Comparative Study of the Structural and Vibroelectronic Properties of Porphyrin and Its Derivatives

Density functional theory (DFT and time-dependent-DFT (TD-DFT) were employed to investigate the vibroelectronic structural properties of porphyrin and some derivatives: unsubstituted porphyrin (TPyr), meso-tetraphenylporphyrin (TPP), meso-tetrakis(p-sulfonatophenyl)porphyrin (TSPP), protonated-TPyr (H2TPyr), deuterated-H2TPyr (D4TPyr), protonated-TPP (H2TPP) and deuterated-H2TPP (D4TPP), protonated TSPP (H2TSPP), deuterated-H2TSPP (D4TSPP), dicationic TSPP (H6TSPP) and deuterated-H6TSPP (D8TSPP). The possible internal conversion (IC) and intersystem crossing (ISC) processes of these compounds were investigated. Finally, the relaxed ground state potential energy surface (PES) (S0), and singlet (Sn, n = 1–24) and triplet (Tn) excited state PESs of the TSPP molecule were calculated as function of the dihedral angle (Cα-Cm-Cϕ-C(ph)) rotation. The results of the calculations indicated that while the meso-substitutions caused a significant shift in frequencies when the meso-carbons within the parent-porphine (or TPyr) are involved in the vibrational motion of molecules; the protonation of the N atoms at the porphine/porphyrin core causes a significant blue shift when the H on the N atoms within the pyrroline are dominantly involved in the vibrational motions. The deuteration of N atoms not only caused a red-shift in the frequencies of the corresponding peaks below 1600 cm−1, but also produced new vibrational modes of frequencies in the 2565–2595 cm−1 range caused by the N-D bond stretching. Similarly, the deuteration of O atoms within the sulfonato groups (-SO3−) exhibited a new peak at around 2642 cm−1 due to O-D bond stretching. The measured Raman spectrum of the H2TSPP is assigned based on the predicted Raman spectra of the compounds studied here and measured Raman spectrum of the TPP (from our previous work). The IR spectrum is assigned based on our calculations and measured IR spectra obtained from the literature. The results of the TD-DFT calculations did not only indicate that the meso-substitution and protonation of the porphyrin bring about a significant read shift in the electronic transitions; but also provided a strong evidence for the IC from the Soret band to Q-bands beside possibility of the ISC process; its existence depend on the other excited state process such as much faster vibrational relaxation; the IC and etc. The ground state PES curve (S0) of the ionic TSPP exhibited two minima at the dihedral angle (Cα-Cm-Cϕ-C) of about 66° (corresponds to the lowest ground state) and 110° (corresponds to next energetically stable state or the local minima). The energy deference between these two minima is 0.0132 eV (or 106 cm−1) and the highest potential energy barrier when undergoing from the lowest ground state to this local state is only 0.0219 eV (177 cm−1; which is compatible with the thermal energy (kT) at 298 K is 207.2 cm−1.


Introduction
Porphyrin and its derivatives have attracted considerable attention from both experimentalists and theoreticians for the last few decades and still remain an attractive research subject due to their broad applications in industrial and biomedical fields. The ubiquity of porphyrin derivatives in Nature and their subtle yet crucial chemical and biological functions have motivated scientists to study the unique structure/dynamics characteristics of molecules of this family, and to attempt to mimic their properties, such as high efficiency utilization of solar energy [1][2][3][4][5], and in synthetic molecular analogs, active elements in molecular electronic devices [6,7]. Enormous interest has also arisen in exploiting porphyrin-like molecular systems for the use as therapeutic drugs, photosensitizers in photodynamic therapy of cancer [8], as well their potential applications in the treatment of nonmalignant conditions such as psoriasis, blocked arteries, and pathological and bacterial infections [9], as well as HIV [10]. The biological effects of porphyrins basically depend on their physicochemical properties that essentially cause important changes in their photophysical behavior, for instance, aggregation and axial ligation cause significant changes on their absorption spectra, quantum yield, fluorescence lifetime, and triplet state lifetime [11][12][13]. A inclusive collection entirely devoted to porphyrins may be found in the Handbook of Porphyrin Science [14,15].
Very few porphyrins are known to form J-aggregates, the main requisite being the zwitterionic character with the protonation of the pyrrole nitrogen within the macrocycle. It has also been reported that these aggregates may be promoted by interaction with proteins [16,17] and surfactants [18]. The aggregation of the anionic porphyrin meso-tetrakis(p-sulfonatophenyl)porphyrin sodium salt (H2TSPP) has been studied extensively. In aqueous solutions, at neutral pH, the electronic absorption spectrum of meso-tetrakis(p-sulfonatophenyl)porphyrin (H2TSPP) is usual of free base porphyrins (D2h symmetry) and is characterized by an intense Soret band at around 420 nm and four Q bands in the region of 500-700 nm. In very acidic medium, H2TSPP forms highly ordered molecular J and H aggregates [9,[19][20][21]. The absorption spectrum of aggregated H2TSPP in acidic medium exhibits two new bands at 490 and 707 nm [21].
Quantum chemical calculations are expected to play a crucial role in promoting the ends mentioned above since the ideal approach for acquisition of intrinsic structural information of molecules, especially those of large sizes such as the porphyrinoids, would be through theoretical calculations, in which structural information would not be influenced by solvent interaction or crystal packing effects-though correction for such phenomena might be accomplished through appropriate modeling; moreover, quantum chemical calculations would be inherently free of the arbitrariness associated with deciphering structure characteristics from spectroscopic observations. Recent advances in computing facilities and the development of sophisticated computation programs, with increasingly efficient algorithms, especially the fundamental improvements in the treatment of electron correlation based on density-functional theory (DFT) [22], have also combined to allow quantum chemical methods to routinely handle molecular systems containing hundreds of atoms. Density functional theory (DFT) is also one of the most important techniques used by theoreticians to provide deep insight into spectroscopic and structural properties, even for complex molecular systems, especially those of large sizes such as the porphyrinoids [23][24][25][26][27][28].
