Theoretical study on pentiptycene molecular brake: photoinduced isomerization and photoinduced electron transfer

The isomerization of the double bond plays an important role in the braking and de-braking of the light-controlled molecular brake. Therefore, the pentiptycene-type (Pp-type) light-controlled molecular brake system ((E)- and (Z)-4ʹ-pentiptycyl vinyl-[1,1ʹ-biphenyl]-4-carbonitrile) containing the C = C double bond was theoretically studied. Combining the 6-31G(d) basis set, the ωB97XD functional with dispersion correction was applied to implement the (E)-configuration and (Z)-configuration initial optimization. Next, using the 6-311G(d,p) basis set, the relaxed potential energy surface scans of the rotation angle were operated, and then the optimization calculations of the transition states at the extremum high points. Analyzing the stagnation points and the rotational transition states on the potential energy profiles, the rotation mechanism and basic energy parameters of the molecular brake were obtained. Then, the DFT computations at ground states and the TD-DFT computations of vertical excitation energy were put into practice at the accuracy of the def-TZVP basis set for the two configurations, and using the natural transition orbital (NTO) analyses combining the excitation energies and absorption spectra, the electronic transition characteristics and electron transfer properties of light-controlled molecular brake were studied. Afterwards, in order to investigate the photoinduced isomerization reaction, the C = C double bond was scanned on the relaxed potential energy surface, and the intermediates of the isomerization reaction were searched and analyzed; thus, the braking mechanism of the light-controlled molecular brake was proposed.


Introduction
Artificial molecular machines are uniquely positioned to play a significant role in nano science and technology; it has been becoming a new and rapidly emerging field of chemistry and physics. In fact, the level of control of the motions of molecular brakes  is still and will be in the stage of development for a quite long time. The light-controlled molecular brake is a typical rotary motion controller which could be defined as a molecular or supramolecular system that effectively controls intramolecular or inter-fragment rotational motion via photochemical reactions such as photoisomerization and photooxidation [17,29]. In recent years, the concept of green chemistry is gradually attracting attention since the environmental protection issues are valued by all walks of life, especially scientific researchers. Light is considered to be one of the cleanest, fastest input, and most accessible energy sources, so it is favored strongly by researchers.
Herein, the molecular brake system((E)-and (Z)-4ʹpentiptycyl vinyl-[1,1ʹ-biphenyl]-4-carbonitrile) containing a C = C double bond and a pentiptycenyl (Pp) group was selected as the research object (Scheme 1). This type of molecular brake uses Pp as the rotator and styryl group as the brake pad, and the rotator has a huge influence on the performance of the molecular brake, so it is called Pp-type light-controlled molecular brake. The potential application value of π-extended stilbene (the part consisting of brake pad and Pp center benzene) that undergoes efficient singlet-state (E)-to (Z)-or (Z)-to (E)-isomerization for the design of high-performance light-controlled molecular devices such as molecular switches has been demonstrated with molecule 1 [17]. Since light-induced excitation of C = C double bonds can give rise to an excited state isomerization, the molecular configuration can be controllably transformed from (E)-to (Z)-or (Z)-to (E)-by irradiation with light of different frequencies. That is, the styryl group is the brake pad [15][16][17][18]. Recognized as a four-bladed model, the Pp segment was the rotator with excellent performance of the molecular brake. On the one hand, Pp has been well studied as molecular gears and brakes, in which the phenyl moieties in the center may give rise to pronounced electron delocalization, enabling a photoinduced configuration change. On the other hand, Pp is not a complete spatial quadruple structure, which is facilitating to add some other modification groups between the two more distant blades on the same side (blue labeled in Scheme 1), so as not to make the atom density too large. It can freely and fast rotate around the single bond (C2-C39) due to the low rotating energy barrier when the (E)-type configuration ((E)-1) is adopted. While the (Z)-type formed, a pad snaps into the middle of the two blades, leading to resistance increase; thence, the energy barrier is higher and the rotational motion slows down. Plausibly, almost all molecules that are sensitive to light stimulation display a high degree of conjugation, which leads to the very strong electron delocalization. Therefore, the molecule is excited by light, triggering the electron transitions, further causing the occurrence of photoinduced electron transfer (PET) process. In view of this, to investigate the electronic properties in the process of photochemical reactions, the dimethylamino group and phenylstilbene chromophore were introduced as electron donors and acceptors, respectively.
