Theoretical Study of Topographical Features around the Conical

Apr 4, 2013 - Another CIX reported at the present time (CIX2) exclusively goes back to .... orbital) ascribable to the ethylenic π and π* characters...
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Theoretical Study of Topographical Features around the Conical Intersections of Fluorene-Based Light-Driven Molecular Rotary Motor Yoshiaki Amatatsu* Faculty of Engineering and Resource Science, Akita University, Tegata Gakuen-cho, Akita 010-8502, Japan S Supporting Information *

ABSTRACT: Topographical features around the conical intersection (CIX) of a fluorene-based light-driven molecular rotary motor have been examined by means of ab initio molecular orbital calculations. The model molecule is a derivative of 9-(2-phenyl-2-cyclopenten-1-ylidene)-9H-fluorene (PCPF) where PCPF is bridged by a pentamethylene chain between the 2 position of the phenyl group and the pseudoaxial position of the C5 atom in the 2-cyclopenten-1ylidene ring. This model molecule (denoted by M5-PCPF) has been very recently reported as a candidate for a light-driven molecular motor with constant rotation. The conical intersection for the photoprocess of the ethylenic CC torsion reported there (denoted by CIX1), which exclusively leads to a product of P′M5-PCPF, is found to be classified as a sloped-type CIX. Another CIX reported at the present time (CIX2) exclusively goes back to a reactant of P-M5-PCPF, whereas CIX2 is also classified as a sloped-type CIX. At the stable geometry in S1 around the CIX region (S1-geometry), the 2-cyclopenten-1-ylidene rotor takes a perpendicular twist against the fluorene stator, but the fluorene stator does not wag so much against the CC rotary axis. The wagging motions of the fluorene stator from S1-geometry to the opposite directions lead to CIX1 and CIX2, respectively. very preliminary level as a nanomachine.17−20 The molecular car cannot always control a scrawling motion on a metal surface by external stimuli.19 In conventional light-driven molecular motors, two factors have been considered in molecular modeling. One is a rigid and overcrowded rotor which induces helicity by steric repulsion with the stator. The other is a stereogenic center in the rotor which discriminates between two helical isomers and controls unidirectional rotation from a metastable helical isomer into a stable one. In our modeling, we discarded the former factor and designed a model molecule to interchange helicity by a floppy internal motion in the rotor part, such as a phenyl torsion. An actual model molecule is 9-(5-methyl-2-phenyl-2-cyclopenten1-ylidene)-9H-fluorene (denoted by MPCPF).21 By means of ab initio molecular orbital (MO) calculations, we found that MPCPF has helicity due to steric repulsion between the phenyl group and the fluorene stator, and in addition, the helical interchange from a metastable M-isomer into a stable P-isomer takes place with a much lower energy barrier (∼1.4 kcal/mol) due to a floppy phenyl torsion. Unfortunately, however, MPCPF also has a disadvantage that the energy difference between the two helical isomers are very small (∼1.6 kcal/ mol). In other words, a photoprocess of backward rotation from the M-helical isomer cannot be suppressed effectively because of a fast equilibration between the two helical isomers.

1. INTRODUCTION A light-driven molecular rotary motor is a molecular device which transforms photon energy into internal rotational motion and then transmits it to another part of a molecular machine. Photoisomerization around the CC double bond of ethylenoids is a suitable photoreaction for a light-driven rotary motor, if the following two conditions are satisfied: unidirectionality and constancy of the CC rotation. Unidirectionality in the photoisomerization of ethylenoids was first realized in symmetrical overcrowded biphenanthrylidene with helicity.1 However, the overcrowded ethylenoid seriously prevents thermal conversion from a metastable Mhelical isomer into a stable P-helical one, which follows extremely fast photochemical conversion from a stable P-helical isomer into a metastable M-helical one. In other words, the overcrowded ethylenoid with helicity realized unidirectional rotation but also causes a terrible disadvantage about constant rotation. Since then, much effort has been made to improve the rate of thermal helical conversion by reducing the steric repulsion between the overcrowded substituents experimentally2−11 and theoretically.12−16 So far helical inversions take place with a half-lifetime of 70 ms for the fluorene-based molecular motor10 and of 574 ns for the acridane-based molecular motor,8 respectively. Considering that the photochemical conversion takes place at most within a few picoseconds, however, constant speed in unidirectional rotation has not been realized yet. Due to a lack of effective molecular rotary motor, for instance, a molecular car which is a composite of light-driven molecular rotary motors, axles, and wheels is at a © 2013 American Chemical Society

