Theoretical Study of Topographical Features around the Conical

Article pubs.acs.org/JPCA

Theoretical Study of Topographical Features around the Conical Intersections of 9‑(2-Cyclopenten-1-ylidene)‑9H‑fluorene Yoshiaki Amatatsu* Faculty of Engineering and Resource Science, Akita University, Tegata Gakuen-cho, Akita 010-8502, Japan S Supporting Information *

ABSTRACT: Ab initio molecular orbital calculations have been performed to examine the topographical features around the conical intersections (CIXs) for the photoisomerization of 9-(2-cyclopenten-1-ylidene)-9H-fluorene (CPF). The present study is motivated by the computational findings of the topographical features in the CIX region of a fluorene-based light-driven molecular motor with smooth rotation (denoted by M5-PCPF). CPF is a parent molecule of M5-PCPF but exhibits neither helicity nor unidirectionality. A stable geometry in S1 (S1-geometry) is located in the region where the ethylenic rotary axis is perpendicularly twisted, but the fluorene part wags little against the rotary axis, as is the case of M5-PCPF. However, the topographical features around the CIXs of CPF are different from those of M5PCPF. The wagging motion of the fluorene stator to the negative direction from S1geometry leads straight to a CIX which implements forward and backward rotations. On the other hand, only the wagging motion to the positive direction does not lead to a CIX, and additional geometrical deformations are needed. Depending on the directions of additional geometrical deformations, two CIXs, which play the roles of respective exit channels for forward and backward rotations, are located in the positive wagging region. The difference in the topographical features in the CIX region between CPF and M5-PCPF is ascribed to the effect of the pentamethylene chain. By virtue of much less computational labor of CPF as well as the electronic structures being similar to those of M5-PCPF, the intrinsic reaction coordinate was followed from the ethylenic ππ* state at the stable geometry in S0 into S1-geometry. Thereby, it was confirmed that a spectroscopically dark state due to the π(fluorene)π*(ethylene) excitation contributes less to the photochemical process of the ethylenic bond torsion, as is the case of M5-PCPF.

1. INTRODUCTION Molecular rotary motors are one of the most important molecular devices in nanomachines.1 Various types of molecular rotary systems fueled by external stimuli, such as photon,2−17 chemical,18−20 or electrical21−23 energy, etc., have been presented both from the experimental and theoretical sides, and new ideas for a better molecular rotary motor continue to be presented. For instance, a combined system of a conventional fluorene-based molecular motor with a triplet sensitizer of palladium tetraphenylporphyrin was synthesized to cause a unidirectional rotation by triplet energy transfer from the triplet sensitizer.8 A molecular motor comprising a pianostool complex was realized, which controls clockwise and anticlockwise rotation by means of electric energy from the tip of a scanning tunneling microscope.21 From a theoretical viewpoint, a new type of molecular motor which makes good use of a chiral hydrogen-bond environment was proposed.17 Ethylenoids with rigid and overcrowded substituents have been extensively studied as a candidate of UV light-driven molecular rotary motors since the first realization of unidirectionality.2 The rigid and overcrowded substituents of ethylenoids ensure unidirectionality around the ethylenic double bond but also give rise to a large energy barrier in the subsequent thermal helical conversion. In other words, the full © 2013 American Chemical Society

rotary process of ethylenoids with rigid and overcrowded substituents, which consists of four consecutive steps (i.e., two fast photochemical steps each followed by an extremely slow thermal conversion step), is not smooth and is rather awkward from the viewpoint of a molecular rotary motor. Despite much effort to modify the rigid and overcrowded substituents,3−7 smooth unidirectional rotation has not been realized yet. In order to overcome the disadvantages, we proposed a new approach in the modeling of a light-driven molecular rotary motor, where a conventional overcrowded and rigid substituent for unidirectional rotation is replaced by an overcrowded but floppy one.13,15 Thereby, a derivative of 9-(2-phenyl-2-cyclopenten-1-ylidene)-9H-fluorene (PCPF), where PCPF is bridged by pentamethylene chain between the 2 position of the phenyl group and the pseudoaxial position of the C5 atom in the 2-cyclopenten-1-ylidene ring (we call it 2-cyclopentenylidene hereafter for convenience), is found to be a promising candidate for a UV light-driven molecular motor with smooth rotation by means of ab initio molecular orbital (MO) calculations. That is, the full rotary process of the Received: June 28, 2013 Revised: October 15, 2013 Published: October 16, 2013 12529

dx.doi.org/10.1021/jp4063912 | J. Phys. Chem. A 2013, 117, 12529−12539

The Journal of Physical Chemistry A

Article

sponding π* orbitals are taken into account. Thereby, the following were found out: PRCI1 - In the Franck−Condon region, S1 with π(fluorene)π*(ethylene) excitation is a dark state, while S2 with ethylenic ππ* excitation is a bright state.

derivative of PCPF (denoted by M5-PCPF hereafter) consists of two consecutive photochemical processes of the P-helical isomer → P′-helical isomer and P′-helical isomer → P-helical isomer. As a consequence, a smooth rotation in the full rotary process could be realized. In addition, it is found that M5-PCPF has the following topographical features in the conical intersection (CIX) region where the rotary axis of the ethylenic CC bond is highly twisted.16 TP1 - A stable geometry in S1 (S1-geometry) is located in the CIX region. S1-geometry diabatically correlates with a spectroscopically bright state with ethylenic ππ* character in the Franck−Condon region. TP2 - There are two CIXs which play exclusive roles of forward and backward rotations, respectively. TP3 - Two CIXs are accessed by the wagging motions to the opposite directions from S1-geometry. Thus, we come up with a question whether TP1−TP3 are intrinsic in M5-PCPF, or are these topographical features also true for fluorene-based ethylenoids without unidirectionality? In order to answer this question, we theoretically examine the topographical features in the CIX regions of 9-(2-cyclopenten1-ylidene)-9H-fluorene (CPF) in Figure 1. CPF is a parent

