Chinese Chemical Letters 25 (2014) 727–731

Original article

A semiclassical molecular dynamics of the photochromic ring-openingreaction of spiropyran

Gao-Hong Zhai a,*, Pei Yang a, Shao-Mei Wu a, Yi-Bo Lei a,*, Yu-Sheng Dou b

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, Chinab Department of Physical Sciences, Nicholls State University, PO Box 2022, Thibodaux, LA 70310, USA

A R T I C L E I N F O

Article history:

Received 20 December 2013

Received in revised form 6 January 2014

Accepted 21 January 2014

Available online 19 March 2014

Keywords:

Semiclassical dynamical simulation

Spiropyran

Photochromic ring-opening reaction

Internal conversion

A B S T R A C T

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 ring-

opening process of trans-SP to form the most stable merocyanine (MC) product. These findings provide

more important complementarity for interpreting experimental observations.

� 2014 Gao-Hong Zhai and Yi-Bo Lei. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All

rights reserved.

Contents lists available at ScienceDirect

Chinese Chemical Letters

jo u rn al h om epag e: ww w.els evier .c o m/lo cat e/cc le t

1. Introduction

Photochromic molecules have been widely used in a variety ofnew techniques and processes, such as sunglasses, opticalswitching, optical date storage, nonlinear optical devices, opticalnanoparticles, and photonic crystal because of their controllablelight-induced change of color [1,2]. Among these molecules, asuitable spiropyran (SP) leading to a fast bidirectional photo-switching processes is one of the very recent most studiedmolecules [3–6].

In Spiro-type compounds, the indole and benzopyran planarheterocycles are joined orthogonally by a common spiro carbonatom, which constrains the conjugation of the two p-electronicsystems so that the lowest electronic transition occurs in the nearUV region (l < 400 nm). Correspondingly, this molecule iscolorless. After this excitation, the break of the bond betweenthe Spiro-C and O atoms takes place and this spiropyran convertsto a planar form in a few picoseconds [7]. This form is an openphotoisomer of spiropyran, called merocyanine (MC) withabsorption in the visible region (l = 500–700 nm) (see Scheme1), since the planar conjugation leads to p-electronic delocaliza-tion. This process corresponds to a photocoloration reaction. As a

* Corresponding authors.

E-mail addresses: zgh@nwu.edu.cn (G.-H. Zhai), leiyb@nwu.edu.cn (Y.-B. Lei).

1001-8417/$ – see front matter � 2014 Gao-Hong Zhai and Yi-Bo Lei. Published by Els

http://dx.doi.org/10.1016/j.cclet.2014.01.050

photoreversible and thermal reaction, MC can switch back to theclosed form SP by heating or irradiation in the visible region. Thereversible process, accompanied by remarkable changes ingeometries and charge distribution, can be used in variousapplications.

Thus, the photochromic reactions of SP have been widelystudied by time resolved spectroscopy to find the complexmechanism [8–12]. In this paper, we only pay attention to thephoto induced ring-opening reaction of BIPS, which is the primaryprocess of SP, although several reactions exist with differentsubstituents on the SP and experimental conditions. Recentspectroscopic investigations reveal the following aspects: (1)The efficient internal conversion from the excited state S1 to theground state S0 leads to a ring-opening process to formphotoproducts (MC), corresponding to quantum yields less than10% in gas phase [9] and 3.3% in water [12]; (2) The MC productscan not be directly produced from the excited SP, and someintermediate species/state are assumed in the ring-openingprocess [9]; (3) The formation of MC is likely to be barrierlessand generally fast in 0.9 ps [7] or 1.6 ps [12], measured byfemtosecond absorption spectroscopy or subpicosecond transientspectroscopy in water, respectively.

To clarify the mechanisms of the photo triggered ring-openingreactions of SP, various high level quantum calculations have beencarried out, including time-dependent density functional theory(TD-DFT) [13], the complete active space self-consistent field

evier B.V. on behalf of Chinese Chemical Society. All rights reserved.