In the present work, in order to investigate the effect of meso-substitution groups on the geometric and vibroelectronic properties of the parent-porphine or porphyrin macrocycle, density functional theory (DFT) and time-dependent-DFT (TD-DFT) were employed to investigate the vibroelectronic structural properties of porphyrin and derivatives: unsubstituted porphyrin (TPyr), meso-tetraphenylporphyrin (TPP), meso-tetrakis(p-sulfonatophenyl)porphyrin (TSPP), protonated-TPyr (H2TPyr), deuterated-H2TPyr (D4TPyr), protonated-TPP (H2TPP or dicationic TPP) and deuterated-H2TPP (D4TPP), protonated TSPP (H2TSPP or dianionic TSPP), deuterated-H2TSPP (D4TSPP), dicationic TSPP (H6TSPP) and deuterated-H6TSPP (D8TSPP). The possible internal conversion (IC) and intersystem crossing (ISC) processes for the porphyrin and derivatives were also investigated by using the TD-DFT technique. Furthermore, the relaxed potential energy surface scan were employed to study the minimum potential energy pathways for the ground and excited states of the TSPP molecule as a function of rotation Cm-Cϕ bond (or dihedral angle (Cα-Cm-Cϕ-C(ph)). We, further, ascertain that the experimental Raman bands of the H2TSPP molecule can most appropriately be described in terms of the concerted vibrations of local structural units such as the pyrrole/pyrroline rings, the sulfonatophenyl groups, and their combinations, rather than as vibrations of isolated chemical bonds, as has been the common practice. The calculated IR spectra of the H2TSPP were assigned by comparison with the calculated IR spectra of other porphyrin derivatives studied here and the experimentally measured IR spectra obtained from the literature.

Structures of Porphyrin and Its Derivatives
In brief, the predicted ground state geometry and selected bond angles and dihedral (torsional) angles of the porphyrin and its derivatives in water, used as a solvent, at B3LYP/6-311G(d,p) level of the DFT are provided in Figure 1 and Table 1. the results of the calculations indicated that while the meso-substitution of porphyrin with tetraphenyl or tetrasulfonatophenyl cause slightly out-of-plane distortion from the planar structure of the macrocycle (within 3° to 5°) for TPP and TSPP; the protonation of the porphyrin core leads to a significant distortion from its planarity within 10° to 20° for H2TPyr, H2TPP, H2TSPP and H6TSPP. Furthermore, with respect to the average plane of porphryin to macrocycle as seen in Figure 1 and Table 1, the peripheral phenyl and sulfonatophenyl substituents are oriented at a tilt angle of about 72° for the TPP and TSPP (unprotonated structures) and about 48° for the H2TPP, H2TSPP and H6TSPP (protonated structures). , meso-tetraphenylporphyrin (TPP), and anionic meso-tetrakis(p-sulfonatophenyl)porphyrin (TSPP) as well as their protonated structures (H2TPyr, H2TPP, H2TSPP and H6TSPP) in water at the B3LYP/6-311G(d,p) level of the DFT. Table 1. Selected dihedral angles (D) and bond angles (A) of free-base porphyrin (TPyr), meso-tetraphenylporphyrin (TPP), and the anionic meso-tetrakis(p-sulfonatophenyl)porphyrin (TSPP) as well as their protonated structures (H2TPyr, H2TPP, H2TSPP and H6TSPP). The calculations were done in water at the B3LYP/6-311G(d,p) level of the DFT. The calculated bond lengths are in agreement with X-ray measurements within ca. ±0.01 Å. As result, the calculations indicated clearly indicated that the protonation of the porphyrin core does not only destroy planarity of the macrocycle, but also, has an effect on the tilt angle of the phenyl and p-sulfonatophenyl substitution groups.

Raman Spectra of Porphyrin and Derivatives
Figure 2 provides the measured Raman spectra of the TPP ( Figure 2B, from our previous work [23] and H2TSPP ( Figure 2G), which reveal many Raman peaks with strong and medium intensity as well as many weak or very weak features dispersed through the spectrum. When comparing the observed Raman spectrum of the H2TSPP with the TPP, the Raman patterns in spectra of both molecules are very similar, but some of the Raman peaks positions are significantly shifted in frequency. For instance, while the most intense peak at 1564 cm −1 and relatively weak peaks at 1595, 1577, 1438, 1327, 1234 and 334 cm −1 in the spectrum of TPP are red-shifted to 1537 cm −1 (the strongest one), 1494, 1562, 1427, 1339, 1229 and 312 cm −1 , respectively. The peaks at 1002, 962, 334 and 201 cm −1 are respectively blue-shifted to 1014, 983, 314 and 236 cm −1 in the spectrum of H2TSPP. Also, the Raman bands at 1476 and 701 cm −1 Raman spectrum of the H2TSPP are significantly enhanced reference to corresponding peaks in the TPP spectrum. Figure 2 provide the calculated Raman spectra of the TPyr/D2TPyr, H2TPyr/ D4TPyr, TPP/D2TPP, H2TPP/(D4TPP), TSPP/D2TSPP, H2TSPP/D4TSPP, and H6TSPP/D8TSPP in water (used as a solvent), with the observed Raman spectra of the TPP and H2TSPP for comparison. (It is worthy to note that where D indicates that deuterium atoms covalently bound to the N atoms at porphyrin core; for dicationic D6TSPP, four of eight D atoms covalently bound to O atoms within sulfonato group, -SO3 − , other four covalently bound to the N atoms at the core). While only the data for the Raman features of TPP, TSPP and H2TSPP are presented in Table 2; the observed Raman spectrum of the H2TSPP is assigned in connection with the calculated Raman spectra of the compounds studied here and observed Raman spectrum of TPP (from our previous work [23]). Our conclusion may be summarized as follows: (1) the Raman peak at 1593 cm −1 : as seen in Figure 2, the calculations produced an active Raman band at about 1600 cm −1 for all of the porphyrin derivatives. However, the nuclear motion of the molecules showed that this calculated Raman band is due to C-C bond stretching ν(C-C) within phenyl rings and rocking of their H ρ(CH), no any contribution comes from macrocycle and sulfonato groups (-SO3 − ). The spectra of the free base porphyrin (TPyr) and protonated TPyr (H2TPyr) produced a peak around 1600 cm −1 , which results from asymmetric stretching of the Cα-Cm-Cα (νa(C-Cm-C)) and bending deformation of the C-N(H)-C/C-N-C bonds, θ(C-N(H)-C/C-N-C), and rocking of H on Cm atoms (ρ(CmH)), as seen in Figure 3. Therefore, the vibrational motion of the phenyl substitution is responsible for the observed Raman band at 1593 cm −1 in the observed spectrum of protonated TSPP (H2TSPP). Furthermore, in our previous work [23], the measured and calculated Raman spectrum of the TPP revealed the same result and also these results are shown in Table 2 and Figure 2.  [23]) and (G) H2TSPP. It should be noted that the plot Raman spectra in the gray color belong to the deuterated molecules, and the line arrows show the frequency shift in the deuterated molecule.