PRCI2 - In the region where the C9C1′ rotary axis is perpendicularly twisted, the ethylenic ππ* state becomes S1. PRCI3 - The HOMO (highest occupied MO) and LUMO (lowest unoccupied MO) are mainly characterized by the ethylenic π and π* orbitals irrespective the conformations, while fluorenic π and π* orbitals are HOMO−1 and LUMO+1. From the preliminary CI calculations, two electrons in two orbitals by the complete active space self-consistent field (CASSCF) (denoted by (2,2)CASSCF) approach is enough to describe the electronic states in our main interest, as is the case of M5-PCPF.15,16 In addition, a two-state averaged (2,2)CASSCF (SA2-(2,2)CASSCF) method, where two-particle density matrices of S1 and S0 are equally weighted, was adopted for scanning of the potential energy surfaces due to the closeness of S1 and S0 surfaces in the CIX region, although an S0-specific (2,2)CASSCF was adopted in optimizations of stable geometries in S0. By virtue of less computational labor of CPF, we checked whether a spectroscopically bright state due to the ethylenic ππ* excitation diabatically correlates to the S1 state in the CIX region where the C9C1′ rotary axis is perpendicularly twisted, although we previously checked it on M5-PCPF by easier approaches.15,16 In the first step, we followed the intrinsic reaction coordinate (IRC) in S1 from the stable geometry in S0 (S0-geometry) by means of the SA2-(2,2)CASSCF method. Thereby, a spectroscopically bright state with ethylenic ππ* character at S0-geometry is connected with a stable geometry in S1 in the CIX region (S1-geometry) at least artificially. In the second step, we evaluated the energies of S0, S1, and S2 at each IRC point by a larger three-state averaged (4,4)CASSCF (SA3(4,4)CASSCF) where two-particle density matrices of S0, S1, and S2 are equally weighted. The SA3-(4,4)CASSCF approach is based on the preliminary CI results. The three-state average of two-particle density matrices is because only the S1 and S2 states are important in the Franck−Condon region but the S0 state becomes also important in the CIX region. In this step, we can check whether a spectroscopically bright S2 state in the Franck−Condon region diabatically correlates with the S1 state in the CIX region. In other words, we can validate whether our approach of (2,2)CASSCF is reasonable. In the Appendix, we further validated the truncation of the active space by larger (10,10)CASSCF optimizations at the key geometries. The basis sets are reduced as in the previous calculations on M5-PCPF because larger basis sets were previously confirmed to affect the computational results a little.15 A Huzinaga− Dunning double-ζ quality augmented by polarizations (DZP) (αd = 0.75 for C atoms) were applied to the five-membered rings in the stator and rotor (i.e., C9,C9a,C4a,C4b,C8a and C1′ to

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

molecule of M5-PCPF but exhibits no unidirectionality, as will be mentioned later. By comparing the topographical features of CPF in the CIX region with those of M5-PCPF, therefore, we probably obtain a new insight into the effect of the pentamethylene chain on the photochemical reaction in the CIX region. By virtue of much less computational labor of CPF, we can also analyze the intrinsic reaction coordinate (IRC) from the ethylenic ππ* state at the stable geometry in S0 into the CIX region easily. Thereby, we validate a dark state due to the π(fluorene)π*(ethylene) excitation that contributes less to the photochemical process of fluorene-based ethylenoids in a more rigorous way, although we have already done it on M5PCPF by easier ways.15,16 We also expect to obtain geometrical changes along IRC which are transferable to a discussion on M5-PCPF except for the effects of the pentamethylene chain.

C5′), which ensures the spatial flexibility of the electronic populations on these atoms dependent on the conformations. On the other hand, the C and H atoms except for the C atoms in the five-membered ring of the stator and rotor are applied to a minimal basis set (so-called MINI) because the hybridizations of the remaining skeletal C atoms are almost unchanged irrespective of the conformations.

2. METHOD OF CALCULATIONS In the present ab initio MO calculations including the determination of CIXs, we used the GAMESS program.24 We preliminarily performed configuration interaction (CI) calculations where as much as triple excitations of the π orbitals from the Hartree−Fock closed-shell configuration into the corre12530



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3. RESULTS AND DISCUSSION 3.1. IRC Analysis of CPF from the Franck−Condon Region into the CIX Region. Before discussions on the present computational results, we comment on the notations of geometries. In the present paper, we will refer to the key geometries for CPF as well as those of M5-PCPF many times. For instance, S1-geometry indicates a stable geometry of S1 in the CIX region of CPF as well as that of M5-PCPF. As far as which of the molecules is indicated is clear, we will use a simple notation of S1-geometry. In some cases, however, we refer S1geometry as S1-geometry(CPF), S1-geometry(M5-PCPF) to clarify which of molecules is indicated. We also comment on phrases of forward and backward rotations in the present paper. In any case, the forward and backward rotations mean increase and decrease of the torsional angle (τ) around the C9C1′ rotary axis, respectively. The definition of τ as well as those of the wagging angles (ω and ω′) is shown in Figure 2 so as to characterize the geometries subsidiarily.

character is S1. This is also confirmed by the energy profile along IRC in Figure 3a. In addition, the IRC analyses in a−d of Figure 3 give us detailed information on the photochemical process from the Franck−Condon region into the CIX region. In the early stage of IRC < 1.1 amu1/2 Bohr, the spectroscopically bright S2 state (and also the dark S1 state) is drastically lowered in energy (see Figure 3a). From a viewpoint of geometry, the C9C1′ bond becomes longer quickly (Figure 3d), while τ and ω (b and c of Figure 3) remain almost unchanged. The quick elongation of the C9C1′ bond makes it possible to relax the excited state due to the ethylenic ππ* character, which leads to the quick lowering in energy (∼14 kcal/mol) in the stage of IRC < 1.1 amu1/2Bohr. Interestingly, the geometry at IRC∼1.1 amu1/2Bohr is similar to that of TS1FC. Therefore, the early stage upon ethylenic ππ* excitation corresponds to a process of S0-geometry → TS1FC (refer to the relevant part of Table 2). TS1FC is a transition state of S1 in the Franck− Condon region which separates the forward region with the backward one and is hence the origin of no unidirectionality of CPF. Once CPF is geometrically relaxed into the TS1FC region by the C9C1′ elongation without the τ torsion (and the ωwagging motion), the τ torsion easily takes place to the forward and backward directions. In the present case, we forced the IRC to be followed in the forward region. As the τ-torsional angle monotonically increases in the second stage of IRC > 1.1 amu1/2Bohr, the ethylenic ππ* state is stabilized so as to cross with a dark state of π(fluorene)π*(ethylene) at IRC ≈ 13.5 amu1/2Bohr (τ ≈ 54°). Finally, the ethylenic ππ* state correlates to the S1 state in the perpendicularly twisted S1geometry where S1 and S2 are well separated from each other. It is found that the fluorene stator (see Figure 3c) as well as the 2cyclopentenylidene rotor (not shown) wags little against the C9C1′ rotary axis on the way from S0-geometry to S1-geometry. On the basis of the computational findings of CPF along IRC, we can deduce the photochemical behavior of M5-PCPF, although we have already mentioned it roughly by means of the energy gradient analysis.15 Upon ethylenic ππ* excitation at S0geometry(M5-PCPF), a main event is the C9C1′elongation in the initial stage, as is the case of CPF. However, M5-PCPF inherently puts on a downhill surface with respect to τ in the spectroscopically bright state because the stator and rotor are twisted with each other against the C9C1′ rotary axis even at S0-

Figure 2. Definitions of τ, ω, and ω′ of CPF and M5-PCPF. Numberings of atoms are the 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 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.

