Excited States of a Significantly Ruffled Porphyrin: Computational

Article pubs.acs.org/JPCA

Excited States of a Significantly Ruffled Porphyrin: Computational Study on Structure-Induced Rapid Decay Mechanism via Intersystem Crossing Fu-Quan Bai,†,‡ Naoki Nakatani,§ Akira Nakayama,§ and Jun-ya Hasegawa*,§,∥ †

Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano-Nishihiraki, Sakyo, Kyoto 606-8103, Japan Catalysis Research Center, Hokkaido University, Kita 21, Nishi 10, Kita-ku, Sapporo 001-0021, Japan ∥ JST-CREST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan §

S Supporting Information *

ABSTRACT: The compound meso-tetra-tert-butylporphyrin (H2T(t-Bu)P) is a significantly ruffled porphyrin and known as a good quencher. Compared with planar porphyrins, H2T(t-Bu)P showed bathochromic shift and rapid radiationless decay of the 1(π, π*) excited state. Density functional theory, approximated coupled-cluster theory, and complete active space self-consistent field method level calculations were performed for the potential energy surface (PES) of the low-lying singlet and triplet states of H2T(t-Bu)P. The origin of the bathochromic shift in the absorption and fluorescence spectra was attributed to both steric distortions of the ring and electronic effects of the substituents. The nonradiative deactivation process of H2T(t-Bu)P via intersystem crossing (ISC) is proposed as (S1 → T2 → T1 → S0). Along a nonplanar distortion angle, the PESs of the S1 and T2 states are very close to each other, which suggests that many channels exist for ISC. For the T1 → S0 transition, minimum energy ISC points were located, and spin−orbit coupling (SOC) was evaluated. The present results indicate that the ISC can also occur at the T1/S0 intersection, in addition to the vibrational SOC promoted by specific normal modes.

1. INTRODUCTION Nature preserves good quencher molecules such as purine and pyrimidine bases in DNA and RNA,1,2 which exhibit high stability against sunlight irradiation. Nonplanar porphyrins are also commonly found in biological systems3−5 and, therefore, are often synthesized to gain insights into the mechanism behind the nonplanar structure.6−10 To acquire photostability in artificial systems, a systematic understanding of the quenching mechanism should be explored at an atomic resolution. The out-of-plane macrocycle distortion in a series of sterically crowded porphyrins results in unusual optical properties. The enhanced radiationless decay of the 1(π, π*) excited state8−13 is comparable to those of the DNA bases. Both ruffled metalloporphyrins and ruffled free-base porphyrins reduce the excited-state lifetime by a factor of 200,9,11 which indicates that the rapid decay can be attributed to not only the metal d−d deactivation but also the excited state of the distorted porphyrin ring. This raises the possibility that the excited-state properties of the porphyrin can be adjusted systematically through the introduction of distortions into the tetrapyrrole skeleton. Therefore, it is important to understand how the structural distortion is linked with the photochemical and photophysical properties. In the past decade, there has been significant progress, particularly in quantitative computational studies on the excited states of porphyrins (for example, see refs 12 and 14−20 and references therein). To elucidate the excited-state decay via © 2014 American Chemical Society

intersystem crossing (ISC), Marian and co-workers performed density functional theory (DFT)/multireference configuration interaction (MRCI) calculations for an unsubstituted planar free-base porphyrin and found two possible decay pathways from the S1 to T1 state.19 It was shown that out-of-plane vibrations of the porphyrin ring increase as spin−orbit coupling (SOC) increases.19,21 For ruffled porphyrins, there is some controversy in the literature regarding the origin of the bathochromic shift of the Q-band (the lowest-energy absorption) in the absorption spectrum, as some researchers attribute the shift to the out-of-plane distortion of the ring,22 while others attribute it to the electronic effect of substituents.12 However, we have found no report on the excited-state potential surface to explain the origin of the fast deactivation process. In this paper, excited states of a significantly ruffled porphyrin, meso-tetra-tert-butylporphyrin (H2T(t-Bu)P) are compared with those of free-base porphyrin (H2P). In particular, we focus on the nonradiative decay process of H2T(t-Bu)P via ISC because the time constant of this process is 200 times smaller than those of normal planar free-base porphyrins.9 We first investigated the computational performance of several electronic structure methods. Next, we calculated the vertical and adiabatic excitation energies of Received: March 7, 2014 Revised: May 15, 2014 Published: May 19, 2014 4184

dx.doi.org/10.1021/jp502349h | J. Phys. Chem. A 2014, 118, 4184−4194

The Journal of Physical Chemistry A

Article

Table 1. Calculated and Experimentally Observed Excitation Energies of Singlet States of H2Pa SAC-CI

a

CAM-B3LYP

B3LYP

level 1

level 3

CIS

CIS(D)