Received: February 20, 2013 Revised: April 4, 2013 Published: April 4, 2013 3689

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ize topography in the CIX region. On the basis of the topographical features in the CIX region, we give a picture on the photochemistry of M5-PCPF which is more elaborate than the previous one.22

In order to overcome the defect of MPCPF for a light-driven molecular rotary motor, we chemically modified MPCPF into its analogue (M5-PCPF) by a bridge of pentamethylene chain between the 2 position of the phenyl group (i.e., C7′ atom in Figure 1) and the pseudoaxial position of the C5′ atom in the 2-

2. METHOD OF CALCULATIONS In our previous paper, we confirmed how much the computational results are affected by wave functions and basis sets.22 Thereby, a computational strategy described below is enough to pinpoint the photochemistry of M5-PCPF. That is, we adopted two electrons in two orbitals complete active space self-consistent field (CASSCF) (denoted by (2,2)CASSCF) method. This is because the potential energy surfaces in the CIX region are well described by the HOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupied molecular orbital) ascribable to the ethylenic π and π* characters respectively. A two-state-averaged (2,2)CASSCF (SA2-(2,2)CASSCF) where the two density matrices of S0 and S1 are weighted equally was adopted in order to scan the potential energy surfaces in the CIX region because of the closeness of S1 and S0 surfaces, except for the case that an S0specific (2,2)CASSCF was adopted in following the IRC in S0. In some cases, we further validated (2,2)CASSCF approach in comparison with a larger (6,6)CASSCF one. Concerning the basis sets, a Huzinaga-Duunning double-ζ quality augmented by polarizations (DZP) (αd = 0.75 for C atoms) was applied to the five-membered rings in the stator and rotor (i.e., C9, C9a, C 4a , C 4b , C 8a , and C 1′ to C 5 ′), considering that the hybridizations of these atoms are sp2 or sp3, strongly dependent on the torsional motion around the C9C1′ axis. Thereby, the spatial flexibility of the electronic population is ensured. On the other hand, the hybridizations of the remaining skeletal C atoms are almost unchanged irrespective of the conformations. Therefore, the C and H atoms except for the C atoms in the five-membered rings of the stator and rotor are applied to a minimal basis set (so-called MINI). In the present ab initio MO calculations including determination of CIXs, we used GAMESS program.23 In addition, we changed the definitions of ω and ω′ in a simpler form (see Figure 2), although the discussion remains unchanged.

Figure 1. Labeling of atoms of M5-PCPF. Labeling of the C atoms of the pentamethylene chain colored in red is presented in the lower panel.

cyclopenten-1-yliene (note; we call it 2-cyclopentenylidene hereafter for convenience).22 Thereby, we found that M5PCPF no longer takes a metastable M-helical isomer and directly goes to a stable P-helical isomer after relaxation at the conical intersection (CIX). This implies that M5-PCPF is a promising candidate for a light-driven molecular rotary motor with constant speed. From a computational viewpoint, however, the photochemistry of M5-PCPF should be further examined whether M5-PCPF works as a light-driven molecular rotary motor. The issues of the photochemical behavior coming out of our previous study22 are summarized as follows. (IS1) M5-PCPF possibly takes many conformations arising from flexibility of the pentamethylene chain as well as the 2cyclopentenylidene ring. So a question is whether the photochemical behavior depends on a conformation of the pentamethylene chain, although we partly mentioned it previously. (IS2) Is only the bright state of the ethylenic ππ* excitation enough to discuss the photochemistry? Or does the dark state assignable to the π(fluorene)π*(ethylene) excitation play an important role around the CIX region? These questions were also answered partly in our previous paper but might not be necessarily enough. (IS3) The CIX reported previously (denoted by CIX1 hereafter) is exclusively connected with the P′-helical region in S0 without any local minimum around the M′-helical region. In other words, once M5-PCPF relaxes into S0 at CIX1, only the forward reaction takes place. So a question is whether the backward reaction to P-M5-PCPF never takes place from CIX1. Otherwise, is there another CIX (CIX2) leading back to P-M5PCPF? In the present paper, we focus our interest on IS3. In relation with our main interest, we also make a little comment on IS2. In the next section, we describe a computational strategy to examine the model molecule of M5-PCPF. In section 3, we first make comments on the key geometries in the CIX region. Then we analyze the intrinsic reaction coordinate (IRC) in S0 staring from a CIX newly located (denoted by CIX2) to clarify a role of CIX2 in the photochemical behavior. In addition, the relationship between CIX1 and CIX2 is examined to character-

3. RESULTS AND DISCUSSIONS 3-1. Key Geometries in the CIX Region. We first tried to perform an S1-optimization from CIX1 by SA2-(2,2)CASSCF.

