ARTICLE pubs.acs.org/JPCA
Theoretical Design of a Light-Driven Molecular Rotary Motor with Low Energy Helical Inversion: 9-(5-Methyl-2-phenyl-2-cyclopenten-1ylidene)-9H-fluorene Yoshiaki Amatatsu* Faculty of Engineering and Resource Science, Akita University, Tegata Gakuen-cho, Akita 010-8502, Japan ABSTRACT: A light-driven molecular rotary motor of 9-(5-methyl-2-phenyl-2-cyclopenten-1-ylidene)-9H-fluorene (MPCPF) has been designed by means of ab initio complete active space self-consistent field and its second order multireference MøllerPlesset perturbation methods. In the present model molecule of MPCPF, 9Hfluorene (as a stator) and 5-methyl-2-phenyl-2-cyclopenten-1-ylidene (as a rotor) are directly linked with each other by a CdC double bond. Even by a substitution of phenyl group, MPCPF comes to have a stable P-helical MPCPF and a metastable M-helical MPCPF, and exhibits unidirectionality around the CdC double bond. In addition, interchange of the helicity can proceed with a low energy barrier through a floppy phenyl torsional motion. This is in contrast to previous light-driven molecular rotary motors where the unidirectionality is ensured by rigid and sterically overcrowded rotors. In the full rotary process of MPCPF, therefore, constancy of the rotation speed is expected to be much more improved as well as unidirectionality.
1. INTRODUCTION Light-driven molecular rotary motors118 are one of the most important molecular devices fueled by light, as well as molecular scissors19 and switches.20,21 Feringa and co-workers first reported an artificial light-driven molecular rotary motor which realizes a 360° unidirectional rotation around the ethylenic double (CdC) bond.1 In their model molecule, two factors for a unidirectional rotation have been considered. One factor is a helical chirality which is realized by connection of two sterically overcrowded tetrahydrophenanthrylidenes with each other. The second factor is a presence of chiral centers which governs the relative stability between the two helical conformations. Upon irradiation of UV light, the model molecule proposed there realizes a 360° unidirectional rotation, which is composed of four consecutive steps; two photochemical steps each followed by a thermal conversion step. The first and the third steps of the photoisomerization around the ethylenic double bond are very fast, in which processes a stable conformer is transformed into a metastable one. On the other hand, the second and the forth steps, where a metastable conformer is transformed into a stable one through a thermal helical inversion, are terribly slower than the preceding photochemical process. Therefore, this model molecule has a serious problem in a constancy of rotation speed, despite that it ensures a 360° unidirectional rotation. Since this pioneering work, many challenges have been made to realize more effective transformation from a metastable conformer into a stable one in the thermal helical inversion process.28,1118 According to recent reports, the helical inversions take place with half-lifetimes of 70 ms for the fluorene-based molecular motor15 and 574 ns for the acridane-based molecular motor,13 respectively. In spite of great improvement of a thermal helical inversion process, however, r 2011 American Chemical Society
the rotation speed in a 360° unidirectional rotary process is still awkward because a photochemical process of the CdC torsion takes place at most in a few picoseconds and the ratio of the rates between the thermal process and the photochemical process is still large. In previous model molecules, rigid and sterically overcrowded rotors, such as tetrahydrophenanthryl and dihydroindenyl skeletons, and their analogues, ensure helicity and unidirectionality but may also prevent low energy helical inversion between a metastable conformer and a stable one. In modeling a lightdriven molecular rotary motor, therefore, we do not make use of a rigid and sterically overcrowded rotor to ensure helicity and unidirectional rotation. Alternatively we make use of an overcrowded rotor with a floppy internal motion such as phenyl torsion, possibly leading to a much lower energy barrier in the helical interchange. The present paper is organized as follows. In section 2, we model a new light-driven molecular rotary motor based on the above idea. Then, in section 3, we describe a computational strategy to examine the present model molecule of 9-(5-methyl-2phenyl-2-cyclopenten-1-ylidene)-9H-fluorene (denoted by MPCPF hereafter) shown in Figure 1. In section 4, we mention the geometric features at important conformations of MPCPF and then discuss the full rotary cycle. Last, in section 5, we give a summary on the molecular character of MPCPF from the viewpoint of the performance of a light-driven molecular rotary motor. Received: July 29, 2011 Revised: September 21, 2011 Published: October 03, 2011 13611
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0
Figure 1. Numbering of atoms in MPCPF. Only the H12 atom out of the H atoms is drawn.
