On the Light-Driven Isomerization of a Model Asymmetric Molecular

Aug 12, 2010 - Mariana Assmann , Cristina Sanz Sanz , Guillermo Pérez-Hernández , Graham A. Worth , Leticia González. Chemical Physics 2010 377, 86...
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J. Phys. Chem. A 2010, 114, 9342–9348

On the Light-Driven Isomerization of a Model Asymmetric Molecular Rotor: Conformations and Conical Intersections of 2-Cyclopentylidene-tetrahydrofuran Mariana Assmann, Guillermo Pe´rez-Herna´ndez, and Leticia Gonza´lez* Institut fu¨r Physikalische Chemie, Friedrich-Schiller-UniVersita¨t Jena, Helmholtzweg 4, 07743 Jena, Germany ReceiVed: May 28, 2010; ReVised Manuscript ReceiVed: July 16, 2010

The ground state potential energy surface of the model molecular rotor 2-cyclopentylidene-tetrahydrofuran (CPTHF) has been characterized by calculating minimum energy conformations, racemization pathways, and rotational barriers with high level ab initio electronic structure calculations. Two conformers with their corresponding enantiomers are found. The activation barriers for racemization are negligible, therefore thermal racemization takes place at room temperature. Torsional transition states, calculated using multiconfigurational CASSCF calculations, show twisted and pyramidalized biradical structures. Additionally, the photochemistry of CPTHF has been investigated using the accurate MS-CASPT2/CASSCF methodology. In the UV spectrum it is found that the spectroscopic state is the S1, which corresponds to a ππ* transition within the ethylene moiety. To understand light-triggered isomerization around the CdC bond, five conical intersections between the S0 and S1 have been located for each conformer of CPTHF, which allow the system to rapidly decay to the electronic ground state. Introduction

SCHEME 1: Rotary Cycle of A. Adapted from Ref 7

An important branch of nanoscience is the construction of molecules capable of mimicking mechanical machines. The operating principle of a molecular machine is the rearrangement of electrons or nuclei induced by external chemical, photochemical, or electrochemical stimulation.1,2 A particularly promising class of molecular machines are those that exploit photochemical processes. Powering a machine with light has important advantages, for example, the fact that waste products are avoided and that spectroscopic methods can be used to follow the state of the machine itself. As a consequence, a considerable effort has been done in the last two decades to design photochemically driven molecular machines.3 Among the components that comprise a molecular machine, an essential part is the motor because it allows to convert energy into mechanical motion. One of the most exciting directions of constructing motors at a molecular level is to functionalize chiral overcrowded alkenes.4 The first example of an artificial molecular motor based on a chiral overcrowded alkene was reported in 1999.5 This was a symmetric biaryl overcrowded alkene in which repetitive unidirectional 360° rotation around a carboncarbon double bond is achieved in four steps: two light-induced cis/trans isomerizations are each followed by a thermal-induced helicity inversion. Since 1999, a large number of molecular rotors that exploit the same photochemical and thermal scheme have been synthesized.6 One of the smallest (and latest) molecular rotors based on overcrowded alkenes is shown in Scheme 1, where also the four steps of the rotary cycle are lined out. In this rotor, A, the upper and lower halves consist of dimethyl-substituted phenyl groups that are easy to synthesize and provide faster rotations than the first and second generation rotors designed by the same authors.7 Other successful rotors have been synthesized, with distinct upper and lower halves as well as with heteroatoms.8 Such asymmetric molecular rotors are particularly interesting since * To whom correspondence should be addressed: E-mail: leticia.gonzalez@ uni-jena.de.

they could be recently anchored on gold surfaces,9 gold nanoparticles,10 and quartz surfaces.11 The upper half acts as a propeller and it is free, while the lower half of the rotor, the stator, is immobilized to the surface by two legs terminated with thiol groups. In this way, uncontrolled thermal rotation of the entire motor can be avoided, and the rotor is prepared to be linked to macroscopic parts. Regardless of whether the molecules are free or anchored, two features stand out as mandatory for unidirectional rotation within the mentioned variety of rotors. First, when photoisomerizing the central double bond with unshaped UV-light, the rotation must occur only toward one of the two possible directions, namely the positive or negative variation of the dihedral angle. This is granted by the rotors’ built-in asymmetry around the central double bond. Different steric impediments arise in both directions, and net rotation will occur along the