The thermodynamic properties of ground and excited states, spectral properties, molecular dynamic properties, braking mechanism, and the electron transfer were studied by computational method using the Kohn-Sham density functional theory (KS-DFT, abbreviated as DFT). The mechanism of the photoinduced isomerization reaction has been unraveled by the group of Yang [17], and there are some theoretical supports of the previous standpoints. It is a lightinduced angular torsion reaction that occurs on the potential energy surface of the singlet excited state (S1) undergoing p and p* states. Therefore, all calculations regarding excited states are based on singlet states.

Computational details
The DFT and TD-DFT were used to investigate the interesting issues of molecular brake system. The object is a huge conjugation system, which requires proper long-range corrected (LC) functionals to describe correctly. At the same time, the molecule contains several electronegative atoms and different types of non-covalent interaction (NCI), which requests reasonable NCI options to reflect. Based on this, the popular ωB97XD [30] functional which includes 100% long-range exact exchange and empirical dispersion corrections was an excellent choice for the majority task in this paper. All of the quantum models were created, drawn, and exported by the visualization software of Gauss View 5.0.8 [31] and VMD 1.9.3 [32].
First step, the (Z)-1 and (E)-1 were fully optimized with the acetonitrile solvent considered at the level of ωB97XD/6-31G(d) [33]. Then, the relaxed potential energy surface scan procedures of (Z)-1 and (E)-1 were carried out with the dihedral angle (denoted as θ) of C3-C2-C39-C40 as the variable (the step size is 5°) under the 6-311G(d,p) [34] basis set. Except for the corresponding dihedral angle, there are no other restrictions. Second step, the transition Scheme 1 Pp-type light-controlled molecular brake system based on Pp rotator and the styryl brake pad state optimization processes were performed using the high energy points as initial guesses at the level of ωB97XD/6-311G(d,p), and the two stable conformers of (Z)-1 and (E)-1 were also re-optimized under the 6-311G(d,p) basis set. As a result, the energy barriers of fast and slow rotation would be figured out. In order to investigate the propagating progress of double bond during the braking process, third step, without any other restricted conditions, the dihedral angle of C2-C39-C40-C41 represented as α has been scanned using relaxed potential energy surface with a step size of 5° at the accuracy of ωB97XD/6-311G(d,p). Fourth step, for the aim of understanding the mechanism of photoinduced configuration transformation, starting from the highest energy structure, the unrestricted DFT calculation of the Berny algorithm [35] was proceeded using the 6-311G(d,p) basis set to obtain the intermediate. Fifth step, for the conformers of (Z)-1 and (E)-1, the time-dependent density functional theory (TD-DFT) method under several functionals was used to calculate the 6 lowest excited energies with solvent to obtain the theoretical UV absorption spectra. And then, the databases were compared to illustrate more convincing conclusions; besides, the excited state databases were also utilized in subsequent natural transition orbital (NTO) and PET analyses using Multiwfn 3.7 program [36][37][38]. All of the above computations were completed by Gaussian 09 [39] quantum chemistry package.

