Excited States of a Significantly Ruffled Porphyrin: ComputationalStudy on Structure-Induced Rapid Decay Mechanism via IntersystemCrossingFu-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 signifi-cantly 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 completeactive space self-consistent field method level calculations were performed for the potentialenergy surface (PES) of the low-lying singlet and triplet states of H2T(t-Bu)P. The origin ofthe bathochromic shift in the absorption and fluorescence spectra was attributed to bothsteric distortions of the ring and electronic effects of the substituents. The nonradiativedeactivation 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 veryclose to each other, which suggests that many channels exist for ISC. For the T1 → S0 transition, minimum energy ISC pointswere located, and spin−orbit coupling (SOC) was evaluated. The present results indicate that the ISC can also occur at the T1/S0intersection, in addition to the vibrational SOC promoted by specific normal modes.

1. INTRODUCTION

Nature preserves good quencher molecules such as purine andpyrimidine bases in DNA and RNA,1,2 which exhibit highstability against sunlight irradiation. Nonplanar porphyrins arealso commonly found in biological systems3−5 and, therefore,are often synthesized to gain insights into the mechanismbehind the nonplanar structure.6−10 To acquire photostabilityin artificial systems, a systematic understanding of thequenching mechanism should be explored at an atomicresolution.The out-of-plane macrocycle distortion in a series of

sterically crowded porphyrins results in unusual opticalproperties. 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 porphyrinsreduce the excited-state lifetime by a factor of 200,9,11 whichindicates that the rapid decay can be attributed to not only themetal d−d deactivation but also the excited state of thedistorted porphyrin ring. This raises the possibility that theexcited-state properties of the porphyrin can be adjustedsystematically through the introduction of distortions into thetetrapyrrole skeleton. Therefore, it is important to understandhow the structural distortion is linked with the photochemicaland photophysical properties.In the past decade, there has been significant progress,

particularly in quantitative computational studies on the excitedstates of porphyrins (for example, see refs 12 and 14−20 andreferences therein). To elucidate the excited-state decay via

intersystem crossing (ISC), Marian and co-workers performeddensity functional theory (DFT)/multireference configurationinteraction (MRCI) calculations for an unsubstituted planarfree-base porphyrin and found two possible decay pathwaysfrom the S1 to T1 state.19 It was shown that out-of-planevibrations of the porphyrin ring increase as spin−orbit coupling(SOC) increases.19,21 For ruffled porphyrins, there is somecontroversy in the literature regarding the origin of thebathochromic shift of the Q-band (the lowest-energyabsorption) in the absorption spectrum, as some researchersattribute the shift to the out-of-plane distortion of the ring,22

while others attribute it to the electronic effect ofsubstituents.12 However, we have found no report on theexcited-state potential surface to explain the origin of the fastdeactivation process.In this paper, excited states of a significantly ruffled

porphyrin, meso-tetra-tert-butylporphyrin (H2T(t-Bu)P) arecompared with those of free-base porphyrin (H2P). Inparticular, we focus on the nonradiative decay process ofH2T(t-Bu)P via ISC because the time constant of this processis 200 times smaller than those of normal planar free-baseporphyrins.9 We first investigated the computational perform-ance of several electronic structure methods. Next, wecalculated the vertical and adiabatic excitation energies of

Received: March 7, 2014Revised: May 15, 2014Published: May 19, 2014

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singlet and triplet states of H2T(t-Bu)P, and the results werecompared with available experimental data. The origin of thebathochromic shift was then rationalized by a stepwisemodification of the computational model. Next, we studiedthe potential energy surface (PES) of the ground and excitedstates along the distortion of the porphyrin ring. Minimum-energy intersystem crossing points (MEISC) between T1 andS0 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 thesecomputational data, we propose the nonradiative deactivationpathway via intersystem crossing.

