Chinese Chemical Letters  2014, Vol.25 Issue (05):727-731   PDF    
A semiclassical molecular dynamics of the photochromic ring-opening reaction of spiropyran
Gao-Hong Zhaia , Pei Yanga, Shao-Mei Wua, Yi-Bo Leia , Yu-Sheng Doub    
a Key Laboratory of Synthetic and Natural Functional Molecule Chemistry of Ministry of Education, College of Chemistry & Materials Science, Shaanxi Key Laboratory of Physico-Inorganic Chemistry, Northwest University, Xi'an 710069, China;
b Department of Physical Sciences, Nicholls State University, PO Box 2022, Thibodaux, LA 70310, USA
Abstract: The photochromic ring-opening reaction of spiropyran (SP) has been investigated by a realistic semiclassical dynamics simulation, accompanied by SA3-CASSCF(12,10)/MS-CASPT2 potential energy curves (PECs) of S0-S2. The main simulation results show the dominate pathway corresponds to the ringopening process of trans-SP to form the most stable merocyanine (MC) product. These findings provide more important complementarity for interpreting experimental observations.
Key words: Semiclassical dynamical simulation     Spiropyran     Photochromic ring-opening reaction     Internal conversion    
1. Introduction

Photochromic molecules have been widely used in a variety of new techniques and processes,such as sunglasses,optical switching,optical date storage,nonlinear optical devices,optical nanoparticles,and photonic crystal because of their controllable light-induced change of color [1, 2]. Among these molecules,a suitable spiropyran (SP) leading to a fast bidirectional photoswitching processes is one of the very recent most studied molecules [3, 4, 5, 6].

In Spiro-type compounds,the indole and benzopyran planar heterocycles are joined orthogonally by a common spiro carbon atom,which constrains the conjugation of the two p-electronic systems so that the lowest electronic transition occurs in the near UV region (l < 400 nm). Correspondingly,this molecule is colorless. After this excitation,the break of the bond between the Spiro-C and O atoms takes place and this spiropyran converts to a planar form in a few picoseconds [7]. This form is an open photoisomer of spiropyran,called merocyanine (MC) with absorption in the visible region (l = 500-700 nm) (see Scheme 1),since the planar conjugation leads to p-electronic delocalization. This process corresponds to a photocoloration reaction. As a photoreversible and thermal reaction,MC can switch back to the closed form SP by heating or irradiation in the visible region. The reversible process,accompanied by remarkable changes in geometries and charge distribution,can be used in various applications.

Thus,the photochromic reactions of SP have been widely studied by time resolved spectroscopy to find the complex mechanism [8, 9, 10, 11, 12]. In this paper,we only pay attention to the photo induced ring-opening reaction of BIPS,which is the primary process of SP,although several reactions exist with different substituents on the SP and experimental conditions. Recent spectroscopic investigations reveal the following aspects: (1) The efficient internal conversion from the excited state S1 to the ground state S0 leads to a ring-opening process to form photoproducts (MC),corresponding to quantum yields less than 10% in gas phase [9] and 3.3% in water [12]; (2) The MC products can not be directly produced from the excited SP,and some intermediate species/state are assumed in the ring-opening process [9]; (3) The formation of MC is likely to be barrierless and generally fast in 0.9 ps [7] or 1.6 ps [12],measured by femtosecond absorption spectroscopy or subpicosecond transient spectroscopy in water,respectively.