Figure 2. Definitions of τ, ω, and ω′. Numberings of atoms are same as those in Figure 1. Vectors of r(C9Xo) and r(C1′Yo) are outer products of r(C9C9a) × r(C9C8a) and r(C1′C5′) × r(C1′C2′), respectively. In the case of a negative value of τ, τ is replaced by a value of τ + 360°. Thereby τ is a parameter representing a unidirectional rotation from 0° to 360°. The definitions of ω and ω′ are changed to be simpler than the previous ones in ref 22. The values of (1/2π + ω) and (1/2π + ω′) are determined by the angles of r(C9Xo) and r(C9C1′) and r(C1′Yo) and r(C1′C9), respectively. 3690

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Table 1. Characteristic Optimized Parameters at Key Geometries of M5-PCPF geometry C9C1′ τb φ(C9C1′C2′C6′) ϕ(C1′C2′C6′C7′) C1′C2′C3′C4′ C2′C3′C4′C5′ CeC5′C4′C3′ H5′C5′C4′C3′ C2′C6′C7′Ca C6′C7′CaCb C7′CaCbCc CaCbCcCd CbCcCdCe CcCdCeC5′ CdCeC5′C4′ ωb ω′b a

P-M5-PCPFa 1.364 10.8 30.3 53.9 −2.0 −15.7 −100.1 141.4 2.8 78.7 −141.7 91.5 −98.2 104.9 42.6 −2.9(−3.2) 4.0(5.2)

CIX1a 1.419 67.0 28.6 67.0 2.9 −17.3 −95.6 140.1 −2.3 80.2 −149.7 85.3 −83.1 111.8 23.1 −51.2(−58.5) 5.2(6.8)

S1-geometry

CIX2

P′-M5-PCPFa

Bond Distances (Å) 1.430 1.419 1.364 Dihedral Angles (degree) 85.7 103.7 191.1 20.9 17.0 30.4 67.6 65.7 54.1 −5.4 −10.3 −2.0 −7.9 −5.7 −15.8 −103.8 −99.4 −100.0 133.7 138.2 141.5 −3.3 −1.1 2.9 70.4 73.0 78.7 −142.9 −140.4 −142.0 102.2 96.0 91.3 −95.3 −98.5 −97.6 98.1 104.6 105.1 41.0 41.3 42.1 Wagging Angles (degree) 17.1(20.0) 55.9(60.2) 3.3(3.6) 8.3(8.4) 6.8(7.2) 4.0(5.2)

CIX1′a

S1′-geometry

CIX2′

1.422

1.430

1.428

246.6 25.8 69.4 1.1 −15.4 −94.9 140.0 −2.6 78.1 −148.3 87.8 −83.8 111.7 22.2 52.5(58.9) 5.0(7.0)

265.6 20.7 67.7 −5.4 −7.8 −103.8 133.7 −3.3 70.1 −143.0 102.4 −95.0 98.0 40.9

285.1 21.3 68.3 −10.7 −7.9 −96.4 140.3 −0.5 76.8 −143.0 88.7 −92.8 112.0 33.0

−16.6(−19.5) 8.2(8.3)

−58.4(−62.4) 6.0(6.3)

The optimized parameters are taken from ref 22. bFor comparison, ω and ω′ by previous definitions are given in the parentheses.