We start with mentioning that the spectroscopically bright state with ethylenic ππ* character of CPF in the Franck− Condon region diabatically correlates to the S1 state in the CIX region. Although we have already confirmed it on M5-PCPF by easier ways,15,16 we confirm it on CPF by a more rigorous way as mentioned in METHOD OF CALCULATIONS. We first follow the IRC in S1 from the stable geometry in S0 (S0geometry or S0-geometry(CPF), more precisely) to S1geomerty by SA2-(2,2)CASSCF. Thereby, we obtain the IRC which diabatically follows the ethylenic ππ* state from S0geometry into the CIX region. Then we calculate the potential energies in S0, S1, and S2 at each IRC point by a larger SA3(4,4)CASSCF where two-particle density matrices of S0, S1, and S2 are equally weighted. Table 1 lists the electronic structures at S0-geometry, of which geometrical parameters are listed in Table 2. It can be seen that the spectroscopically bright state with ethylenic ππ* character is S2 in the Franck−Condon region, whereas the dark state with π(fluorene)π*(ethylene)

geometry(M5-PCPF). Therefore, once the C9C1′ double bond is geometrically relaxed in the Franck−Condon region, M5-PCPF exclusively forwards a rotation into S1-geometry. In order to obtain a more detailed picture, of course, we should examine the photochemical process in relation with a conformational effect of the pentamethylene chain. In summary, electronically excited CPF diabatically correlates to the S 1 state in the CIX region, which validates our

Table 1. Electronic Structures of CPF at S0-geometrya S0 S1 S2

energy (kcal/mol)b

dipole moment (Debye)

oscillator strengthc

main CSFsd

0.0(0.0) 119.4(93.8) 136.3(104.9)

1.43 6.01 4.07

− 2.8 × 10−3 1.40

0.99(closed-shell) 0.93(HOMO−1-LUMO) 0.99(HOMO-LUMO)

a The geometrical parameters of S0-geometry is taken from Table 2. The values are evaluated by SA3-(4,4)CASSCF. bThe values in the parentheses are MRMP2 corrections of SA3-(4,4)CASSCF energies. cThe oscillator strengths are given in length form. dThe absolute values of the coefficients of CSFs(configuration state functions) greater than 0.30 are listed.

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Table 2. Characteristic Optimized Parameters at Important Geometries of CPF in the Former Half of Rotary Cyclea geometry

S0-geometryb

S1TSFC

C9C1′

1.343(1.364)

1.467

C9aC9C1′ C8aC9C1′ C9aC9C8a

128.6(129.2) 126.5(126.6) 104.9(104.2)

125.0 127.4 107.6

τ C1′C2′C3′C4′ C2′C3′C4′C5′ H5a′C5′C4′C3′c H5b′C5′C4′C3′c

1.7(10.8) 0.5(−2.0) −1.6(−15.7) −118.3(−100.1) 122.8 (141.4)

0.0 0.7 −0.9 −119.0 120.9

ω ω′

−1.0(−2.9) −0.4(4.0)

−0.3 −0.1

CIX1b

S1-geometryb

Bond Distance (Å) 1.431(1.419) 1.432(1.430) Bond Angles (deg) 104.4(93.4) 125.6(114.8) 105.4(126.7) 126.2(134.3) 101.3(102.0) 108.0(107.1) Dihedral Angles (deg) 88.8(67.0) 89.7(85.7) 0.2(2.9) −0.4(−5.4) 0.1(−17.3) −0.1(−7.9) −119.2(−95.6) −118.2(−103.8) 117.8(140.1) 119.7(133.7) Wagging Angles (deg) −66.1(−51.2) 3.6(17.1) 0.1(5.2) 0.3(8.3)

CIX2b

CIX3

S0′-geometryb

1.429(1.419)

1.429

1.343(1.364)

99.6(96.2) 107.9(121.0) 100.6(102.1)

107.7 99.7 100.5

126.4(126.6) 128.7(129.1) 104.9(104.2)

98.1(103.7) −6.4(−10.3) −4.9(−5.7) −97.1(−99.4) 140.2(138.2)

82.2 6.5 4.6 −139.7 97.6

180.2(191.1) 0.4(−2.0) −1.1(−15.8) −119.1(−100.0) 122.0(141.5)

67.5(55.9) 1.4(6.8)

67.6 −1.5

−0.5(3.3) 0.2(4.0)

a

All Cartesian coordinates are provided in the Supporting Information. The characteristic optimized parameters and their Cartesian coordinates in the latter half of rotary cycle are also provided in the Supporting Information. bThe values in the parentheses are the optimized parameters of M5PCPF taken from refs 15. and 16, where S0-geometry(M5-PCPF) and S0′-geometry(M5-PCPF) were referred as P-M5PCPF and P′-M5-PCPF, respectively. cIn the case of M5-PCPF, the dihedral angles of H5a′C5′C4′C3′ and H5b′C5′C4′C3′ are replaced by those of CeC5′C4′C3′ and H5′C5′C4′C3′, respectively.

Figure 3. IRC (in amu1/2 Bohr) of the ethylenic ππ* state from S0-geometry(CPF) into S1-geometry(CPF) by SA2-(2,2)CASSCF. (a) energy profiles of the ethylenic ππ* excited state (in red line) and the π(fluorene)π*(ethylene) state (blue line) evaluated by SA3-(4,4)CASSCF for each IRC point by SA2-(2,2)CASSCF. The energies are relative to that in S0 by SA3-(4,4)CASSCF at S0-geometry(CPF). (b) τ, (c) ω, d) C9 C1′ bond distance.

coordinates are provided in the Supporting Information). At a stable geometry in S1 (S1-geometry) in the CIX region, the 2cyclopentenylidene rotor is perpendicularly twisted against the fluorene stator (τ = 89.7°), but the fluorene stator wags little against the C9C1′ rotary axis (ω = 3.6°). Other important geometries are three CIXs. CIX1 has a geometrical feature that

computational strategy of (2,2)CASSCF in a series of our studies on the fluorene-based ethylenoids.13,15,16 3.2. Topographical Features of CPF in the CIX Region. Now we mention the main interest of the topographical features of CPF by refering to the optimized parameters at the key geometries of CPF in Table 2 (note: all Cartesian 12532