(2) The observed peak at 1563 cm −1 : while the measured Raman spectrum of the H2TSPP displayed a relatively weak bands at 1563 cm −1 , its calculated Raman spectrum displayed only an extremely very weak peak at 1568 cm −1 in this region (as a result of C-C bond stretching within phenyl rings and rocking of their H, accompanied by relatively weak asymmetric stretching of Cα-Cm-Cβ bond stretching, no any contribution comes from sulfonato groups). When we examined this peak caused by the same vibrational motion for the TPP, TSPP, H2TPP and H6TSPP, their calculated Raman spectra again exhibited an extremely very weak peak at 1588, 1574, 1585 and 1578 cm −1 , respectively. Actually, the calculated spectrum of the TSPP produced the most intense Raman band at 1,564 cm −1 , but its vibrational motions indicated that this mode of frequency shifted to 1524 cm −1 in the spectrum of H2TSPP. This problem is not only observed for H2TSPP, but also, we found the same problem for the TPP (seen Figure 2 and Table 2). Therefore, we believe that the DFT calculations might underestimate the intensity of this peak. (3) The observed Raman spectra of TPP and H2TSPP exhibited a strong band at 1553 cm −1 (with a shoulder ca. at 1540 cm −1 ) and at 1537 cm −1 (with a shoulder at ca. 1528 cm −1 ), respectively. Their calculated spectra displayed the strongest Raman band at 1564 and 1524 cm −1 , respectively, as a results of the same vibrational motion: Cβ-Cβ bond stretching, ν(Cβ-Cβ), symmetric stretching of Cα-Cm-Cα bonds, νs(Cα-Cm-Cα), which lead to bending deformation of the C-N-C bonds, θ(C-N(H)-C). The observed shoulders at 1540 cm −1 (TPP) and at 1528 cm −1 (H2TSPP) correspond to the calculated peaks at 1559/1540 cm −1 (in the TPP/H2TSPP and caused by νs(Cα-Cm-Cα)/ρ(C-N(H)-C)/ρ(NH)) and 1555/1529 cm −1 (in the TPP/H2TSPP, owing to ν(Cβ-Cβ)/ρ(CβH) and relatively weak θ(C-N(H)-C)). Both of the experimental and calculated Raman spectra showed that the strongest band in the TPP spectrum is significantly red shifted in the H2TSPP spectrum. This large red-shift in this peak position (about exp. 14 cm −1 and ca. 40 cm −1 ) is mainly caused by the out-of-plane distortion of the macrocycle as a result of protonation of the N atoms at porphyrin core, not due to the substitution effect, which is responsible from the observed Raman band at 1563 cm −1 in the spectrum of H2TSPP. Also, the frequency shift of this peak in the calculated spectra of the TPyr, TPP and TSPP is found in the calculated spectrum of the H2TPyr, H2TPP and H6TSPP. Table 2. Observed and calculated Raman active modes of frequencies (in cm −1 ) of the H2TSPP (C2v) with the TPP (C2v point group) and TSPP (C2v) for comparison. The calculations were carried out in water used as solvent at B3LYP/6-311G(d,p) level of the DFT. Where ∆νsc stands for the scaled vibrational frequencies (∆νsc. = 0.96∆νcalc +40) and SR and IR indicate the calculated Raman scattering activity and intesity, respectively; ∆νexp and IR/exp stand for the observed Raman frequency and Intensity, respectively. The experimental values of Raman spectrum of the TPP are taken from our previous work [23].
leads to bending deformation of the C-N-C bonds, θ(C-N(H)-C).    Out of plane wagging of phenyl rings and relatively weak out of plane wagging macrocycle.
(4) The calculated Raman spectra of the TPP, H2TPP, TSPP, H2TSPP and H6TSPP revealed a relatively strong peak around 1238 cm −1 , arise from the ν(Cϕ-Cm) (predominantly), νs(C-N(H)-C), ρ(CH) and ν(Cβ-Cβ) (relatively weak). This vibrational mode of frequency is assigned to the observed Raman bands at 1229 cm −1 (H2TSPP) and 1234 cm −1 (TPP). It is clear that this mode is mainly due to bond stretching between the meso-position C atom (Cm within macrocycle) and the adjacent C atom (within the meso-substituted phenyl or p-sulfonatophenyl groups). For the unsubstituted free base porphyrin molecules, this peak is red-shifted to 1194 cm −1 and 1217 cm −1 in the calculated spectra of the TPyr and H2TPyr, respectively, which mainly result from rocking of the H atom (covalently bound to meso-carbon atom), ρ(CmH), including vibrational bond stretching within the macrocycle (see Figure 3). The question here is that why this peak is not shifted in the meso-substituted phenyl/sulfonatophenyl porphyrin molecules, but it is shifted in the TPyr and H2TPyr? This may be explained by the existence of the electrostatic repulsion interactions between the H atoms on the Cm atoms and H atoms on the β-C atoms (Cβ) within the pyrrole/pyrroline rings in the case of the TPyr and H2TPyr. For instance, this frequency shift in the TPyr (1194 cm −1 ) is larger than in the H2TPyr (214 cm −1 ) due to the out of plane distortion from planarity of the protonated porphyrin (H2TPyr, see Figure 1) that leads to decreasing electrostatic repulsion interaction between the H atoms on the Cβ and Cm atoms resulting from increasing distance between them.