RICC2

SCS-RICC2

exptlb

2.20 2.42 3.55 3.65 4.26 4.79

2.26 2.42 3.30 3.44 3.79 4.05

1.67 2.06 3.41 3.57 4.13 4.68

1.69 2.18 3.41 3.53 4.19 4.75

2.39 2.50 4.44 4.62 5.23 5.60

2.46 2.61 4.13 4.45 4.97 5.30

2.30 2.50 4.38 4.72 5.23 6.54

2.13 2.51 3.45 3.78 4.38 4.66

2.16, Qx(1−0) 2.56, Qy(1−0) 3.33, B 3.65, N 4.25−4.67, L

Unit is in eV. bIn gas phase. Reference 31. Experimentally observed Qx(0−0) and Qy(0−0) transition energies were 1.98 and 2.42 eV, respectively.

SCS-RICC2 result was a systematic overestimation ranging from +0.03 to +0.15 eV, and this result was deemed to be satisfactory to investigate the potential energy surface of excited states, in terms of accuracy versus computational cost. A previous benchmark study also showed that the SCS treatment improved the 0−0 excitation energies of π−π* states of organic chromophores.34 The SAC-CI/6-31G* results underestimated the transition energy of the Qx and Qy bands but showed reasonable agreements for higher excited states. The TD-CAMB3LYP/6-31+G** and TD-B3LYP/6-31+G** calculations were performed at the closed-shell geometry optimized at the CAM-B3LYP/6-31+G** and B3LYP/6-31+G** levels, respectively. These DFT results also produced energy levels at a reasonable accuracy. The deviations from the experimental data were small for the low-lying excited states. With these benchmark results, we adopted SCS-RICC2 and B3LYP for investigating the potential energy surfaces of the nonradiative decay processes. The ISC point was also explored using a method proposed ́ by Martinez and co-workers,39 which is originally designed to obtain minimum energy conical intersection (MECI) without derivative coupling vectors. In the present study, a program package developed by one of the authors was used.40 The parameter σ was set to values of 35.0 and 10.0 for H2P and H2T(t-Bu)P, respectively. With this setting, the energy difference between the S0 and T1 states was within 0.4 kcal/ mol at the converged geometries. Calculations were performed at the B3LYP/6-31+G** level. The TURBOMOLE 6.4 package41 was used for all RICC2 and SCS-RICC2 calculations. Complete active space selfconsistent field (CASSCF)42 and CAS state interaction (CASSI)43 calculations were performed using MOLCAS 7.4.44,45 The remainder of the calculations were performed using Gaussian 09 revision C02.46 Molecular orbitals were drawn using GaussView 5 software.

singlet and triplet states of H2T(t-Bu)P, and the results were compared with available experimental data. The origin of the bathochromic shift was then rationalized by a stepwise modification of the computational model. Next, we studied the potential energy surface (PES) of the ground and excited states along the distortion of the porphyrin ring. Minimumenergy intersystem crossing points (MEISC) between T1 and S0 states were also located for both H2P and H2T(t-Bu)P. Electronic structures at the MEISC points were characterized, and the role of the ring distortion was clarified. With these computational data, we propose the nonradiative deactivation pathway via intersystem crossing.