2. COMPUTATIONAL DETAILS

The ground-state equilibrium geometries were computed usingthe Kohn−Sham DFT,23 employing the hybrid functionalB3LYP.24,25 Singlet- and triplet-state equilibrium geometrieswere 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 anunrestricted single determinant using the B3LYP functional.Frequency analysis was carried out at calculated stationarypoints. The basis sets used were the 6-31+G** sets29,30 (6-31Gsets augmented by a single polarization function and diffusefunctions, for the H, C, N, and O atoms). The molecular spatialsymmetry of H2P was D2h at all the stationary points, while thatof 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 electronicstructure methods were compared. In Table 1, the calculatedexcitation energies of the optically allowed π−π* singlet-statesof H2P are compared with experimental data.31 Among theDFT functionals, the B3LYP24,25 and CAM-B3LYP28 wereadopted. For wave function methods, the performance of CIsingles (CIS) and their second-order perturbative correction(CIS(D))32 were examined, in addition to the second-orderapproximated coupled-cluster model with the resolution ofidentity approximation33 (RICC2), spin-component scaledRICC2 (SCS-RICC2),34 and symmetry-adapted cluster-config-uration interaction (SAC-CI) method.35−37 The electronicstructures of these states have been presented in severalprevious publications.14,15,38

The CIS/6-31+G**, CIS(D)/6-31+G**, and RICC2/def-SV(P) calculations were performed using the B3LYP/6-31+G** optimized geometry. The basis sets “def-SV(P)”denote split-valence basis sets with a d-type polarizationfunction. These calculations overestimated experimental datafor the Qx transition by 0.5 eV at the largest case. A previousCC2 study20 showed a similar trend. However, the SCStreatment produced significant improvements. The error in the

SCS-RICC2 result was a systematic overestimation rangingfrom +0.03 to +0.15 eV, and this result was deemed to besatisfactory to investigate the potential energy surface of excitedstates, in terms of accuracy versus computational cost. Aprevious benchmark study also showed that the SCS treatmentimproved the 0−0 excitation energies of π−π* states of organicchromophores.34 The SAC-CI/6-31G* results underestimatedthe transition energy of the Qx and Qy bands but showedreasonable agreements for higher excited states. The TD-CAM-B3LYP/6-31+G** and TD-B3LYP/6-31+G** calculationswere performed at the closed-shell geometry optimized at theCAM-B3LYP/6-31+G** and B3LYP/6-31+G** levels, respec-tively. These DFT results also produced energy levels at areasonable accuracy. The deviations from the experimental datawere small for the low-lying excited states. With thesebenchmark results, we adopted SCS-RICC2 and B3LYP forinvestigating the potential energy surfaces of the nonradiativedecay processes.The ISC point was also explored using a method proposed

by Martinez and co-workers,39 which is originally designed toobtain minimum energy conical intersection (MECI) withoutderivative coupling vectors. In the present study, a programpackage developed by one of the authors was used.40 Theparameter σ was set to values of 35.0 and 10.0 for H2P andH2T(t-Bu)P, respectively. With this setting, the energydifference between the S0 and T1 states was within 0.4 kcal/mol at the converged geometries. Calculations were performedat the B3LYP/6-31+G** level.The TURBOMOLE 6.4 package41 was used for all RICC2

and SCS-RICC2 calculations. Complete active space self-consistent field (CASSCF)42 and CAS state interaction(CASSI)43 calculations were performed using MOLCAS7.4.44,45 The remainder of the calculations were performedusing Gaussian 09 revision C02.46 Molecular orbitals weredrawn using GaussView 5 software.

3. RESULTS AND DISCUSSION

3.1. Geometries of H2P and H2T(t-Bu)P in S0, S1, and T1states. To understand the nonadiabatic decay process ofH2T(t-Bu)P, the excited-state structures were expected toprovide important information. Therefore, the energy mini-mum structures of H2T(t-Bu)P in low-lying singlet and tripletstates were compared.Ground-state equilibrium geometries of H2P and H2T(t-

Bu)P were optimized at the B3LYP/6-31G** level and arepresented in Figure 1. At the calculated energy minimum, H2Pand H2T(t-Bu)P exhibited D2h and C1 symmetry, respectively.The structure of H2T(t-Bu)P was in the so-called ruffledconformation as shown in Figure 1d and e. To avoid stericrepulsion with the tert-butyl group, the neighboring pyrrole

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

SAC-CI

CAM-B3LYP B3LYP level 1 level 3 CIS CIS(D) RICC2 SCS-RICC2 exptlb

2.20 2.26 1.67 1.69 2.39 2.46 2.30 2.13 2.16, Qx(1−0)2.42 2.42 2.06 2.18 2.50 2.61 2.50 2.51 2.56, Qy(1−0)3.55 3.30 3.41 3.41 4.44 4.13 4.38 3.45 3.33, B3.65 3.44 3.57 3.53 4.62 4.45 4.72 3.78 3.65, N4.26 3.79 4.13 4.19 5.23 4.97 5.23 4.38 4.25−4.67, L4.79 4.05 4.68 4.75 5.60 5.30 6.54 4.66

aUnit 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.