2. MODELING OF MOLECULAR ROTARY MOTOR As pointed out in the Introduction, rigid and sterically overcrowded rotors such as the dihydroindenylidene skeleton serve to form a local helical structure but also prevent an interchange between the two helical isomers. Therefore, we tried to modify a model molecule of 9-(2,4,7-trimethyl-2,3-dihydro-1H-inden-1ylidene)-9H-fluorene, whose performance as a light-driven molecular rotary motor has been recently examined by Filatov and co-workers.12,18 We adopt MPCPF as the present model in Figure 1. Our modification against the previous model is quite simple. A rigid and sterically overcrowded 2,4,7-trimethyl-2,3dihydro-1H-inden-1-ylidene rotor is replaced by 5-methyl-2phenyl-2-cyclopenten-1-ylidene (hereafter we call it 5-methyl2-phenyl-2-cyclopentenylidene for convenience) and the rotor of 5-methyl-2-phenyl-2-cyclopentenylidene is directly linked with the stator of 9H-fluorene (we call it fluorene hereafter) by an ethylenic double bond. Thereby the present rotor is sterically overcrowded similar to the rotor in the previous model, but a floppy phenyl torsional motion is expected to lead to an easy helical inversion. A schematic representation of the full rotary cycle of MPCPF is shown in Figure 2, although the conformations in this figure will be discussed later, based on the computational findings. The geometry of P-MPCPF, which is the most stable in S0, takes a P-helical structure due to a steric repulsion between the phenyl group and the fluorene stator. P-MPCPF is excited into S1 and then reaches the conical intersection between S0 and S1 (denoted by CIX) through torsion of the ethylenic double bond which links the rotor with the stator. Once MPCPF electronically relaxes into S0 in the vicinity of CIX, MPCPF is able to take a metastable geometry in S0 (M0 -MPCPF) through a further CdC torsion accompanied by the phenyl torsion. M0 MPCPF and another globally stable geometry of P0 -MPCPF are separated by a transition state (TS0 ). However, M0 -MPCPF is expected to easily change into P0 -MPCPF through a floppy phenyl torsion. A similar discussion can be done on the latter half-rotary cycle of P0 -MPCPF f CIX0 f M-MPCPF f TS f P-MPCPF. Our present purpose is to examine the potential energy surfaces of the full rotary cycle and to validate the present model as a lightdriven molecular rotary motor by means of a reliable level of ab initio calculations.
Figure 2. Schematic representation for the full rotation cycle of MPCPF. See the text for abbreviations of the conformers. The substituent R is a 6 0 70 8 0 methyl group. The red and cyan parts correspond to C C C and 0 0 0 C6 C11 C10 in Figure 1, respectively. The solid and the dotted parts colored red, cyan, and green are above and below the fluorene stator, respectively. The solid and wavy lines for each step represent that MPCPF is in S0 and S1, respectively.
3. METHOD OF CALCULATIONS We preliminarily performed configuration interaction (CI) calculations where up to triple excitations from the Hartree Fock configuration were taken into account at various geometries possibly contributing to the 360° unidirectional rotation process of MPCPF. Thereby we found the following. CI1. Both the ground and the excited states in our present interest are well described by the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) irrespective of the conformations. CI2. The HOMO and LUMO are mainly located on the ethyleninc double bond which links the rotor with the stator of MPCPF. From these computational findings, we adopted the two electrons in two orbitals complete active space self-consistent field (CASSCF) (denoted by (2,2)CASSCF) method as a present standard computational approach in scanning the potential energy surfaces. In order to compare with the energies at various geometries (including CIX and CIX0 ) for each electronic state, we adopted two state averaged (2,2)CASSCF (denoted by SA2(2,2)CASSCF) methods where the two-particle density matrices in S0 and S1 are equally weighted. From necessity for quantitative discussion, we made the energetic correction by the second order multireference MøllerPlesset perturbation (MRMP2) method where all valence and virtual orbitals were included. First we optimized the important geometries schematically shown in Figure 2. Then we tried to connect these geometries with each other by following reaction paths. Except for the determination of CIX by Gaussian 03,22 we used the GAMESS program in the present ab initio calculations.23 The basis sets used in the present calculations are classified into three parts. A HuzinagaDunning double-ζ quality 13612
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Table 1. Characteristic Optimized Parameters at Important Geometries of MPCPF geometry P-MPCPF
CIX
M0 -MPCPF
TS0
P0 -MPCPF
CIX0
M-MPCPF
TS
TSX
1.369
1.472
91.8
TSX0
bond distance (Å) 0
C9C1
1.363
1.427
1.369
1.369
τa,b
13.0
96.1
158.3
170.8
1.363
1.427
1.369
1.472
dihedral angle (deg)
0
0
9 10
20
0
0
192.8
276.2
338.8
351.6
(167.2)
(83.8)
(21.2)
(8.4)
271.7 (88.3)
9.7
51.3
156.9
162.9
172.2
56.5
18.5
2.0
82.9
101.9
33.4
0.2
8.6
10.6
32.8
0.2
8.5
12.3
9.9
10.5
37.0
93.0
130.0
95.8
37.3
93.1
129.6
92.8
46.5
47.1
1.7 17.4
2.3 3.9
0.7 0.5
0.7 11.7
1.5 17.5
2.3 4.0
1.0 1.2
0.0 11.4
1.9 10.5
1.3 8.6
92.0
135.0
121.4
102.3
92.1
135.1
120.3
102.1
139.4
136.6
145.8
101.2
117.8
136.1
145.8
101.1
118.8
136.3
99.8
102.6
ωa
1.9
63.4
3.0
9.5
2.1
63.3
3.2
10.2
3.2
3.5
ω0 a
5.5
5.7
2.7
4.5
5.2
5.6
2.8
4.7
14.9
14.6
C9aC9C1 C2
j (C C C C6 ) 0
0
0
0
0
0
ϕ (C1 C2 C6 C7 ) 0
C1 C2 C3 C4 0 0 0 0 C2 C3 C4 C5 0
0
0
0
30
40
50
120
C3 C4 C5 C12 C C C H
wagging angle (deg)
The definitions of τ, ω, and ω0 are described in the Appendix. b The values in parentheses are τ values which are defined as 180 to 180°. In some cases, these values are referred in the text for convenience. a
augmented by polarizations (DZP) (αd = 0.75 for C atoms) is applied to the five-membered rings0 in the stator and the rotor 0 (i.e., C9, C9a, C4a, C4b, C8a, and C1 C5 ) to ensure the conformational flexibility. A HuzinagaDunning double-ζ quality (DZ) is applied to the remaining part of the fluorene stator (i.e., C1C4 and C5C8). The DZ basis set is also applied to the H atoms in the stator and in the 2-cyclopentenylidene ring of the rotor. A minimal basis set (so-called MINI) is applied to the phenyl and methyl groups of the rotor, which mainly play a role of steric repulsion with the stator. In the determination of CIX, the basis set is further reduced by replacing the DZ quality on the C and H atoms into MINI, while the five-membered skeletal C atoms in the stator and the rotor keep the DZP quality.