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the fluorene stator greatly wags to the negative direction (ω = −66.1°) against the C9C1′ rotary axis, whereas the 2cyclopentenylidene rotor remains to wag little (ω′ = 0.1°). Concerning CIX2, the fluorene stator wags in the positive direction (ω = 67.5°) against the C9C1′ rotary axis with little wagging of the 2-cylopentenylidene rotor. In addition, the rocking deformation of the fluorene stator against the C9C1′

parameters which are mutually different among three geometries are ensured to smoothly change in the CIX region. Q i1 = σ1Q i(CIX1) + (1 − σ1)Q i(S1‐geometry), 0 ≤ σ1 ≤ 1

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

axis, which is defined by β = C9aC9C1′-C8aC9C1′, takes place at CIX2 (β = −8.3°), whereas it does not take place at CIX1 (β = −1.0°). This implies that another CIX in the positive ωwagging region possibly exists in the opposite region with respect to the β-rocking deformation. Actually, CIX3 is located in the positive ω-wagging region (ω = 67.6°) with a positive βvalue (β = 8.0°). In addition, we tried to search for a CIX where the 2-cyclopentenylidene rotor greatly wags (i.e., large ω′) against the C9C1′ rotary axis but did not find any CIX in the large ω′-wagging region. Figure 4 is useful to obtain the

where Qi1 and Qi2 are the ith internal coordinates in the region between CIX1 and S1-geomerty and in the region between S1geometry and CIX2, respectively. As shown in Figure 5a, the

Figure 4. Side (left) and front (right) views of CIX1, S1-geometry, CIX2 and CIX3 of CPF. The rotary axis of C9C1′ is colored in yellow. In order to see the β-rocking directions of the fluorene stator against the C9C1′ rotary axis, the C atoms of the 2-cyclopentenylidene ring in the front views of CIX2 and CIX3 are colored in cyan. The notation of ω+β−, for instance, means that the ω-wagging and β-rocking motions of the fluorene stator take place to the positive and negative directions, respectively, for the process of S1-geometry → CIX2. The captions in the parentheses for CIXs indicate the direction of the τ rotation after electronic relaxation into S0.

Figure 5. (a) Potential energy surfaces of S1 (solid line) and S0 (dashed line) with respect to ω in the CIX region ranging over CIX1, S1-geometry, and CIX2. The energies are relative to that in S0 by SA2(2,2)CASSCF at S0-geometry. Note that the energy in S1 at S1geometry is 83.2 kcal/mol, while that in Figure 3a (i.e., IRC ≈ 25 amu1/2 Bohr) is ∼89 kcal/mol. This difference is due to the fact that the former is evaluated by SA2-(2,2)CASSCF, while the latter is evaluated by SA3-(4,4)CASSCF. (b) Relationship between ω and τ in the CIX region. For comparison with those of M5-PCPF in ref 16, the scales of abscissas and ordinates are adjusted to be the same as those of M5-PCPF.

geometrical relationship among the key geometries in the CIX region visually. In the access from S1-geometry to CIX1, only the ω-wagging motion to the negative direction is needed. In the access to CIX2 and CIX3, on the other hand, the β-rocking motions to the negative and positive directions are needed in addition to the ω-wagging motion in the positive direction. We will make more detailed comments on the couplings among the internal motions later. We confirmed that three CIXs are directly connected with S1-geometry by geometry optimizations in S1 from three CIXs. In order to show the topographical features of the CIX region over CIX1, S1-geometry, and CIX2, we introduce linear interpolation parameters σ1 and σ2. Thereby, the geometrical

potential energy surfaces of S1 and S0 with respect to ω are characterized by a positive curvature around S1-geometry. However, considering that CPF obtains an excess energy of 46.7 kcal/mol in the process of S0-gemetry → S1-geometry (note: the energy difference in S1 between S0-geometry and S1geometry is evaluated by SA2-(2,2)CASSCF but a similar energy difference of 47.1 kcal/mol between IRC = 0 and ∼25 amu1/2 Bohr for the ethylenic ππ* state in Figure 3a is obtained by SA3-(4,4)CASSCF), CPF easily accesses from S1-geometry to CIX1 and CIX2 (8.7 and 12.3 kcal/mol, respectively). These 12533



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are similar to the case of M5-PCPF.16 On the other hand, τ is almost independent of ω (see Figure 5b), especially in the negative ω-wagging region. This contrasts with the case of M5PCPF where the τ torsion is strongly coupled with the ωwagging motion under constraint of the pentamethylene bridge. By a similar treatment among CIX1, S1-geometry, and CIX3, we obtain a and b of Figure 6. It is found that the τ-torsional angle decreases to access CIX3, contrary to accessing CIX2.

for instance, never obtained by the linear interpolation between CIX1(104.4°) and CIX2(99.6°). As shown in Figure 5a where two types of linear interpolations (i.e., CIX1 and S1-geometry, S1-geometry and CIX2) are done properly, on the other hand, it can be seen that S1-geometry is a minimum in the region ranging from CIX1 to CIX2. For confirmation, we performed S1 geometry optimizations from σ1 = 0.0 (i.e., CIX1), 0.5, 0.7, and σ2 = 0.3, 0.5, 1.0 (i.e., CIX2). Thereby, we found that all the optimizations go to S1-geometry. This means that the curvature in S1 around S1-geometry is positive with respect to ω, although the geometry for each σ1 and σ2 is not a minimum for each ω. Therefore, the potential energy surfaces with respect to ω in Figure 5a, which is built by the linear interpolation, is useful to roughly grasp the topographical features in the CIX region. As a good case for the linear interpolation approach, we previously examined the S2−S1 internal conversion of phenylacetylene.25 The potential energy surfaces in this process built by the linear interpolation well describes the photochemical process, which was validated by the intrinsic reaction coordinate analysis in S2 in a more rigorous way.26 In the latter half of rotary cycle, the key geometries of TS1FC′, CIX1′, CIX2′, CIX3′, and S1′-geometry, which are provided in the Supporting Information, can be related to TS1FC, CIX1, CIX2, CIX3 and S1-geometry by τ torsion of ∼180° and ω inversion, respectively. In addition, a puckering of the 2-cyclopentenylidene ring and interchange between the relative positions between the H5a′ and H5b′ atoms are also found to take place between CIX2 and CIX2′ (CIX3 and CIX3′). Therefore, a similar discussion on the topographical features of the CIX′ region can be done. 3.3. Internal Mode Couplings on the S1 Surface in the CIX Region. As pointed out in the previous subsection, the τ−ω coupling of CPF in the CIX region is different from that of M5-PCPF. The strong τ−ω coupling of M5-PCPF can be ascribed to a constraint of the pentamethylene chain between the 2 position of the phenyl group and the 5 pseudoaxial position of the 2-cyclopentenylidene ring. This constraint