10.1021/jp104898t  2010 American Chemical Society Published on Web 08/12/2010

Ground State Potential Energy Surface of CPTHF

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Figure 1. CPTHF with used atom labels and coordinate system.

least energetic pathway. The second criterion concerns the thermal steps of the rotatory cycle. The stability difference between the two helicity isomers must be large enough for the thermal equilibrium to be totally displaced to the product side. Again, this stability difference has its origin in the specific interplay of the moieties crowding the fjord-region (see Scheme 1). Just by warming up the sample, the rotors irreversibly undergo the helicity-inversion. This helicity-inversion bears an associated twist of the central double bond that keeps the same direction as the torsion of the photoinduced isomerization, so that the overall unidirectionality is conserved. In this paper we investigate a reduced model for a molecular rotor: 2-cyclopentylidene-tetrahydrofuran (abbreviated CPTHF), see Figure 1. Rotation around the CdC bond connects two isomers that are indistinguishable. Several reasons have been considered for choosing the present system. Inspired by the rotors based on alkenes, CPTHF shares the central bicyclopentylidene scaffolding of the rotor shown in Scheme 1, but one of the carbon atoms has been substituted by an oxygen atom. It lacks, however, the steric crowding of A. Nevertheless, we emphasize that our long-term interest is the ignition of unidirectional rotations in molecular rotors using ultrafast laser pulses,12-16 where, as opposed to A, rotation does not involve thermal steps. In this respect, in our model the control parameter is not the difference in stability, but rather the dipole moment, or more precisely, its asymmetry along the torsion coordinate. This asymmetry is a desired feature to induce direct and efficient laser transitions from the ground to the excited state in the case of symmetric potential energy surfaces (PES).16 This is the reason why the bicyclopentylidene scaffolding has been doped with an oxygen atom. Finally, given its reduced size, CPTHF allows for accurate ab initio electronic structure calculations and laser-driven quantum dynamical simulations. As a first step toward the goal of inducing unidirectional rotations using laser pulses, in this paper we investigate the PES of CPTHF both in the ground and in the first singlet electronically excited state. CPTHF has different enantiomeric forms, both in the local minima of the PES as well as in the transition states (TSs). A complex PES arises, and different pathways for rotation are possible. In this paper, we investigate the landscape of the electronic ground state of CPTHF and try to establish possible rotation mechanisms. Because the rotation can be triggered with light via an excited state, the photochemistry of CPTHF is also characterized. The UV-vis absorption spectrum is computed and critical points in the excited state PES are optimized. Of particular interest will be the existence of conical intersections (CIs) that play a key role in the relaxation to the ground state and thus in the overall rotation mechanisms in the excited state. Computational Methods The equilibrium structures of CPTHF in the electronic ground state were optimized at the MP2/6-31G(d,p) level of theory. The five-membered rings adopt nonplanar puckered conformation and thus, several minima are possible depending whether

Figure 2. (a) CPTHF. (b-d) Orbitals included in the CASSCF(4,3)/ 6-31G* calculations.

