The list of the solvents with their dielectric constants (ε) used in this work.
We have calculated the solvent effects on the ground state and the lowest triplet state absorption spectra of meso-tetraphenylporphyrin (TPP), meso-tetrakis(p-sulfonatophenyl)porphyrin (TSPP) and their diprotonated forms (H4TPP and H4TSPP) in thirty-nine different solvent using time-dependent-DFT density functional theory (TD-DFT) coupled with CPCM method. The results of the calculations show that the Q-bands and Soret-bands (or B-bands) in the absorption spectra of these compounds substantially change as function of solvent dielectric constant (ε) up to 20.493 (acetone), but become stabile in high polar solvents with dielectric constants ε > 20. The relative shifts in the B-bands are more significant than that in the Q-bands. The magnitude of the shifts in the spectral position of the Q and B bands are in the following order: H4TSPP > H4TPP > TPP > TSPP for the B-bands and H4TSPP > H4TPP > TSPP > TPP for the Q-bands. We also have determined that the energy-gaps between the B/Q-bands and their nearest triplet states are also solvent dependent for ε < ~ 20.493.
- solvent effect
Porphyrins are tetrapyrrolic macrocycles with conjugated electronic systems that exist in nature and have a large number of applications in several fields of research from biomedicine to materials science. The ubiquity of porphyrins in natural systems and their subtle yet important biological and chemical functions have inspired scientists to explore the unique structure/dynamics characteristics of compounds of this family, and to endeavor to imitate their properties in synthetic molecular analogs that display efficient use of solar energy [1, 2, 3, 4, 5] and could be used as active elements in molecular electronic devices [6, 7]. Furthermore, in recent times, porphyrin-like molecular systems have drawn a great deal of interest due to the use of therapeutic drugs, photosensitizers in photodynamic therapy of cancer , several applications in the treatment of nonmalignant conditions such as psoriasis, blocked arteries and pathological and bacterial infections , as well as in HIV research . As known, biological effects of porphyrins generally derive from their photophysical and physicochemical properties, such as the formation of molecular aggregates and axial ligation that give rise to significant modifications in absorption spectra, quantum yields, and fluorescence and triplet state lifetimes [11, 12, 13, 14, 15].
Along with rapid development in computer technology and computational quantum chemical methods, molecular properties have been intensively investigated in gas-phase and solvent-phase. Computational quantum chemistry is a powerful tool for understanding real-world chemical problems. Several molecular properties can be obtained by solving quantum mechanical equations. When the results of calculations are in agreement with their experimental results, we can interpret the experimental results more reasonably. Computational studies are not only performed to provide an understanding of experimental data, for instance the position and source of spectroscopic peaks, but also may be used to explore reaction mechanisms and molecular environment effect on the molecular properties.
Photophysical and photochemical properties of porphyrin and its derivatives have been widely studied by experimentalists and theoreticians [16, 17, 18, 19]. Dipole allowed electronic excitation spectra of porphyrin compounds exhibit two major absorption bands in which are called as the Q-band in the visible region and the Soret band (or B-band) in the near UV region ; both of which have been the subject for a number of quantum chemical studies [21, 22, 23, 24, 25, 26, 27, 28, 29]. It has been experimentally reported that when porphyrin molecules are excited in the Soret- or B-band region, internal conversion (IC) takes place from the B-band to the Q-band, which is then followed by a fluorescence from the Q-band to the ground state S0; i.e., S0 + hν0 → S2(B-band) → S1(Q-band) → S0 + hν. During relaxation of the S1 state, a fraction of molecules also relaxes to the triplet T1 via intersystem crossing (ISC).
The electrostatic interaction between a molecular system and its surrounding environment leads to change in geometric and spectroscopic properties. For instance, Jun Takeda and Mitsuo Sato  have experimentally studied solvent effect on the absorption spectra of meso-tetraphenylporphyrin (TPP) and dodecaphenylporphyrin (H2DPP) in thirty-seven different neat solvent. The authors reported that the solvent leads to red shifts in Q-bands and B-band (Soret-band) in their absorption spectra, and that red shifts in H2DPP are greater than those in TPP due to the nonplanarity of the H2DPP macrocycle. The authors concluded that these red shifts in the absorption spectra of both compounds are caused by the hydrogen-bonding interactions of pyrrole NH protons and pyrrolenine nitrogen lone pairs with solvent.
Li Ye  used steady-state and time-resolved spectroscopic techniques to investigate photophysical properties of several metalloporphyrins have been examined in several different solvents. The author reported that the absorption spectrum of the Cu(TPPCl8) in nonpolar solvents does not display a shift in the spectral position of the absorption bands and there is no evidence found for charge transfer (CT) transitions in the visible or near UV regions, however, in the polar solvent, blue shifts are observed in the absorption spectrum of the Cu(TPPCl8) an intramolecular CT band takes place in absorption spectra. The author concluded that the activation free energy of the charge-transfer transition decreases with increasing outer reorganizational energy owing to increasing solvent polarity.