Molecular geometry optimization
The Pp-type light-controlled molecular brake can be recognized as a device which could realize the control of the rotation motions through the conversion of the C = C double bond configuration. Therefore, in order to study the braking mechanism of the light-controlled molecular brake, the different configurations must be analyzed. In the ground state, the C = C double bond in molecule 1 has two configurations, namely (E)-1 and (Z)-1, which can be transformed in a controllable manner at different frequency illuminations. Under gas phase conditions, the initial geometric structure optimizations of the ground states (E)-1 and (Z)-1 were carried out at the ωB97XD/6-31G(d) level, and the single-point energies of the two stereoisomers after optimizations were calculated using the method of ωB97XD/def-TZVP [40], the obtained relative single-point energies Δε ele are listed in Table 1. It can be seen from the table that the energy of (Z)-type is ca. 6 kcal·mol −1 lower than of (E)-type. In order to verify the stability of the two isomers, the NCI analyses were performed to visualize the intramolecular NCIs; the reduced density gradient (RDG) isosurface maps and the RDG scatter plots were drawn and exported (as shown in Fig. 1). It can be figured that the types of NCIs in the two isomers are roughly the same, mainly the van der Waals (vdW) interactions, and all the NCIs in the (E)-type are very weak. Whereas, in the (Z)-type configuration, a benzene ring in the styrene moiety is in a dislocation parallel position with a paddle benzene ring in the Pp, allowing the two benzene rings face to face and forming a π···π stacking effect, which is much stronger than any of the (E)-type configuration, further reducing the energy of the system and stabilizing the molecules. Therefore, even if the steric hindrance effect is weak in the (E)-type configuration, the π···π stacking effect of the (Z)-type configuration is stronger, making the total energy of the system lower than the (E)-type configuration and the molecule becomes more stable. The molecular structures of the two configurations are shown in Fig. 1, and Table 1 also gives some key parameters of the ground state (E)-1 and (Z)-1 configurations. Due to the existence of NCIs and steric hindrances, the benzene rings on both sides of the C = C double bond in (E)-1 and (Z)-1 are not in the same plane. The calculated angle between the planes according to atomic coordinates is ca. 69.53° in (E)-1, while the angle in (Z)-1 is about 64.69°, indicating that the conjugated planar structures on both sides of the C = C double bond of the two configurations are destroyed to a certain extent, which will affect the intramolecular electron transition and electron transfer properties.

Minimum energy profiles and thermodynamic properties
The rotation process would theoretically produce countless conformations, each of which has different physical and chemical properties, and some of them are the most specific. In order to investigate the dynamic features and operating mechanism of the rotational motion of the molecular brake, it is necessary to analyze these conformations. Starting from the two optimized configurations (E)-1 and (Z)-1, respectively, the dynamic characteristics of the two configurations are studied by the method of relaxed potential energy surface scanning. The scanning results of the single bond rotating dihedral angle are shown in Fig. 2. It can be seen that the potential energy profile of (E)-configuration is relatively smooth, and there is no obvious sudden drop in potential energy. The energy difference between the highest and lowest energy points is ca. 6 kcal·mol −1 ; according to statistical thermodynamics, it is considered that this value is in the free rotation interval [8,[41][42][43], indicating that the rotation of the single bond is relatively free, and it is not restricted by too much resistance; thus, it is in a state of rapid rotation (OFF in Scheme 1). In addition, the relative free energies of the four stable conformations (A, C, E, and G) of (E)-configuration are 0.14, 0 (reference point), 0.44, and 0.35 kcal·mol −1 , respectively; it is obvious that the difference is small (the conformational isomerization caused by the side chain of the C-O bond is not considered, the same below). It can be seen that the relation between the relative position of the aminoalkyl and styrene moiety of (E)-configuration has little effect to free energy, because the styrene moiety and the aminoalkyl are far apart, which is not enough to generate mutual influence. However, the potential energy profile of (Z)-configuration has two obvious potential energy sudden drops (J → K, O → P), and the energy difference between the highest and lowest energy points rises to ca. 20 kca·mol −1 ; in stereochemistry, it is considered to be in the range of hindered rotation [8,[41][42][43], and the rotation of single bonds is largely forbidden. The styrene brake pad is inserted between the Pp paddle, and the rotation resistance increases sharply; thereby, the rotation motion becomes slow or even stops; as a result, it is in the state of slow rotation (ON in Scheme1). There are certain differences in the stable conformational energies of (Z)-configuration. With the lowest energy conformation L as the reference point, the relative free energies of I, N, and Q are 1.72, 1.24, and 0.70 kcal·mol −1 , respectively; therefore, (Z)-configuration has four stable conformations. Due to the relatively close distance between the styrene moiety and the side chain of the aminoalkyl, the interaction could be generated, which further reduces the free energy of the system and the molecule becomes more stable. Specifically, in (E)-configuration, due to the styrene moiety extending from the C2 position of Pp to the side away from Pp (as shown in Fig. 3a), during the rotation of the C2-C39 and C-O single bond, it will not cause a significant change in the distance between styrene moiety and aminoethyl; of course, the interaction will not change a lot either. Therefore, the free energy of each stable conformation point during the rotation process is basically the same. The styrene moiety in the (Z)-configuration is inserted transversely between the Pp paddles (as shown in Fig. 3b). Due to the effect of space resistance, the C2-C39 single bond is not easy to rotate, but it is going back and forth between the two blades (vibration). However, the C-O single bond is not affected by resistance raise. During the process of rotation, the carbon chain plane and styrene plane will form four limit positions of nearly 0°(cis coplane), 90°, 180° (trans coplane), and 270°, making the distance between styrene Fig. 1 The reduced density gradient (RDG) isosurface map of (a) (E)-and (b) (Z)-configuration of molecule 1 and the RDG scatter plots of (c) (E)-1 and d (Z)-1. The white are H, the cyan are C, the red are O, and the blue are N moiety and aminoethyl to vary greatly. Therefore, the interaction will also vary greatly. The free energy of each stable conformation point will not be the same, and four stable conformations (I, L, N, and Q) will be located.