C10

C11C8

N

C1

C2

C3

C6 C9

C12

C15C13

O

CH3

CH3H3C

H21

H27

H26N O

CH3

H3C CH3

UV

Δ or Vi sible

Spiropy ran Merocy anine(M C,TTC)

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

G.-H. Zhai et al. / Chinese Chemical Letters 25 (2014) 727–731728

(CASSCF) [14], complete active space second-order perturbationtheory (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 otherapproximations [13,20]. The primary theoretical investigationshave proposed three different pathways for the photochromicreaction of the electronically excited SP. All three pathways rely onthe internal conversion through conical intersections. The first andsecond kinds of paths are both associated with the Cspiro–Ostretching and hydrogen-out-of-plane (HOOP) torsion modes (theC atom is connected by Spiro-C) of the excited SP. The first routestarts from the excitation of one isomer of SP (trans-SP), whichtransitions first to TCC(S1), which in turn forms CIS1/S0(TCC), whichcan transition to MC intermediates or back to the original SPmolecule [18,19]. Alternatively, cis-SP can become CCC(S1) afterphoto initialization, then decaying to CIS1/S0(CCC) and finally eitherMC isomers or the ground state SP, as reported by Liu andMorokuma [19]. The very recent theoretical study implies thatthese two channels involve not only a one-bond-flipping (OBF)path on the S1 state, but also a HOOP valley following the Cspiro–Ostretching and H–C out-of-plane torsion modes as mentionedabove [19]. The last pathway involves the lengthening Cspiro–Nbond and the internal conversion from the electronically excitedstates to the SP ground state through CIS1/S0(CN) [18,19]. All ofthese pathways play an important role in the effective internalconversion yields of SP.

Theoretical investigations on the photochromic reaction of SPtypically use static quantum calculations with mode compounds tolocate energy minima on the potential energy surfaces andderiving the minimum energy path by connecting the criticalpoints. These calculations are fundamental and important inunderstanding the main features of the reaction mechanisms.However, the static calculations alone can not provide detailedinformation for a specific reaction path that is actually realized in aphotochromic reaction due to the following limitations: (1) thesimplified model can not represent the real molecular structuresand conformational adaptability; (2) they are incapable ofdescribing the time-dependent properties of the ring-openingprocess; (3) they are usually performed along one or two reactioncoordinates with the other coordinates fixed or optimized andconsequently are insufficient in characterizing a real photochromicprocess where all reaction coordinates are involved and play a non-negligible role; and (4) they do not include the laser pulseproperties and subsequently cannot provide detailed explanationsfor photochemical experiments in which the laser pulse param-eters strongly influence the reaction.

To more directly interpret the mechanisms of this reaction, inthis work, we study the dynamics of the radiationless deactivation,which is necessary for the photo-induced chemical reaction [21] ofthe low-lying excited states of SP following the excitation usingseveral laser pulses, by a semiclassical dynamics simulationapproach. In our simulation study, all degrees of freedom of themolecule are included in the calculations and the laser pulse isexplicitly coupled to electrons. By monitoring the nuclear motions

triggered by a specific laser pulse, we are able to describe a realisticphoto ring-opening reaction path. The more accurate potentialenergy curves (PECs) of the ground state and the low-lying excitedstates along the reaction path will be supplied for the explanationof the simulation results.

2. Methodology

In our semiclassical dynamics simulation approach, calledsemiclassical electron-radiation-ion dynamics (SERID), the time-dependent quantum states are calculated for the valence electrons,while the radiation field and the motion of the nuclei are treatedclassically.