Figure 6. (a) Potential energy surfaces of S1 (solid line) and S0 (dashed line) with respect to ω in the CIX region ranging over CIX1, S1-geometry, and CIX3. The energies are relative to that in S0 by SA2(2,2)CASSCF at S0-geometry. As noted in the caption of Figure 5a, the energies are also evaluated by SA2-(2,2)CASSCF. Hence, the energies are different from those at IRC ≈ 25 amu1/2 Bohr by SA3(4,4)CASSCF in Figure 3a. (b) Relationship between ω and τ in the CIX region. For comparison, the scales of abscissas and ordinates are adjusted to be the same as those in a and b, respectively, of Figure 5.

serves the Ce atom (corresponding to the H5a′ atom of CPF in Figure 1) to keep an pseudoaxial position on the C5′ atom irrespective of the conformations of M5-PCPF. This causes an energetic instability of the M-helical region in the rotary cycle and in consequence an M-helical conformation is forced to be only a transient one. In the case of CPF without constraint of pentamethylene chain, on the other hand, the relative positions of the H5a′ and H5b′ atoms are interchangeable depending on the geometries. In addition, the conformation of the 2cyclopentenylidene ring changes in accord with the relative

Here, it is worthwhile making comment on the linear interpolation approach of the potential energy surfaces. As mentioned above, in the case that the two geometries to be connected by an interpolation are different from each other, the linear interpolation approach is an easy way to build the potential energy surfaces between the two geometries. However, we have implicit assumptions on building them. All geometrical parameters between the two geometries change in accord with linear interpolation parameter, σ. What is more important is that the two geometries are directly connected in a chemical sense. For instance, we can build the potential energy surfaces between CIX1 and CIX2 formally by the linear interpolation. However, the potential energy surface in S1 (also in S0) does not lead to the fact that the S1-geometry is a minimum in the CIX region. This is easily understood by the fact that the C9aC9C1′ bending angle at S1-geometry (125.6°) is,

positions of the H5a′ and H5b′ atoms. At S1-geometry, the 2cyclopentenylidene ring substantially takes a planar conformation and the H5a′ and H5b′ atoms take equivalent positions against the planar 2-cyclopentenylidene ring (i.e., H5b′C5′C4′C3′(119.7°) ≈ −H5a′C5′C4′C3′(−118.2°)). At CIX1 in the negative ω-wagging region, a similar geometrical feature is found. This implies that the ω-wagging motion to the negative direction is a main factor in the process of S1-geometry → CIX1, and other motions such as the β-rocking motion of the fluorene stator are not so important. This is indicated by the notation of ω−β0 in the process of S1-geometry → CIX1 of Figure 4. 12534



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At CIX2 which is located in the positive ω-wagging region, on the other hand, the 2-cyclopentenylidene ring puckers to the negative direction where the dihedral angles of C1′C2′C3′C4′ and C2′C3′C4′C5′ are −6.4° and −4.9°, respectively. Accompanied with the ring puckering to the negative direction, the relative positions of the H5a′ and H5b′ atoms take pseudoaxial (−97.1°) and pseudoequatorial (140.2°) positions, respectively. In addition, the β-rocking deformation of the fluorene stator against the C9C1′ axis takes place to the negative direction (β = −8.3°). In Figure 4, the process of S1-geometry → CIX2 is characterized by the notation of ω+β−. At CIX3 which is also located in the positive ω-wagging region (ω = 67.6°), the 2cyclopentenylidene ring puckers to the positive direction (i.e.,

Figure 7. Potential energy surfaces of S1 (in solid line) and S0 (in dashed line) with respect to τ in the region accessed by the ω-wagging motion to the positive direction. The curves in black are those in the CIX2 region, whereas the curves in red are those in the CIX3 region. The geometries are taken from the region of IRC < 5.0 amu1/2Bohr for CIX2 as well as CIX3, where the IRC was evaluated by an S0-specific (2,2)CASSCF from CIX2 (as well as CIX3). The energies are evaluated by SA2-(2,2)CASSCF for each IRC point and are relative to that in S0 by SA2-(2,2)CASSCF at S0-geometry(CPF).

C1′C2′C3′C4′ = 6.5°, C2′C3′C4′C5′ = 4.6°) and in accord the relative positions of the H5a′ and H5b′ atoms interchange with each other in comparison with those of CIX2. That is, the H5a′ and H5b′ atoms take pseudoequatorial(−139.7°) and pseudoaxial(97.6°) positions, respectively. The β-rocking deformation of the fluorene stator takes place to the positive direction (β = 8.0°). Hence the process of S1-geometry → CIX3 is characterized by the notation of ω+β+ in Figure 4. In summary, the accesses from S1-geometry into CIX2 and CIX3 in the positive ω-wagging region are determined by three geometrical factors; the directions of the β-rocking deformation and the ring puckering of the 2-cyclopentenylidene, and the interchange of the relative positions between the H5a′ and H5b′ atoms. 3.4. Topographical Features around Each CIX. We turn to mention the topographical features around each CIX. In order to examine the topography around CIX2, we performed additional calculations by a similar way which allowed us to characterize the topographical features around CIX2(M5PCPF).16 First we follow the IRC in S0 from CIX2(CPF) by an S0-specific (2,2)CASSCF and then evaluated the S1 and S0 energies at each IRC point by SA2-(2,2)CASSCF. We also examined the topography around CIX3(CPF) by a similar approach. Figure 7 show the potential energy surfaces with respect to τ in the CIX2 and CIX3 regions which can be accessed from S1-geometry by the ω-wagging motion to the positive direction. It is found that both of CIX2 and CIX3 are classified as a sloped-type CIX.27 CIX2 serves to exclusively backward a rotation as is the case of M5-PCPF. Interestingly, CIX3 serves to forward a rotation in spite of the ω-wagging motion to the same (positive) direction. This means that a

Figure 8. Potential energy surfaces of S1 (in solid line) and S0 (in dashed line) with respect to τ in the region accessed by the ω-wagging motion to the negative direction. The crossing point of the curves in black, the minimum of the S1 curves in red and blue correspond to CIX1(i.e., ω = −66.1°), the geometries at ω = −58.9° and −29.7° in Figure 5a, respectively. Note that the geometries at ω = −58.9° and −29.7° are obtained by setting the linear interpolation parameter σ1 = 0.1 and 0.5, respectively, and are not minimum in S1 at each ω. The potential energy surfaces are obtained by varying τ, whereas the other geometrical parameters are fixed to those of CIX1 and the geometries at ω = −58.9° and −29.7° in Figure 5a, respectively. The energies are relative to that in S0 by SA2-(2,2)CASSCF at S0-geometry(CPF).