In the case of meso-phenyl/sulfonatophenyl-substituted porphyrin molecules, this electrostatic repulsion interaction between the H atoms on the Cβ atoms and H atoms on the meso-phenyl substituent lead to rotation of the meso-phenyl/sulfonatophenyl groups about Cm-Cϕ bond, up to the tilt angle of 71° for unprotonated structures and about 48° for the protonated porphyrin molecules (relative to macrocycle, see Figure 1 and Table 1). Therefore, due to decreasing in these electrostatic repulsion interactions, the calculations did not produced a significant frequency shift in this peak position (~1238 cm −1 ) in the Raman spectra of the substituted porphyrin molecules.
(5) In the range of 1050-950 cm −1 , there are two well-known Raman band that are influenced by the protonation and deuteration of the macrocycle. While the observed Raman spectrum of the TPP (excited at 488 nm) exhibited two bands at 1002 and 962 cm −1 , which are respectively blue shifted to 1016 and 986 cm −1 in the H2TSPP spectrum (excited at 514 nm). These large shift in the peak positions may be due to protonation of the porphyrin core, which leads to saddle-type distortions of the porphyrin core (in the other words, leading to increasing the degree of the freedom of the rocking of the N-H bonds as a result of decreasing electrostatic repulsion between these H atoms). Furthermore, the Gaussview animation software showed that the band at 1036 cm −1 (H4TSPP) is due to expansion of the pyrrole/pyrroline groups along N(H)…N(H) direction in opposite direction (Figure 3), as a result of the ν(Cα-Cβ), leading to macrocycle getting rectangular shape instead of square shape, and the bands at 1005 cm −1 (H4TSPP) is due to expansion of the pyrrole/pyrroline groups along N(H)…N(H) direction in the same phase like macrocycle getting square shape or similar to breathing of the macrocycle or the breathing of the pyrrole rings as assigned by Rich and McHale [29].
(6) Two other important peaks in low frequency region are predicted at 248 and 338 cm −1 for H2TSPP and 235 and 365 cm −1 for TPP are due to out of plane twisting of the macrocycle only and breathing of entire molecule, respectively, which are consistent with their experimental values (242 and 338 cm −1 for the H2TSPP; 235 and 334 cm −1 for the TPP). These observed and calculated Raman bands of TPP are red and blue shifted as a result of the protonation of the macrocycle, not due to sulfonato-substituted groups. The rest of the assignments of the observed Raman bands are given in Table 2.

Isotopic Effect on the Raman Spectrum
The results of the calculations showed that the deuteration of the N atoms at the porphyrin core also produce a significant red shift in their frequencies. There is a strong evidence on this observation comes from the polarized resonance Raman scattering (RRS) spectra of the aggregated H2TSPP (protonated TSPP) and D2TSPP (deuterated TSPP) by Rich and McHale [29]. The authors reported that the RRS spectra of the aggregated H2TSPP and D2TSPP (excited at 488 nm) exhibits frequency shifts of some of the well-known Raman modes besides changes in the relative intensities of the Raman modes upon deuteration. They found the most notable frequency shifts observed for the Raman bands at 983 cm −1 and 1013 cm −1 in the Raman spectrum of protonated TSPP (H2TSPP) aggregate that shift to 957 and 1004 cm −1 in the spectrum of aggregated D2TSPP. They also concluded that these two modes are pyrrole breathing modes and thus the red shifts can be attributed to the substitution of deuterium ions with the labile protons in the porphyrin core [29]. Our measured Raman spectra of the TPP and H2TSPP, and protonated and deuterated spectra of aggregated H2TSPP and D4TSPP clearly showed that while the protonation of the porphyrin core leads to blue shift in the frequency, the deuteration leads to red shift in the spectral position of these two Raman bands.
By comparing the spectral positions of these two peaks in the calculated Raman spectra of protonated and deuterated porphyrin core with their corresponding unprotonated ones (see Table 3), we can see that while the protonation of the free base and meso-substituted porphyrin core caused a blue shift in frequency of these two bands, the deuteration caused a red shift. For instance, while these two Raman band at 1020 and 985 cm −1 in the spectrum of TSPP are blue shifted to 1036 and 1005 cm −1 in the protonated TSPP (H2TSPP), these peaks are red shifted to 1012 and 980 cm −1 in the spectrum of deuterated TSPP (D2TSPP). When the four N atoms at the core are deuterated (D4TSPP), then, these two peaks are shifted from 1036 and 1005 cm −1 (in the H4TSPP) to 1026 and 983 cm −1 in the D4TSPP. Table 3. The predicted Raman active bands of frequencies (for the protonated (see Table 2 for TPP and H2TSPP) and deuterated (Ref. [29]) porphyrin derivatives) that experimentally exhibited significant frequency shift in the range of 1040-950 cm −1 . The effect of the deuteration of the N atoms on the frequency shift in the rest of intense Raman bands in the calculated spectrum are less than 5 cm −1 , which is consistent with the experimental observation [29], but there are many predicted Raman bands with weak intensities which exhibited large shift in the frequency (see Figure 2). The other meso-substituted and free base porphyrin derivatives showed the similar results, which are in accordance with experimental observations as discussed above. Furthermore, the theoretical calculations indicated that the meso-substituted groups do not any significant effect on the spectral position of these two Raman bands. The blue shift of these two peaks for the protonation of the porphyrin core is not so surprising when taking into account of the electrostatic repulsion effect between H atoms (covalent bonded to N atoms) at the porphyrin core. This effect can be minimized by out of plane distortion (or deviation from the planarity) of the macrocycle as discussed above. The red shift also can be expected due to isotopic effect since the vibrational frequency is inversely proportional to the square root of mass of atoms that contribute to the vibrational mode. Furthermore, the deuteration of the porphyrin core and one of oxygen atoms within the sulfonato (SO3D) groups exhibited new Raman peaks in the range of 2630-2720 cm −1 .