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

HabðX � X0Þ ¼ H0abðX � X0Þexp

iq

�hcA � ðX � X0Þ

� �(1)

Here HabðX � X0Þ is the Hamiltonian matrix element for basisfunctions a and b on atoms at X and X0 respectively, and q = �e isthe charge of the electron. The one-electron wave function isupdated at each time step by solving the time-dependentSchrodinger equation with an algorithm based on the time-evolution operator and conservation of probability [25]. Density-functional-based tight-binding (DFTB) is employed to calculate theelectronic structure, in which only the valence electrons aretreated and the remaining electrons plus nucleus are representedas a core [26].

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

Mld2Xla

dt2¼ � @Eelec

@Xla

¼ �1

2

Xj

Cþj �

@H

@Xla� i�h

1

2

@S

@Xla� @@t

� �� C j

� @Ure p=@Xla (2)

where Xla ¼ Xla

D Eis 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 isthe overlap matrix for the atomic orbitals, and Eelec is the electronicenergy of the system. This equation is numerically integrated bythe velocity Verlet algorithm [27], and a time step of 0.1 fs wasused to preserve energy conservation.

3. Results and discussion

The ground state geometries of trans-SP conformer was obtainedwithin 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)

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.

G.-H. Zhai et al. / Chinese Chemical Letters 25 (2014) 727–731 729

are hereafter labeled asa,b,g andt, respectively, consistent with theprevious work [19].

To produce an excited state, in which the photochromic ring-opening process of SP is appreciably activated, an 80 fs (FWHM)laser pulse was applied to trans-SP conformer with an effectivephoton energy of 3.972 eV, corresponding to 312.1 nm light, whichis in agreement with the mentioned experimental conditions [9].The energy selected matches the energy gap between theHOMO � 1 and LUMO + 1 in the present density-functional basedapproach for the equilibrated ground state geometry. Simulationswere run for more than 100 different fluences, corresponding toseveral initial conditions, but only representative results will bepresented for a fluence of 0.139 kJ/m2 that generates the desiredvibrational 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 areconstructed at the three state average (SA3)-CASSCF and thefollowing CASPT2 level with a level shift 0.1 of a.u. and the 6-31G(d) basis set employing the MOLCAS 7.5 quantum chemistrypackage [28]. The active space is constructed with 12 electronsdistributed in 10 molecular orbitals, consistent with the previouscalculations [19].

Six snapshots from the simulation at different times for thephoto induced ring-opening process of trans-SP are shown in Fig. 1.The laser excitation starts at 0 fs and the initial molecule becomeselectronically excited after about 50 fs. The most impressivefeatures shown in Fig. 1 are the lengthening of the C1–O bond, thetwist around C3–C6 bond, and the HOOP torsion of phenyl ringconnected to the O atom, which is shown by the dihedral angleH27–C13–C9–C15, denoted by u.

The important nuclear motions for ring-opening reaction of SP,described by the variations of C1–O bond and dihedral angles a, b, gare presented in Fig. 2a and b, respectively. The evident variationsof these nuclear motions start at 422 fs. After this time, it can be

Fig. 2. Changes in (a) C1–O (b) the a, b and g (c) t and u of trans-SP subjected excitation

3.972 eV.

seen in Fig. 2a that the C1–O bond is gradually lengthened from theinitial 1.404 A to 3.618 A at 616 fs, and then the bond lengthoscillates around an average value 3.5 A until about 4848 fs, whenthis bond is broken and the six membered ring with the O atom isaccordingly opened. This bond is again elongated to 3.945 A at thismoment. After that, an average value of about 4.000 A is kept untilthe end of this simulation. Correspondingly, Fig. 2b shows that thedihedral angle a increases rapidly to the peak value 272.68 at 616 fsand then decrease gradually to 158.48 at 4848 fs. After that, thistwist angle maintains an average value of 180.08 to the end. Thedihedral angles b and g are also speedily enlarged after 422 fs andtheir values are basically kept until 4848 fs. At this moment, theangle 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 retainaverage values of 180.08 and 0.08 up to the end, respectively. Withthese results, it can be indicated that the initial MC conformer atthe beginning of the ring-opening is MC-TCC. After that, thetransient MC-CCC form appears at 616 fs. Then, this isomer isgradually switched back to the MC-TCC conformer. After 4848 fs,MC-TCC isomerizes to the final form MC-TTC, which is the moststable isomer of MC as observed previously by experimentalobservations [8–12]. In fact, the molecular vibration is initializedfrom two cooperative HOOP distortions of two connected sixmembered rings, corresponding to the changes of dihedral angles tand u as presented in Fig. 2c. These two dihedral angles vary visiblyfrom the beginning until about 422 fs. Then, they are changed backto their initial values with large oscillations up to the end. TheseHOOP distortions imply the presence of HOOP valleys as proposedvery recently [19].