4. RESULTS AND DISCUSSION 4.1. Geometric Features at Important Conformations in S0. We begin by mentioning the geometric features at important
conformations of MPCPF in S0. The characteristic optimized parameters are listed in Table 1. Three additional parameters of are τ, ω, and ω0 , whose definitions are described in the Appendix, 0 also listed. The torsional angle τ around the C9C1 rotary axis, which takes a value from 0 to 360°, is a measure for how many degrees the rotor twists against the stator. The wagging angle ω is a measure0 for how many degrees the fluorene stator wags against the C9C1 rotary axis, although the fluorene stator itself is almost planar irrespective of conformations in the full rotary cycle. The wagging angle ω 0 is a measure for how many0 degrees the 2-cyclopentenylidene ring wags against the C9C1 axis. In other how many degree pyramidal words, ω and ω0 are measures for 0 structures around the C9 and C1 atoms are, respectively. At P-MPCPF, which is the globally stable conformation in S0, 0 the fluorene stator wags little against the C9C1 rotary axis (refer to ω = 1.9° in Table 1). The 2-cyclopentenylidene rotor also does not wag much (ω0 = 5.5°), which is irrespective of the conformations in the full rotary cycle. (Note that TSX and TSX0 with
large nonzero ω0 values are not directly related to the conformations in the full rotary cycle, as discussed later.) On the other hand, the 2-cyclopentenylidene rotor itself is slightly tilted against the fluorene stator (τ = 13.0°). This serves to avoid a steric repulsion between the stator and the phenyl group of the rotor. In addition, the phenyl group is also twisted so0 as0 to0 be0 0 0 0 away from the stator (C9C1 C2 C6 (j) = 33.4° and C1 C2 C6 C7 (ϕ) = 37.0°). This means that the local structure of the 0 0 0 0 C1C9aC9C1 C2 C6 C7 skeleton (a so-called fjord region) takes a P-helical conformation. In other words, a helical structure can be realized even by a sterically overcrowded 2-phenyl-2-cyclopentenylidene rotor and the fluorene stator, not necessarily by a much more rigid and sterically overcrowded rotor previously reported.17,1315 Furthermore, the 2-cyclopentenylidene ring is 0 0 0 0 nonplanar (C2 C3 C4 C5 = 17.4°). The methyl group takes a pseudoaxial position to be away from the fluorene stator, whereas 0 0 the less bulky H12 atom (bonded to the C5 atom) takes a pseudo30 40 50 120 equatorial position (see the dihedral angles of C C C C = 0 0 0 0 92.0° and C3 C4 C5 H12 = 145.8°). The nonplanarity of the 2-cyclopentenylidene ring and the pseudoaxial position of the methyl group serve to stabilize the P-helical conformer more than an M-helical conformer. We also found another globally stable P-helical conformer of P0 -MPCPF at τ = 192.8°. Comparing the optimized geometric parameters with those of P-MPCPF, 0we can interpret that P0 -MPCPF is a conformation with the C9C1 rotary axis of P-MPCPF twisted by ∼180°. M-MPCPF is a locally stable conformation in S0 but energetically unstable compared with P-MPCPF. That is, M-MPCPF is a so-called metastable conformation. In a comparison of M-MPCPF with P-MPCPF in Table 1, the geometric feature of M-MPCPF is clarified. At first the phenyl torsional angle ϕ (129.6°) is very different from0 that of P-MPCPF (37.0°). The dihedral angle of 0 0 0 C1 C2 C6 C11 (52.8°, not shown in Table 1) is also 0different 0 0 from that of P-MPCPF (145.0°). This means that the C6 C11 C10 part of the phenyl group at M-MPCPF faces the fjord region, 0 0 0 whereas the C6 C7 C8 part faces it at P-MPCPF. The dihedral 13613
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Table 2. Electronic Structures at CIX chargea energyb (kcal/mol)
dipole moment (D)
fluorene (C9)
S0
83.43
8.66
0.75 (0.45)
S1
86.76
0.58
0.02 (0.13)
0
2-cyclopentenylidene (C1 )
main CSFsc
phenyl
methyl
0.12 (0.31)
0.47
0.40
0.99 (closed shell)
0.88 (0.24)
0.47
0.39
0.99 (HOMOLUMO)
0
a
The charges were evaluated by L€owdin population analysis. The values in parentheses are charges on the C9 and C1 atoms. b The energies, which are evaluated by SA2-(2,2)CASSCF with the present standard basis set, are relative to that in S0 at P-MPCPF. The energy difference is, of course, 0 in the case of energy evaluation by SA2-(2,2)CASSCF with the smaller basis set mentioned in the text. c The absolute values of the coefficients of CSFs (configuration state functions) greater than 0.30 are listed.