IR Spectra of Porphyrin and Derivatives
We also calculated the IR spectra of TPyr, TPP, TSPP, H2TPyr, H2TPP, H2TSPP and H6TSPP as well as their deuterated structures (D2TPyr, D2TPP, D2TSPP, D4TPyr, D4TPP, D4TSPP and D6TSPP, where D2 and D4 indicate the number of D atoms at porphyrin core and D6 stands for the deuteration of the porphyrin core and sulfonato groups) at the same level of the DFT. Their spectra exhibited many IR features with medium and relatively weak intense in addition intense IR bands, which are dispersed throughout the full spectral range as seen in Figure 4. The calculations coupled with the animated motions indicated that these calculated IR vibrational modes are principally associated with: (a) symmetric and asymmetric skeletal deformations of the macrocycle and phenyl rings; (b) out-of-plane deformation of the macrocycle and the phenyl rings; and (c) rocking and wagging of the CH and NH bonds. The assignments of selected IR features for these molecules are provided in Table 4. In order to test the reliability of the calculated IR spectra of the molecules investigated here, we also compared their IR peaks in the calculated spectra of the TPP and H2TSPP (protonated TSPP) with its experimentally measured IR spectra of TPP [30] and H2TSPP [31]. As seen in Table 4, the calculated and measured IR frequencies are well correlated, which indicates that the calculated IR spectra of the molecules investigated in this work are reasonable. We should point out that two types of scaling factors used for the IR spectrum of TPP: one (0.96 × ωcal + 40 in cm −1 ) that we used through paper for the Raman and IR spectra discussed here, but a scaling factor of 0.976 provided best fit to experimentally measured IR data (not for Raman) of TPP only. Only the latter one is given in Table 4.
The key conclusions on the calculated IR spectra as following: (1)  (4) the bond stretching, bending deformation and rocking of CH bonds within sulfonatophenyl substitutes; ν(S-C)), θ(C-C(S)-C) and ρ(CH on phenyl only) produced a very weak IR peak at about 1108 cm −1 in spectra of the porphyrins substituted with sulfonatophenyl groups.
The frequency shift predicted is that of 1108 cm −1 mode in the sulfonatophenyl-substituted porphyrin which shift to 1049 cm −1 in the spectra of phenyl substituted porphyrin; (5) the predicted IR peaks result from due to ν(S-C)/θ(phenyl) and relatively weak w(CH and NH) and out of plane bending (or twisting) deformation of macrocycle (at 748 cm −1 ) and out of plane twisting of the entire molecule, including θ(O-S-O)/w(CH and NH) (at 566 cm −1 ) have very weak intensity, where the θ and w represent the bending deformation and wagging vibration, respectively; (6) the vibrational mode of frequency only result from the H atoms at porphyrin core (NH) caused two IR peaks at low frequency region of 510 and 559 cm −1 (due to w(NH)), with very weak intensity; (7) the IR band caused by only rocking of the CβH produced a very weak peak at 1089 cm -1 , which is appeared almost at same position for the other systems; (8) the vibrational mode of frequencies caused by the bond stretching (ν), rocking (ρ), wagging (w) and bending deformation (θ) of the C and H atoms within macrocycle are predicted at 751, 825, 848, 1036, 1240, 1299 and 1386 cm −1 with a very weak or very weak intensity. These predicted IR features of frequencies are somewhat shifted in spectra of the protonated porphyrins, which are in agreement with experimental observation as provided in Table 4 from refs. [30,31]. It is worth noting that each assignment made in Table 4 was carried out based on the nuclear motion of the atoms within molecule using the Gaussview visualization program; (9) the bonding stretching between the meso-C atoms (Cm within the macrocycle) and Cϕ atom within the phenyl substitution involved in the mode of frequencies (due to νs/a(Cϕ-Cm-Cα)/θ(Cϕ-Cm-Cα)/νa(Cβ-Cβ-Cα)/θ(Cα-N-Cα)/ρ(CH) are found at 1220 and 1348 cm −1 . The peaks caused by symmetric/asymmetric bond stretching, bending deformation or wagging/rocking vibrational motion of the atoms within free base porphyrin (macrocycle) are predicted at 1004, 1460 and 1545 cm −1 ; (10) while in-plane rotational motion of the pyrroline rings, including relatively weak out-of-plane twisting deformation of the phenyl rings produced a weak peak at 439 cm −1 , a weak peak at 427 cm −1 (rocking of phenyl rings (ρ(phenyl) and wagging of macrocycle w(macrocycle and another weak peak at 484 cm −1 (caused by twisting of phenyl (phenyl) and w(macrocycle)) are found in the calculated spectrum of H2TSSP. Detailed descriptions for each band are given in Table 4.