the carbon atoms of the ring are below or above the molecular plane defined by the ethylene backbone. This out-of-plane movement provides a very flat ground state PES. The TSs connecting the different minima are also optimized at MP2/631G(d,p) level of theory. The vertical absorption spectrum of CPTHF was calculated using the complete active space self consistent field17 (CASSCF) method with the 6-31G(d) basis set. Different active spaces, ranging from (2,2) to (8,6), have been tested. The minimum active space CAS(2,2) consists of the πCCπ*CC molecular orbitals situated at the central CdC bond. The larger active spaces systematically add the πOCC orbital located at the oxygen atom (CAS(4,3)), the lone pair of the oxygen (CAS(6,4)), and a σCOσ*CO pair (CAS(8,6)). As it will be shown in Section 3, the intermediate active space (4,3) is enough to describe the system adequately, and therefore, the rest of the calculations are carried out with this active space. The πOCC orbital and the pair of πCCπ*CC orbitals are shown in Figure 2. Depending on the size of the active space, different numbers of states have been equally averaged, so that the wave functions are properly balanced. The resulting energies have been corrected with complete active space second-order perturbation theory in its multistate version,18 MS-CASPT2, and the same 6-31G(d) basis set. The level shift technique19 with a parameter value of 0.2 au was employed to correct for intruder states. This parameter was chosen after a careful examination of the stability of the excitation energies and the comparison of the excited states reference weight with that of the ground state. The rotational motion of CPTHF around the CdC bond involves twisted TSs of biradical nature, for which the use of multiconfigurational methods is mandatory. Following the analysis of the active space to calculate vertical excitations, the biradical TSs have been optimized using CASSCF(4,3)/6-31G(d) in the ground state. For consistency, the energies of the minima in the electronic ground state were also recalculated at the CASSCF(4,3)/6-31G(d) level of theory. The optimization of CIs between the ground and first electronically excited singlet states (S0 and S1, respectively) is performed using state-averaged wave functions of the two involved states (SA2) at the CASSCF(4,3) level with the 6-31G(d) basis set. Starting at the Franck-Condon geometries in the S1, a minimum energy path (MEP) calculation was carried out in the

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Assmann et al. TABLE 1: Position of the Atoms C4, C5, C8, and C9 in All Geometries Including the Enantiomersa

Figure 3. Front and side view of the ground state isomers (1 and 2) and enantiomers (1′ and 2′) of CPTHF. MP2/6-31G(d,p) and CASSCF(4,3)/6-31G(d) (in brackets) energies in kcal/mol.

excited state surface, leading to the geometry of one CI, which was then used as starting point to obtain further nine CIs. The so obtained CIs were then connected with the corresponding minima in the ground state using intrinsic reaction coordinate20,21 (IRC) calculations. TS geometries were also associated to their minima through IRC calculations. Except for the MS-CASPT2/CASSCF calculations of the UV-vis absorption spectrum and the MEP calculation, which are done with the MOLCAS 7.0 package,22 the rest of optimizations and single point calculations are done with the Gaussian 03 package.23 Results and Discussion Conformational Studies in the Ground State. As shown in Figure 3, both five-membered rings of CPTHF are puckered in a half-chair conformation. As a consequence, CPTHF possesses two stereoisomers, 1 and 2, each of them with a corresponding enantiomer, 1′ and 2′. The four minima can be distinguished by the atoms C4, C5, C8, and C9 (recall atom numbering in Figure 1) which are differently above or below the molecular plane. The molecular plane is described by the xz-plane of the coordinate system in Figure 1, and it corresponds to the plane formed by the ethylenic backbone. Then, above and below the plane is positive and negative y-direction. With this definition, stereoisomer 1 has the carbons C4 and C8 above the plane, whereas C5 and C9, at the other side of the double bond, are below the plane. Stereoisomer 2 has the carbons C5 and C8 above the plane and C4 and C9 below the plane. The position of the four carbons is reversed for the mirror images 1′ and 2′. Thus, the stereoisomers 1 and 2 have a similar disposition of the ring containing exclusively carbon atoms (henceforth called carbon-ring) and differ in the five-membered ring containing the oxygen atom (henceforth called oxygenring). In Table 1 we specify the position of the carbon atoms of all the structures here reported and corresponding enantiomers. The position of the relevant C atoms is labeled with “d” for down, that is, below the molecular plane, and with “u” for up, that is, above the plane. The stereoisomers 1 and 2 are related by a floppy skeleton motion of the carbons and therefore, within the accuracy of the employed method, they can be considered degenerated. For pragmatic reasons, the rest of the energies will be given with respect to 1. The geometrical parameters of 1 and 2 are summarized in Table 2. Here, the bond lengths of the C1-C2 double bond and

structure

C 4 C5

C 8 C9

enantiomer

C 4 C5

C8 C9

1 2 TS12u TS12d TS1′2u TS1′2d TS11L/R TS22L/R CI1-C1 L/R CI1-C2 L/R CI1-C1 Le CI2-C1 L/R CI2-C2 L/R CI2-C1Re

ud du uu dd du du ud du ud ud ud du du du

ud ud ud ud uu dd ud ud ud ud uu ud ud dd

1′ 2′ TS1′2′d TS1′2′u TS12′d TS12′u TS1′1′R/L TS2′2′R/L CI1′-C1R/L CI1′-C1R/L CI2′-C1Re CI2′-C1R/L CI2′-C2R/L CI1′-C1Le

du ud dd uu ud ud du ud du du du ud ud ud

du du du du dd uu du ud du du uu du du dd

a “u” (up) means the C atom is above and “d” (down) means it is below the plane defined by the ethylene moiety. The labels u and d correspond to the unrotated and unpyramidalized structures.