angle j takes a negative value (8.5°) at the M-isomer, whereas it is0 positive (33.4°) at the P-isomer. Furthermore, the C1C9aC9C1 angle (15.0°, not shown in Table 1) relevant to the helical structure is negative at the M-isomer, whereas it is positive (6.5°) at the P-isomer. These computational findings imply that a helical interchange takes place between P-MPCPF and M-MPCPF through a phenyl torsional motion. In accordance with the interchange from P-isomer into M-isomer, other geometric parameters are also changed for M-MPCPF to be stabilized. The 2-cyclopentenylidene ring of0 M-MPCPF is sub0 0 0 0 0 0 0 stantially planar (C1 C2 C3 C4 = 1.0° and C2 C3 C4 C50 = 1.2°). This leads to the fact that the methyl group and the H12 atom take equivalent positions with each other against the planar 2-cyclo0 0 0 0 0 0 0 0 pentenylidene ring (C3 C4 C5 C12 = 120.3° and C3 C4 C5 H12 = 118.8°), whereas those of globally stable P-MPCPF take pseu30 40 50 120 C C C = 92.0°) and pseudoequatorial doaxial (C 0 0 0 0 (C3 C4 C5 H12 = 145.8°) positions, respectively. In addition, τ, which is a main geometric parameter for the rotary cycle, takes a negative (21.2°, i.e., 338.8°) value at the M-isomer, whereas it is positive (13.0°) at the P-isomer, In summary, two helical isomers of P-MPCPF and M-MPCPF are originated from a sterically overcrowded fjord structure, which is the same as the case of previous light-driven molecular motors. On the other hand, the helical structures of M-MPCPF and P-MPCPF interchange with each other through a floppy phenyl torsional motion, in contrast to the case where two helical isomers in previous lightdriven molecular motors interchange with each other by a rigid helical inversion between the stator and the rotor in the fjord region.17,1315 The other metastable helical conformation of M0 MPCPF, 0which is possibly a product from P-MPCPF by a twist of the C9C1 axis, has a geometric feature similar to that of M-MPCPF except for τ (158.3° for M0 -helix and 21.2° for M-helix). Considering the relationship τ(M0 -MPCPF) ∼ τ(M-MPCPF) + 180°, M0 -MPCPF is found to be a conformation obtained by a simple τ-twist of 180° from M-MPCPF, although a more delicate geometric relationship between them will be pointed out later. Next we mention the transition state (TS) between the P-isomer and the M-isomer. The torsional angle τ (8.4°) takes an intermediate value between those of the M-isomer (21.2°) and the P-isomer (13.0°). This implies that TS is located between M-MPCPF and P-MPCPF from a viewpoint of geometry. The dihedral angles relevant to the 2-cyclopentenylidene ring, the 0 0 methyl group, and the H12 atom bonded to the C5 atom are also intermediate values between two helical isomers. As mentioned above, the dihedral angles j and ϕ relevant to the phenyl torsion determine a helical structure in the fjord region. These values at TS are also intermediate between two helical isomers. Especially, the phenyl group is almost perpendicularly twisted (ϕ =0 92.8°). 0 0 0 0 0 This leads to the fact that the C6 C7 C8 and C6 C11 C10 parts in the phenyl group are equivalently away from the fluorene stator,
0
0
0
0
0
0
whereas the C6 C7 C8 and C6 C11 C10 parts are closer to the fluorene stator at P-MPCPF and M-MPCPF, respectively. In other words, TS corresponds to a switching point of the helicity through the phenyl torsional motion. It is interesting that the fluorene stator is more wagging than those of the P- and M-helical isomers (see ω’s, 10.2° (TS), 1.9° (P-MPCPF), and 3.2° (M-MPCPF)). Considering that ω is a measure for pyramidal structure around the C9 atom, sp3 character on the C9 atom at TS increases from sp2 in the helical interchange between the P-helix and the M-helix. TS0 is another transition state between M0 -MPCPF and P0 MPCPF. The torsional angle τ (170.8°) is intermediate between M0 -MPCPF(τ = 158.3°) and P0 -MPCPF(τ = 192.8°), implying that TS0 is located between the M0 -isomer and the P0 -isomer from a geometric viewpoint. In a comparison of τ(TS0 ) with τ(TS), the relationships of τ(TS0 ) ∼ τ(TS) + 180° and ω(TS0 ) ∼ ω(TS) are found. However, the other geometric features of TS0 are similar to those of TS. In other words, TS0 can be related to TS by a τ-twist of 180° and a wagging inversion of the fluorene stator. Incidentally, the relationships of ω(M0 -MPCPF) ∼ ω(M-MPCPF) and ω(P0 -MPCPF) ∼ω(P-MPCPF) are also found, although both absolute values are much smaller than those at TS and TS0 . This means that, strictly speaking, M0 -MPCPF and P0 -MPCPF are also related respectively to M-MPCPF and P-MPCPF in the same manner of a τ-twist of 180° and a wagging inversion of the fluorene stator, although we previously mentioned that M0 -MPCPF and P0 -MPCPF are related respectively to M-MPCPF and P-MPCPF by a simple τ-twist of 180°. 4.2. Conical Intersections (CIX and CIX0 ). The CIX (and CIX0 ) is one of the most important geometries in discussing the light-driven molecular rotary motor of MPCPF. Before describing the geometric feature of CIX, we validate our computational strategy that a smaller basis set was used in the determination of CIX. As seen in Table 2, the energy difference between S0 and S1 is small (3.33 kcal/mol) enough to be a CIX. This implies that the CIX is similar to a CIX by much more computational demand with the present standard basis set. Concerning the geometry of CIX, it is found that the 2-cyclopentenylidene rotor is almost perpendicularly twisted against the fluorene stator (τ = 96.1°) and is located on the way from P-MPCPF (13.0°) to M0 -MPCPF (158.3°). Other geometric features at CIX are clarified in comparison with those at P-MPCPF and M0 -MPCPF. In the process of P-MPCPF f from CIX f M0 -MPCPF, the phenyl torsional angle ϕ changes 0 0 0 0 37.0° f 93.0° f 130.0°, while the dihedral angle of C1 C2 C6 C11 (not shown in Table 1) changes from 145.0° f 90.8° f 52.2°. The dihedral angle j changes from a positive value (33.4° at P-MPCPF) to a negative value (8.6° at M0 -MPCPF) 0 0 0 and is close to zero at CIX (0.2°). This means that the C6 C7 C8 60 110 100 and C C C parts face the fjord regions at P-MPCPF and 13614