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groups had twisted conformations. A previous study8 showedthe possibility of a saddle-shaped conformation in a porphyrinin a more crowded situation. In the H2T(t-Bu)P case, however,the saddle conformation was obtained as a transition state thatwas 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 bondlengths 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, thebond lengths of the S0 and S1 structures were very similar toeach other in both H2P and H2T(t-Bu)P. However, those inthe T1 structure exhibited differences from the singlet states asbond-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 dihedralangles of H2P and H2T(t-Bu)P are also summarized in Figure2c and d. In H2T(t-Bu)P, the C4−C5−C6−N4 angles wereobserved 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 toeach other in both H2P and H2T(t-Bu)P. The triplet statestended to have larger deviations. Because the electronicstructures of triplet states, particularly the T1 state, weredominated by a single configuration (HOMO to LUMOtransition, see Figure 3 and discussion in subsection 3.2), thebonding/antibonding character of these MOs clearly reflectedthe minimum energy structure.3.2. Low-Lying Singlet and Triplet Excited States of

H2P. The singlet and triplet π → π* excited states related tophotoabsorption, fluorescence, and phosphorescence of H2Pare summarized in Table 2. Vertical transition energies at the S0and S1 structures were compared with the peak position ofQx(1−0) in the photoabsorption spectrum and Qx(0−1) in thefluorescence spectrum, respectively. On the basis of theabsorption and emission spectra,9 it is reasonable to assume

that the Qx(1−0) and Qx(0−1) peaks have the largest Franck−Condon overlap in the photo absorption and emissionprocesses, respectively. However, the calculated verticaltransition energies were not a very comparable quantity tothe experimentally observed Qx(1−0) and Qx(0−1) energies.The 0−0 transition energy, Qx(0−0), which is discussed in thenext paragraph and listed in Table 3, was expected to be morereasonably comparable. The vertical excitation energiescalculated by SCS-RICC2 (2.13 eV) and B3LYP (2.26 eV)were close to the experimental Qx(1−0) peak position (2.16 eVin the gas phase). With regard to fluorescence energy, thecalculated vertical transition energy (2.09 eV by SCS-RICC2)overestimated the experimentally obtained energy for theQx(0−1) peak in an EPA (ethyl ether:isopentane:ethanol involume ratio of 5:5:2) solution by 0.27 eV. However, thecalculated Stokes shift of 0.04 eV reasonably agreed with that infree-base tetraphenylporphyrin (0.02 eV).9

In Table 3, the calculated adiabatic transition energies for theS1 (2.10 eV) and T1 states (1.73 eV) are compared with theexperimentally observed Qx(0−0)

31,47 and T(0−0)47 energies.

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). (dand e) The side view of part c along the C10−C20 axis and the N1−N3 axis, respectively.

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 theB3LYP SCF level. For atom indices, see Figure 1.

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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 theS1 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 arrowsalong with their coefficients.

Table 2. Vertical Transition Energies and Main Configurations of the Singlet and Triplet π → π* States of H2P at Energy-Minimum Structuresa

TD-B3LYP/6-31+G** SCS-RICC2/def-SV(P)

state main configurations (|C| > 0.3)b EE(f)d main configurations (|C| > 0.3)b EE(f)c exptl

Photo Absorption at S0 Minimum Structure Optimized with B3LYP/6-31+G**S1 +0.54 (81(5b1u) → 83(4b3g)) 2.26 (<1.0 × 10−5) +0.78 (80(5b1u) → 83(4b3g)) 2.13 (1.67 × 10−3) 2.16e in vapor

+0.46 (80(2au) → 82(4b2g)) +0.58 (81(2au) → 82(4b2g)) 2.18e in CHCl3T1 +0.64 (81(5b1u) → 82(4b2g)) 1.48 +0.93 (80(5b1u) → 82(4b2g)) 1.94

−0.32 (80(2au) → 83(4b3g))Fluorescence at S1 Minimum Structure Optimized with TD-B3LYP/6-31+G**S1 +0.55 (81(5b1u) → 82(4b2g)) 2.23 (1.10 × 10−3) +0.78 (80(5b1u) → 83(4b3g)) 2.09 (2.09 × 10−4) 1.83f in EPA