2. COMPUTATIONAL DETAILS The ground-state equilibrium geometries were computed using the Kohn−Sham DFT,23 employing the hybrid functional B3LYP.24,25 Singlet- and triplet-state equilibrium geometries were computed using the time-dependent approach (TDDFT)26,27 with the B3LYP and CAM-B3LYP functionals.28 For the lowest triplet state, optimization was performed with an unrestricted single determinant using the B3LYP functional. Frequency analysis was carried out at calculated stationary points. The basis sets used were the 6-31+G** sets29,30 (6-31G sets augmented by a single polarization function and diffuse functions, for the H, C, N, and O atoms). The molecular spatial symmetry of H2P was D2h at all the stationary points, while that of H2T(t-Bu)P was finally relaxed into C1 symmetry. To investigate the PES of the ground and excited states, vertical excitation energies calculated from several electronic structure methods were compared. In Table 1, the calculated excitation energies of the optically allowed π−π* singlet-states of H2P are compared with experimental data.31 Among the DFT functionals, the B3LYP24,25 and CAM-B3LYP28 were adopted. For wave function methods, the performance of CI singles (CIS) and their second-order perturbative correction (CIS(D))32 were examined, in addition to the second-order approximated coupled-cluster model with the resolution of identity approximation33 (RICC2), spin-component scaled RICC2 (SCS-RICC2),34 and symmetry-adapted cluster-configuration interaction (SAC-CI) method.35−37 The electronic structures of these states have been presented in several previous publications.14,15,38 The CIS/6-31+G**, CIS(D)/6-31+G**, and RICC2/defSV(P) calculations were performed using the B3LYP/631+G** optimized geometry. The basis sets “def-SV(P)” denote split-valence basis sets with a d-type polarization function. These calculations overestimated experimental data for the Qx transition by 0.5 eV at the largest case. A previous CC2 study20 showed a similar trend. However, the SCS treatment produced significant improvements. The error in the

3. RESULTS AND DISCUSSION 3.1. Geometries of H2P and H2T(t-Bu)P in S0, S1, and T1 states. To understand the nonadiabatic decay process of H2T(t-Bu)P, the excited-state structures were expected to provide important information. Therefore, the energy minimum structures of H2T(t-Bu)P in low-lying singlet and triplet states were compared. Ground-state equilibrium geometries of H2P and H2T(tBu)P were optimized at the B3LYP/6-31G** level and are presented in Figure 1. At the calculated energy minimum, H2P and H2T(t-Bu)P exhibited D2h and C1 symmetry, respectively. The structure of H2T(t-Bu)P was in the so-called ruffled conformation as shown in Figure 1d and e. To avoid steric repulsion with the tert-butyl group, the neighboring pyrrole 4185



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Figure 1. (a) Chemical structures of H2P and H2T(t-Bu)P. (b and c) Ground-state optimized structures of H2P and H2T(t-Bu)P, respectively. The green area denotes the dihedral angles C4−C5− C6−N4 and C14−C15−C16−N2 (see part a for atomic indices). (d and e) The side view of part c along the C10−C20 axis and the N1− N3 axis, respectively.

groups had twisted conformations. A previous study8 showed the possibility of a saddle-shaped conformation in a porphyrin in a more crowded situation. In the H2T(t-Bu)P case, however, the saddle conformation was obtained as a transition state that was connected to the steady ruffled conformation. The ruffled conformation of H2T(t-Bu)P in the singlet and triplet states was then investigated. Figure 2 shows the bond lengths and dihedral angles of H2P and H2T(t-Bu)P in the S0, S1, and T1 optimized structures. As seen in Figure 2a and b, the bond lengths of the S0 and S1 structures were very similar to each other in both H2P and H2T(t-Bu)P. However, those in the T1 structure exhibited differences from the singlet states as bond-length alternation became more apparent. In particular, the C5−C6 and C15−C16 bonds were stretched to 1.48 Å, which is similar to that of a C−C single bond. The dihedral angles of H2P and H2T(t-Bu)P are also summarized in Figure 2c and d. In H2T(t-Bu)P, the C4−C5−C6−N4 angles were observed to be 18.5, 25.5, and 56.6° in the S0, S1, and T1 states, respectively. Again, the S0 and S1 structures were very similar to each other in both H2P and H2T(t-Bu)P. The triplet states tended to have larger deviations. Because the electronic structures of triplet states, particularly the T1 state, were dominated by a single configuration (HOMO to LUMO transition, see Figure 3 and discussion in subsection 3.2), the bonding/antibonding character of these MOs clearly reflected the minimum energy structure. 3.2. Low-Lying Singlet and Triplet Excited States of H2P. The singlet and triplet π → π* excited states related to photoabsorption, fluorescence, and phosphorescence of H2P are summarized in Table 2. Vertical transition energies at the S0 and S1 structures were compared with the peak position of Qx(1−0) in the photoabsorption spectrum and Qx(0−1) in the fluorescence spectrum, respectively. On the basis of the absorption and emission spectra,9 it is reasonable to assume