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Figure 3. Snapshot of CIX. The C09 and C10 atoms are in red. The C9a 1 60 and C atoms in the stator, C , C7 , and C8 of the0 phenyl group in the 0 0 rotor are also in red in order to depict that the C6 C7 C8 part no longer faces the C1C9aC9 part in the fjord region of the stator and alternatively faces the C8C8aC9 part.
M0 -MPCPF, respectively. At CIX, on the other hand, the phenyl group is perpendicularly twisted against the 2-cyclopentenylidene ring (i.e., ϕ = 93.0°) in addition to the perpendicular twist of the 2-cyclopentenylidene rotor against the fluorene0 stator (i.e., 6 70 80 C C and τ =0 96.1°) (see Figure 3). Thereby both the C 0 0 C6 C11 C10 parts of the phenyl group in the rotor come to face region0 of 0the stator, the C9C8aC8 and C9C9aC1 parts in 0the0 fjord 0 0 respectively. In other words, the C6 C7 C8 and C6 C11 C10 parts face respective benzene 0rings in0 the stator. This0 is in contrast to 0 0 0 the fact that both the C6 C7 C8 and C6 C11 C10 parts face one of the benzene rings in the stator at TS (and TS0 ). Except for this point, however, the discussion is similar to that in the helical interchange between P-helix and M-helix at TS. Therefore, we interpret that a helical interchange takes place at CIX. Our interpretation is supported also by a negatively large value of ω (63.4°). As pointed out in the discussion of TS, a helical interchange is accompanied by a wagging motion of the fluorene stator. This is also true in the case of CIX. As seen in a snapshot of0 CIX in Figure 3, the fluorene stator highly wags against the C9C1 rotary axis so that a local geometry around the C9 atom is pyramidal, not planar. On the other hand, the 2-cyclopentenylidene rotor does not wag as much (ω0 = 5.7°) as the cases 0 of other conformations. That is, a local geometry around the C1 remains almost planar trigonal.0 In0 addition, the 2-cyclopentenylidene ring 0 0 0 0 0 0 is almost planar (C1 C2 C3 C4 = 2.3°, C2 C3 C4 C5 = 3.9°). Concomitant with a planarity of the 2-cyclopentenylidene ring, 0 the methyl group and the H12 atom interchange relative positions. The methyl group takes a pseudoequatorial position 0 0 0 0 120 (C3 C4 C5 C012 0= 135.0°), while the H atom takes a pseudo0 0 0 axial one (C3 C4 C5 H12 = 101.2°). The C9C1 rotary axis (1.427 Å) is longer than a normal CdC double bond, although those of other conformations mentioned above (1.361.37 Å) are a normal CdC double bond. In comparison of CIX0 with CIX in Table 1,
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CIX0 can be related to CIX by a τ-twist of 180° and a wagging inversion of the fluorene stator, as found in the relationships of TS and TS0 , P- and P0 -MPCPF, and M- and M0 -MPCPF. We turn to discuss the electronic structure at CIX. As listed in Table 2, the dipole moment in the state described by a closed shell (S0 in this case) is large (8.66 D), while that by HOMO LUMO single excitation (S1) is small (0.58 D). Therefore, we examined why the dipole moments are very different from each other in terms of the charge populations. The charge populations for each fragment are listed in Table 2. In the electronic state with a small dipole moment (i.e., S1), the 2-cyclopentenylidene rotor is high negatively charged due to an electron donation from the phenyl and methyl groups, whereas the fluorene stator is almost neutral. In the state with a large dipole moment (i.e., S0), on the other hand, the fluorene stator is high negatively charged due to an electron flow 0from the 2-cyclopentenylidene rotor. Focusing on the C9 and C1 charges in S0 and S1, we conclude that the state with 0a large dipole moment is a zwitterionic state where the 0 C9C1 bond is greatly polarized as a C9‑-C1 + bond. The counter state 0with a small dipole moment is a diradical state 0 where the C9C1 bond is a nonpolar diradical like a C9•C1 •. From a viewpoint of geometry, CIX is characterized by a perpendicular τtwist accompanied by a pyramidalization around the C9 atom of the fluorene stator, not by a simple perpendicular τ-twist. The geometric feature at CIX is in close relation to the electronic structures mentioned above. The hybridization on the negatively charged C9 atom is sp3, whereas that on the positively charged 10 C remains to sp2. As 0a consequence, the fluorene stator greatly wags against the C9C1 axis (ω = 63.4°), whereas the 2-cyclopentenylidene rotor does not wag as much (ω0 = 5.7°). Here it is worthwhile making a comment on why ω takes a large negative value, not a positive one. As mentioned above, the C9 atom has sp3 character in the CIX region, which leads to a large positive or negative ω. As deduced from Figure 3, however, a large positive ω causes a serious