+0.44 (80(2au) → 83(4b3g)) −0.62 (81(2au) → 82(4b2g))Phosphorescence at T1 Minimum Structure Optimized with TD-B3LYP/6-31+G**T1 +0.71 (81(5b1u) → 82(4b2g)) 1.12 +0.97 (80(5b1u) → 82(4b2g)) 1.55Phosphorescence at T1 Minimum Structure Optimized with B3LYP/6-31+G**T1 81 (5b1u) → 82(4b2g) (SCF

d) 1.54 +0.97 (80(5b1u) → 82(4b2g)) 1.57

aUnits are in eV. bMO indices are shown with number. HOMO and LUMO are 81 and 82, respectively. cExcitation energy. Number in parenthesesis oscillator strength in au. dT1 state was obtained as B3LYP/6-31+G** SCF solution. eQx(1−0) peak31 in the absorption spectrum; fQx(0−1) peakin the fluorescence spectrum.47 EPA denotes a mixed solvent (ethyl ether:isopentane:ethanol in a volume ratio of 5:5: 2).

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The adiabatic energies were approximated by the potentialenergy differences between the S0 and S1 minima and betweenthe S0 and T1 minima. We note that the zero point energycorrections were not included. The results showed that thecalculation reproduced the experimental values with anacceptable deviation of approximately 0.1 eV. A previousDFT/MRCI calculation19 also gave an acceptable agreement(1.61 eV) with the experiment.Wave functions of the excited states are also summarized in

Table 2. The main configurations are also illustrated in Figure3, together with the molecular orbital energy levels. The S1 statewas dominated by two main configurations within theGouterman’s four orbitals, comprising the highest occupiedmolecular orbital (HOMO), next HOMO, lowest unoccupiedMO (LUMO), and next LUMO. The present resultsreproduced the traditional picture.48 On the other hand, theT1 state was dominated by a single configuration. Excitationsobtained with TD-B3LYP were very similar to those in SCS-RICC2.Regarding the phosphorescence energy, the vertical

phosphorescence energy calculated with TD-B3LYP was 0.43eV smaller than the value calculated by SCS-RICC2. Since theelectronic wave function obtained with SCS-RICC2 wasdominated by a single configuration, the unrestricted B3LYPSCF (UB3LYP-SCF) solution was examined for calculating thestructure and phosphorescence energy. This approach signifi-

cantly improved the underestimation of the phosphorescenceenergy, and the result (1.54 eV) was in close agreement withthe SCS-RICC2 one (1.57 eV). The fine performance of theB3LYP SCF was also reported in previous reports.17 The failurein the TD approach could be due to the calculated energyrelative to the singlet state. A similar amount of under-estimation (by 0.46 eV compared with SCS-RICC2) wasobserved when calculating the excitation energy of the T1 stateat the S0 geometry. Because optimized structures by the TDand SCF approaches were not significantly different, the SCS-RICC2 phosphorescence energy with the two structures was1.55 and 1.57 eV, respectively. With this result, the potentialenergy calculated by UB3LYP-SCF was expected to produce asemiquantitative agreement with the SCS-RICC2 one.

3.3. Low-Lying Singlet and Triplet Excited States ofH2T(t-Bu)P. The calculated vertical transition energies of thesinglet and triplet π→π* excited states of H2T(t-Bu)P atminimum energy structures are summarized in Table 4. Theexperimentally reported Qx(1−0) energy in the absorptionspectrum and the Qx(0−1) energy in the fluorescence spectrumwere used as the reference values to compare the calculatedvertical absorption energy and vertical fluorescence energy,respectively. On the basis of the absorption and emissionspectra,9 it is reasonable to assume that the Qx(1−0) andQx(0−1) peaks have the largest Franck−Condon overlap in thephoto absorption and emission processes, respectively. In Table3, the calculated adiabatic transition energies for the S1 and T1states are compared with the experimental Qx(0−0) and T(0−0) energies, respectively, which are a better measure to assessthe reliability of the calculation.With the SCS-RICC2 calculations, the calculated vertical

excitation (1.89 eV) and fluorescence (1.81 eV) energies of theS1 state were in reasonable agreement with the experimentalQx(1−0) (1.95 eV) and Qx(0−1) (1.76 eV) energies,respectively. As shown in Table 3, the calculated adiabatictransition energy of the S1 state (1.82 eV) agreed very well withthe experimental Qx(1−0) energy (1.76−1.78 eV).Table 4 also shows the main configurations in the wave

functions. Similar to the H2P case, the S1 state could bedescribed within the four-orbital model. Because the molecularsymmetry was reduced to the C1 symmetry, all four