The thermodynamic quantities at room temperature (298.15 K) including single-point energies ε ele , enthalpy corrections H corr , and free energy corrections G corr of several special conformations are listed in Table 2. Among them, the thermodynamic correction amounts were derived from the frequency calculation tasks including zero-point energy (ZPE) correction (the correction scale under the combination of ωB97XD/6-311G(d,p) is 0.957 [44][45][46]). The free energy G of each conformations was figured out via the formula G = ε ele + G corr .
It can be seen from the potential energy profiles that there is no obvious energy sudden drop in (E)-1. At room temperature, it is almost in a state of free rotation. The rotation energy barrier is calculated from the difference between the highest and lowest free energy points in the first half of the cycle and the second half of the cycle, respectively. They are 7.29 kcal·mol −1 and 6.58 kcal·mol −1 . Yet, in (Z)-1, there are two obvious energy sudden drops at points J and O, respectively, indicating that there are rotating transition states near points J and O. Therefore, taking these points as the initial structures, the transition state search tasks were performed at ωB97XD/6-311G(d,p) accuracy. The calculated result is that both structures have unique imaginary frequencies, which are 26.69 cm −1 and 23.50 cm −1 , respectively. The thermodynamic quantities of the two transition states are also listed in Table 2 and their free energies are almost equal. The transition state structures are verified by the intrinsic reaction coordinate (IRC) calculation. The molecular structures of the two transition states are shown in Fig. 4, and their key structural parameters are given in Table 3. The IRC curves (Fig. 5)  backward the transition state. The results of the transition state search show that the styrene moiety forms a point-topoint spatial structure with the intersection line of the Pp paddle; that is, the planarity of the styrene moiety is broken again, causing a sharp increase in energy. The rotational transition state is extremely unstable; thus, it would quickly adjust the structure to release energy and form a stable conformation. At this time, the probability of the styrene moiety rotating to both sides is almost the same, so the ratios of forming two different conformations will theoretically be the same. The free energies of the transition states were figured out via the single-point energies and the free energy correction amount calculations. Based on these data, the rotational free energy barriers can also be derived from the differences between the free energies of the transition states and the lowest points, which are 17.68 and 17.55 kcal·mol −1 , respectively. In summary, the rotation mechanisms of (E)-1 and (Z)-1 can be described as a and b in Fig. 6, respectively, where A-H, I, L, M, N, Q, and R are the macroscopic models of different conformations during the rotation of (E)-1 and (Z)-1, respectively. TS1 and TS2 are the macroscopic models of the two transition states that appear during the 360° rotation of (Z)-1. The conformations K and P are the same in structure as the conformations L and Q, reflected on the potential energy surface; they are just not optimized to the local minimum energy point.