rocking motion of the C5′H2 part (i.e., the interchange of pseudoaxial and pseudoequatorial positions between the H5a′ and H5b′ atoms), which is strongly coupled with a puckering of the 2-cyclopentenylidene ring, is also important to determine a direction of the τ rotation after electronic relaxation at CIX. The topographical features around CIX1 are different from those of CIX2 and CIX3. This is due to the fact that CIX1 is accessed from S1-geometry only by the ω-wagging motion to the negative direction and additional geometrical changes mentioned above are no longer needed, unlike the cases of the accesses to CIX2 and CIX3. Figure 8 shows the potential energy surfaces of S1 and S0 in the CIX1 region with respect τ. It is found that CIX1 is a peaked-type CIX.27 For confirmation, we optimized CIXs starting from two geometries where the ωwagging angles are negatively large but the other parameters are

taken from those of CIX2 and CIX3. As a result, we obtained the optimized geometries substantially same as CIX1. As seen in Figure 8, the topographical features of S0 are common to the region ranging from CIX1 (i.e., ω = −66.1°) to S1-geometry. In τ < 90° (note: τ = 88.8° is a crossing point of CIX1), the S0 surface is open to the reactant region, whereas it is open to the product region in τ > 90°. This means that CIX1 is a branching point to determine the direction of rotation, unlike the case of CIX2 and CIX3. We further mention what makes the difference of the topographical features among CIX1, CIX2 and CIX3 from a viewpoint of the β-rocking motion of the fluorene stator. By the ω-wagging motion to the negative direction (i.e., S1-geometry 12535



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Depending on the total signs of ω+β− (− for CIX2) and ω+β+ (+ for CIX3), the directions of the τ rotations after electronic relaxation into S0 are backward and forward, respectively. In the case of CIX1 with ω−β0, a notation of ± is assigned and hence indicates that CIX1 serves to forward and backward rotations. For summary, we tabulated the relationship between the direction of the τ rotation and the ω−β coupling for CIXs of CPF as well as M5-PCPF (see Table 3).

→ CIX1), the bending angles of C9aC9C1′, C8aC9C1′ and C9aC9C8a around the C9 atom of the fluorene stator become small, while β remains close to 0°. This means that the fluorene stator (the C9aC9C8a part more precisely) greatly wags but little rocks against the C9C1′ rotary axis. By the ω-wagging motion to the positive direction, on the other hand, β becomes negatively large (β = −8.3°) in accord with the wagging motion to the positive direction to reach CIX2, whereas β becomes positively large (β = 8.0°) to reach CIX3. This means that the β-rocking motions of the fluorene stator to the negative and positive directions are also important to reach CIX2 and CIX3, respectively. In order to validate that β is a deterministic factor for the direction of rotation, we will discuss a role of the βrocking motion of the C9aC9C8a part of M5-PCPF in the following. M5-PCPF has two relaxation channels of CIX1(M5-PCPF) and CIX2(M5-PCPF) which can be accessed from S1geometry(M5-PCPF) by the ω-wagging motions to the opposite directions, as already reported.16 At both of them, the 2-cyclopentenylidene ring puckers to the negative direction

Table 3. Relationship between the Direction of τ-Rotation and the ω−β Coupling geometry

ω

β

ωβ

τ-rotation

CPF CIX1 CIX2 CIX3

− + +

CIX1 CIX2

− +

±a − + M5-PCPF − + − −

0 − +

forward and backward backward forward forward backward

A notation of ± is assigned in the case that a CIX serves to forward and backward rotations. This is due to the fact that the β-rocking deformation is small (i.e., β ≈ 0°). a

and the Ce atom (corresponding to the H5a′ atom of CPF) takes a pseudoaxial position (refer to Table 1). This means that the pentamethylene chain prevents the 2-cyclopentenylidene part from changing into other conformations by the ring puckering motion. At both CIX1(M5-PCPF) and CIX2(M5PCPF), actually, the 2-cyclopentenylidene ring remains to pucker to the negative direction. Nevertheless, CIX1(M5PCPF) and CIX2(M5-PCPF) are classified as a sloped-type CIX and serve to exclusively forward and backward rotations, respectively. Therefore, the β-rocking motion of the fluorene stator is possible to be more important in couple with the ωwagging motion, although the importance of the β-rocking motion in CPF seems to be at most comparable to those of the other two factors (i.e., a puckering of the 2-cyclopentenylidene

Before closing this subsection, it is worthwhile to comment on why there are two types of CIXs (i.e., CIX2(CPF) and CIX3(CPF)) in the positive ω-wagging motion, whereas there is only CIX1(CPF) in the negative direction. In the case that only the wagging motion takes place to the positive direction, the C9a and C8a atoms of the fluorene stator are close to the H5b′ and H5a′ atoms in the 2-cyclopentenylidene rotor, respectively. Actually, we calculated the nonbonded distances of C9a−H5b′ and C8a−H5a′ at an artificial geometry, where τ and ω are adjusted to be 89.7° (i.e., τ at S1-geometry) and 67.5° (i.e., ω at CIX2), respectively, and the C9aC9C1′ and C8aC9C1′ angles are set to 103.0° (hence, β = 0°), while the other geometrical parameters are fixed to those of S1-geometry. The nonbonded distances of C9a−H5b′ and C8a−H5a′ at the artificial geometry are calculated to be 2.565 and 2.573 Å, whereas they are 2.686, 2.963 Å at CIX2, and 2.954, 2.682 Å at CIX3. This means that three additional geometrical deformations are effective to reduce the steric repulsion between the stator and rotor, although the directions of these deformations discriminate between CIX2 and CIX3. In the case of the ω-wagging motion to the negative direction, the H2′ atom of the 2cyclopentenylidene rotor is close to the C9a and C8a atoms of the fluorene stator but the nonbonded distances of C9a−H2′