the C2-C3 bond as well as some selected angles and dihedrals are given. It can be seen that the length of the double bond is nearly the same in 1 and 2; the same applies to the C2-C3 bond. The C1-C2 bond with values around 1.339 Å is in the range of a typical C-C double bond, whereas the C2-C3 bond with values of 1.390 Å is shorter than the C4-C3 bond, which is about 1.438 Å in all stereoisomers, and is shorter than in free THF (1.430 Å, value calculated at MP2/6-31G(d,p) level of theory). The shortening of the C2-C3 bond is a hint for the participation of the p-orbital of the oxygen atom in the double bond system. The dihedrals C6-C2-C1-C7 are all very close to 180°, showing that the system formed by the double bond and the neighbored atoms is nearly planar. The presence of the oxygen atom obviously makes the oxygen-ring not symmetric. The other selected dihedrals show that the carbon-ring is also not symmetric. The minima 1 and 2 are linked by TSs in which two neighbored carbon atoms, either C4 and C5 or C8 and C9, are both above (denoted by u) or below (denoted by d) the molecular plane, so that the five-membered ring takes an envelope form, see Figure 4. Note that in the minima these atoms are never on the same side of the ethylenic plane. The TSs are named after the minima they connect, as confirmed with the help of IRC calculations. The corresponding geometrical parameters are listed in Table 2. The interconversion between 1 and 2 proceeds via two possible TSs: TS12u and TS12d. Both have similar very small activation energies, 2.81 and 2.88 kcal/mol, respectively. As shown in Table 1, TS12u has the C4 and C5 atoms up, so that the oxygen-ring takes an envelope form, while the carbon-ring is twisted in a half-chair as in the minima. In TS12d, the C4 and C5 atoms also take an envelope form, but they are down. The imaginary frequencies of both TSs are 153i and 154i cm-1, respectively, and as expected, they correspond to the movement of C4 and C5 in opposite directions, from envelope to the halfchair form. The racemization pathway of 1 into 1′ has also been calculated. For this purpose, the TSs connecting 2 and 1′ are necessary. The corresponding saddle points, TS1′2u and TS1′2d have relative energies of 2.82 and 2.94 kcal/mol at MP2/631G(d,p) level of theory, respectively, see Figure 4. Both TSs have the atoms C8 and C9 simultaneously up or down so that the carbon-ring is in envelope form, whereas the oxygen-ring is twisted in half-chair conformation. The corresponding

Ground State Potential Energy Surface of CPTHF

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TABLE 2: Selected Bond Lengths (in Å), Angles, and Dihedral Angles (Both in Degrees) of the Geometries of CPTHF Optimized with MP2/6-31G(d,p) (Minima and Planar TSs) or CASSCF(4,3)/6-31G(d) (Twisted TSs and CIs)a structure 1 1′ 2 2′ TS12u TS12d TS1′2u TS1′2d TS11L TS11R TS22L TS22R CI1-C1L CI1-C1R CI1-C1Le CI1-C2L CI1-C2R CI2-C1L CI2-C1R CI2-C1Re CI2-C2L CI2-C2R a

C1-C2 C2-C3 C6-C2-C1-C7 C1-C2-C3-C4 C1-C2-C6-C5 C2-C1-C7-C8 C2-C1-C10-C9 C2-C1-X25 C1-C2-X26 1.339 1.339 1.338 1.338 1.338 1.339 1.339 1.334 1.472 1.472 1.471 1.472 1.405 1.400 1.410 1.451 1.451 1.405 1.400 1.403 1.460 1.452

1.390 1.390 1.390 1.390 1.384 1.384 1.391 1.373 1.379 1.377 1.377 1.378 1.269 1.286 1.279 1.523 1.510 1.270 1.287 1.295 1.490 1.509