In order to take the solvent effect on the molecular properties into account in calculations, a number of implicit (continuum) theoretical models have been developed in the last decade, such as the polarizable continuum model (PCM), the dielectric PCM (DPCM), conductor-like PCM (CPCM), integral equation formalism PCM (IEFPCM), and the conductor-like screening model (COSMO)); see refs. [32, 33] for more details. Density functional theory (DFT) and Time-dependent DFT (TD-DFT) coupled with one of the PCM methods, which is becoming a general routine in most quantum chemical software packages like Gaussian, can be used to compute solvent effect on the geometric and spectroscopic properties [34, 35, 36, 37]. Results from such calculations has been shown to be successful in supporting analyses of experimental data with useful insights for better understanding of photophysical and photochemical pathways in solution.
L. Edwards et al.  have experimentally studied solvent effect on the spectral positions of dipole allowed singlet-singlet transitions (S0 → Sn) of the free-base porphyrin (FBP). Their experimental results shows that the Q-bands at 626 and 512 nm and the Soret band at 372 nm in gas-phase spectrum were respectively significantly shifted to 614, 519 and 391 nm in ethanol.
As far as we know, there is no theoretical study systematically investigating the solvent effect on porphyrin compounds in the literature, except our previous work  where we have studied solvent effect on the absorption spectra of the free-base porphyrin (FBP) and diprotonated form (H4FBP) in the ground state and the lowest triplet state by using TD-DFT/CPCM techniques in thirty-nine different solvent (with solvent dielectric constant (ε) changes from 1 to 181.56). The results from calculations show that dipole allowed electronic transitions in each absorption spectrum change as function of increasing solvent dielectric constant up to about ε = 20.493 and remain almost constant with further increment of the solvent dielectric constant. We have also studied meso- substitution effect on the absorption spectra of the porphyrin (parent porphyrin) such as the meso-tetraphenylporphyrin (TPP), mesotetrakis (p-sulfonatophenyl) porphyrin (TSPP) and their diprotonated forms (H4TPP and H4TSPP), where the results from the calculations have shown that the meso-substituted functional groups result in a significant read shift in the electronic transition energies in the porphyrin absorption spectrum [19, 40].
2. Calculation section
The singlet-singlet and triplet-triplet electronic absorption spectra of the porphyrins and their derivatives in the gas phase and thirty-eight solvents were calculated using the Gaussian 09 software package . Geometries for the ground and the lowest triplet states in each solvent were optimized using unrestricted density functional theory (at B3LYP level) [42, 43] with the 6-311G(d,p) basis set for C and H atoms and 6-311 + G(d.p) basis set  used for N, O and S atoms. Solvent effects were taken into account using self-consistent reaction field (SCRF) calculations , with the conductor-like polarizable continuum model (CPCM) [46, 47, 48] as contained in the Gaussian 09 software package. Type of solvent used in calculations are listed in Table 1. All compounds in both gaseous and solvents phases were optimized to minima on their ground and lowest triplet state potential energy surfaces (PESs) that is verified by the absence of imaginary frequencies in calculated vibrational spectra.
Time-dependent-DFT (at TD-B3LYP level) coupled with CPCM solvation method was used to calculate the first 24 singlet-singlet vertical electronic transitions (S0➔Sn) and 25 triplet-triplet vertical electronic transitions (T1➔Tm) in the gas and solvent phases. The GaussSum 0.8 freeware program  was used to check outputs and to generate computed absorption spectra from the output file of the Gaussian 09 software.
Additionally, we obtained a best fit to the calculated relative shifts in the Q and B bands positions by using the following equation: where ε is the dielectric constant of the solvent and Cn is a constant. We would like to point out that in the fitting equations is part of the solvent correction in the CPCM method.
3. Results and calculations
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 , which is considerably shifted to 420 nm in toluene (ε = 2.374) , 419 nm in benzene (ε = 2.271) , 417 nm in
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.
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).
The calculated triplet-triplet electronic transitions up to 25000 cm−1 (400 nm) are given in Figure 2
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
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(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
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  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) . 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 ca. 550-575 nm and third one at 624 nm . For the H4TSPP (at pH = 3), their triplet-triplet 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
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.
As seen in Figure 6A and B, the calculated dependence of the dipole triplet-triplet 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
3.4 Solvent dependence of the H4TSPP
Likewise, the nearly degenerated B-bands at 12720/12796 cm−1 (or 786.1/781.5 nm) in gas phase spectrum are respectively 9839/9755 cm−1 blue shifted to 22559/22551 cm−1 (443.3/443.4 nm) in acetone (ε =20.493) and to 22755/22751 cm−1 (439.5/439.5 nm) in water (ε =78.355). Relatively very weak bands with relatively weak intensity (labeled as L-bans) at 14211/14189 cm−1 (703.7/704.8 nm) are substantially blue-shifted (9139/9108 cm−1) to 23350/23297 cm−1 (428.3/429.2 nm) in acetone and to 23907/23861 cm−1 (528.2/528.2 nm) in water, respectively.