The populations and energies of HOMO � 1, HOMO, LUMO andLUMO + 1 for this reaction path are also shown in Fig. 3a and b,respectively. It can be seen in Fig. 3a that the electronic populationof HOMO � 1 decreases while that of LUMO increases from theinitial photon excitation until 244 fs. When the energy gap

by a 80 fs (FWHM) laser pulse with a fluence of 0.139 kJ/m2 and photon energy of

0 20 0 4 0 0 6 0 0 8 0 0 1 0 0 00 . 00 . 10 . 20 . 30 . 40 . 50 . 60 . 70 . 80 . 91 . 0

Elec

troni

c po

pula

tion

t i m e / f s

H O M O - 1 H O M O L U M O L U M O + 1

( a )

0 2 0 0 4 0 0 60 0 8 0 0 1 0 0 0- 7 . 0- 6 . 5- 6 . 0- 5 . 5- 5 . 0- 4 . 5- 4 . 0- 3 . 5- 3 . 0- 2 . 5- 2 . 0- 1 . 5

Ener

gy /e

V

tim e / f s

H O M O - 1 H O M O L U M O L U M O + 1

( b )

Fig. 3. Variations with time of (a) the electronic populations and (b) energies of the HOMO � 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.

G.-H. Zhai et al. / Chinese Chemical Letters 25 (2014) 727–731730

between HOMO and LUMO is diminished according to the suddendescent of LUMO energy and slight ascent of HOMO energy, thenthe gap is enlarged till 422 fs. At this moment, these two orbitalsare again degenerate, corresponding to the fact that the electronicpopulation of LUMO decreases while that of HOMO increases. Afterthat, no remarkable change of the electron population occursbetween these four interesting frontier molecular orbitals.

To gain a deeper understanding of the reaction path, thefollowing CASSCF(12,10)/MS-CASPT2 potential energy curves(PECs) of the ground state and two low-lying excited states alongthe representative trajectory are presented in Fig. 4. It is evidentthat 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. Correspondingto the electron population in Fig. 3a, the electrons would be excitedto S1 from S0 at the beginning. At about 230 fs, the energydifference between S1 and S0 is diminished to 0.503 eV (0.524 eVfor CASSCF), and the dominant configuration of S1 is changed toHOMO ! LUMO, consistent with the simulation findings in Fig. 3.Then, these two states are obviously separate until they areroughly degenerate again from 560 fs to 640 fs with the smallestenergy difference 0.576 eV (0.182 eV for CASSCF). Particularly, at560 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 andS1 at MS-CASPT2 level. These results imply that electron transitionfrom S1 to S0 would occur at this moment, which is a little later

110010009008007006005004003002001000-862 .65

-862 .60

-862 .55

-862 .50

-862 .45

-862 .40

-862 .35

-862 .30

-862 .25

-862 .20

Ener

gy /a

.u.

tim e /fs

S0 S1 S2

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).

than 422 fs for the simulation in Fig. 3. Subsequently, these threeelectronic states are not degenerate until the end.