-180 180 -180 180 180 180 180 180 128 74 124 71 -58 -120 -55 161 21 -62 -126 -128 165 21

-175 175 176 -176 -156 157 180 -172 -155 167 -166 155 -179 -176 -178 -115 116 179 176 176 -109 112

-161 161 160 -160 161 -162 157 166 169 -140 140 -169 -167 -171 -166 109 -111 166 170 170 68 -71

170 -170 168 -168 164 173 -142 -147 -178 155 156 154 120 -146 166 169 155 125 -145 -165 165 157

165 -165 167 -167 171 162 -143 148 155 -178 -179 -177 -145 121 -166 168 -178 -148 121 166 173 178

165 165 166 164 127 126 127 175 172 127 124 126 172 173

150 150 150 149 177 173 177 106 106 177 173 173 108 107

The corresponding labels of the atoms in the different structures can be seen in Figures 1 and 5.

Figure 4. Interconversion and racemization pathways from 1 to 1′ via 2 and 2′. MP2/6-31G(d,p) energies in kcal/mol.

Figure 5. Biradical transition states of CPTHF. CASSCF(4,3)/6-31G(d) energies in kcal/mol. In panel (a), the atom numbering with dummy atoms X25 and X26 is given.

imaginary frequencies of ca. 111i cm-1 show a similar movement of these C atoms as in the case of TS12u and TS12d. Therefore, the racemization of 1 goes first to 2 through either TS12u or TS12d and then to 1′ via TS1′2u or TS1′2d. The

racemization of 1 to 1′ is also possible through 2′. This pathway includes the enantiomers of the TSs considered above, see Figure 4. For completeness, we report that CPTHF with both fivemembered rings planar corresponds to a saddle point of fourth order, SP4, with an MP2/6-31G(d,p) energy of 7.72 kcal/mol. Its four imaginary frequencies show movements of C4 and C5 or C8 and C9 in the same or the opposite direction, leading to the TSs described above. For further investigations of the PES we shall consider only geometries connected to the stereoisomers 1 and 2. The corresponding enantiomers of these and other critical points (listed in Table 1) will not be shown. The TSs reported so far keep the double bond planar. However, a rotation of a double bond in the electronic ground

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TABLE 3: Excitation Energies ∆E (in eV) Obtained with MS-CASPT2/CASSCF/6-31G(d)a MS-CASPT2(2,2) configuration 2

(πCC) (πCC)1(π*CC)1 (πOCC)1(π*CC)1 (nO)1(π*CC)1 (πCC)1(σ*CO)1 (πCC)0(π*CC)2

MS-CASPT2(4,3)

MS-CASPT2(6,4)

MS-CASPT2(8,6)

c

∆E (eV)

f

c

∆E (eV)

f

c

∆E (eV)

f

c

∆E (eV)

f

0.989 0.998

6.61(8.36)

0.475

-0.981 0.991

6.57(8.46)

0.483

-0.980 -0.964 -0.857 0.936

6.39(8.29) 9.13(10.55) 9.22(9.93)

0.482 0.123 0.015

-0.975 0.921 0.845 -0.925 0.921 0.900

6.46(8.27) 9.56(10.69) 9.71(10.12) 8.15(9.16) 11.79(12.85)

0.433 0.061 0.014 0.007 0.012

a CASSCF energies are given in parentheses. Also given are the configuration interaction coefficients, c, of the contributing wave function and the oscillator strength, f.