Figure 2. Optimized structural parameters of H2P and H2T(t-Bu)P. Bond angles of (a) H2P and (b) H2T(t-Bu)P. Dihedral angles of (c) H2P and (d) H2T(t-Bu)P. The S0 and T1 states were optimized at the B3LYP SCF level. For atom indices, see Figure 1.

that the Qx(1−0) and Qx(0−1) peaks have the largest Franck− Condon overlap in the photo absorption and emission processes, respectively. However, the calculated vertical transition energies were not a very comparable quantity to the experimentally observed Qx(1−0) and Qx(0−1) energies. The 0−0 transition energy, Qx(0−0), which is discussed in the next paragraph and listed in Table 3, was expected to be more reasonably comparable. The vertical excitation energies calculated by SCS-RICC2 (2.13 eV) and B3LYP (2.26 eV) were close to the experimental Qx(1−0) peak position (2.16 eV in the gas phase). With regard to fluorescence energy, the calculated vertical transition energy (2.09 eV by SCS-RICC2) overestimated the experimentally obtained energy for the Qx(0−1) peak in an EPA (ethyl ether:isopentane:ethanol in volume ratio of 5:5:2) solution by 0.27 eV. However, the calculated Stokes shift of 0.04 eV reasonably agreed with that in free-base tetraphenylporphyrin (0.02 eV).9 In Table 3, the calculated adiabatic transition energies for the S1 (2.10 eV) and T1 states (1.73 eV) are compared with the experimentally observed Qx(0−0)31,47 and T(0−0)47 energies. 4186



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Figure 3. MO energy levels of H2P and H2T(t-Bu)P at S0, S1, and T1 optimized geometries (isosurface value = 0.02). The main configurations of the S1 states at the S0 and S1 structures, and those of the T1 states at the T1 structure which are listed in Tables 1 and 2, are marked by the orange arrows along with their coefficients.

Table 2. Vertical Transition Energies and Main Configurations of the Singlet and Triplet π → π* States of H2P at EnergyMinimum Structuresa TD-B3LYP/6-31+G** state

main configurations (|C| > 0.3)

b

SCS-RICC2/def-SV(P) EE(f)

d

main configurations (|C| > 0.3)b

Photo Absorption at S0 Minimum Structure Optimized with B3LYP/6-31+G** S1 +0.54 (81(5b1u) → 83(4b3g)) 2.26 ( 0.3)b

SCS-RICC2/def-SV(P) EE(f)c


Photo Absorption at the S0 Minimum Structure Optimized with B3LYP/6-31+G** S1 +0.44 (145 → 146) + 0.35 (145 → 147) 2.00 +0.53 (144 → 146) + 0.46 (145 → 147) −0.32 (144 → 147) (9.30 × 10−3) +0.52 (144 → 147) + 0.44 (145 → 146) T1 +0.50 (145 → 146) − 0.45 (145 → 147) 1.13 +0.83 (144 → 146) − 0.45 (144 → 147) +0.26 (145 → 146) Fluorescence at the S1 Minimum Structure Optimized with TD-B3LYP/6-31+G** S1 −0.49 (145 → 146) + 0.31 (145 → 147) 1.92 0.63 (144 → 146) + 0.64 (145 → 147) −0.32 (144 → 147) +0.34 (145 → 146) Phosphorescence at the T1 Minimum Structure Optimized with TD-B3LYP/6-31+G** T1 −0.71 (145 → 146) −0.54 0.97 (145 → 146) Phosphorescence at the T1 Minimum Structure Optimized with B3LYP/6-31+G** T1 145 → 146 (SCF)d 0.39 0.96 (145 → 146) + 0.22 (145 → 147)

EE(f)c

exptl

1.89 (1.22 × 10−3) 1.65

1.95e

1.81 (4.68 × 10−3)

1.76f

0.49 0.74

a Units are in eV. bMO indices are shown with number. HOMO and LUMO are 145 and 146, respectively. cExcitation energy. Number in parentheses is oscillator strength in au. dT1 state was obtained as B3LYP/6-31+G** SCF solution. eQx(1−0) peak in the absorption spectrum.9 f Qx(0−1) peak in the fluorescence spectrum.9