In literature, we could not find an experimentally observed electronic spectrum of H4TSPP in the gas-phase or in a less polar solvent environment to compare with our calculated results. In high polar or acidic solutions, the observed B- and Q-bands in the electronic spectra of H4TSPP have been published by several researchers as discussed in the TSPP section, which are in agreement with the results presented here. Furthermore, results also shows that the stability of the electronic spectrum of the diprotonated TSPP (H4TSPP) rapidly increases with increasing polarity or dielectric constant of the solvent (Figure 7A and B).
The solvent-dependency of the smallest energy gap between the singlet and SCF corrected-triplet states, ΔE(singlet-triplet, ε), are estimated to be around 2300 cm−1 (T4-Q states) and about 300 ± 150 cm−1 (T9-B) and (T11-L).
Results from calculated electronic spectra of the TPP, TSPP and their diprotonated structures in gas-phase and thirty eight different solvent showed that solvent gives rise to a blue/red shifts in the singlet-singlet and triplet-triplet dipole allowed vertical electronic transition energies as a function of solvent dielectric constant only in the region of ε = 1 to about 20.493 (acetone), but no significant spectral shifts found for the solvent dielectric constant ε ≥ about 20.493.
In the low energy region (Q-band region), the Q-bands of the TPP first exhibit a red-shift (of about 70 cm−1) with increasing solvent dielectric constant up to ε = 5.32 (diiodomethane) and then to a blue shift with increasing of the ε (from 5.32 to 20.493), However, the Q-bands of the TSPP display only a blue shift (as much as 295 cm−1) with increasing of solvent dielectric constant up to 20.493. The Q-bands in both H4TPP and H4TSPP spectra exhibits a rapid blue-shift with increasing of solvent dielectric constant, but the shifts in the H4TSPP is much stronger than that in the H4TPP spectrum; such as 4480 cm−1 in the H4TSPP and 490 cm−1 in the H4TPP in acetone as solvent.
In the high energy region, the solvent effect on the Soret band (B-band) of the TPP is stronger than on that of the TSPP. The B-band of both molecules first display a red-shift in range from 1 to 5.32 and then turn to blue shift up to acetone (ε = 20.493). In both H4TPP and H4TSPP compounds, the B-band exhibit a strong blue-shift with increase of ε, but the shift in the B-band position of H4TSPP is much stronger than that of the H4TPP. With the further increase of the solvent dielectric constant (ε), spectral position of the Q- and B-bands become almost stabile within a few-tens wavenumber ranges. Furthermore, the intensity of the B-band slightly increases with increase of solvent dielectric constant.
The solvent results in both red- and blue-shifts in the triplet-triplet transition energies in the TPP, H4TPP and TSPP spectra in the calculated spectral region, but only blue-shift takes place in the H4TSPP. Furthermore, the calculations also showed that the ISC process many not only take place between the Q-bands and the nearest triplet states, but also it is possible between the B- and L-bands and the nearest triplet states because these singlet states almost overlapping with the higher triplet states. Therefore, the ISC may occurs in the singlet state B (or B-band) via surface touching, based on the competition between the IC (from the B- to Q-bands) and the ISC process. This energy gaps between Q/B-bands and the nearest triplet states is also solvent dependent for ε < 20.
The results of calculations also indicate that solvent effect on the nonplanar macrocycle conformation of porphyrin (H4TPP/H4TSPP) is more significant than that on the planar macrocycle conformation of porphyrin (TPP/TSPP). This observation suggest that the nonplanar macrocycle conformation increase the electrostatic/electronic interaction between the four hydrogen atoms at the macrocycle core and molecular environment.
The results from calculations suggest that the polarized porphyrin molecule may interact strongly with increasing solvent polarity and lead to modification of dipole allowed vertical electronic transition energies with increasing solvent polarity arising from partial charge transfer between solvent and the porphyrin macrocycle and/or the intramolecular charge transfer. Moreover, in terms of the electronic configuration of the molecular orbitals of the porphyrin, the additional charge partially may occupy a nonbonding and/or antibonding orbitals that brings about the weakening of the chemical bonding in porphyrin. Also, the partial charge transfer from an occupied nonbonding (atomic orbital of the N atom) and/or antibonding orbital results in the strengthening of the chemical bonding in porphyrin. The change in occupancy of the bonding/nonbonding orbitals affect the electronic excited state, which gives rise to shift in the electronic absorption spectrum of the porphyrin molecule.
As a result, the solvent-dependence of the spectroscopic features of porphyrin can be used to monitor micro environmental changes of porphyrin-like compounds incorporated in biological systems and nanoparticles, which also may be appropriate for study and monitoring changes of the chemical environment in different solutions and interactions in biological systems, as well as deal with nonspecific
We would like to thank TUBITAK ULAKBIM, High Performance and GridComputing Center (TR-Grid e-Infrastructure) for the calculations reported in the theoretical part of this paper.