Electron transfer
The photoinduced electron transfer (PET) process is closely related to the electronic excitation and transition of molecules. It is involved to the differences in electronic structure between the excited states and the ground states. For the analyses of electronic excitation and transition, a more accurate and convenient method of natural transition orbital (NTO) can be used. The electronic transition is essentially a transition between a certain electronic state and another electronic state of the system. In order to facilitate the understanding and study of the transition mode, the electronic transition is usually described as the model of the transition of an occupied orbital electron to a certain non-occupied orbital. When calculating the molecular excited state, the transition mode can be expressed as a linear combination of different transition forms between occupied orbitals and non-occupied orbitals of the ground states, and the contribution rate of one or several transitions to the total transition is dominant; this transition model is NTO. In order to investigate the electron transfer characteristics of the molecular brake system, under the ωB97XD/def-TZVP level and solvent (acetonitrile) condition, the ground states and excited states were theoretically computed by DFT and TD-DFT, respectively; thereby, the NTOs were obtained. Because the photoisomerization reaction is a singlet excited state reaction in the absence of other photosensitizers, and it is a reaction in the first excited state [17], only the first excited state S1 was considered when the NTO analyses were performed. Figure 7 shows the dominant NTO model diagrams and points out the percentage of such transition modes in the electronic transition components. It can be seen from the figure that the NTOs of (E)-1 and (Z)-1 are basically distributed in the conjugated part; that is, the conjugate  bridge connected by the Pp center benzene-styrene-benzenecyano group is the active part. The ether bond oxygen has a lone pair of electrons and forms a p-π conjugate effect with the π-conjugated chain; as a result, there will be a certain orbital distribution on the oxygen. The distributions of aminoethyl chain and Pp paddle benzene rings are less; it is because aminoethyl is a single bond of σ, the excitation energy level is very high, and it is not prone to electronic transitions and difficult to participate in the transmission of electrons; however, it can expand the delocalization range of electrons and plays a role in promoting the electronic transitions. The paddle benzene rings are also difficult to participate in the transitions due to the isolation of the σ single bond structure of bridge ring. It can also be figured that the two modes that contribute the most to the electronic transitions of (E)-1 and (Z)-1 are π → π* transitions, which are the transitions from No. 190  For the purpose of further clarifying the characteristics of electron transfer, the charge density difference (CDD) analyses between the excited states and the ground states were carried out, and the CDD isosurface diagrams are shown as Fig. 8. Among them, the green area is the place where the electron density increases after excitation, and the blue (a) TS1 (b) TS2 Fig. 4 The molecular structure of the two rotating transition states: a TS1 and b TS2 of (Z)-1  It can be seen that in (E)-1 and (Z)-1, the electrons are still concentrated in the conjugated part, and due to the auxiliary effect of the aminoethyl chain, the electron activity range is expanded, and almost penetrating all of the conjugated parts, and it is worth to note that the type of electronically excited transition is π → π* transition. The final results of electron transfer are as follows: the electrons in (E)-1 are transferred from the benzene in the center of the Pp to the cyano-substituted phenylstyrene, while the electrons in (Z)-1 are transferred from the C = C double bond to the cyano group. The reason for it is that the ethylenic double bond and the Pp center benzene are not in the same plane because of the (Z)-type steric hindrance effect; thence, it destroys the conjugation of the chain and shortens the conjugate bridge, which reduces the electron distribution on the Pp center benzene. In contrast, the electron distribution of the C = C double bond increases. In conclusion, the two are almost the same in transfer mode, but there is a slight difference in the position of electron transfer.

Ultraviolet absorption spectrum
