to a maximum value of 972 cm−1 (ε = 5.32), then follow an exponentially decrease to 110 cm−1 (ε = 78.355). The triplet state T7 lies about 191 cm−1 above the L1-band in gas-phase, which start to decrease to 130 cm−1 with increase in the ε.

#### **3.2 Solvent dependence of the H4TPP**

The UV–vis absorption spectrum of the diprotonated TPP (H4TPP) exhibited a Soret band (B-band) at 22272 cm−1 (449 nm) in *acidic* chloroform solutions [56], 22831 cm−1 (438 nm) in acidic dichloromethane solution [57], 23419 cm−1 (427 nm) in acidified THF solution [58], and 22422 cm−1 (446 nm) *and* 22272 cm−1 (*449* nm) in acidic dichloromethane solution containing chloride *anion* (Cl<sup>−</sup> ) and bromide anion (Br<sup>−</sup> ), respectively [59]. The Q(0,0)-band was observed at 14837 cm−1 (674 nm) in acidic chloroform solutions [56], 15337 cm−1 (652 nm) in acidic

*Density Functional Theory Study of the Solvent Effects on Electronic Transition Energies… DOI: http://dx.doi.org/10.5772/intechopen.99613*

dichloromethane solution [57], 15432 cm−1 (648 nm) in acidic (H2SO4) dichloromethane solution, and 15129 cm−1 (661 nm) *in* acidic (H2SO4) dichloromethane solution containing chloride *anion* (Cl<sup>−</sup> ) [59]*.* These experimental results reveal that the solvent's polarity has significantly effects on the absorption spectrum of diprotonated TPP (H4TPP). The calculated solvent effect on the absorption spectra of the H4TPP in thirty nine different solutions can summarized as follows.

**Singlet H4TPP:** On contrary to red-shifts of the bands in the absorption spectrum TPP, the solvent leads to substantial blue-shifts of the absorption bands in the protonated TPP (H4TPP) spectrum as seen in **Figure 3(A** and **B)**. For instance, the calculated Q (14761 cm−1/ 677.5 nm), B (20583 cm−1/485.8 nm), L1 (21803 cm−1/458.7 nm), L2 (24095 cm−1/415.0 nm) and M (28465 cm−1/351.3 nm) bands in gas phase spectrum are progressively blue shifted to 15352, 22981, 25069, 25731, and 29355 cm−1 (or 651.4, 435.2, 404.4, 398.9 and 388.6 nm), respectively, as function of solvent dielectric constant (ε) from 1.00 to 20.493. With further increase in ε, these electronic bands remain almost constant within a few ten of wavenumbers fluctuation. These calculated results are consistent with the experimentally observed dependence of the absorption spectrum of H4TPP on molecular environments as discussed above.

**Triplet H4TPP:** While **Figure 4(A)** provides the calculated electronic spectra of the triplet H4TPP in the solvents used in this work, **Figure 4B** provides the shifts in the peak positions as function of the solvent dielectric constant relative to their corresponding positions in the gas phase spectrum. The results from calculations show that the solvent gives rise to change in dipole allowed triplet-triplet vertical electronic transition energies in the H4TPP spectrum as well energy level of the lowest triplet state (T1) as a function of solvent dielectric constant only in the region of solvent dielectric constant from ε = 1 to 28.493 and, with further increase of solvent dielectric constant, remain unchanged within a few wavenumber variations, see **Figure 4A** and **B**. Therefore, we only provide the maximum shifts when molecular environment changes from the gas phase to acetone (ε = 28.493). It is worthy to point that the shift in the energy level of the lowest triplet state (T1) was estimated from the equation: ΔE(T1,ε) = E(T1,ε)-E(S0,ε).

The predicted T1 lowest triplet state gradually blue shifts from 8232 cm−1 (1215 nm) in gas phase to 8767 cm−1 (1141 nm) in acetone solvent medium. The T4

#### **Figure 3.**

*(A) The calculated solvent-dependence of the singlet-singlet electronic absorption spectrum of the H4TPP in the thirty-nine different environments, where the dielectric constant of the molecular environment increases from bottom (*ε *= 1.00) to top (*ε *= 181.560); (B): The red-shifts in the absorption band positions as function of dielectric constant of the solvent (*ε*), reference to their corresponding values in gas-phase spectrum.*