ring, and interchange of the relative positions between the H5a′ and H5b′ atoms). Actually, β-values are much larger in negative (β = −33.3° for CIX1(M5-PCPF) and β = −24.8° for CIX2(M5-PCPF)) than that of CIX2(CPF) (β = −8.3°). In other words, in the case that the changes of the two factors are suppressed by the pentamethylene chain (i.e., M5-PCPF), only the β−ω coupling is important. In the case of no constraint such as pentamethylene chain (i.e., CPF), on the other hand, the other two factors also become important superficially. Considering that the changes of the two factors are strongly affected by β and ω; however, they are subsidiary to the β−ω coupling. In summary, the β−ω coupling of CPF and its derivatives determines a type of CIX and direction of the τ rotation. The direction of the τ rotation (also type of CIX) can be related with the β−ω coupling by the following arithmetic operations. Depending on the positive and negative directions of the ω-wagging motion of the fluorene stator, ω is supposed to be assigned to +1 and −1, respectively. Similarly β is assigned to +1, −1, and 0 (no rocking motion), respectively. Thereby, the product of ωβ gives +1, −1, and 0. The value of 0 corresponds to a peaked-type CIX and the CIX serves to forward and backward rotations (i.e., CIX1(CPF)). Nonzero values of ±1 correspond to a sloped-type CIX. Furthermore, a CIX with +1 is an exit channel for forward rotation (i.e., CIX3(CPF) and CIX1(M5-PCPF)), whereas a CIX with −1 is for backward rotation (CIX2(CPF) and CIX2(M5-PCPF)). This relationship is also confirmed by the notations in Figure 4.

and C8a−H2′ even at CIX1 are large (2.958 and 2.970 Å, respectively). Therefore, no further deformations are needed for the H2′ atom of the 2-cyclopentenylidene rotor to escape from the nonbonded C9a and C8a atoms of the fluorene stator. As a result, only a CIX (i.e., CIX1(CPF)) is located in the negative ω-wagging region. Consequently, CIX1(CPF) plays a role of forward rotation as well as backward rotation, whereas the other two CIXs (i.e., CIX2 and CIX3) play respective roles of forward and backward rotations in the positive ω-wagging region. 3.5. Relationship between Topographical Features and Electronic Structures in the CIX Region. We mentioned above that fluorene-based ethylenoids in S1 have a 12536



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positive curvature with respect to ω around S1-geometry. In this subsection, we try to rationalize it from a viewpoint of electronic structures. Table 4 lists the one-electron properties

Similar discussions can be done in other cases. In summary, the ω-wagging motion leads to a pyramidal geometry around the C9 atom as well as a change of the hybridization on the C9 atom from sp2 into sp3 and consequently destroys a 14π delocalized system of the anionic fluorene. This is an explanation from the viewpoint of the electronic structures for the reason that the potential energy surface of S1 has a positive curvature with respect to ω around S1-geometry. In real systems, molecular rotary motors including fluorenebased rotary motors work well both in polar and nonpolar solvents. Our computational results where M5-PCPF (and CPF) is treated as an isolated molecule are true for the case in nonpolar solvent. Considering that the S1 state is wholly polarized over the CIX region and hence the S1 surface is evenly shifted down in polar solvent, however, our results are also transferrable to the case in polar solvent with minor revisions.

Table 4. One-Electron Properties in the CIX Regionsa chargeb dipole moment(Debye) S0 S1

0.64 11.63

NPR ZWI

0.49 7.92

NPR ZWI

1.02 8.44

NPR ZWI

1.01 7.80

S0 S1

0.84 10.65

NPR ZWI

0.45 7.51

NPR ZWI

1.09 6.80

fluorene (C9)

S1-geometry(CPF) 0.06(0.03) −0.76(−0.46) CIX1(CPF) 0.09(0.07) −0.59(−0.48) CIX2(CPF) 0.12(0.09) −0.62(−0.50) CIX3(CPF) 0.06(0.04) −0.57(−0.45) S1-geometry(M5-PCPF) 0.04(0.03) −0.76(−0.48) CIX1(M5-PCPF) 0.07(0.03) −0.59(−0.47) CIX2(M5-PCPF) −0.03(−0.04) −0.53(−0.39)

2-cyclopentenylidene (C1′) −0.06(−0.20) 0.76(0.35) −0.09(−0.22) 0.59(0.28) −0.12(−0.22) 0.62(0.29)

4. CONCLUDING REMARKS In the present paper, we computationally examined CPF which is a parent molecule of a light-driven molecular rotary motor of M5-PCPF. By means of the intrinsic reaction coordinate analysis of the excited state from S0-geometry to S1-geometry, we reconfirmed that a dark state of π(fluorene)π*(ethylene) less contributes to the photochemistry and hence our approach of (2,2)CASSCF is reasonable. In addition, we obtained a new insight of the photochemical process of CPF as well as M5PCPF. Upon ethylenic ππ* excitation of CPF, the rotary axis of the ethylenic double bond first becomes longer, and then the torsional motion around the rotary axis easily takes place into the forward and backward regions to reach stable geometries in the perpendicularly τ-twisted regions (i.e., S1-geometry and S1′geometry). In the case of M5-PCPF, the elongation of the rotary axis is also an initial event. Once the rotary axis is elongated in the Franck−Condon region, however, only a forward rotation takes place because M5-PCPF inherently puts on a downhill surface with respect to the τ torsion in the spectroscopically bright state, and a backward rotation is prohibited by the overcrowded substituents in the 2-cyclopentenylidene rotor. Concerning the CIX regions which are the main interest in the present study, we found out the similarities and differences between CPF and M5-PCPF. In both cases, the S1 state is highly polarized so that the anionic fluorene part with the 14π system is stabilized. Therefore, the curvature in S1 with respect to the ω-wagging motion of the fluorene stator is positive around S1-geometry. Contrary to the case wherein the photochemical rotary process of M5-PCPF takes place under constraint of the pentamethylene chain, that of CPF takes place without such a constraint. The difference between them causes a difference of the topographical features around CIXs. By the ω-wagging motion of the fluorene stator from S1-geometry to the negative direction, CPF reaches a peaked-type CIX which is a branching point for forward and backward rotations. On the other hand, CPF reaches other CIXs by the ω-wagging motion to the positive direction and three additional geometrical deformations (i.e., the puckering of the 2-cyclopentenylidene ring, interchange of the relative positions between the two H atoms bonded to the C5′ atom, and the rocking motion of the fluorene stator against the rotary axis). Depending on the directions of three additional deformations, two sloped-type CIXs serve to rotate exclusively forward and backward,

−0.06(−0.18) 0.57(0.25) −0.04(−0.25)c 0.76(0.29) −0.07(−0.27) 0.59(0.22) 0.03(−0.18) 0.53(0.15)

a

Except for S1-geometry(CPF) and S1-geometry(M5-PCPF), the terms of S0 and S1 at CIX are meaningless, and alternatively, the nonpolar diradical state and zwitterionic state are denoted by NPR and ZWI, respectively. bThe charges were evaluated by Löwdin population analysis. The values in the parentheses are charges on the C9 and C1′ atoms. cIn the case of M5-PCPF, the charges of the phenyl and pentamethylene parts are included as those of the 2-cyclopentenylidene part.