Due to the long-range conjugated structure in the molecules, the two isomers can absorb ultraviolet light [17]. Based on the optimized structures of (E)-1 and (Z)-1, four different functionals of ωB97XD [30], M06-2X [47], BMK [48], and CAM-B3LYP [49] are combined with TD-DFT, respectively. Using the def-TZVP base set, the lowest vertical excitation energies of the two stereoisomers were calculated under acetonitrile solvent conditions. Figure 9 shows the theoretical simulation electronic absorption spectra of (E)-1 and (Z)-1 under different functionals. Table 4 gives the key data of the absorption spectra, where E ex refers to the excitation energy, λ max refers to the wavelength of the maximum absorption, configuration refers to the contribution rate of the transition mode, and N refers to NTO. It is obvious that the characteristic absorption wavelengths of the two isomers range from 260 to 400 nm, and the shapes of the absorption peaks of the two isomers are also very similar. The characteristic absorption wavelengths of (E)-1 under the four functionals are 311, 315, 324, and 317 nm, respectively; noticing, the experimental value is 320 nm [17]. It can be seen from the data that the characteristic absorption peaks are mainly contributed by S0 → S1 excitation, and the vibrator intensities f are very high. According to reference [17], the isomerization reaction occurs in the S1 excited states, and the S0 → S1 excitation corresponds to the characteristic absorption peaks on the spectra. Therefore, the characteristic absorption peaks of (E)-1 can be attributed to the π → π* transitions in direction of the Pp center benzene to phenylstyrene (Fig. 7). Owing to undergoing the expanded conjugate bridge, the energy level of electron transitions is not high, and the characteristic peaks are near the ultraviolet region. This is the most major transition mode of the (E)-type configuration; hence, the absorption intensity is strong, and the width of half-peak is also relatively large. Compared with (E)-1, the absorption wavelength range of (Z)-1 is narrowed (270-360 nm). Specifically, using four type functionals, the computed characteristic absorption wavelengths mainly caused by S0 → S1 excitation are 291, 295, 302, and 296 nm, respectively, and the experimental result is 309 nm [17]; thus, the blue shift under the same functional is ca. 20 nm; in addition, the absorption intensity is also reduced nearly 25%. The reason is that after the (E)type is isomerized to the (Z)-type, the coplanarity between the ethylenic double bond and the benzene in the Pp center is broken, and the dihedral angle θ between the two planes is 71.06° (absolute value; the one of (Z)-type is 48.54°). The result is that the conjugation of the molecule is destroyed, (b) NTO diagrams of (Z)-1 and the conjugate bridge that promotes electron transition and transfer is partially blocked, which makes the π → π* transition of Pp center benzene to phenylstyrene more difficult; instead, it becomes the π → π* transition from the C = C double bond to cyanobenzene. The electron delocalization is weakened due to the shortening of the conjugate bridge, and the excitation energy is increased. Therefore, the absorption wavelength will shift to the shortwave direction. As for the decrease in absorption intensity, it may be because of the formation of π···π stacking in (Z)-type configuration, which leads to a more compact molecular structure, resulting in a decrease in absorbance. In comparison, it is noticed that the characteristic absorption wavelengths calculated using the BMK functional are closer to the experimental value. For (E)-1 and (Z)-1, the calculation errors δ are: The accuracy is already very good. The other three errors are listed in Table 4. The error of (Z)-1 is generally larger than that of (E)-1, which may have a great relation with the compactness of the molecular structure. Thence, for the spectral simulation of the huge conjugate system, among the four functionals, the BMK functional has the best performance, which is also mentioned in reference [50]. In summary, the (E)-type has better conjugation than the (Z)-type, so the main form of electronic transition (S0 → S1) that promotes the isomerization reaction is easier to proceed. In other words, (E)-type conversion to (Z)-type is easier than (Z)-type to (E)-type, and the required radiation wavelength is longer. These computational results and conclusions are in good agreement with the experimental results [17].

Isomerization reaction
In order to study the dynamic properties of the isomerization reaction, the relaxed potential energy surface scanning calculation of the C = C double bond is required. With (E)-type as the initial structure, the ωB97XD/6-311G(d,p) method was applied to implement 36 steps in total (step size is 5°) scanning task. The obtained potential energy profile of double bond is shown as Fig. 10a. The figure shows that there is an obvious energy sudden drop from point p to p + 1, indicating that there is a transition state near the p point. Regarding p as the initial guess structure and keeping basis set same, the UωB97XD functional was used for transition state optimization (gas phase), where U stands for unrestricted calculation. The reason is that during the process of double bond rotation, the issue of π bond destruction (opening) is involved, so that the system would be a certain nature similar to radicals; consequently, the restricted calculations will be unreasonable. The optimization result is shown in Fig. 10b. In the optimized structure, the dihedral angle α (C2-C39-C40-C41), which is also called the twist angle, is − 87.43°. That is, the planes of the atoms on both sides of the C = C double bond are almost perpendicular to each other. The unique imaginary frequency of the transition state is 579.13 cm −1 , and the vibration modes are the twisting motions of the C-H