state involves a twisted and biradical TS. These TSs are much higher in energy than that of the planar TSs, since the rotation involves the rupture of the CdC bond. We have found two twisted TSs for each of the stereoisomers, 1 and 2, see Figure 5. Their imaginary frequencies are between 260i and 270i cm-1 and correspond to the torsion around the CdC bond. As it can be seen in Table 2, the C1-C2 bond of all the twisted TSs is as expected elongated to a C-C single bond (1.47 Å). Moreover, the twisted TSs are slightly pyramidalized in C1 and C2. This is best appreciated in the angles C2-C1-X25 and C1-C2-X26, which indicate the grade of pyramidalization with the aid of the dummy atoms X25 and X26. The atom X25 is situated in the middle of an imaginary line between C7 and C10. Likewise, X26 is in the middle of the line joining C3 and C6, see Figure 5a. Compared with 180°, which correspond to a nonpyramidalized structure, the angles C2-C1-X25 and C1-C2-X26 indicate a pyramidalization at C1 and C2 of ca. 165 and 150°, respectively. In all twisted TSs, the degree of pyramidalization of C2 is higher than the one of C1. The TSs corresponding to the torsion of 1 or 2 are named TS11 or TS22, respectively. These saddle points of first order show the same configurations of the C4, C5, C8, and C9 atoms as the stereoisomers they come from (cf. Table 1). Moreover, we indicate with L (left) or R (right) in which direction along the x-axis the oxygen-ring is pyramidalized. We define left to be in negative and right to be in positive x-direction. The CASSCF(4,3)/6-31G(d) energies amount to ca. 74 and 62 kcal/ mol for the left- and right-pyramidalized TSs, respectively. Therefore, the activation barriers are ca. 10 kcal/mol lower for the saddle points TS11/22R. UV-vis Absorption Spectrum of CPTHF. Table 3 collects the CASSCF and MS-CASPT2 vertical excitation energies obtained for CPTHF with different active spaces. The smallest active space (2,2), including the πCC and the π*CC orbitals localized mainly at the CdC bond (see Figure 2), predicts an intense bright S1 state of ππ* character at 6.61 eV (SA2CASSCF: 8.36 eV) with an oscillator strength f ) 0.475. This energy is typical of olefinic systems. The valence state of ethylene itself is obtained experimentally at 7.65 eV,24 and theoretically at MS-CASPT2 level of theory at 7.98 eV.18 In related systems, such as bicyclohexylidene25 or 4-(methylcyclohexylidene)fluoromethane,26 similar levels of theory predict the bright π f π* transition at ca. 6.5-6.8 eV, in accordance to available experimental values, see, for example, ref 27. The inclusion of the p-orbital of the oxygen (πOCC) in the active space (4,3) allows for resonance within the π-system formed by the p-orbitals of the atoms C1, C2, and C3. As expected, the S1 ππ* excited state is stabilized and thus, the excitation energy decreases to 6.57 eV. The oscillator strength is very similar to that obtained with CAS(2,2) (f ) 0.483). To investigate the effect of the nonbonding electron pair of the oxygen, the nO-orbital was included and SA4-CASSCF(6,4)

calculations were performed. The S1 state corresponds to the ππ* excitation at 6.39 eV. The S2 state is ca. four times weaker than the ππ* S1 state and corresponds to a πOCC f π*CC transition with an excitation energy of 9.13 eV. The S3 is very weak, and it is a nO f π*CC excitation predicted at 9.22 eV. The influence of σ-orbitals was investigated using the active space (8,6) by adding the σCO σ*CO pair to the (6,4) active space. In this case, six states need to be included in the averaged calculation, otherwise the πOCC f π*CC transition does not appear within the calculated wave functions. In the SA6-CASSCF(8,6) calculations, the πCC f π*CC transition at 6.46 eV is still the brightest state with an oscillator strength of 0.433ssimilar to the results obtained with other active spaces. However, the S2 state, predicted at 8.15 eV, corresponds now to a dark πCC f σ*CO transition. This state has intercalated between the ethylenic ππ* state and the πOCCπ*CC, which now is the S3 state at 9.56 eV. The S4 state corresponds to the weak nO f π*CC state (9.71 eV), and the S5 state is a double excitation from the πCC to the π*CC-orbital (11.79 eV). As we can see, all the calculations are consistent with the fact that CPTHF should show a band peaking around 6 eV and a shoulder at around 9 eV. The S1 is the brightest state, and corresponds to a ππ* (HOMO-LUMO) transition within the carbon-carbon double bond. Because of the presence of the oxygen atom, an additional ππ* state weaker than the previous one is responsible for the shoulder at higher energies. To the tail of the band contributes a weak state of nπ* character. The excitation energy of the ππ* S1 state is robust regardless of the active space, so are the associated oscillator strengths. However, at MS-CASPT2/SA6-CASSCF(8,6) level of theory, the πOCCπ*CC transition is predicted much weaker than at MSCASPT2/SA4-CASSCF(6,4), and it is destabilized by 0.4 eV because a πσ* state intercalates in between. Obviously, the SACASSCF procedure is more accurate when few states are calculated, and it can deteriorate very quickly if a large number of states are calculated with the same set of averaged orbitals. Since the πσ* as well as nπ* states are very weak and do not play a role in the photochemistry of CPTHF, we consider that the (4,3) active space provides a satisfactory description of the bright states. From those, the spectroscopic one is the S1 of ππ* character, in analogy to the valence state of ethylene.28,29 Following this analysis, we shall employ SA2-CASSCF(4,3) to study the radiative and nonradiative (via CIs) relaxation pathways from the S1 excited state of CPTHF. Relaxation Pathways and Conical Intersections. Five CIs coupling the S1 and S0 states have been located for 1 and five analogous for 2, see Figure 6. Their labels CI1 and CI2 refer to the stereoisomers 1 and 2, respectively. All 10 CIs are twisted and pyramidalized at either C1 or C2. Accordingly, they are denoted by CI-C1 or CI-C2 and R or L, with the same meaning as in the TSs. Six CIs were found pyramidalized at C1, these are CI1-C1L, CI1-C1R, CI1-C1Le, CI2-C1L,