To clarify the mechanisms of the photo triggered ring-opening reactions of SP,various high level quantum calculations have been carried out,including time-dependent density functional theory (TD-DFT) [13],the complete active space self-consistent field (CASSCF) [14],complete active space second-order perturbation theory (CASPT2) [15] level,density matrix renormalization group (DMRG) based CASSCF,CASPT2 [16] from simplified [17] to more [18] and even more [19] realistic models of SP,and other approximations [13, 20]. The primary theoretical investigations have proposed three different pathways for the photochromic reaction of the electronically excited SP. All three pathways rely on the internal conversion through conical intersections. The first and second kinds of paths are both associated with the Cspiro-O stretching and hydrogen-out-of-plane (HOOP) torsion modes (the C atom is connected by Spiro-C) of the excited SP. The first route starts from the excitation of one isomer of SP (trans-SP),which transitions first to TCC(S1),which in turn forms CIS1/S0(TCC),which can transition to MC intermediates or back to the original SP molecule [18, 19]. Alternatively,cis-SP can become CCC(S1) after photo initialization,then decaying to CIS1/S0(CCC) and finally either MC isomers or the ground state SP,as reported by Liu and Morokuma [19]. The very recent theoretical study implies that these two channels involve not only a one-bond-flipping (OBF) path on the S1 state,but also a HOOP valley following the Cspiro-O stretching and H-C out-of-plane torsion modes as mentioned above [19]. The last pathway involves the lengthening Cspiro-N bond and the internal conversion from the electronically excited states to the SP ground state through CIS1/S0(CN) [18, 19]. All of these pathways play an important role in the effective internal conversion yields of SP.

Theoretical investigations on the photochromic reaction of SP typically use static quantum calculations with mode compounds to locate energy minima on the potential energy surfaces and deriving the minimum energy path by connecting the critical points. These calculations are fundamental and important in understanding the main features of the reaction mechanisms. However,the static calculations alone can not provide detailed information for a specific reaction path that is actually realized in a photochromic reaction due to the following limitations: (1) the simplified model can not represent the real molecular structures and conformational adaptability; (2) they are incapable of describing the time-dependent properties of the ring-opening process; (3) they are usually performed along one or two reaction coordinates with the other coordinates fixed or optimized and consequently are insufficient in characterizing a real photochromic process where all reaction coordinates are involved and play a nonnegligible role; and (4) they do not include the laser pulse properties and subsequently cannot provide detailed explanations for photochemical experiments in which the laser pulse parameters strongly influence the reaction.

To more directly interpret the mechanisms of this reaction,in this work,we study the dynamics of the radiationless deactivation, which is necessary for the photo-induced chemical reaction [21] of the low-lying excited states of SP following the excitation using several laser pulses,by a semiclassical dynamics simulation approach. In our simulation study,all degrees of freedom of the molecule are included in the calculations and the laser pulse is explicitly coupled to electrons. By monitoring the nuclear motions triggered by a specific laser pulse,we are able to describe a realistic photo ring-opening reaction path. The more accurate potential energy curves (PECs) of the ground state and the low-lying excited states along the reaction path will be supplied for the explanation of the simulation results. 2. Methodology

In our semiclassical dynamics simulation approach,called semiclassical electron-radiation-ion dynamics (SERID),the timedependent quantum states are calculated for the valence electrons, while the radiation field and the motion of the nuclei are treated classically.

The details of this method have been described elsewhere [22, 23],so only a brief outline is present here. The radiation field is directly introduced in the electronic Hamiltonian though a vector potential A,and the time-dependent Peierls substitution is used to couple the radiation field and electrons [24].

Here Hab(X - X') is the Hamiltonian matrix element for basis functions a and b on atoms at X and X0 respectively,and q = -e is the charge of the electron. The one-electron wave function is updated at each time step by solving the time-dependent Schro¨ dinger equation with an algorithm based on the timeevolution operator and conservation of probability [25]. Densityfunctional- based tight-binding (DFTB) is employed to calculate the electronic structure,in which only the valence electrons are treated and the remaining electrons plus nucleus are represented as a core [26].

The nuclear motion is treated classically and described by the Ehrenfest’s theorem [22, 23]

where Xlα = is the expectation value of the time-dependent Heisenberg operator for the a coordinate of the nucleus labeled by l (with a = x,y,z). Urep is the nucleus-nucleus repulsive potential,S is the overlap matrix for the atomic orbitals,and Eelec is the electronic energy of the system. This equation is numerically integrated by the velocity Verlet algorithm [27],and a time step of 0.1 fs was used to preserve energy conservation. 3. Results and discussion

The ground state geometries of trans-SP conformerwas obtained within 5000 fs of simulation. The primary dihedral angles N-C1-C3- C6,C1-C3-C6-C9,C3-C6-C9-C12,and H21-C3-C1-C6 (see Scheme 1) arehereafter labeledasa,b,gandt,respectively,consistentwiththe previous work [19].