Isotopic (or Deuteration) Effect on the IR Spectrum
The calculated IR spectra of the molecules studied here clearly indicated that there are not some shifted in the vibrational frequency, but also, the deuterated porphyrin core or sulfonato groups exhibit relatively intense IR peaks in the range of 2630-2660 cm −1 (unscaled values) due to N-D bond stretching and around 2711 cm −1 (unscaled value) resulting from the O-D bond stretching. The most momentous frequency shifts predicted are those of 540 and 490 cm −1 (H2TSPP, where all N atoms at porphyrin core are hydrogenated or protonated) shifted to 396 and 366 cm −1 in the D4HTSPP (indicates that all N atoms at porphyrin core were deuterated) in the range of low frequency region (below 700 cm −1 ) due to wagging of the N-D bond, w(ND). Table 4. Assignments of the IR active modes of frequencies (in cm −1 ) of the meso substituted porphyrin derivatives: TPP (C2v point group), TSPP (C2v), H2TSPP (C2v) and H6TSPP (C2v) for comparison. The calculations were carried out in water used as solvent at B3LYP/6-311G(d,p) Level of the DFT. Where ∆νsc stands for scaled vibrational frequencies ((a) ∆νsc = 0.96∆νcalc +40 as used for the Raman spectra for all molecules studied here) and IIR indicate the calculated IR intensity. In the assignments, the signs ν, θ, ρ and w indicates the bonding stretching, bending deformation, rocking and wagging, respectively. It should be noted that two different scaling factor used for the TPP: (a) ∆νsc = 0.96∆νcalc +40) and (b) ∆νsc = 0.976∆νcalc. The latter one (b) yields best fitting to observed IR spectrum (from refs. [30,31]) of the TPP only, not for others; however, the scaling factor of ∆νsc = 0.96∆νcalc +40 yields the best fitting to observed IR spectrum of H2TSPP (from ref. [31]) and Raman spectra of the TPP (our previous work, ref. [23]) and H2TSPP (present work).      In the high or mid frequency region, when the deuterium atom(s) is involved in the vibrational mode of frequency that lead to a red shift in the frequency as much as up to 10 cm −1 for the D2TSPP spectrum. The deuteration also have an effect on the relative intensity of the IR peaks in some cases, see Figure 4. These shift in the high frequency shift for the D2TPyr, D4TPyr and D4TPP are more significant than these for D2TSPP and D4TSPP. This observation indicates that above the low frequency region, the frequency shift due to deuteration decreases with increasing size of the substituent group.

Solvent Effect on the IR Spectrum
Also, the solvent effect on the IR spectrum of the H2TSPP was investigated. We used dimethylsulfoxide (DMSO) and toluene instead of water as solvent beside vacuum (gas-phase) in the calculations. The calculations indicated that, below 1100 cm −1 , there is no any significant frequency shift in the peak positions, but there are above 1100 cm −1 . For instance, while the IR peak centered at around 1200 cm −1 in gas phase is shifted to 1188 cm −1 (toluene), 1166 cm −1 (DMSO), and 1160 cm −1 (water), the IR peaks centered around 1477 and 1453 cm −1 in gas phase spectrum that are shifted to 1490 and 1468 cm −1 (toluene), 1497 and 1480 cm −1 (DMSO), and 1499 and 1481 cm −1 (water). These results indicate that the IR features, in high energy region, of the porphyrin and its derivatives, at least for H2TSPP, are sensitive to its environment. For that reason, the experimentally measured IR spectrum may exhibits frequency shifts in the spectral location of peaks in the different environments; accordingly we need to be careful about the assignment of the IR features.
Furthermore, the calculations produced twenty-four triplet states in the range of 822-249 nm for the TPyr molecule (in water used as solvent). There are two triplet states at 373 nm with symmetry B3g, T8(B3g), and at 366 nm (T9(B2u)) that are almost overlap with the strongly dipole allowed singlet electronic state at 367 nm (S4(B2u)). This finding indicate that there is no only possibility of the internal-conversion (IC) process between the S4(B2u at 376 nm) and S1(B1u at 540 nm) and S2(B2u at 506 nm), but also, the possibility of the inter-system-crossing (ISC) process through potential energy surface (PES) touching or strong vibrational coupling between S4 and T8/9 electronic states in the excited state.
For the protonated TPyr (H2TPyr) molecules exhibited similar futures such as: the IC between the S3/4 (the strongest bands or B-band) at 366 nm (with the symmetry E) and the S1 (at 538 nm with symmetry E); the ISC process between the S1 (at 538 nm with symmetry E) and T7/8 (triplet states at 367 nm with the symmetry E), see Table 5.

The Electronic Spectra of TPP and H2TPP
While the TPP molecule exhibited two weak peaks at 571 nm (S0→S1, f = 0.00337) and 535 nm (S0→S2, f = 0.0359) in Q-band region, the H2TPP produced only a double degenerated peak that is red shifted to 645 nm (S0→S1/2, f = 0.3040). In the B-band region, two strong peaks at 401 and 393 nm (S0→S3/4, f = 1.2834/1.6972) in the TPP absorption spectrum and a doubly degenerated band at 430 nm (S0→S3/4, f = 1.209) in the H2TPP. Both spectra exhibited a few weak and very weak allowed electronic transitions in the high energy region as seen in Table 5 and Figure 5. Jiang et al. [32] measured absorption and EPR spectra of some porphyrins (TPP and derivatives) and metalloporphyrins compounds. The measured absorption spectrum of the TPP produced an intense electronic transition at 417 nm (B-band) and several Q-bands with weak intensity at 514, 550, 593 and 646 nm. As seen in Table 5 and Figure 5, while these observed electronic bands are consistent with the calculated values as mentioned above, the electronic transition at 646 nm is not. The calculations did not even produce any dipole forbidden singlet-singlet electronic transition with wavelength longer than 571 nm, but, a weak singlet-singlet transition was predicated at 645 nm for the protonated TPP (H2TPP) molecule. This observation suggest that the H2TPP might be formed in the TPP solution with a low concentration and high pH value (pH > 7) or there might be singlet-triplet transition (predicted at 623 nm) through the intensity borrowing process. The authors have also reported that both steric hindrance and electron effects of the functional groups influenced the UV-vis absorption indicate that the TPP of Soret bands of the studied para-substituted meso-tetraphenylporphine derivatives moved slightly toward short wavelength (3-5 nm). This experimental observation is consistent with our calculations, for instance, when molecular system going from the TPyr, TPP to TSPP or from the H2TPyr, H2TPP to H2TSPP (see Figure 5 or Table 5).

Calculated Electronic Spectra of the TSPP, H2TSPP and H6TSPP
The experimentally observed absorption spectra of the free base TSPP exhibited an intense band (S-band, also known as B-band) at ~410 nm and several weak bands (known as Q-bands) at about 515, 550, 580, 640 nm by Akins et al. [21] and Zhang et al. [31]. Also, the authors have reported that the absorption spectrum of the dianionic TSPP (here we referred as H2TSPP) displayed the S-band at 432 nm and Q-bands at 540, 580 and 642 nm. Also, Akins and coworkers have measured fluorescence spectra of free-base TSPP (pH = 12) and monomeric H2TSPP (pH = 4.5), and aggregate TSPP. Their measured fluorescence spectra at excitation 412, 432, and 488 nm (the B-bands for the TSPP, H2TSPP and the aggregated-TSPP, respectively) showed that emission arises from the lowest excited electronic singlet state (S1) associated with the Q-bands, while excitation might be to the S2 state, the higher excited state associated with the B-band. (The fluorescence spectrum at excitation 412 nm exhibited a broadened and red degraded peak at 642 nm and a weak one at 702 nm; at the excitation 432 nm, they observed an intense broadened peak with a shoulder at 655 nm. These experimental clearly indicate an internal conversion (CI) from the B-band to the Q-band [21].