Ground State Potential Energy Surface of CPTHF

Figure 6. CIs of CPTHF. CASSCF(4,3)/6-31G(d) energies in kcal/ mol.

CI2-C1R and CI2-C1Re. Among them, CI1-C1Le and CI2-C1Re show a carbon-ring in an envelope form (e), while the others adopt half-chair conformations in all the rings. A closer inspection on the configurations (recall Table 1) reveals that CI1-C1Re is the enantiomer form of CI2-C1Re, and likewise CI2-C1Le is not reported in Figure 6 and Table 2 since it is the enantiomer of CI1-C1Le. The remaining four CIs, CI1-C2L, CI1-C2R, CI2-C2L, and CI2-C2R, are pyramidalized at C2. At CASSCF(4,3) level of theory, the energies of the CI-C1s are around 105 kcal/mol (ca. 4.5 eV), whereas the CIs pyramidalized at C2 (CI-C2s) are higher in energy, at ca. 128 kcal/mol (ca. 5.5 eV). The geometrical parameters which characterize the CIs are listed in Table 2. Similar to the twisted TSs, the CIs have biradical character and hence, the C1-C2 distance is elongated to a single bond. In the case of the CI-C2 structures the C1-C2 bond is slightly longer than in the CI-C1 ones. Furthermore, the CI-C1 structures show a contraction of the C2-C3 bond (around 1.27 Å) toward a CdO bond. In the CI-C2s the C2-C3 bond (around 1.5 Å) is longer than a typical C-O single bond. Observing the dihedrals C6-C2-C1-C7, one can see that in the CI-C2s the torsion differs only around 20° from a planar structure but the C2-C3 bond arranges nearly perpendicular to the molecular plane. Therefore, the displacement of the oxygen-ring with respect to the planar structure is higher than in the CI-C1 s and the pyramidalization of C2 is much larger than the one of C1 in the CI-C1s. This is best observed comparing the angles C1-C2-X26 and the angles C2-C1-X25. As in the twisted TSs, X25 and X26 are dummy atoms, situated as shown in Figure 5a. In the CI-C1s the angle C2-C1-X25 is around 126°, which corresponds to a deviation from the planar structure (180°) of about 54°. In the CI-C2s the angle C1-C2-X26 is around 107°, indicating a larger deviation from the planar structure of ca. 73°. An IRC calculation along the gradient difference vector of CI1-C1L in the ground state leads to 1 (in one direction) and to 2 (in the other direction). Furthermore, the optimization of the Franck-Condon geometry of 1 in the S1 as well as a MEP calculation beginning at the same point ends in CI1-C1L. Thus, it appears that this CI is the most important one to relax to the electronic ground state S0. Conclusions In this paper, the ground and first excited state potential energy surfaces of the model molecular rotor CPTHF have been investigated. In the electronic ground state, two degenerated stereoisomers are possible. The two stereoisomers appear due to the distortion suffered in cyclopentane and tetrahydrofuran rings to release strain. Both stereoisomers have enantiomeric