Scheme 1.The scheme of photo induced reaction between spiropyran and merocyanine.

To produce an excited state,in which the photochromic ringopening process of SP is appreciably activated,an 80 fs (FWHM) laser pulse was applied to trans-SP conformer with an effective photon energy of 3.972 eV,corresponding to 312.1 nm light,which is in agreement with the mentioned experimental conditions [9]. The energy selected matches the energy gap between the HOMO - 1 and LUMO + 1 in the present density-functional based approach for the equilibrated ground state geometry. Simulations were run for more than 100 different fluences,corresponding to several initial conditions,but only representative results will be presented for a fluence of 0.139 kJ/m2 that generates the desired vibrational motions necessary for the ring-opening reaction. Along the typical trajectory,the potential energy curves (PECs) of the ground state and the low-lying two excited states are constructed at the three state average (SA3)-CASSCF and the following CASPT2 level with a level shift 0.1 of a.u. and the 6- 31G(d) basis set employing the MOLCAS 7.5 quantum chemistry package [28]. The active space is constructed with 12 electrons distributed in 10 molecular orbitals,consistent with the previous calculations [19].

Six snapshots from the simulation at different times for the photo induced ring-opening process of trans-SP are shown in Fig. 1. The laser excitation starts at 0 fs and the initial molecule becomes electronically excited after about 50 fs. The most impressive features shown in Fig. 1 are the lengthening of the C1-O bond,the twist around C3-C6 bond,and the HOOP torsion of phenyl ring connected to the O atom,which is shown by the dihedral angle H27-C13-C9-C15,denoted by θ.

Fig. 1. Snapshots taken at different times in a simulation of trans-SP in response to excitation by a 80 fs (FWHM) laser pulse with a fluence of 0.139 kJ/m2 and photon energy of 3.972 eV,Atom C,H,N,and O are respectively denoted by dark gray,French gray,blue,and red,(a)-(f) are at 0 fs,244 fs,422 fs,616 fs,4848 fs and 15,000 fs,respectively.

The important nuclear motions for ring-opening reaction of SP, described by the variations of C1-O bond and dihedral angles a,b,g are presented in Fig. 2a and b,respectively. The evident variations of these nuclear motions start at 422 fs. After this time,it can be seen in Fig. 2a that the C1-O bond is gradually lengthened from the initial 1.404Å to 3.618Å at 616 fs,and then the bond length oscillates around an average value 3.5Å until about 4848 fs,when this bond is broken and the six membered ring with the O atom is accordingly opened. This bond is again elongated to 3.945Å at this moment. After that,an average value of about 4.000Å is kept until the end of this simulation. Correspondingly,Fig. 2b shows that the dihedral angle a increases rapidly to the peak value 272.68 at 616 fs and then decrease gradually to 158.48 at 4848 fs. After that,this twist angle maintains an average value of 180.08 to the end. The dihedral angles b and g are also speedily enlarged after 422 fs and their values are basically kept until 4848 fs. At this moment,the angle b increases to 180.48,while the angle g decreases to -37.78. Similar with the angle a,the angles b and g then respectively retain average values of 180.08 and 0.08 up to the end,respectively. With these results,it can be indicated that the initial MC conformer at the beginning of the ring-opening is MC-TCC. After that,the transient MC-CCC form appears at 616 fs. Then,this isomer is gradually switched back to the MC-TCC conformer. After 4848 fs, MC-TCC isomerizes to the final form MC-TTC,which is the most stable isomer of MC as observed previously by experimental observations [8, 9, 10, 11, 12]. In fact,the molecular vibration is initialized from two cooperative HOOP distortions of two connected six membered rings,corresponding to the changes of dihedral angles t and u as presented in Fig. 2c. These two dihedral angles vary visibly from the beginning until about 422 fs. Then,they are changed back to their initial values with large oscillations up to the end. These HOOP distortions imply the presence of HOOP valleys as proposed very recently [19].