Table 3. Adiabatic Excitation Energies of H2P and H2T(t-Bu)P Calculated with the SCS-RICC2 Method

H2P H2T(t-Bu)P

state calc exptl calc exptl

S1 2.10 1.98a 1.82 1.78e

2.02b 1.76f

2.03c

T1 1.73 1.58d 1.07aQx(0−0)

31 in gas phase. bQx(0−0)31 in CH2Cl2.

cQx(0−0)47 in EPA.

EPA is a mixed solvent (ethyl ether:isopentane:ethanol in a volumeratio of 5:5:2). dQx(0−0)47 in EPA:EtI. EPA:EtI denotes a mixedsolvent EPA:EtI = 1:1. EtI is ethyl iodide. eQx(0−0) peak.9 fIn theabsorption spectrum; Qx(0−0)9 peak in fluorescence spectrum.

Table 4. Vertical Transition Energies and Main Configurations of the Singlet and Triplet π → π* States of H2T(t-Bu)P atEnergy-Minimum Structuresa

TD-B3LYP/6-31+G** SCS-RICC2/def-SV(P)

state main configurations (|C| > 0.3)b EE(f)c main configurations (|C| > 0.3)b EE(f)c exptl

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) 1.89 1.95e

−0.32 (144 → 147) (9.30 × 10−3) +0.52 (144 → 147) + 0.44 (145 → 146) (1.22 × 10−3)T1 +0.50 (145 → 146) − 0.45 (145 → 147) 1.13 +0.83 (144 → 146) − 0.45 (144 → 147) 1.65

+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) 1.81 (4.68 × 10−3) 1.76f

−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) 0.49Phosphorescence 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) 0.74

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

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configurations were mixed with similar coefficients. Theelectronic structure of the T1 state was also dominated by asingle configuration, as in the H2P case. However, thesymmetry-lowering introduced some configuration mixing tothe main configurations.The problem of applying TD-B3LYP to calculate the T1

energy became more prominent. As shown in Table 4, TD-B3LYP produced negative phosphorescence energy at the T1

optimized structure, as the lowest triplet state was calculated tobe lower than the S0 state by 0.54 eV. Again, the SCF solutionfor the T1 state produced a better result (0.39 eV), which wasmuch closer to that of the SCS-RICC2 solution. Because thedeviation in the SCS-RICC2 result with the TD and SCFstructures was 0.25 eV, we could conclude that the TD-B3LYPcalculation also introduced some error in the optimizedgeometry, in addition to the relative energy between S0 andT1 states.To summarize, we observed that SCS-RICC2 produced a

quantitative agreement with the experimental spectroscopicdata on the potential surfaces of the S0, S1, and T1 states. TheTD-B3LYP calculation was applicable to the S0 and S1 surfaces,but not to the T1 one. Instead, UB3LYP-SCF reproduced theSCS-RICC2 potential surface of the T1 state with semi-quantitative accuracy.3.4. Effect of Distortion in the H2P Skeleton on the

Excitation Energies of H2T(t-Bu)P. The origin of thesignificant low-energy shift in the calculated energy levels ofH2T(t-Bu)P in the low-lying singlet and triplet states wasinvestigated. The strategy employed here was to adopt adistorted H2P skeleton.12,49,50 The tert-butyl groups at the mesopositions of the ruffled H2T(t-Bu)P were replaced by hydrogenatoms to obtain H2P in the H2T(t-Bu)P geometry. TheC(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 statesare summarized in Table 5, together with the results of H2Pand H2T(t-Bu)P. Comparing the result of the ruffled H2P withH2T(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 hypsochro-mic shifts when going from the ruffled H2P to planar H2P, andthe amounts of the shifts were 0.17 and 0.20 eV for the S1 andT1 energies at the S0 geometry, respectively. The results clearlyshowed that the structural distortion in the H2P skeleton wasthe major origin of the strong bathochromic shift in H2T(t-

