**1. Introduction**

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 [1–5] 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 [8], several applications in the treatment of nonmalignant conditions such as psoriasis, blocked arteries and pathological and bacterial infections [9], as well as in HIV research [10]. 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 [11–15].

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 [16–19]. 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 [20]; both of which have been the subject for a number of quantum chemical studies [21–29]. 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 + hν<sup>0</sup> → 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 [30] 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 hydrogenbonding interactions of pyrrole NH protons and pyrrolenine nitrogen lone pairs with solvent.

Li Ye [31] 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

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

general routine in most quantum chemical software packages like Gaussian, can be used to compute solvent effect on the geometric and spectroscopic properties [34–37]. 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. [38] 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 [39] 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 mesotetraphenylporphyrin (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].

This *work is a continuation* of our previous studies as mentioned above. In this present work we used TD-DFT/CPCM method to investigated solvent effect on the singlet-singlet and triplet-triplet electronic spectra of the TPP, TSPP and their protonated derivatives (H4TPP and H4TSPP).

## **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 [41]. 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 [44] used for N, O and S atoms. Solvent effects were taken into account using self-consistent reaction field (SCRF) calculations [45], with the conductor-like polarizable continuum model (CPCM) [46–48] 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 [49] was used to check outputs and to generate computed absorption spectra from the output file of the Gaussian 09 software.


#### **Table 1.**

*The list of the solvents with their dielectric constants (*ε*) used in this work.*

Additionally, we obtained a best fit to the calculated relative shifts in the Q and B bands positions by using the following equation: ( ) ( ) ( ) <sup>5</sup> <sup>1</sup> <sup>f</sup> , *n n n C* ε ε <sup>−</sup> ε = <sup>∑</sup> where ε is the dielectric constant of the solvent and Cn is a constant. We would like to point out that (ε 1) ε <sup>−</sup> in the fitting equations is part of the solvent correction in the CPCM method.