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Table 5. Photoabsorption, Fluorescence, and Phosphorescence Energies and Related π → π* States of Distorted H2P with a Porphyrin Skeleton Geometry Taken from H2T(t-Bu)Pa distorted H2P (skeleton taken from H2T(t-Bu)P) state


H2T(t-Bu)P

H2P

EE(f)

EE(f)

1.89 (1.22 × 10−3) 1.65

2.13 (1.67 × 10−3) 1.94

1.81 (4.68 × 10−3)

2.09 (2.09 × 10−4)

0.49

1.55

0.74

1.57

EE(f)

Photo Absorption at the S0 Minimum Structure Optimized with B3LYP/6-31+G** S1 +0.67 (80 → 83) −0.66 (81 → 82) 1.96 (2.50 × 10−3) T1 +0.90 (80 → 82) 1.74 Fluorescence at the S1 Minimum Structure Optimized with TD-B3LYP/6-31+G** S1 +0.72 (80 → 83) −0.67 (81 → 82) 1.88 (5.23 × 10−3) Phosphorescence at the T1 Minimum Structure Optimized with TD-B3LYP/6-31+G** T1 0.95 (81 → 82) 0.50 Phosphorescence at the T1 Minimum Structure Optimized with B3LYP/6-31+G** T1 0.94 (81 → 82) 0.76 a

Calculations were performed using SCS-RICC2/def-SV(P). Units are in eV. bMO indices are shown with number. HOMO and LUMO are 81 and 82, respectively. cExcitation energy. Number in parentheses is oscillator strength in au.

Bu)P. The electronic effect of tert-butyl groups produced a secondary contribution but was not negligible. This result was comparable with that in β-trifluoromethylporphycene in our previous study,50 in which trifluoromethyl groups at the β-carbons of pyrrole rings introduced structural distortion into the porphycene skeleton and caused a hypsochromic shift in the absorption spectrum. The electronic effect of the trifluoromethyl groups was secondary but was not negligible. The present result also agreed with the results obtained by Parusel and co-workers,22 in which ruffling and saddling resulted in a bathochromic shift. Although DiMagno and co-workers12 concluded that the ruffling effect caused a negligible shift; in a free-base porphyrin with CH3 groups at the meso position, the calculated bathochromic shift (0.19 eV) was interpreted by the substituent effect (0.17 eV).12 However, the balance between the ruffling and electronic effects seemed to depend on the system. In their result for a free-base porphyrin with CF3 groups at the meso position, the ruffling and electronic effects induced shifts of 0.04 and 0.09 eV, respectively, with a total bathochromic shift of 0.15 eV.12 A much larger shift due to the nonplanar distortion was observed for the calculated excitation energy of the T1 state at the T1 geometry. The relative energy difference between the T1 and S0 states appeared to be much more sensitive to the distortion. This result indicated that the nonplanar distortion could be relevant to the nonradiative decay via ISC. 3.5. On the Nonradiative Relaxation Pathway of H2T(tBu)P. To understand the nonradiative relaxation pathway in the excited state of H2T(t-Bu)P, the potential energy curves of the singlet and triplet states were investigated at the SCSRICC2 level. On the basis of the Kasha rule, it was assumed that H2T(t-Bu)P was in the S1 state after relaxation from highlying singlet excited states. Because the dihedral angle C4−C5− C6−N4 and its symmetric counterpart C14−C15−C16−N2 were the most prominent structural variables that characterize the structural change in the excited states (see Figure 2d), the structure of the H2T(t-Bu)P in the S1 state was optimized at several C4−C5−C6−N4 angles (20, 40, 60, and 80°), and the single-point SCS-RICC2 calculations for the low-lying singlet and triplet states were performed. The result is shown in Figure 4. The potential energy surface of the S1 state had an energy minimum at 25.5°, and the energy of the S1 state monotonically increased when the angle increased. Figure 4 clearly shows that the energies of the S1 and T2 states were close to each other in their energy levels, even at the energy minimum of the S1 state. Because both of