Thereby, we obtained a stable geometry in S1 (S1-geometry) in the highly τ-twisted region. As seen in Table 1, the 2cyclopentenylidene rotor at S1-geometry is almost perpendicularly twisted against the fluorene stator (τ = 85.7°) but the fluorene stator wags a little against the C9C1′ rotary axis (ω = 17.1°). We further confirmed that a larger SA2-(6,6)CASSCF optimization of S1 leads to a geometry similar to S1-geometry by SA2-(2,2)CASSCF. This means that the spectroscopically bright state with ethylenic ππ* character in the Franck− Condon region diabatically correlates to the S1 state in the perpendicularly τ-twisted region, as commented previously.22 Therefore, our computational strategy of (2,2)CASSCF pinpoints enough to describe the photochemistry of M5-PCPF. Then we mention a topographical feature around CIX1. Figure 3a shows the potential energy surfaces of S0 and S1 as a function of τ, which are evaluated by SA2-(2,2)CASSCF along the IRC previously reported (IRC < 5 amu1/2Bohr). Thereby, it is found that the S0 state is quickly stabilized by an increase of τ. In Figure 3b, it can be seen that the fluorene stator recovers from a highly wagged position against the C9C1′ rotary axis in accord with increase of τ (note: the definitions of ω and ω′ depicted in Figure 2 are changed to be simpler than the previous ones and therefore the values are slightly different from the previous ones, although the discussion remains unchanged). Contrary to a drastic stabilization of the S0 state with respect to τ, the S1 state is stabilized a little but two surfaces are found to cross each other at CIX1 as is the case of a so-called sloped-type surface crossing.24 This validates that CIX1 serves M5-PCPF to be exclusively forwarded to a product of P′-M5-PCPF. Here we have a question about whether electronically excited P-M5-PCPF never goes back to P-M5PCPF in S0 through a CIX and exclusively goes to P′-M5-PCPF through CIX1. So we tried to search another CIX in the region with a highly τ-twisted value. Thereby, we found another CIX (CIX2) listed in Table 1. The difference between CIX1 and CIX2 is characterized as τ and ω. Figure 4 is helpful to understand the difference of these geometrical features as well as that of S1-geometry. At both CIX1 and CIX2, the fluorene

Figure 3. (a) Potential energy surfaces of S1 (in solid line) and S0 (in dashed line) with respect to τ in the CIX1 region. The geometries are taken from the region of IRC < 5 amu1/2Bohr in ref 22. The energies are relative to that in S0 by SA2-(2,2)CASSCF at P-M5-PCPF. So the energy of S0 at CIX1 is, for instance, different from previous one by an S0-specific (2,2)CASSCF. (b) Relationship between τ and ω in the CIX1 region. For comparison, the full ranges of τ, ω and energy are adjusted to be same as those in Figures 8 and 9.

stator highly wags against the C9C1′ rotary axis but the directions of wagging motions are opposite to each other, whereas it wags a little at S1-geometry. At CIX1, the fluorene 3691

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Figure 4. Side views of CIX1, S1-geometry and CIX2. The rotary axis of C9C1′ is colored in yellow. In order to show that the C6′C7′C8′ and C6′C11′C10′ parts of the phenyl group are almost equivalently away from the fluorene stator in all cases, the C7′C8′ and C9aC1 parts which face each other at P-M5-PCPF are colored in red, whereas the C11′C10′ and C8aC8 parts are colored in cyan.

Table 2. Electronic Structures at CIX2 chargea dipole moment (Debye)

fluorene (C9)

2-cyclopentenylidene (C1′)

phenyl

pentamethylene

main CSFb

S0 S1

−0.03(−0.04) −0.53(−0.39)

−0.84(−0.18) −0.36(0.15)

0.39 0.39

0.49 0.50

0.43(closed-shell) + 0.90(HOMO−LUMO) 0.90(closed-shell) − 0.43(HOMO−LUMO)

1.09 6.80

a

The charges were evaluated by Löwdin population analysis. The values in the parentheses are charges on the C9 and C1′ atoms. bThe absolute values of the coefficients of CSFs (configuration state functions) greater than 0.30 are listed.