#### **Figure 4.**

*(A) The calculated solvent-dependence of the triplet-triplet electronic absorption spectrum of the H4TPP in the thirty-nine different environments, where the dielectric constant of the molecular environment increases from bottom (*ε *= 1.00) to top (*ε *= 181.560); (B): The shift in the energy level of the Tn state reference to their corresponding value in gas-phase spectrum as function of dielectric constant of the solvent (*ε*). The shift in the energy level of the T1 state is obtained using the equation:* Δ*E(T1,*ε*) = E(T1,*ε*)-E(S0,*ε*).*

(at 11900 cm−1/840.3 nm), T5 (13093 cm−1/763.8 nm), T6 (13955 cm−1/716.6 nm), T7 (13291 cm−1/752.4 nm), and T12 (16236 cm−1/615.9 nm) in the gas phase spectrum are 500, 1344, 1083, 2176, and 631 cm−1 blue shifted in spectrum of H4TPP in acetone, respectively. However, the T14 (19024 cm−1/525.7 nm) and T18 (21607 cm−1/462.8 nm) are 210 and 890 cm−1 red shifted in acetone as solvent, respectively, see **Figure 4A** and **B**.

The SCF corrected triplet states showed there are four ISC pathway below 30000 cm−1, which also are solvent dependent. The solvent dependence of the energy gap between the singlet and triplet excited states, ΔE(T-S; ε) = E(triplet; ε)-E(singlet; ε), decreases with increase of solvent dielectric constant up to acetone and remain almost constant with further increase of ε. For instance, when molecular environment changes from gas-phase to acetone medium, the computed energy gap (ΔE(T-S; ε)) between the closest singlet and triplet state changes from −2602 to −2458 cm−1 (T2-Q ), from 3269 to 2138 cm−1 (T3-Q ), from 743 to 208 cm−1 (T5-B), from 348 to 65 cm−1 (T11-L1), from 373 to 105 cm−1 (T12-L2), from 1076 to 5 cm−1 (T17-M) and from 1375 to 151 cm−1 (T18-M).

#### **3.3 Solvent dependence of TSPP**

Akins *et al.* [60] and Zhang *et al*. [61] also have measured the UV–vis spectra of the free-base TSPP and the H4TSPP (diprotonated- or dianionic-TSPP). The author reported that the absorption spectrum of the TSPP exhibited Q(0-0)-bands at about 517 (± 2) and 640 (± 3) nm and the B-band at ~412 nm, the H4TSPP spectrum revealed a weak broad Q(0-0)-band at 645 nm and an intense B-band at 432 nm. Furthermore, the UV–vis spectra of the singlet TSPP and H4TSPP in the region of 420-460 nm indicated that the maximum peak position of the B-band in the ethanol, methanol, and DMSO solvents is red shifted with respect to water [62].

The excited-state dynamics of the TSPP has been experimentally studied by several research groups. The lowest triplet state (T1) of the TSPP has been observed at 862 nm [63] and the energy gap between the Q1 band and the T1 state in the TSPP, ΔE(T1-Q1), is measured to be about 4000 cm−1 (48 kJ mol−1) [64]. Moreover, the measured triplet– triplet absorption spectrum of the TSPP (at pH = 7) exhibited a strong peak between 440 and 450 nm with a three weak transitions: at 524 ± 2 nm, a broad peak between

*Density Functional Theory Study of the Solvent Effects on Electronic Transition Energies… DOI: http://dx.doi.org/10.5772/intechopen.99613*

ca. 550-575 nm and third one at 624 nm [65]. For the H4TSPP (at pH = 3), their triplettriplet absorption spectrum in the range of 450-700 nm displayed two relatively strong and one weak peaks. Their estimated peak positions: at ~500 ± 2 nm with a shoulder (at about 530 nm) and 650 ± 5 nm; a weak one at about 596 ± 2 nm. Jirsa and *et al*. also observed a strong triplet band at 444 nm in the TSPP absorption spectrum [66].

Our calculated dipole allowed singlet-singlet and triplet-triplet electronic transition energies of the TSPP and H4TSPP are in good agreement with these experimentally observed absorption spectra discussed above. The results from calculations show that the spectral position of the calculated absorption bands gradually change as a function of solvent dielectric constant only in the region of ε = 1 to about 20.493 (acetone) and remain unchanged with further increase of ε. Thus, we only discuss the shifts in the band position when molecular environment changes from gas phase to acetone medium and the results may be summarized as follows.