configurations were mixed with similar coefficients. The electronic structure of the T1 state was also dominated by a single configuration, as in the H2P case. However, the symmetry-lowering introduced some configuration mixing to the main configurations. The problem of applying TD-B3LYP to calculate the T1 energy became more prominent. As shown in Table 4, TDB3LYP produced negative phosphorescence energy at the T1 optimized structure, as the lowest triplet state was calculated to be lower than the S0 state by 0.54 eV. Again, the SCF solution for the T1 state produced a better result (0.39 eV), which was much closer to that of the SCS-RICC2 solution. Because the deviation in the SCS-RICC2 result with the TD and SCF structures was 0.25 eV, we could conclude that the TD-B3LYP calculation also introduced some error in the optimized geometry, in addition to the relative energy between S0 and T1 states. To summarize, we observed that SCS-RICC2 produced a quantitative agreement with the experimental spectroscopic data on the potential surfaces of the S0, S1, and T1 states. The TD-B3LYP calculation was applicable to the S0 and S1 surfaces, but not to the T1 one. Instead, UB3LYP-SCF reproduced the SCS-RICC2 potential surface of the T1 state with semiquantitative accuracy. 3.4. Effect of Distortion in the H2P Skeleton on the Excitation Energies of H2T(t-Bu)P. The origin of the significant low-energy shift in the calculated energy levels of H2T(t-Bu)P in the low-lying singlet and triplet states was investigated. The strategy employed here was to adopt a distorted H2P skeleton.12,49,50 The tert-butyl groups at the meso positions of the ruffled H2T(t-Bu)P were replaced by hydrogen atoms to obtain H2P in the H2T(t-Bu)P geometry. The C(meso)−H bond length was set to be 1.08 Å. Calculations with SCS-RICC2 were performed for the ruffled H2P at the S0, S1, and T1 geometries. Calculated excited states are summarized in Table 5, together with the results of H2P and H2T(t-Bu)P. Comparing the result of the ruffled H2P with H2T(t-Bu)P, the calculated excitation energies of the S1 and T1 states at the S0 geometry increased by 0.07 and 0.09 eV, respectively. Meanwhile, there were more obvious hypsochromic shifts when going from the ruffled H2P to planar H2P, and the amounts of the shifts were 0.17 and 0.20 eV for the S1 and T1 energies at the S0 geometry, respectively. The results clearly showed that the structural distortion in the H2P skeleton was the major origin of the strong bathochromic shift in H2T(t4189



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base porphyins.19,21 In these previous studies, it was pointed out that a spin−orbit promoting normal mode enhances the SOC. In addition, another decay mechanism could be attributed to the crossing from the T1 surface to the S0 surface, such as a conical intersection. To investigate this possibility, the MEISC point was computationally located. The B3LYP SCF solution for the T1 and S0 states was adopted for calculating the potential energy. The basis set of 6-31+G* was employed. Figure 5 shows a schematic diagram of the PES for H2P and H2T(t-Bu)P. In the case of H2P, two S0/T1 MEISC points were obtained. The first point, (S0/T1)meso, was associated with the C−H flip motion at the meso position. The crossing structure was located at 2.52 and 1.15 eV above the minimum energy structure in the singlet (S0min) and triplet (Tmin 1 ) multiplicities, respectively. This C−H flip movement was similar to the prefulvene structure at a conical intersection in benzene.52,53 The second point, (S0/T1)Py, was associated with the Cβ-Cβ bond stretching at a pyrrole ring. The Cβ−Cβ bond elongated to be a single bond (1.53 Å), which was associated with the Cβ−H flip motions (see inset in Figure 5a). This ISC point was suggested by a previous study,19 and it was related to the stretching Cβ−Cβ bond that leads to crossing between the singlet and triplet states at the DFT/MRCI level. The energy of and the ISC point was 3.54 and 2.17 eV above the Smin 0 Tmin 1 energies, respectively, which was qualitatively similar to previous results.19 In the distorted H2T(t-Bu)P case, the ISC was found at only 0.04 eV above the Tmin 1 level. Even though the initial structure mimics the (S0/T1)Py MEISC structure in H2P, the present one was finally obtained. In addition, the molecular structure at the MEISC point was very similar to that at the energy minimum of the T1 state. As shown in Figure 2b, the bond length alternation in the MEISC point resembled that in the T1 structure, suggesting that the electronic structures were also similar to each other. As seen in Figure 2d, the same was true for the

Figure 4. Potential energy curves of H2T(t-Bu)P in the singlet and triplet excited states. The reaction coordinates are defined by the dihedral angles, C4−C5−C6−N4, and the other structural parameters were optimized for the S1 state at the TD-B3LYP/6-31+G** level. Single-point calculations were performed at the optimized geometry with SCC-RICC2/def-SV(P).