4. Conclusion

In summary, we have investigated the photochromic ring-opening reaction mechanism of SP employing a realistic simulationapproach that couples the dynamics of electrons and nuclei and thefollowing SA3-CASSCF(12,10)/MS-CASPT2 PECs. The typical simu-lation trajectory firstly involves two cooperative HOOP torsions oftwo connected six membered rings. After the electronic transitionat about 560 fs, the C1–O bond is broken and the MC-TCC is formedbefore 616 fs, at this moment the unstable product MC-CCC,assigned to appear shortly after photo excitation, emerges andrapidly converts back to the original MC product MC-TCC until4848 fs. Then, the final stable TTC form of MC is created and kept upto the end. This means that the ring-opening process takes about616 fs, which basically agrees with the 900 fs measured by theexperiments on the gas phase [9]. The subsequent isomerization onthe ground state takes about 4 ps, which is less than the about20 ps obtained by the previous studies [10,13]. This simulationtrajectory also provides a direct proof for confirming the proposedmechanism suggested by Liu and Morokuma in more accuratetheoretical computations [19].

Acknowledgments

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

References

[1] B.L. Feringa, Molecular Switches, Wiley-VCH, Weinheim, Germany, 2011, p. 476.[2] M. Heilemann, P. Dedecker, J. Hofkens, M. Sauer, Photoswitches: key molecules for

subdiffraction-resolution fluorescence imaging and molecular quantification,Laser Photonics Rev. 3 (2009) 180–202.

[3] J. Buback, M. Kullmann, F. Langhojer, et al., Ultrafast bidirectional photoswitchingof a spiropyran, J. Am. Chem. Soc. 132 (2010) 16510–16519.

[4] G. Berkovic, V. Krongauz, V. Weiss, Spiropyrans and spirooxazines for memoriesand switches, Chem. Rev. 100 (2000) 1741–1754.

[5] S. Silvi, A. Arduini, A. Pochini, et al., A simple molecular machine operated byphotoinduced proton transfer, J. Am. Chem. Soc. 129 (2007) 13378–13379.

[6] (a) D.S. Achilleos, T.A. Hatton, M. Vamvakaki, Light-regulated supramolecularengineering of polymeric nanocapsules, J. Am. Chem. Soc. 134 (2012) 5726–5729;(b) Z. Si, Q. Zhang, M. Xue, et al., Synthesis of novel chalcone derivatives and theirstabilization effect of spiropyran in PMMA films, Chin. Chem. Lett. 22 (2011)1025–1028.

G.-H. Zhai et al. / Chinese Chemical Letters 25 (2014) 727–731 731

[7] N.P. Ernsting, T. Arthen-Engeland, Conformational dynamics of the merocyanine,J. Phys. Chem. 95 (1991) 5502–5509.

[8] N. Tamai, H. Miyasaka, Ultrafast dynamics of photochromic systems, Chem. Rev.100 (2000) 1875–1890.

[9] M. Rini, A.K. Holm, E.T.J. Nibbering, H. Fidder, Ultrafast UV-mid-IR investigation ofthe ring opening reaction of a photochromic spiropyran, J. Am. Chem. Soc. 125(2003) 3028–3034.

[10] L. Poisson, K.D. Raffael, B. Soep, J.M. Mestdagh, G. Buntinx, Gas-phase dynamics ofspiropyran and spirooxazine molecules, J. Am. Chem. Soc. 128 (2006) 3169–3178.

[11] M. Kullmann, S. Ruetzel, J. Buback, P. Nuernberger, T. Brixner, Reaction dynamicsof a molecular switch unveiled by coherent two-dimensional electronic spec-troscopy, J. Am. Chem. Soc. 133 (2011) 13074–13080.

[12] J. Kohl-Landgraf, M. Braun, C. Ozcoban, D.P.N. Goncalves, A. Heckel, J. Wachtveitl,Ultrafast dynamics of a spiropyran in water, J. Am. Chem. Soc. 134 (2012) 14070–14077.