in Figure 6c,d, C2′C6′C7′Ca, C6′C7′CaCb, C7′CaCbCc in Figure 7) are also affected in recovery from a highly wagged fluorene stator. Interestingly, however, the phenyl torsion of ϕ and the conformational changes of the pentamethylene chain in the backward process are much smaller than those in the forward process (refer to the Supporting Information). This difference can be discussed in close relation to the conformational effect on the photochemistry (i.e., IS1) which is not the main issue in the present paper and will be discussed elsewhere. In the same manner as the case of CIX1, the potential energy surfaces of S1 and S0 around CIX2 (i.e., IRC2 < 5 amu1/2Bohr) are shown as a function of τ (see Figure 8a). Under condition of a strong coupling between τ and ω (Figure 8b) in the CIX2 region, two surfaces cross each other at CIX2 as a so-called sloped-type surface crossing.24 This topographical feature around CIX2 is also confirmed by the computational findings that geometry optimizations of S0 and S1 from CIX2 lead to P-M5-PCPF and S1-geometry, respectively. Concerning the latter half rotary cycle of P′-M5-PCPF → PM5-PCPF, we also found that there are two types of CIXs (denoted by CIX1′ and CIX2′,respectively) and the stable geometry in S1 (S1′-geometry) (see Table 1). The optimized CIX1′, CIX2′, and S1′-geometry are related to CIX1, CIX2 and S1-geometry by τ-torsion of ca.180° and ω inversion, respectively. As is the case of CIX1 correlating to the product of P′-M5-PCPF, CIX1′, which is characterized by the fact that the fluorene stator faces the phenyl group, correlates to a product of P-M5-PCPF in the latter half rotary cycle. As same as CIX2, CIX2′ is characterized by the fact that the fluorene stator is far away from the phenyl group and correlates to a reactant of P′-M5-PCPF in S 0 . In addition, both S 1 optimizations from CIX1′ and CIX2′ result in S1′-geometry and therefore CIX1′ and CIX2′ are also classified as a slopedtype CIX, as are the cases of CIX1 and CIX2. All Cartesian coordinates in Table 1 are provided in the Supporting Information.

stator and phenyl group are close to each other, whereas they are further away at CIX2. Concerning the electronic structures at CIX2, we found a feature similar to that at CIX1. That is, CIX2 is a crossing region between the zwitterionic and the nonpolar biradical state (see Table 2), as already pointed out in the case of various ethylenoids.21,22 We also located a CIX2 by a larger SA2-(6,6)CASSCF to confirm that our SA2-(2,2)CASSCF approach is enough to describe the photochemistry of M5-PCPF. We checked where electronically relaxed M5-PCPF at CIX2 goes by following the IRC in S0 (denoted by IRC2 hereafter). From the energy profile and τ torsion (Figures 5 and 6a), it is

Figure 5. Energy profile in S0 along IRC2 (in amu1/2Bohr) from CIX2 to P-M5-PCPF. The scales of the abscissa and ordinate are adjusted so as to be the same as those in the forward process provided in the Supporting Information (and also in ref 22), for comparison.

found that electronically relaxed M5-PCPF at CIX2 exclusively goes back to P-M5-PCPF without any trap by monotonically decreasing τ. At the early stage after electronic relaxation at CIX2 (i.e., IRC2 < 5 amu1/2Bohr), a highly wagged geometry around the C9 atom quickly tends to become planar in accordance with a decrease of τ (see Figure 6a,b). The geometrical parameters relevant to the phenyl torsion (i.e., ϕ, φ 3692

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Figure 7. Dihedral angles relating to the pentamethylene chain along IRC2 (in amu1/2Bohr). The scale of the abscissa is adjusted to be that of the forward process, for comparison. Each dihedral angle is adjusted within a full range of 0° to 90° as same as in the case of the forward process provided in the Supporting Information (and also in ref 22.). This is because the behaviors of dihedral angles along IRC2 are important rather than the actual values. In order to give information on the actual dihedral angles, however, a set of values are provided in the parentheses for each dihedral angle. The first and second values are the actual dihedral angle at IRC2 = 0 amu1/2Bohr and the adjustment value to be within the full range of ordinate, respectively. For instance, the value at IRC2 = 0 amu1/2Bohr for C6′C7′CaCb, 58.0 in this figure is obtained by a sum of 73.0 + (−15.0). Each adjustment value is as same as that in the forward process except for that of C7′CaCbCc. C6′C7′CaCb (73.0,−15.0; black solid line); C7′CaCbCc (−140.4, 160.0; red solid line); CaCbCcCd (96.0, −70.0; cyan solid line); CbCcCdCe (−98.5, 150.0; green solid line); CcCdCeC5′ (104.6, −50.0; blue solid line); CdCeC5′C4′ (41.3, 0.0; red dashed line); CeC5′C4′C3′ (−99.4, 130.0; black dashed line).

between the fluorene stator and the phenyl group, which is managed by ω and τ (refer to Table 1 and Figure 4). In addition, both CIX1 and CIX2 are directly connected with S1geometry, as confirmed by SA2-(2,2)CASSCF optimization in S1. So we tried to calculate the potential energy surfaces connecting CIX1 with CIX2 to characterize the topography around the CIX1 and CIX2 region including S1-geometry. Considering that the geometrical parameters, especially τ and ω, are mutually different among CIX1, CIX2, and S1-geometry, we introduce new parameters σ1 and σ2 to smoothly change the geometrical parameters among them Q i1 = σ1Q i(CIX1) + (1 − σ1)Q i(S1 − geometry), 0 ≤ σ1 ≤ 1