Bu)P. The electronic effect of tert-butyl groups produced asecondary contribution but was not negligible.This result was comparable with that in β-trifluoromethyl-

porphycene in our previous study,50 in which trifluoromethylgroups at the β-carbons of pyrrole rings introduced structuraldistortion into the porphycene skeleton and caused ahypsochromic shift in the absorption spectrum. The electroniceffect of the trifluoromethyl groups was secondary but was notnegligible. The present result also agreed with the resultsobtained by Parusel and co-workers,22 in which ruffling andsaddling resulted in a bathochromic shift. Although DiMagnoand co-workers12 concluded that the ruffling effect caused anegligible shift; in a free-base porphyrin with CH3 groups at themeso position, the calculated bathochromic shift (0.19 eV) wasinterpreted by the substituent effect (0.17 eV).12 However, thebalance between the ruffling and electronic effects seemed todepend on the system. In their result for a free-base porphyrinwith CF3 groups at the meso position, the ruffling andelectronic 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 wasobserved for the calculated excitation energy of the T1 state atthe T1 geometry. The relative energy difference between the T1and S0 states appeared to be much more sensitive to thedistortion. This result indicated that the nonplanar distortioncould be relevant to the nonradiative decay via ISC.

3.5. On the Nonradiative Relaxation Pathway of H2T(t-Bu)P. To understand the nonradiative relaxation pathway inthe excited state of H2T(t-Bu)P, the potential energy curves ofthe singlet and triplet states were investigated at the SCS-RICC2 level. On the basis of the Kasha rule, it was assumedthat H2T(t-Bu)P was in the S1 state after relaxation from high-lying singlet excited states. Because the dihedral angle C4−C5−C6−N4 and its symmetric counterpart C14−C15−C16−N2were the most prominent structural variables that characterizethe structural change in the excited states (see Figure 2d), thestructure of the H2T(t-Bu)P in the S1 state was optimized atseveral C4−C5−C6−N4 angles (20, 40, 60, and 80°), and thesingle-point SCS-RICC2 calculations for the low-lying singletand 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 energyof the S1 state monotonically increased when the angleincreased. Figure 4 clearly shows that the energies of the S1and T2 states were close to each other in their energy levels,even at the energy minimum of the S1 state. Because both of

Table 5. Photoabsorption, Fluorescence, and Phosphorescence Energies and Related π → π* States of Distorted H2P with aPorphyrin Skeleton Geometry Taken from H2T(t-Bu)P

a

distorted H2P (skeleton taken from H2T(t-Bu)P) H2T(t-Bu)P H2P

state main configurations (|C| > 0.3)b EE(f) EE(f) 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) 1.89 (1.22 × 10−3) 2.13 (1.67 × 10−3)

T1 +0.90 (80 → 82) 1.74 1.65 1.94Fluorescence 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) 1.81 (4.68 × 10−3) 2.09 (2.09 × 10−4)Phosphorescence at the T1 Minimum Structure Optimized with TD-B3LYP/6-31+G**T1 0.95 (81 → 82) 0.50 0.49 1.55Phosphorescence at the T1 Minimum Structure Optimized with B3LYP/6-31+G**T1 0.94 (81 → 82) 0.76 0.74 1.57

aCalculations were performed using SCS-RICC2/def-SV(P). Units are in eV. bMO indices are shown with number. HOMO and LUMO are 81 and82, respectively. cExcitation energy. Number in parentheses is oscillator strength in au.

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the S1 and T2 states can be characterized as combinations ofexcited configurations within the four orbitals,51 the energies ofthese states were expected to show similar behavior uponstructural perturbations. In previous DFT/MRCI calculations,19

the energies associated with the S1 and T2 states of H2P lieclose to each other along N−H stretching and C−C stretchingreaction coordinates. With these results, many nonradiativedecay channels via ISC could be expected from the S1 to T2state.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 decayprocess, therefore, was expected to involve ISC. However, asseen in Figure 4, the energy level of the T1 state was wellseparated from that of the S0 state. A possible decay processwould be a vibronic SOC as discussed in unsubstituted free-

base porphyins.19,21 In these previous studies, it was pointedout that a spin−orbit promoting normal mode enhances theSOC.In addition, another decay mechanism could be attributed to

the crossing from the T1 surface to the S0 surface, such as aconical intersection. To investigate this possibility, the MEISCpoint was computationally located. The B3LYP SCF solutionfor the T1 and S0 states was adopted for calculating thepotential 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 pointswere obtained. The first point, (S0/T1)

meso, was associated withthe C−H flip motion at the meso position. The crossingstructure was located at 2.52 and 1.15 eV above the minimumenergy structure in the singlet (S0

min) and triplet (T1min)

multiplicities, respectively. This C−H flip movement wassimilar to the prefulvene structure at a conical intersection inbenzene.52,53 The second point, (S0/T1)