bond with the line where the double bond carbon is located as the axis (as shown by the arrow in Fig. 10b). If it is vibrated in manner (i), it will finally be transformed into (Z)-configuration, and if it is vibrated in manner (ii), the product will be the (E)-configuration. The transition state is a very unstable structure, which will undoubtedly lead to an increase in the energy of the system. The single-point energy calculated using the def-TZVP basis set for this structure is ε ele = − 1.39829072 × 10 6 kcal· mol −1 , and the free energy correction value calculated at the 6-311G(d,p) basis set is 422.00 kcal·mol −1 . Based on this, the energy barrier ΔG E-Z of the (E)-1 → (Z)-1 isomerization process is calculated to be 42.75 kcal·mol −1 , and the barrier ΔG Z-E of the reverse isomerization process ((Z)-1 → (E)-1) is 45.96 kcal·mol −1 . In order to verify the transition state, the IRC (Fig. 11) was computed using the 6-311G(d,p) basis set. The IRC curve can continuously and smoothly connect the product ((Z)-1) and the reactant ((E)-1), revealing that the optimized vertical-type transition state is the ground state intermediate p ≠ [17] of photoisomerization reaction. Because the intermediate is a saddle point on the S0 potential energy surface, the probability of its evolution to both sides is almost equal. That is, the molecule is excited to the S1 state, and after structural relaxation and evolution to p*, it releases energy and transitions back to the ground state intermediate p ≠ . When the structure relaxes to steady state, the probability of propagating to the product direction and the reactant direction is almost 50/50. This does not mean that the yields of (E)-type → (Z)-type or (Z)-type → (E)type photoisomerization reactions are equal. Because, for most such reactions, the energy level relations between the structures on the S1 potential energy surface corresponding to the product, the reactant, the excited state intermediate p*, and the ground state intermediate p ≠ are not certain. In other words, the relations between the energies of product, reactant, and hν 1 and hν 2 are not easy to determine (shown in Fig. 12). Most of the time it includes complex processes such as thermodynamic activities of vibration relaxation, energy transfer, radiation transitions of fluorescence, and delayed fluorescence, as well as non-radiative transitions of internal conversion and intersystem cross; hence, the yield Fig. 7 The dominant and sub-dominant natural transition orbital models of a (E)-1 and b (Z)-1 ◂ of isomerization and reverse isomerization will not be the same. Due to the high energy barrier of the double bond isomerization reaction, it is extremely difficult to realize by thermochemical methods; moreover, the action time is such long, so it is realized by photochemical method. As mentioned above, the vertical excitation energies (S0-S1) of (E)-1 and (Z)-1 are 3.98 eV (91.78 kcal·mol −1 ) and 4.26 eV (98.24 kcal·mol −1 ), respectively. After absorbing the light quantum energy, if the other excited state decay processes are controlled as weak as possible, then the photochemical isomerization processes of (E)-1 → (Z)-1 and (Z)-1 → (E)-1 are relatively easy, which is also in good agreement with the experimental conclusions.

Conclusions
The analyses indicate that when the molecule adopts the (E)-type, the energy barrier is small due to the low rotation resistance, and it is in fast rotation. After being irradiated by light, a photoisomerization reaction occurs and it is converted into (Z)-type, which makes the brake pad insert into the pentiptycene paddle, and the rotation resistance increases. What's more, the energy barrier rises to the rotation hindered range, and the rotation speed significantly reduces, so as to achieve the purpose of braking. In the process, the electron transition caused by light excitation further leads to the partial transfer of the electron, and this exists in both configurations. The results of NTOs and absorption spectra analyses show that the ratio of (E)-configuration Fig. 8 The charge density difference (CDD) between the computed excited state (S1) and the ground state of a (E)-1 and b (Z)-1. The green is where the electron density increases, while the blue is where the electron density decreases Fig. 9 The absorption spectra of (E)-1 and (Z)-1 simulated by different functionals in solvent of acetonitrile Table 4 The characteristic absorption (S0-S1) spectrum data table of (E)-1 and (Z)-1 computed by different functionals [a] f refers to the vibrator intensity.
[b] Refers to the relative error compared with the experimental value.
[c] N stands for natural transition orbital (NTO). has stronger conjugation and electron delocalization than (Z)-configuration, and the wavelengths of light radiation required for excitations are longer. The discussions of the mechanisms of the isomerization reveal that the reaction occurs in the S1 excited state and undergoes an intermediate with a torsion angle of nearly 90°. If the molecule is converted back and forth under different wavelengths of light, it can be like a macro brake to realize the controllable adjustments of rotation motions in molecular level.