Q i2 = σ2Q i(S1 − geometry) + (1 − σ2)Q i(CIX2), 0 ≤ σ2 ≤ 1

Figure 6. Geometrical changes along IRC2 (in amu1/2Bohr). (a) τ, (b) ω, (c) ϕ, and (d) φ. The full range of ordinate in a is 130° but the others are 60°. In order to be compared with those in the forward process of CIX1 → P′-M5-PCPF provided in the Supporting Information (and also in ref 22), the scales of the abscissas and ordinates are adjusted so as to be same as those in the forward process. In comparison with the ω behavior with that in the forward process, b should be compared only with Figure SI-1b drawn by the present definition of ω.

where Qi1 and Qi2 are the ith internal coordinates in the region between CIX1 and S1-geometry and in the region between S1geometry and CIX2, respectively. Figure 9a shows the potential energy surfaces with respect to ω. It is found that both S1 and S0 surfaces have a positive curvature with respect to ω around S1-geometry. In other words, M5-PCPF around S1-geometry is accessible to CIX1 and CIX2 by wagging motions with large negative and positive ω values, respectively. In accord with the wagging motions to the negative and positive directions around S1-geometry, the τ torsion is back and forth to reach CIX1 and CIX2, respectively.

3.2. Topographical Feature in the CIX Region. The main difference between CIX1 and CIX2 is a relative position 3693

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Figure 9. (a) Potential energy surfaces of S1 (in solid line) and S0 (in dashed line) with respect to ω in the CIX region. The energies are relative to that in S0 by SA2-(2,2)CASSCF at P-M5-PCPF. (b) Relationship between ω and τ in the CIX region. For comparison, the full ranges of τ, ω and energy are adjusted to be same as those in Figures 3 and 8.

Figure 8. (a) Potential energy surfaces of S1 (in solid line) and S0 (in dashed line) with respect to τ in the CIX2 region. The geometries are taken from the region of IRC2 < 5 amu1/2Bohr in Figure 5. The energies are relative to that in S0 by SA2-(2,2)CASSCF at P-M5PCPF. So the energy of S0 at CIX2 is, for instance, different from that by an S0-specific (2,2)CASSCF in Figure 5. (b) Relationship between τ and ω in the CIX2 region. For comparison, the full ranges of τ, ω and energy are adjusted to be same as those in Figures 3 and 9.

other words, neither CIX1 nor CIX2 itself plays a decisive role in branching for the forward and backward rotation. In the latter half of rotary cycle (P′-M5-PCPF → P-M5-PCPF), a similar discussion among CIX1′, S1′-geomerty, and CIX2′ can be done. These are schematically shown in Figure 10, which gives a more elaborate picture on the photochemistry of M5PCPF than previous one.22 The present computational findings give a guiding principle for a further modification of fluorene-based light-driven molecular rotary motor. As mentioned above, M5-PCPF has two relaxation channels which exclusively forward and backward rotations around the CC rotary axis respectively.

We also performed an S1-optimization from P-M5-PCPF by SA2-(2,2)CASSCF, which leads to S1-geometry. This is, of course, due to a computational strategy where a spectroscopically bright state with ethylenic ππ* character is included only. As pointed out previously,22 however, this computational strategy is reasonable because the bright ethylenic ππ* state (i.e.S2) in the Franck−Condon region diabatically correlates to the S1 state in the highly τ-twisted region, even though the dark state with π(fluorene)π*(ethylene) character (i.e., S1) in the Franck−Condon region is included by a larger (6,6)CASSCF calculation. As also mentioned above, an S1 optimization from CIX1 by SA2-(6,6)CASSCF leads to a stable geometry similar to S1-geometry by SA2-(2,2)CASSCF. This means that a local minimum of S1 in the perpendicular τ-twisted region is not a computational artifact by SA2-(2,2)CASSCF but a realistic conformation diabatically correlating from the bright ethylenic ππ* state in the Franck−Condon region. Based on the computational findings mentioned above, we deduce the photochemical process as follow. Electronically excited P-M5-PCPF in the Franck−Condon region first goes to the S1-geometry region by perpendicular τ-twist with little wagging motion. Then M5-PCPF at S1-geometry can reach CIX1 and CIX2 by large wagging motions to the negative and positive directions against the C9C1′ rotary axis respectively, which are strongly coupled with τ. CIX1 and CIX2 exclusively connect with P′-M5-PCPF and P-M5-PCPF in S0, respectively. This means that the direction of wagging motion around S1geometry determines the forward or backward reaction. In