steric repulsion between the fluorene stator and the methyl group in the rotor. On the other hand, a large negative ω can successfully escape from the steric repulsion and in addition a flexible phenyl torsional motion can reduce a steric repulsion between the fluorene stator and the phenyl group by a perpendicular twist of the phenyl group (ϕ = 93.0°). In summary, the CIX is a crossing region between a diradical and a zwitterionic state from the viewpoint of the electronic structure, and is characterized as a perpendicular twist of the ethylenic double bond accompanied by a pyramidalization around the negatively charged C atom in the CdC bond (i.e., the C9 atom in this case) from the viewpoint of geometry. Interestingly, the electronic and geometric features at CIX are not intrinsic to MPCPF but rather are common to ethylenoids such as ethylene,24,25 styrene,26,27 stilbene,28,29 their derivatives,30,31 and ethylene-bridged molecular motor.12,16 4.3. Unidirectional Rotary Process. Now we discuss the unidirectional rotary process of MPCPF based on the geometric feature mentioned above. The globally stable P-MPCPF in S0 is excited into S1. In order to theoretically examine how MPCPF behaves in S1 upon electronic excitation, a molecular dynamics simulation or intrinsic reaction coordinate analysis is desirable. However, we checked the behavior of MPCPF by an easier approach of geometry optimization in S1 starting from P-MPCPF. Thereby we found that P-MPCPF in S1 goes to the CIX region. Therefore, our concern is how the geometry in S1 changes in the process of P-MPCPF f CIX. We checked the large geometric difference between P-MPCPF and CIX and then picked up 13615
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The Journal of Physical Chemistry A the large energy gradient components in S1 at P-MPCPF, i.e., 9 10 C ) and 0.0341 au (the dihedral angle C9aC90.0609 au (C 10 20 C C ). It is also found that the energy0 gradient components of 1 double bond (i.e., the the bonds conjugated with the 0C9C 0 0 10 20 2 30 fluorene skeleton, and C C , C C , and C3 C4 ) and those of the dihedral angles relevant to the 2-cyclopentenylidene ring are relatively large. On the other hand, those of the dihedral angles of j and ϕ relevant to the phenyl torsion are small (0.0034 and 0.0015 au, respectively). Based on these findings, the initial event in the0 process of P-MPCPF f CIX in S01 is an elongation of 0 C9C1 and an increase of the C9aC9C1 C2 angle (therefore, τ). Concomitant with the C9C1 bond0 elongation, an alternation of a π bond conjugated with the C9C1 double bond and a planarity of the 2-cyclopentenylidene ring take place. These results are ascribed to a ππ* ethylenic character in S1 at P-MPCPF. Following these geometric changes, two events take place: a phenyl torsion, and pyramidalization around the C9 atom leading to a zwitterionic character at CIX. In order to examine the process where MPCPF behaves after relaxation into S0 at CIX, we followed the geometry in S0 by optimization from CIX. Thereby it is confirmed that MPCPF at CIX in S0 goes forward to the M0 -isomer. The energy gradients at CIX tell us how MPCPF behaves forward to the M0 -isomer after the electronic relaxation at CIX. The energy gradient with respect 0 0 to the C9aC9C1 C2 dihedral angle is small (0.00080 au). On the other hand, the energy gradient of the C4aC9aC9C1 angle related to a wagging motion of the fluorene stator is large (0.1045 au). This means that the first event after electronic relaxation at CIX is reformation of a pyramidal structure into a planar one around the C9 atom of the fluorene stator through a wagging motion. Then a τ-torsional motion takes place for MPCPF to go to the M0 -isomer. In order to check the second thermal process of M0 -MPCPF f 0 P -MPCPF via TS0 in S0, we followed the geometries from TS0 to the forward and backward regions. Thereby, it is confirmed that TS0 goes forward and backward to P0 -MPCPF and M0 -MPCPF, respectively. The latter half-processes of P0 -MPCPF f CIX0 f M-MPCPF f TS f P-MPCPF are similar to the corresponding process mentioned above because the geometric features relevant to the processes are similar to those of the first and second steps of P-MPCPF f CIX f M0 -MPCPF f TS0 f P0 -MPCPF except for τ. Here it is worthwhile focusing our interest on the roles of the phenyl group and the fluorene stator in the full rotary process. In the first process of P-MPCPF f CIX f M0 -MPCPF, the phenyl torsional angle ϕ increases from 37.0 to 130.0°. In the second process of M0 -MPCPF f TS0 f P0 -MPCPF, ϕ does not further increase and in turn decreases from 130.0 to 37.3°. In the latter half rotary cycle of P0 -MPCPF f CIX0 f M-MPCPF f TS f P-MPCPF, ϕ exhibits a trend similar to that of the former half rotary cycle of P-MPCPF f CIX f M0 -MPCPF f TS0 f P0 MPCPF. In summary,0 the0 phenyl group does not take a 360° rotation around the C2 C6 axis but rather it swings back and forth around a perpendicularly twisted conformation (i.e., ϕ∼90°) during the full rotary cycle. The swing of the phenyl group like a pendulum motion serves MPCPF not only to stabilize P-, P0 -, M-, and M0 -helical structures but also to interchange their helicity at CIX, CIX0 , TS, and TS0 . The geometry around the C9 atom of fluorene stator is strongly dependent on the torsional angle τ. This is characterized as a 0 wagging motion of the fluorene stator against the C9C1 rotary axis.