of CPF and M5-PCPF in the CIX regions. From this table, it is found that the S1 state in the CIX region is highly polarized irrespective of CPF and M5-PCPF. In addition, the dipole moments in S1 decrease by the wagging motions to reach CIXs. We explain these findings by referring to the process of S1geometry → CIX1 of CPF. As seen from the charge populations of CPF, the C9C1′ bond is highly polarized like a C9−C1′+ in the S1 state at S1-geometry(CPF). This is due to a charge transfer from the 2-cyclopentenylidene rotor to the fluorene stator. The charge transfer causes a stabilization of the fluorene part at S1-geometry(CPF) because the anionic fluorene are delocalized by the 14π electrons. Therefore, the ω-wagging motion destroys a delocalized 14π system of the anionic fluorene and hence causes an energetic instability. Actually, the electron which is transferred into the fluorene part at S1-geometry is pushed back to the 2-cyclopentenylidene ring by the ω-wagging motion to CIX1. From a geometrical viewpoint, a delocalized system of the fluorene part is also found to be destroyed. The C9C9a and C9C8a bonds become longer (1.441 Å (S1-geometry) to 1.485 Å (CIX1), 1.441 Å (S1geometry) to 1.484 Å (CIX1)). The bond angles of C9aC9C1′, C8aC9C1′ and C9aC9C8a become smaller, as listed in Table 1. 12537



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Table A1. Characteristic optimized parameters by (10,10)CASSCF methodsa geometry

S0-geometry

S1-geometry

CIX1

Bond Distance (Å) C9C1′

1.343(1.343)

1.422(1.432)

1.427(1.431)

Bond Angles (deg) C9aC9C1′ C8aC9C1′ C9aC9C8a

128.7(128.6) 126.5(126.5) 104.8(104.9)

τ C1′C2′C3′C4′ C2′C3′C4′C5′ H5a′C5′C4′C3′c) H5b′C5′C4′C3′ c)

1.8(1.7) 0.6(0.5) −2.0(−1.6) −117.9(−118.3) 123.2(122.8)

ω ω′

−0.9(−1.0) −0.4(−0.4)

125.1(125.6) 126.4(126.2) 108.3(108.0) Dihedral Angles (deg) 90.0(89.7) 0.0(−0.4) −0.0(−0.1) −118.9(−118.2) 119.1(119.7) Wagging Angles (deg) 3.7(3.6) 0.3(0.3)

105.8(104.4) 105.8(105.4) 101.7(101.3) 90.0(88.8) 0.1(0.2) 0.1(0.1) −118.9(−119.2) 118.1(117.8) −64.4(−66.1) 0.2(0.1)

a S0-geometry was optimized by an S0-specific (10,10)CASSCF, whereas the others were optimized by SA2-(10,10)CASSCF. The values in the parentheses are the optimized parameters by (2,2)CASSCF methods in Table 2.

HOMO-1, HOMO-2, etc., and LUMO+1, LUMO+2 etc. at the key geometries are more than 1.9 and less than 0.1, respectively.

respectively. In the case of M5-PCPF where the ring puckering and the CeC5′H5′ rocking (corresponding to the C5′H2 rocking of CPF) motions are prohibited by a constraint of the pentamethylene bridge, the β-rocking motion of the fluorene stator is essential to reach CIXs. The ω-wagging motion to the negative direction is accompanied with the β-rocking motion to the negative direction. This leads to a sloped-type CIX for a forward rotation of M5-PCPF. A constraint of the pentamethylene bridge forces the β-rocking motion of the fluorene stator to take place to the negative direction even by the ωwagging motion to the positive direction, which leads to another sloped-type CIX for a backward rotation. In conclusion, the β-rocking motion of the fluorene stator, which is possible to be strongly coupled with the ω-wagging motion in some cases, is a deterministic factor for a type of CIX and the direction of the τ rotation. From a general viewpoint of the photoisomerization of ethylenoids, the present computational findings of the CIX region can be paraphrased into the following:

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ASSOCIATED CONTENT

S Supporting Information *

Table for characteristic optimized parameters in the latter half of rotary cycle of CPF. All Cartesian coordinates of the key geometries in the full rotary cycle. 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]. FAX: +81-18-889-2625. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

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

(1) A wagging motion of the anionic part of ethylenoids against the ethylenic rotary axis in the CIX region is an essential factor to reach CIX. (2) In some cases, a rocking motion of the anionic part against the rotary axis is needed to reach CIX. (3) The directions of the wagging and rocking motions determine a type of CIX and direction of rotation around the ethylenic bond. Hereby we can examine whether the present computational findings are also true for other (especially nonfluorene-based) ethylenoids or not. Such a work, which is now in progress, will give us a deeper understanding of the photoisomerization of ethylenoids and in addition a guiding principle for a better light-driven molecular rotary motor.

(1) Kottas, G. S.; Clarke, L. I.; Horinek, D.; Michl, J. Artificial Molecular Rotors. Chem. Rev. 2005, 105, 1281−1376. (2) Koumura, N.; Zijlstra, R. W. J.; van Delden, R. A.; Harada, N.; Feringa, B. L. Light-driven monodirectional molecular rotor. Nature 1999, 401, 152−155. (3) ter Wiel, M. K. J.; van Delden, R. A.; Meetsma, A.; Feringa, B. L. Increased Speed of Rotation for the Smallest Light-Driven Molecular Motor. J. Am. Chem. Soc. 2003, 125, 15076−15086. (4) Vicario, J.; Meetsma, A.; Feringa, B. L. Controlling the Speed of Rotation in Molecular Motors. Dramatic Acceleration of the Rotary Motion by Structural Modification. Chem. Commun. 2005, 5910− 5912. (5) Vicario, J.; Walko, M.; Meetsma, A.; Feringa, B. L. Fine Tuning of the Rotary Motion by Structural Modification in Light-Driven Unidirectional Molecular Motors. J. Am. Chem. Soc. 2006, 128, 5127−5135. (6) Kulago, A. A.; Mes, E. M.; Klok, M.; Meetsma, A.; Brouwer, A. M.; Feringa, B. L. Ultrafast Light-Driven Nanomotors Based on an Acridane Stator. J. Org. Chem. 2010, 75, 666−679.

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APPENDIX The ethylenic ππ* state, which is our main interest in the present study, is well described by the HOMO and LUMO of CPF irrespective of the geometries. As listed in Table A1, the key geometries by (10,10)CASSCF are similar to those by (2,2)CASSCF in Table 2. The occupation numbers of the 12538



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Theoretical Study of Topographical Features around the Conical

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