Figure 10. Schematic representation of the full rotary cycle of M5PCPF. The solid and wavy arrows represent that M5-PCPF is in S0 and S1, respectively. The red and blue arrows represent the forward and backward rotations in the full rotary cycle, respectively. Values in the parentheses are the energies (in kcal/mol) relative to that of P-M5PCPF in S0 evaluated by SA2-(2,2)CASSCF. The first and second values are the energies in S0 and S1, respectively. 3694

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Even though a backward rotation takes place via CIX2, however, M5-PCPF can reach S1-geomerty again through electronic excitation of a returnee P-M5-PCPF and therefore has a chance to go to P′-M5-PCPF via CIX1. In other words, electronically excited P-M5-PCPF can be perfectly converted into P′-M5-PCPF after returning from CIX2 into P-M5-PCPF some times. If the branching ratio to CIX1 at S1-geometry is p, P-M5-PCPF is expected to be converted into P′-M5-PCPF after returning from CIX2 (1/p-1) times. In the simplest model, p is supposed to be determined only by two factors. One is the energy difference between CIX1 and CIX2 (5.1 kcal/mol in Figure 10). The other is the available energy which is released in the process of P-M5-PCPF → S1-geometry in S1 (50.6 kcal/mol). From these values, p is estimated to be 0.47, which means that P-M5-PCPF is converted into P′-M5-PCPF after returning from CIX2 1.11 times in average. In order to obtain a more reliable branching ratio around the CIX region, a molecular dynamics simulation is desirable. In summary, the photochemical process of M5-PCPF can be tuned by chemical modifications of steric and electronic factors as well as dynamic modulation. For instance, in M5-PCPF analogue by chemical modification, the energies of CIX1 and CIX2 relative to S1geometry are possibly different from those of M5-PCPF (refer to Figure 9a) and consequently the branching ratio for access from S1-geometry to CIX1 (and CIX2) is different from that of M5-PCPF itself.

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ASSOCIATED CONTENT

S Supporting Information *

All Cartesian coordinates in Table 1 and the geometrical changes along the IRC in the forward reaction. 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: e-mail:[email protected]. Fax: +81-18-8892625. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by a Grant-in-Aid for Scientific Research (C) (No.23550006) from the Ministry of Education, Culture, Sports, Science and Technology.

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REFERENCES

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4. CONCLUDING REMARKS In the present paper we further examined the photochemical behavior of M5-PCPF, where our interest focused on the topographical features in the CIX region. Thereby, we found out the following. 1. Electronically excited M5-PCPF relaxes through two different channels. One of relaxation channels (CIX1) serves to forward a rotation, whereas the other (CIX2) serves to backward a rotation. 2. In the CIX region, there is a stable geometry in S1 (S1geometry) characterized by a conformation where the 2cyclopentenylidene rotor is perpendicularly twisted but the fluorene stator wags a little against the CC rotary axis. S1-geometry is connected with CIX1 and CIX2 by wagging motions to the negative and positive directions against the CC rotary axis, respectively. 3. Electronically excited P-M5-PCPF diabatically correlates to S1-geometry. Thereby, all of P-M5-PCPF finally turn to be P′-M5-PCPF through CIX1 even after backward rotation through CIX2 some times. These findings cause the following questions. (Q1) By a further chemical modification of M5-PCPF, can the relative energies at CIX1 and CIX2 of an M5-PCPF analogue be changed? If yes, the photoreaction rate can be tuned. (Q2) Is the topographical feature in the CIX region for the photoreaction of the CC double bond torsion intrinsic to M5-PCPF? Or is it also found in the case of 9-(2-cyclopenten1-ylidene)-9H-fluorene (CPF) which is parent molecule of M5PCPF, although CPF exhibits neither helicity nor unidirectionality in the photoprocess? Or is the topographical feature in more general found in other ethylenoids? In order to answer these questions, our computational research is now in progress. 3695

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