the S1 and T2 states can be characterized as combinations of excited configurations within the four orbitals,51 the energies of these states were expected to show similar behavior upon structural perturbations. In previous DFT/MRCI calculations,19 the energies associated with the S1 and T2 states of H2P lie close to each other along N−H stretching and C−C stretching reaction coordinates. With these results, many nonradiative decay channels via ISC could be expected from the S1 to T2 state. After the ISC, H2T(t-Bu)P in the T2 state was expected to relax into the T1 state (Kasha rule). The final step of the decay process, therefore, was expected to involve ISC. However, as seen in Figure 4, the energy level of the T1 state was well separated from that of the S0 state. A possible decay process would be a vibronic SOC as discussed in unsubstituted free-

Figure 5. Potential energy profiles of the singlet and triplet excited states of (a) H2P and (b) H2T(t-Bu)P at the equilibrium and intersystem crossing points. Calculations were performed at the B3LYP/6-31+G** level. 4190



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Single-point CASSCF(6e,6o)/ANO-RCC(3s2p1d) calculations were also performed at the B3LYP optimized structures. As Figure 6b shows, the energy levels of the S0 and T1 states came very close to each other at the C4−C5−C6−N4 angle of 80.0°, which supported the present conclusion. In addition, spin−orbit coupling was evaluated at the CASSI level using the CASSCF(6e, 6d) states. As shown in Figure 6b, the SOCs for the S1 and T2 states and for the S0 and T1 states were not very large, but the magnitudes of the SOCs were comparable with those obtained for unsubstituted free-base porphyrin at distorted structures.19,21 Together with the S0/T1 intersection in the PES, these SOCs indicated the possibility of the ISC at the intersection. 3.6. Electronic Structures of H2P and H2T(t-Bu)P at the MEISC Points. To characterize the electronic structure at MEISC points, the differences in spin density (ρα−ρβ) of H2P and H2T(t-Bu)P in the triplet states were compared. As shown in Figure 7a and b, the results at (S0/T1)Py and (S0/T1)meso

dihedral angle C4−C5−C6−N4, although the MEISC structure had a larger angle (68.8°) than the T1 structure (56.6°). The proximity of Tmin 1 to MEISC suggests that the trajectory coming around the Tmin region could easily access the MEISC point 1 and relax to the ground state. The suggested relaxation pathways, however, were based on the B3LYP description; thus, SCS-RICC2 calculations were also performed to confirm the results. Because the structure of the MEISC point was qualitatively characterized as an analogue of the Tmin structure but with a more distorted C4−C5−C6− 1 N4 bond, the potential surfaces of the T1 state were investigated along several dihedral angles (50, 60, 70, 75, and 80°). The UB3LYP-SCF calculations were performed to optimize the structures at each dihedral angle, and these were followed by the single-point SCS-RICC2 calculations. The calculated potential curves for the low-lying singlet and triplet states are shown in Figure 6a. At 80°, the energies of the

Figure 7. Difference in spin densities of triplet states of H2P at (a) (S0/T1)Py and (b) (S0/T1)meso structures, and that of H2T(t-Bu)P at (c) the S0/T1 structure. Blue and green areas show isodensity surfaces (0.01) dominated by alpha- and beta-spin density, respectively. Numbers denote the Mulliken spin population of a specific atom. (d) Highest singly occupied MO of H2T(t-Bu)P in the triplet state at the S0/T1 structure. Orange broken lines indicate the nodal plane.

Figure 6. Potential energy curves of the singlet and triplet states of H2T(t-Bu)P along the C4−C5−C6−N4 angles. Calculations were performed at the (a) SCC-RICC2/def-SV(P) and (b) CASSCF/ ANO-RCC-VDZP levels. The structure was optimized for the T1 state at each angle. Cross marks denote potential energies at the S0/T1 structure that were optimized at the B3LYP/6-31+G** level. Spin− orbit coupling between the S0 and T1 states and between the S1 and T2 states was obtained with the CASSI method.

were clearly different from each other. At (S0/T1)Py, the Cβ−Cβ elongation introduced sp3 character in the Cβ atoms in the pyrrole units, which caused Cβ−H bond flips toward an out-ofplace direction. Because of this structural deformation, the 2pπ electron at the Cβ atom also rotated and increased the unpaired-electron character. The calculated Mulliken spin populations were 1.03 and 0.43 in the two Cβ atoms. Conversely, at the (S0/T1)meso structure, a large alpha electron population appeared at the Cmeso atom and was involved in the C−H flip motion as shown in Figure 6b. The calculated spin