Py, was associated withthe Cβ-Cβ bond stretching at a pyrrole ring. The Cβ−Cβ bondelongated to be a single bond (1.53 Å), which was associatedwith the Cβ−H flip motions (see inset in Figure 5a). This ISCpoint was suggested by a previous study,19 and it was related tothe stretching Cβ−Cβ bond that leads to crossing between thesinglet and triplet states at the DFT/MRCI level. The energy ofthe ISC point was 3.54 and 2.17 eV above the S0

min andT1minenergies, respectively, which was qualitatively similar to

previous results.19

In the distorted H2T(t-Bu)P case, the ISC was found at only0.04 eV above the T1

min level. Even though the initial structuremimics the (S0/T1)

Py MEISC structure in H2P, the present onewas finally obtained. In addition, the molecular structure at theMEISC point was very similar to that at the energy minimum ofthe T1 state. As shown in Figure 2b, the bond length alternationin the MEISC point resembled that in the T1 structure,suggesting that the electronic structures were also similar toeach 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 andtriplet excited states. The reaction coordinates are defined by thedihedral angles, C4−C5−C6−N4, and the other structural parameterswere optimized for the S1 state at the TD-B3LYP/6-31+G** level.Single-point calculations were performed at the optimized geometrywith SCC-RICC2/def-SV(P).

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 intersystemcrossing points. Calculations were performed at the B3LYP/6-31+G** level.

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dihedral angle C4−C5−C6−N4, although the MEISC structurehad a larger angle (68.8°) than the T1 structure (56.6°). Theproximity of T1

min to MEISC suggests that the trajectory comingaround the T1

min region could easily access the MEISC pointand relax to the ground state.The suggested relaxation pathways, however, were based on

the B3LYP description; thus, SCS-RICC2 calculations werealso performed to confirm the results. Because the structure ofthe MEISC point was qualitatively characterized as an analogueof the T1

min structure but with a more distorted C4−C5−C6−N4 bond, the potential surfaces of the T1 state wereinvestigated along several dihedral angles (50, 60, 70, 75, and80°). The UB3LYP-SCF calculations were performed tooptimize the structures at each dihedral angle, and these werefollowed 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

T1 and S0 states became almost degenerated (at a deviation of0.05 eV). The potential energy of the T1 state was surprisinglyflat, as suggested by the B3LYP result in Figure 5b, and thisindicated that there was no energetic barrier to access theMEISC point. The energies of the other singlet and tripletstates, including the S0 state, were observed to increase, whichshowed a peculiarity in the T1 state.

Single-point CASSCF(6e,6o)/ANO-RCC(3s2p1d) calcula-tions were also performed at the B3LYP optimized structures.As Figure 6b shows, the energy levels of the S0 and T1 statescame very close to each other at the C4−C5−C6−N4 angle of80.0°, which supported the present conclusion. In addition,spin−orbit coupling was evaluated at the CASSI level using theCASSCF(6e, 6d) states. As shown in Figure 6b, the SOCs forthe S1 and T2 states and for the S0 and T1 states were not verylarge, but the magnitudes of the SOCs were comparable withthose obtained for unsubstituted free-base porphyrin atdistorted structures.19,21 Together with the S0/T1 intersectionin the PES, these SOCs indicated the possibility of the ISC atthe intersection.

3.6. Electronic Structures of H2P and H2T(t-Bu)P at theMEISC Points. To characterize the electronic structure atMEISC points, the differences in spin density (ρα−ρβ) of H2Pand H2T(t-Bu)P in the triplet states were compared. As shownin Figure 7a and b, the results at (S0/T1)

Py and (S0/T1)meso

were clearly different from each other. At (S0/T1)Py, the Cβ−Cβ

elongation introduced sp3 character in the Cβ atoms in thepyrrole units, which caused Cβ−H bond flips toward an out-of-place direction. Because of this structural deformation, the 2pπelectron at the Cβ atom also rotated and increased theunpaired-electron character. The calculated Mulliken spinpopulations were 1.03 and 0.43 in the two Cβ atoms.Conversely, at the (S0/T1)

meso structure, a large alpha electronpopulation appeared at the Cmeso atom and was involved in theC−H flip motion as shown in Figure 6b. The calculated spin

Figure 6. Potential energy curves of the singlet and triplet states ofH2T(t-Bu)P along the C4−C5−C6−N4 angles. Calculations wereperformed at the (a) SCC-RICC2/def-SV(P) and (b) CASSCF/ANO-RCC-VDZP levels. The structure was optimized for the T1 stateat each angle. Cross marks denote potential energies at the S0/T1structure that were optimized at the B3LYP/6-31+G** level. Spin−orbit coupling between the S0 and T1 states and between the S1 and T2states was obtained with the CASSI method.