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Figure 4. Energy diagram of the full rotary cycle of MPCPF. The points P, M0 , P0 , and M represent the geometries of P-, M0 -, P0 -, and M-MPCPF, respectively, for convenience, although the others have the same meanings in the text and Figure 2. The values in parentheses are MRMP2 energies (in kcal/mol) relative to that of P-MPCPF in S0. The black bold lines represent the excitation processes at P and P0 . The red and green lines indicate that MPCPF is in S1 and S0, respectively.
In the former half rotary cycle, the wagging angle ω, which is a measure for how many degrees the fluorene stator wags against 0 the C9C1 axis, takes a negative value, while it is positive in the latter half-cycle. This means that the fluorene stator in the latter 0 half-cycle is inverted against the C9C1 rotary axis in comparison with the former half-cycle. Especially the conformations where the absolute values of ω’s are large (i.e., CIX, TS0 , CIX0 , and TS) correspond to the switching points of helicity. In conclusion, the fluorene stator also serves to interchange the helical structures by 0 a wagging motion against the C9C1 rotary axis. We turn to discussing the unidirectional rotary process of MPCPF from an energetic point of view. Figure 4 shows an energy diagram of the full rotary cycle. The excitation energy at P-MPCPF (and P0 -MPCPF) is a computational value directly compared with experimental one. The CASSCF excitation energy (122.63 kcal/mol) may be much higher than the experimental one. However, the MRMP2 excitation energy (81.77 kcal/mol in Figure 4) is expected to well reproduce the experimental value. This is because the MRMP2 value is close to the experimental excitation energy (366 nm, i.e., 78.12 kcal/mol) of a previous light-driven rotary motor similar to MPCPF.7 Furthermore, it is found that the MRMP2 energetic corrections little affect the shape of the potential energy surfaces over the unidirectional rotary process. This implies that the CASSCF results are reliable enough to discuss the full rotary cycle and the MRMP2 energies are useful in a quantitative discussion. Electronically excited P-MPCPF directly goes to CIX as discussed above. Then the electronically relaxed MPCPF at CIX goes forward to M0 -MPCPF. However, the energy barrier of M0 -MPCPF f P0 -MPCPF (1.35 kcal/mol) is much smaller than that of a previous overcrowded molecule (18.6 kcal/mol).12 This implies that the excess energy released in the process of CIX f M0 -MPCPF is enough to overcome the energy barrier without any trap around M0 -MPCPF. In other words, a floppy phenyl torsional motion is helpful for MPCPF to smoothly interchange the helical structure from M0 -MPCPF to P0 -MPCPF (also M-MPCPF to P-MPCPF), in contrast to the fact that the previous unidirectional rotary molecular motors with rigid and sterically overcrowded helical structures are prevented from a smooth helical inversion because of a large energy barrier. Again P0 -MPCPF is excited by an incident light with (substantially) the 13616
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The Journal of Physical Chemistry A same wavelength. Then electronically excited P0 -MPCPF goes to P-MPCPF in the itinerary similar to the former half-cycle of P-MPCPF f P0 -MPCPF. In conclusion, a constancy of rotation speed has been much improved because of a much lower energy barrier in the thermal helical inversion. This is realized by the floppy phenyl torsion of MPCPF. We further checked if M0 -MPCPF in S0 has no chance to go back to P-MPCPF and exclusively goes to P0 -MPCPF via TS0 . Therefore, we optimized a transition state (TSX) between the P-isomer and the M0 -isomer. From the torsional angle τ (91.8°) in Table 1, it is found that TSX is located in the intermediate region between the P-isomer and the M0 -isomer. The energy barrier from the M0 -isomer to the P-isomer is calculated to be 21.46 kcal/mol (by MRMP2), which is enough to prevent the backward reaction of M0 -isomer f P-isomer. Similarly, M-MPCPF and P0 -MPCPF are well separated in S0 (21.46 kcal/mol) so that the backward reaction of M-isomer f P0 -isomer is prevented.