T1 and S0 states became almost degenerated (at a deviation of 0.05 eV). The potential energy of the T1 state was surprisingly flat, as suggested by the B3LYP result in Figure 5b, and this indicated that there was no energetic barrier to access the MEISC point. The energies of the other singlet and triplet states, including the S0 state, were observed to increase, which showed a peculiarity in the T1 state. 4191



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population was 1.18, which indicated an unpaired-electron character of the 2pπ electron of the Cmeso atom. The C−H flip movement was rationalized by a nodal structure of the highest singly occupied molecular orbital (HSOMO). In order for a triplet state to have the same energy as the singlet closed-shell state, the HSOMO level should be stabilized. In H2P, HSOMO has a node at the C5−C6 and C15−C16 bonds (see Figure 3). To avoid antibonding interactions at the nodes, the C−H units underwent a significant flip motion. In the case of H2T(t-Bu)P, the calculated spin density distribution was similar to that at the (S0/T1)meso structure of the triplet H2P, as seen in Figure 6c. In particular, blue surfaces were distributed on Cmeso atoms with the largest Mulliken population of 0.56. The HSOMO distribution shown in Figure 6d was similar to that of the triplet H2P. The position of the nodal plane was at the C5−C6 and C15−C16 bonds, where dihedral angles significantly deviated from 180°. The HSOMO decreased the unfavorable antibonding interaction by twisting the dihedral angle.

internal conversion should be additionally investigated and compared with the ISC process via the triplet states.

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ASSOCIATED CONTENT

* Supporting Information S

Full bibliographic information for ref 46. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ‡

(F.-Q.B.) State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, 130023, People’s Republic of China. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by KAKENHI (24350008) from the Japan Society for the Promotion of Science (JSPS), JSTCREST, and Strategic Programs for Innovative Research (SPIRE). A portion of the computations was carried out at RCCS (Okazaki, Japan) and ACCMS (Kyoto University).

4. CONCLUSIONS Ruffled porphyrins were observed to decay 100 times more rapidly from electronic excited states, compared to the ordinary planar porphyrins that are often used for photosensitization applications and as a transportation medium for excitation energy transfer in biology and photochemistry. As Nature shows, stabilization of the chemical system against photoirradiation is achieved by introducing a good quencher molecule that can release extra electronic energy to the thermal bath.2,54 In the present study, we studied the PES of a ruffled porphyrin, H2T(t-Bu)P, to understand the rapid nonradiative decay mechanism via ISC. On the basis of the SCS-RICC2 calculation, which is an approximated coupled-cluster method, we investigated the PESs of H2T(t-Bu)P. We observed that the S1 and T2 states were close in energy from the Smin point to a wide range of 1 structures with distortion angles. There should be many chances of ISC between the S1 and T2 surfaces. Regarding the S0/T1 ISC, we located the MEISC point at the B3LYP/631+G** level. The MEISC structure was similar to that of Tmin 1 ; however, it contained more distorted dihedral angles. The T1 surface along the distortion was also observed to be surprisingly flat. The reason for the flatness was interpreted by the nodal structure of HSOMO, in which the distortion helped to avoid destabilization due to the antibonding interactions at the twisting bond. This result indicated that the trajectory, which comes into the T1 surface, could easily reach the ISC point. Calculations with CASSCF were also performed, and similar results were obtained. The CASSI calculations were also performed for evaluating SOCs between the S1−T2 states and between the T1−S0 states. These results indicated that in addition to the vibronic SOC mechanism as has been proposed for the planar porphyrin,19,21 the ISC through the T1−S0 intersection could also be a possible mechanism for the distorted porphyrin case. The excited-state potential surfaces of H2P were also investigated, and two MEISC points were located. In contrast to the H2T(t-Bu)P case, there was a significant energy barrier in the T1 surface to reach the MEISC points. In the present study, the origin of the accelerated nonradiative decay via ISC was investigated. However, H2T(tBu)P also shows fast internal conversion.9 To discuss the entire photochemistry, nonradiative decay process via the S1−S0

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REFERENCES

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Excited States of a Significantly Ruffled Porphyrin: Computational

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