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 atthe S0/T1 structure. Orange broken lines indicate the nodal plane.

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population was 1.18, which indicated an unpaired-electroncharacter of the 2pπ electron of the Cmeso atom. The C−H flipmovement was rationalized by a nodal structure of the highestsingly occupied molecular orbital (HSOMO). In order for atriplet state to have the same energy as the singlet closed-shellstate, the HSOMO level should be stabilized. In H2P, HSOMOhas a node at the C5−C6 and C15−C16 bonds (see Figure 3). Toavoid antibonding interactions at the nodes, the C−H unitsunderwent 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 surfaceswere distributed on Cmeso atoms with the largest Mullikenpopulation of 0.56. The HSOMO distribution shown in Figure6d was similar to that of the triplet H2P. The position of thenodal plane was at the C5−C6 and C15−C16 bonds, wheredihedral angles significantly deviated from 180°. The HSOMOdecreased the unfavorable antibonding interaction by twistingthe dihedral angle.

4. CONCLUSIONSRuffled porphyrins were observed to decay 100 times morerapidly from electronic excited states, compared to the ordinaryplanar porphyrins that are often used for photosensitizationapplications and as a transportation medium for excitationenergy transfer in biology and photochemistry. As Natureshows, stabilization of the chemical system against photo-irradiation is achieved by introducing a good quenchermolecule that can release extra electronic energy to the thermalbath.2,54 In the present study, we studied the PES of a ruffledporphyrin, H2T(t-Bu)P, to understand the rapid nonradiativedecay mechanism via ISC.On the basis of the SCS-RICC2 calculation, which is an

approximated coupled-cluster method, we investigated thePESs of H2T(t-Bu)P. We observed that the S1 and T2 stateswere close in energy from the S1

min point to a wide range ofstructures with distortion angles. There should be manychances of ISC between the S1 and T2 surfaces. Regardingthe S0/T1 ISC, we located the MEISC point at the B3LYP/6-31+G** level. The MEISC structure was similar to that of T1

min;however, it contained more distorted dihedral angles. The T1surface along the distortion was also observed to be surprisinglyflat. The reason for the flatness was interpreted by the nodalstructure of HSOMO, in which the distortion helped to avoiddestabilization due to the antibonding interactions at thetwisting bond. This result indicated that the trajectory, whichcomes into the T1 surface, could easily reach the ISC point.Calculations with CASSCF were also performed, and similarresults were obtained. The CASSI calculations were alsoperformed for evaluating SOCs between the S1−T2 states andbetween the T1−S0 states. These results indicated that inaddition to the vibronic SOC mechanism as has been proposedfor the planar porphyrin,19,21 the ISC through the T1−S0intersection could also be a possible mechanism for thedistorted porphyrin case. The excited-state potential surfaces ofH2P were also investigated, and two MEISC points werelocated. In contrast to the H2T(t-Bu)P case, there was asignificant energy barrier in the T1 surface to reach the MEISCpoints.In the present study, the origin of the accelerated

nonradiative decay via ISC was investigated. However, H2T(t-Bu)P also shows fast internal conversion.9 To discuss the entirephotochemistry, nonradiative decay process via the S1−S0

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

■ ASSOCIATED CONTENT*S Supporting InformationFull bibliographic information for ref 46. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: hasegawa@cat.hokudai.ac.jp.Present Address‡(F.-Q.B.) State Key Laboratory of Theoretical and Computa-tional Chemistry, Institute of Theoretical Chemistry, JilinUniversity, Changchun, 130023, People’s Republic of China.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis study was supported by KAKENHI (24350008) from theJapan Society for the Promotion of Science (JSPS), JST-CREST, and Strategic Programs for Innovative Research(SPIRE). A portion of the computations was carried out atRCCS (Okazaki, Japan) and ACCMS (Kyoto University).

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