Relaxed Potential Energy Surfaces (PESs) Scan of TSPP Molecule
The ground state (S0) relaxed PES scan of the TSPP molecule was calculated in water (used as a solvent) by rotating one of four dihedral angles θ (Cα-Cm-Cϕ-C) in the region of 40° to 130° with a step size of 10°. As seen in Figure 7B,C, the calculated relaxed PES(S0) curve exhibited two minima at dihedral angles of ~66° and 110°. The calculated electronic spectra (S0→Sn, n = 1-24) and (B) relaxed potential energy surfaces (PESs) scan for the ground state S0 and upper states Sn and Tn (n = 1-24) of the TSPP molecule as function of the dihedral angle (Cα-Cm-Cϕ-C(ph)) rotation in the range of 40° to 130° with a step size of 10°; (C-E) display the change in the PES for the S0 (the ground state), Soret bands (B-bands) and Q-bands in low scale for a better view. It should be noted that only one of the four meso-sulfonatophenyl groups rotated around Cm-Cϕ bond. Note that the S-bands in Figure 7E indicates the Soret bands (or B-bands).
These two minima on the relaxed PES curve of the ground state (S0), at 65° and 110°, correspond to the lowest ground state (with symmetry of C2v) and an energetically more stable local state (with symmetry of C2), respectively. The local minima (at 110° ) lies only 0.0132 eV (or 106 cm −1 ) above the lowest ground state at ~66°) for the TSPP molecule ( Figure 7C). The highest potential energy barrier is only 0.0219 eV (177 cm −1 ) at the dihedral angle of 90° when the molecule going from the lowest ground state to this local state. This finding implies that the meso-sulfonatophenyl substitution groups can be easily rotated around Cm-Cϕ bond at room temperature since the thermal energy (kT) at 298 K is 207.2 cm −1 . Therefore, the self-assembly or arrangement of the TSPP molecules in any environment might be very easily formed since the predicted potential energy barrier is low as much as 0.0132 eV/106 cm −1 (at the dihedral angle of 90°). It is should be point out that the calculated ground state relaxed PES scan was obtained for only one of four meso-sulfonatophenyl groups rotation within the TSPP molecule. If the relaxed PES scan is obtained for the rotations of all four meso-substitutional groups, there would be several different local minimum with a different potential energy barriers on the ground state PES. In this case, these small changes in the potential energy barrier distribution of the TSPP molecules may be used such as scanning nanocalorimetry measurement purpose or other electronic purposes that responding to very small changes in energy.
The PES scan of the singlet (Sn) and triplet (Tn) excited states were obtained by calculating the vertical electronic transitions S0→Sn and S0→Tn (n = 1-24) energies for each optimized ground state geometry of the TSPP molecule at the dihedral angle θ(Cα-Cm-Cϕ-C(ph)) and taking into account of the SCF energy corrections, using the following equation: where E0 and E(θ) correspond to the calculated global (total SCF) energies at the lowest ground state and the relaxed potential energy at the dihedral angle θ(Cα-Cm-Cϕ-C1), respectively; and (S0→Sn/S0→Tn; θ) indicates the vertical electronic transition energy between S0 and excited energy levels S0/Tn at the rotated dihedral angle rotated θ. As seen in Figure 7C-E, change in the electronic energy levels of the singlet and triplet states as function of the dihedral angle rotation, PESs (for Sn and Tn states), are similar to change in the PES(S0) curve. The calculated dipole allowed electronic transitions at each rotated dihedral angle are given in Figure 7A. The results of the calculations displayed that the red shift in spectral position of Soret bands (B-band) increases with the increasing rotational dihedral angle in both right-handed and left-handed rotational direction around its equilibrium dihedral angle of ~66° in the ground state.

Calculation Section
The ground state structures and vibrational modes of frequencies of the porphyrin and its derivatives in water used as solvent were calculated using density functional theory (DFT) with the B3LYP functional [33,34] with 6-311G(d,p) basis set [35]. The solvent effects were taken into account using the self-consistent reaction field (SCRF) calculations [36] with the conductor-like polarizable continuum model (CPCM) [37][38][39] with a dielectric constant of 78.39 for water, SCRF = (CPCM, Solvent = Water) as contained in the Gaussian 09 software package [40]. All compounds were optimized to minima on their ground state relaxed potential energy surfaces (PESs) that were verified by revealing no any imaginary frequency in their calculated vibrational spectra. In order to observe the deuteration effect on the vibrational spectra of the molecules studied here were calculated at same level of the DFT techniques. By using the time dependent DFT (TD-DFT), first twenty four singlet-singlet (S0→Sn) and singlet-triplet (S0→Tn. n = 1 to 24) vertical electronic transitions in water used as solvent were calculated at TD-B3LYP/6-31G(d,p) level of the theory. Finally, to explore the dependence of the potential energy of the ground state (S0) and excited states (Sn and Tn) on the rotation of the Cm-Cϕ bond (or rotation of the dihedral angle θ(Cα-Cm-Cϕ-C(ph)), the relaxed potential energy surface (PES) scan was performed using the scan facility (keyword: "Opt = ModRedundant") implemented within Gaussian09 [40]. The calculated ground state (S0) potential energies at each structure being optimized at the B3LYP/6-31G(d) level were plotted as a function of the rotated dihedral angle θ, ranging from 40° to 130° with a step size of 10°. The excited states (singlet (Sn) and triplet (Tn) states, n = 1 to 24) PES were obtained by calculations of the singlet-singlet (S0→Sn) and singlet-triplet (S0→Tn) electronic transition energies for each optimized structure at the rotated dihedral angle θ, including taking into account of the SCF energy correction (ΔESCF = E(θ) − E0) to the each electronic transition energy, where the E0 and E(θ) indicate the calculated global energies of the energetically most stable structure and the optimized structure at the dihedral angle θ, respectively.