5. CONCLUDING REMARKS In the present paper we theoretically designed a light-driven molecular rotary motor of MPCPF. By means of reliable levels of ab initio CASSCF and MRMP2 calculations, the role of each fragment for a light-driven molecular rotary motor has been clarified. 1. The fluorene stator wags against the CdC rotary axis, which depends on the CdC torsional motion. The flexible wagging motion of the fluorene stator serves the helical structures to be stabilized and to interchange with each other. 2. The 2-cyclopentenylidene ring in the rotor takes a planar or a nonplanar conformation, dependent on the CdC torsion. The degree of nonplanarity is in accordance with a wagging motion of the fluorene stator as well as a pseudoaxial or pseudoequatorial position of the methyl group bonded to the 2-cyclopentenylidene ring. 3. The phenyl group attached to the 2-cyclopentenylidene ring serves MPCPF to take helical structures in the fjord region, the same as in previous light-driven molecular rotary motors which are designed to take helical structures by rigid and sterically overcrowded substituents. However, the phenyl group has a great advantage that an interchange of helicity is governed by a floppy phenyl torsional motion. This leads to the fact that the thermal process of helical inversion has an extremely low energy barrier, in contrast to the fact that those of the previous light-driven molecular rotary motors are too high to be an obstacle for the constant rotation. Furthermore, the phenyl group also serves MPCPF to interchange the helicity at CIX. In the full rotary cycle, the phenyl group swings back and forth around a perpendicularly twisted conformation against the 2-cyclopentenylidene ring, which is like a pendulum. Thereby the phenyl group plays important roles not only in stabilization of the helical structures but also in interchange of the helicity. In summary, a sterically overcrowded substituent with a floppy phenyl torsional motion is expected to realize constant rotation in addition to unidirectionality. In the present computational approach, we found that each fragment of MPCPF is designed so that the internal motions, such as the phenyl torsion and wagging of the fluorene stator, are strongly coupled with the CdC double bond rotation which is the main motion in the light-driven molecular rotary motor. Thereby we believe that the model molecule presented here is promising for a light-driven molecular rotary motor with constant speed.
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However, a light-driven molecular rotary motor of MPCPF should be further improved from the following point. Though a low energy barrier in the thermal helical inversion is a great advantage of MPCPF, the relative stability between the helical isomers is small. This possibly causes a fast equilibration between M0 - and P0 -helices (also M- and P-helices) after relaxation into S0. In order to suppress the backward reaction to the metastable M0 (and M-) helical isomer from the stable P0 - (and P-) helical isomers, we propose two types of prescriptions for chemical modifications of MPCPF. One prescription is that a metastable M0 - (and M-) helical isomer is only a transient species by a chemical modification of MPCPF. In a mathematical sense, the unstable helical isomer no longer corresponds to a local minimum or corresponds at most to an inflection point. Thereby the stable P- and P0 -helical isomers are populated only so that a backward rotation is suppressed. As another idea for a chemical modification, we point out that the energy difference between P0 and M0 -helical isomers should be increased. Thereby the stable P0 - (and P-) helical isomer is populated much more than the metastable M0 - (and M-) helical isomer. In a previous fluorenebased light-driven molecular rotary motor which is similar to MPCPF but has a rigid and overcrowded rotor, the energy difference between the stable and metastable helical isomers is similarly small (2.1 kcal/mol),18 although the backward rotation is successfully suppressed by an large energy barrier. This implies that a fluorene stator and/or 2-cyclopentenylidene of the main rotor part should be replaced by another (other) fragment (fragments) in order to make a larger energy difference between stable and metastable helical isomers. We are now designing a new light-driven molecular rotary motor in line with these ideas.
’ APPENDIX In order to characterize the important conformations of MPCPF, we define additional geometric parameters. As far as the local 0 0 0 0 geometry around the C1 atom (i.e., C1 C9C5 C2 ) and the fluorene stator keep planar structures, the dihedral angle of C9aC910 20 C C is a good measure for how many degrees the rotor twists against the stator. As we mention in the text, however, the local 0 0 0 0 geometry around the C1 atom 0 (i.e., C1 C9C5 C2 ) and that around the C9 atom (i.e., C9C1 C9aC8a) take a nonplanar structure in some cases. Therefore, we alternatively introduce a torsional angle τ which measures how many degrees the rotor twists against the stator. τ0 is0 defined by a dihedral angle of r(C9C9a) 0 9 8a 1 5 10 20 r(C C ) and r(C C ) r(C C ) vectors linked with r(C9C1 ). 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°. We also introduce two wagging angles of many0 degrees the fluorene stator and ω and ω0 to measure how 0 0 0 the local geometry of C1 C9C5 C2 wag against the C9C1 rotary axis, respectively. ω is defined by an angle between the two 0 vectors: r(C1 C9) and a bisector vector between r(C9C9a) and 0 0 is defined by an angle between r(C9C1 ) r(C9C8a). Similarly ω 10 50 10 20 0 and a bisector of r(C C ) and r(C C ). In addition, ω and ω can possibly take positive and negative values. Therefore, the signs of by the signs of (r(C9C09a) r(C9C8a)) 3 ω and ω0 are determined 10 9 10 50 10 20 r(C C ) and (r(C C ) r(C C )) 3 r(C9C1 ), respectively. ’ AUTHOR INFORMATION Corresponding Author
*E-mail: e-mail:
[email protected]. Fax: +81-18-889-2601. 13617
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