**Singlet TSPP:** The solvent-dependence of dipole allowed singlet-singlet electronic transition energies of TSPP is given in **Figure 5A**. **Figure 5B** shows the shifts in band positions caused by solvent, which is similar to the shifts in the TPP absorption spectra. As seen in **Figure 5A** and **B**, the bands at 17064 cm−1 (Q1, 586.0 nm) and 18178 cm−1 (Q2, 550.1 nm) in the gas phase spectrum of singlet TSPP are 576 and 541 cm−1 blue-shifted to 17365 cm−1 (575.9 nm) and 18467 cm−1 (541.5 nm), respectively; however, the Soret-bands B1 at 24692 cm−1 (405.0 nm) and B2 at 25060 cm−1 (399.0 nm) in gas phase spectrum are substantially shifted as function of increasing ε up to about 20.493, such as are first 958 and 1112 cm−1 red shifted to 23734 cm−1 (421.3 nm) and 23948 cm−1 (417.6 nm) with increase of solvent dielectric constant ε from 1.0 to 5.32, and which are then turned to increase up to 24429 cm−1 (409.3 nm) and 24758 cm−1 (403.9 nm) with increase of ε from 5.32 to about 20.493. With further increasing value of ε, they remain constant within ±120 cm−1 fluctuation. The bands at 26319 cm−1 (labeled as L1 at 380.0 nm) in the gas phase spectrum is shifted to 28117 cm−1 (355.7 nm) in the same region.

**Triplet TSPP:** The solvent-dependence of the triplet-triplet vertical electronic transition energies of the TSPP is similar to these in the triplet-TPP spectrum when molecular environment changes from gas phase to solvent phase. For instance, the SCFcorrected the lowest triplet state at 10922 cm−1 (915.6 nm) exhibits a exponentially blue shift up to around 11426 cm−1 (875.2 nm) as function of the ε (up to 20.493), which then

#### **Figure 5.**

*(A) The calculated solvent-dependence of the singlet-singlet electronic absorption spectrum of the TSPP in the thirty-nine different environments, where the dielectric constant of the molecular environment increases from bottom (*ε *= 1.00) to top (*ε *= 181.560); (B): The red-shifts in the absorption band positions as function of dielectric constant of the solvent (*ε*), reference to their corresponding values in gas-phase spectrum.*

remains almost constant within 20 cm−1 with the further increase in ε. This predicted value of the T1 (lowest triplet state) in the solvent with its dielectric constant value ε ≥ 20.493 is consistent with its experimental value of 862 nm as mentioned above.

As seen in **Figure 6A** and **B**, the calculated dependence of the dipole triplettriplet vertical dipole allowed electronic transitions (T1 → Tn) energies also exhibits a exponentially red/blue-shifts as function of the ε. The triplet absorption spectrum displays the maximum shifts in acetone as solvent. For example, while the T7 at 14980 cm−1 (667.5 nm), T8 at 15282 cm−1 (654.4 nm) and T17 at 18757 cm−1 (533.1 nm) in the gas phase spectrum of the TSPP are respectively 2415, 2177 and 902 cm−1 blue-shifted (to 17295 cm−1 (574.9 nm), 17459 cm−1 (572.8 nm) and 19659 cm−1 (508.7 nm)) in acetone medium, the T24 at 22000 cm−1 (454.5 nm) in gas phase is 1036 cm−1 red-shifted to 20964 cm−1 (477.0 nm).

In the same region, T4, T5, T9 and T12 states displayed a relatively weak solvent dependence such as while the triplet states T4 (13248 cm−1/754.8 nm) and T12 (18236 cm−1/548.4 nm) display a maximum blue-shift of about 500 cm−1; the T5 (14022 cm−1/713.2 nm) and T9 (18230 cm−1/548.6 nm) triplet states exhibit about 400 cm−1 red-shift (**Figure 6B**).

For a possible inter system crossing (ISC) process, we also examined the solvent effect on the energy*-*gap between the closest singlet and the triplet states, ΔE(S-T, ISC) = E(T) - E(S). The singlet states Q2, B2 and L2 singlet states are almost overlapping with the T3 (triplet-triplet forbidden state), T4 and T8 triplet states, respectively. For instance, with changes solve ε = 1 to 20.493, ΔE(S-T, ISC) the energy-gap changes from: 234 to −40 cm−1 between the Q2 and T3 state; −2108 to −1829 cm−1 (Q1 and T2); −3322 to −2931 cm−1 (Q2 and T2); 234 to −40 cm−1 (Q2 and T3); −522 to 510 cm−1 (B1 and T4); −890 to 181 cm−1 (B2 and T4); −115 to 767 cm−1 (L1 and T8); and − 576 to 87 cm−1 (L2 and T8) with going from ε = 1 to 20.493. With the further increase in ε, they remain nearly unchanged within a few ten wavenumber variations.