Fig. 2. Changes in (a) C1-O (b) the a,b and g (c) t and u of trans-SP subjected excitation by a 80 fs (FWHM) laser pulse with a fluence of 0.139 kJ/m2 and photon energy of 3.972 eV.

The populations and energies of HOMO - 1,HOMO,LUMO and LUMO + 1 for this reaction path are also shown in Fig. 3a and b, respectively. It can be seen in Fig. 3a that the electronic population of HOMO - 1 decreases while that of LUMO increases from the initial photon excitation until 244 fs. When the energy gap between HOMO and LUMO is diminished according to the sudden descent of LUMO energy and slight ascent of HOMO energy,then the gap is enlarged till 422 fs. At this moment,these two orbitals are again degenerate,corresponding to the fact that the electronic population of LUMO decreases while that of HOMO increases. After that,no remarkable change of the electron population occurs between these four interesting frontier molecular orbitals.

Fig. 3. Variations with time of (a) the electronic populations and (b) energies of theHOMO + 1,HOMO,LUMO and LUMO + 1 orbitals of trans-SP following application of a 80 fs (FWHM) laser pulse with a fluence of 0.139 kJ/m2 and photon energy of 3.972 eV.

To gain a deeper understanding of the reaction path,the following CASSCF(12,10)/MS-CASPT2 potential energy curves (PECs) of the ground state and two low-lying excited states along the representative trajectory are presented in Fig. 4. It is evident that the two excited states S1 and S2 are almost degenerate at 0 fs, corresponding to the dominate configurations HOMO - - 1→LUMO and HOMO→LUMO,respectively. Corresponding to the electron population in Fig. 3a,the electrons would be excited to S1 from S0 at the beginning. At about 230 fs,the energy difference between S1 and S0 is diminished to 0.503 eV (0.524 eV for CASSCF),and the dominant configuration of S1 is changed to HOMO→LUMO,consistent with the simulation findings in Fig. 3. Then,these two states are obviously separate until they are roughly degenerate again from 560 fs to 640 fs with the smallest energy difference 0.576 eV (0.182 eV for CASSCF). Particularly,at 560 fs,the dominant configuration of S0 converts to HOMO - →LUMO,while that for original S0 appears on S2 at CASSCF level, although the dominant configurations are not changed for S0 and S1 at MS-CASPT2 level. These results imply that electron transition from S1 to S0 would occur at this moment,which is a little later than 422 fs for the simulation in Fig. 3. Subsequently,these three electronic states are not degenerate until the end.

Fig. 4. Variations with time of potential energy curves (PECs) of the ground state and two low-lying excited states along the representative trajectory at the level of CASSCF(12,10)/MS-CASPT2 with the basis set 6-31G(d).
4. Conclusion

In summary,we have investigated the photochromic ringopening reaction mechanism of SP employing a realistic simulation approach that couples the dynamics of electrons and nuclei and the following SA3-CASSCF(12,10)/MS-CASPT2 PECs. The typical simulation trajectory firstly involves two cooperative HOOP torsions of two connected six membered rings. After the electronic transition at about 560 fs,the C1-O bond is broken and the MC-TCC is formed before 616 fs,at this moment the unstable product MC-CCC, assigned to appear shortly after photo excitation,emerges and rapidly converts back to the original MC product MC-TCC until 4848 fs. Then,the final stable TTC form ofMCis created and kept up to the end. This means that the ring-opening process takes about 616 fs,which basically agrees with the 900 fs measured by the experiments on the gas phase [9]. The subsequent isomerization on the ground state takes about 4 ps,which is less than the about 20 ps obtained by the previous studies [10, 13]. This simulation trajectory also provides a direct proof for confirming the proposed mechanism suggested by Liu and Morokuma in more accurate theoretical computations [19]. Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 21003100 and 21073242),Natural Science Basic Research Plan in Shaanxi Province of China (No. 2011JQ2013) and Special Fund of Education Department of Shaanxi Province (No. 12JK0619). The authors also thank Professor Zhenyi Wen,Associate Professor Huixian Han,and Bingbing Suo for the helpful suggestions.

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