J. Phys. Chem. A, Vol. 114, No. 34, 2010 9347 counterparts (giving rise to four stereoisomers), related by the position up or down of the carbons of the ring with respect to the plane defined by the ethylene backbone. The racemization pathways have been calculated, finding that the activation barriers are negligible and that thermal racemization takes place at room temperature. The rotational profiles have also been investigated, finding activation energies of 63.25 kcal/mol at CASPT2 level of theory. The UV-vis absorption spectrum of CPTHF has been calculated. The spectroscopic state is the first electronically excited state, which is characterized by a ππ* transition within the ethylene moiety. This state is predicted at ca. 6.5 eV, which is characteristic of olefinic systems. This value is shifted to lower energies in the molecular rotors based on overcrowded alkenes (e.g., 4 eV in ref 7). Because of the oxygen atom, another valence state is present in CPTHF, but it is higher in energy (ca. 9 eV) and well separated from the S1. Therefore, we can consider that the relevant state to describe the photochemistry of CPTHF is the S1. Five different conical intersections have been located for each of the stereoisomers of CPTHF. All of them are twisted and pyramidalized at the ethylenic carbons, as ethylene does. Among the CIs with lower energy, one CI (CI1-C1L) is expected to be first accessed from the S1 to relax to the S0. The low isomerizations barriers in the ground state for the reactions 1 T 2′ and 2 T 1′ point toward no distinction between 1 and 2′ as well as 2 and 1′ at room temperature. Thus, unidirectionality solely by warming it up is only possible if CPTHF is functionalized by crowding the ring moieties. However, ultrafast laser pulses can be used to achieve unidirectional rotation in systems like CPTHF, where the PES are symmetric around the minima, solely with the use of light and thus avoiding the thermal step, see, for example, ref 16. Work along these lines is in progress. Acknowledgment. The authors thank the Deutsche Forschungsgemeinschaft for financial support (GO 1059/2-1). We are grateful to A. Hauser and M. Bra¨utigam for their preliminary calculations on the UV spectrum of CPTHF. Most of the calculations have been performed in the HP computers of the Theoretical Chemistry group at the Friedrich-Schiller-University (FSU) of Jena. The computer center of the FSU is also acknowledged for allocation of computer time. References and Notes (1) Feringa, B. L. Molecular Switches, 1st ed.; Wiley-VCH: Weinheim, 2001. (2) Balzani, V.; Credi, A.; Venturi, M. Molecular DeVices and Machines: A Journey into the Nanoworld, 1st ed.; Wiley-VCH: Weinheim, 2003. (3) Credi, A.; Venturi, M. Cent. Eur. J. Chem. 2008, 6, 325. (4) Feringa, B. L.; van Delden, R. A.; Koumura, N.; Geertsema, E. M. Chem. ReV. 2000, 100, 1789. (5) Koumura, N.; Zijlstra, R. W. J.; van Delden, R. A.; Harada, N.; Feringa, B. L. Nature 1999, 401, 152. (6) Feringa, B. L. J. Org. Chem. 2007, 72, 6635. (7) Pollard, M. M.; Meetsma, A.; Feringa, B. L. Org. Biomol. Chem. 2008, 6, 507. (8) Koumura, N.; Geertsema, E. M.; van Gelder, M. B.; Meetsma, A.; Feringa, B. L. J. Am. Chem. Soc. 2002, 124, 5037. (9) van Delden, R. A.; ter Wiel, M. K. J.; Pollard, M. M.; Vicario, J.; Koumura, N.; Feringa, B. L. Nature 2005, 437, 1337. (10) Pollard, M. M.; ter Wiel, M. K. J.; van Delden, R.; Vicario, J.; Koumura, N.; van den Brom, C.; Meetsma, A.; Feringa, B. Chem.sEur. J. 2008, 14, 11610. (11) Pollard, M. M.; Lubomska, M.; Rudolf, P.; Feringa, B. L. Angew. Chem., Int. Ed. 2007, 46, 1278. (12) Yamaki, M.; Nakayama, S.; Hoki, K.; Kono, H.; Fujimura, Y. Phys. Chem. Chem. Phys. 2009, 11, 1662.

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