Furthermore, vibrational mode descriptions were made on the basis of calculated nuclear displacements associated with measured vibrational frequencies, combined with visual inspection of the animated normal modes, to assess which bond and angle motions dominate the mode dynamics for the molecule. The DFT method was chosen because it is computationally less demanding than other approaches as regards inclusion of electron correlation. Moreover, in addition to its excellent accuracy and favorable computation expense ratio, the B3LYP calculation of Raman frequencies has shown its efficacy in our earlier studies, often proving itself the most reliable and preferable method for many molecular species of intermediate size, including carbon nanotubes (CNTs) and transition metals [41][42][43][44][45][46][47]. We would like to point out that the Raman, IR and electronic spectra of the molecules studied here were plotted using the GaussSum software [48]. The spectral resolutions were taken to be 4 cm −1 with the full width at half maximum (FWHM) of 12 cm −1 for the IR and Raman spectra (with the excitation energy 25,000 cm −1 (400 nm)), and 60 cm −1 with the FWHM of 300 cm −1 for the electronic spectra. The calculated Raman and IR spectra were fitted to observed Raman and IR spectra using a fitting equation of ∆νsc = 0.96∆νcalc + 40.

Experimental Section
TSPP was purchased from Mid-Century Chemicals (Posen, IL, USA) and used without further purification. The protonated TSPP (H2TSPP) solutions were prepared by dissolving TSPP in acidic aqueous medium (HCl was used to adjusting the pH value at ~2 in the concentration of ~5 × 10 −5 M). Raman spectra was excited under ambient temperature condition using a Coherent 899 dye-laser with stilbene as the laser dye, which was optically pumped by 514 nm radiation provided by a Coherent Innova 200 argon-ion laser. Exciting laser radiation was directed through an Olympus BH-2 microscope and focused by a ×50 microscopic objective as a diffraction-limited beam onto the sample. The sample was deposited as a thin film onto a smooth metallic silver surface, with the substrate serving to quench fluorescence of the porphyrin through the "heavy atom effect". Raman scattering signals from the H2TSPP sample were collected through the same microscope in a back-reflection configuration, and dispersed by a 0.6-meter Spex 1877 spectrograph equipped with a 1200 groove/mm grating, a holographic notch filter, and a Spex Spectrum-1 CCD camera cooled to 140 K by liquid nitrogen. The pre-resonance Raman spectrum reported here, unless otherwise stated, result from accumulations of 30 scanned spectra, each with a 5 s integration period, and have been corrected by background subtraction. The uncertainty in Raman shifts with our instrumentation is estimated to be < ±2.0 cm −1 .

Conclusions
The results of the calculated Raman and IR spectra of porphyrin and its derivatives in conjunction with the animation of the vibrational motions of the molecule showed if the peak(s) are only or mainly due to the vibrational motions of the meso-substitutions, H atoms covalently bound to the porphyrin core (and sulfonato groups (-SO3 − )), the meso-substitutions, protonation and deuteration lead to a significant frequency shifts in these peaks positions. For instance, this peak (at about 1600 cm −1 ) in the unsubstituted porphyrin is caused by the macrocycle is red shifted to around 1564 cm −1 in TPP/TSPP (meso-phenyl/sulfonatophenyl substituted porphyrin) and to 1540-1520 cm −1 in H2TPP, H2TSPP and H6TSPP (protonated and meso-substituted porphyrin). The peaks observed and predicted at around 1600 cm −1 in the spectra of TPP/TSPP and their protonated structures are a result of the vibrational stretching of the phenyl rings only. In the low frequency region, the observed and predicted Raman peaks at about 200 and 334 cm −1 in the TPP are respectively shifted to 242 (red shift) and 314 cm −1 (blue shift) in the protonated TSPP (H2TSPP). The red-shift is due to sulfonato (SO3) groups and blue shift is due to the protonation of the porphyrin core. The deuteration of the porphyrin and derivatives exhibited a red shift in the peak positions such as two Raman bands at 1020 and 985 cm −1 in the spectrum of TSPP are blue shifted to 1036 and 1005 cm −1 in the protonated TSPP (H2TSPP), these peaks are red shifted to 1012 and 980 cm −1 in the spectrum of deuterated TSPP (D2TSPP). When the four N atoms at core are deuterated (D4TSPP), then, these two peaks are shifted from 1036 and 1005 cm −1 (in H4TSPP) to 1026 and 983 cm −1 in D4TSPP. The IR spectra of the compounds studied here showed similar trends.
The calculated electronic spectra of these molecules displayed that the Soret band(s) (B-band and Q-bands are red-shifted due to the meso-substitutions and protonation and all spectra indicated the existence of an internal conversion (CI) process from the B-band(s) to the Q-band(s). however, there is a possibility of the intersystem crossing process between the singlet (Sn) and triplet (Tn) excited states due to the potential energy surface touching and vibrational coupling, its occurrence depends on the excited states dynamics such as competition between the vibrational relaxation, the IC and florescence to the ground state and the ISC process, but its observed for the metalloid porphyrin metal complex systems. Finally, the calculated relaxed potential energy surface scan of the TSPP molecules as function of dihedral angle indicated the PES curve of the ground state (S0) of the ionic TSPP exhibited two minima at dihedral angle (Cα-Cm-Cϕ-C) of about 66° (corresponds to the lowest ground state) and 110° (the local minimum on the relaxed PES). The energy deference between these two minima is 0.0132 eV (or 106 cm −1 ) and the highest potential energy barrier is only 0.0219 eV (177 cm −1 when going from the lowest ground state to this local state; which is compatible with the thermal energy (kT) at 298 K is 207.2 cm −1 .