[13] Y. Sheng, J. Leszczynski, A.A. Garcia, et al., Comprehensive theoretical study of theconversion reactions of spiropyrans: substituent and solvent effects, J. Phys.Chem. B 108 (2004) 16233–16243.

[14] K.P. Lawley, Advances in Chemical Physics, vol. 69, John Wiley & Sons Inc., NewYork, 1987, pp. 399–445.

[15] J. Finley, P.A. Malmqvist, O. Roos, L. Serrano-andres, The multi-state CASPT2method, Chem. Phys. Lett. 288 (1998) 299–306.

[16] (a) Y. Kurashige, T. Yanai, High-performance ab initio density matrix renorma-lization group method: Applicability to large-scale multireference problems formetal compounds, J. Chem. Phys. 130 (2009) 234114;(b) D. Ghosh, J. Hachmann, T. Yanai, G.K.L. Chan, Orbital optimization in thedensity matrix renormalization group, with applications to polyenes and beta-carotene, J. Chem. Phys. 128 (2008) 144117;(c) Y. Kurashige, T. Yanai, Second-order perturbation theory with a DMRG self-consistent field reference function: theory and application to the study ofchromium dimer, J. Chem. Phys. 135 (2011) 094104.

[17] (a) P. Celani, F. Bernardi, M. Olivucci, M.A. Robb, Conical intersection mechanismfor photochemical ring opening in benzospiropyran compounds, J. Am. Chem. Soc.119 (1997) 10815–10820;(b) I. Gomez, M. Reguero, M.A. Robb, Efficient photochemical merocyanine-to-spiropyran ring closure mechanism through an extended conical intersectionseam. A model CASSCF/CASPT2 study, J. Phys. Chem. A 110 (2006) 3986–3991.

[18] M. Sanchez-Lozano, C.M. Estevez, J. Hermida-Ramon, L. Serrano-Andres, Ultrafastring-opening/closing and deactivation channels for a model spiropyran–mero-cyanine system, J. Phys. Chem. A 115 (2011) 9128–9138.

[19] (a) F.Y. Liu, K. Morokuma, Multiple pathways for the primary step of the spir-opyran photochromic reaction: a CASPT2//CASSCF study, J. Am. Chem. Soc. 135(2013) 10693–10702;(b) F.Y. Liu, Y. Kurashige, T. Yanai, K. Morokuma, Multireference Ab initio densitymatrix renormalization group (DMRG)-CASSCF and DMRG-CASPT2 study on thephotochromic ring opening of spiropyran, J. Chem. Theory Comput. 9 (2013)4462–4469.

[20] V.I. Minkin, A.V. Metelitsa, I.V. Dorogan, et al., Spectroscopic and theoreticalevidence for the elusive intermediate of the photoinitiated and thermal rearran-gements of photochromic spiropyrans, J. Phys. Chem. A 109 (2005) 9605–9616.

[21] (a) T. Chu, Y. Zhang, K. Han, The time-dependent quantum wave packet approachto the electronically nonadiabatic processes in chemical reactions, Int. Rev. Phys.Chem. 25 (2006) 201–235;(b) K. Han, J.D. Huang, S. Chai, S.H. Wen, W.Q. Deng, Anisotropic mobilities inorganic semiconductors, Nat. Protoc. Exch. (2013), http://dx.doi.org/10.1038/protex.2013.070.

[22] Y.S. Dou, B.R. Torralva, R.E. Allen, Semiclassical electron-radiation-ion dynamics(SERID) and cis–trans photoisomerization of butadiene, J. Mod. Opt. 50 (2003)2615–2643.

[23] Y.S. Dou, B.R. Torralva, R.E. Allen, Another important coordinate in the photo-isomerization of cis-stilbene, Chem. Phys. Lett. 378 (2003) 323–329.

[24] T.B. Boykin, R.C. Bowen, G. Klimeck, Electromagnetic coupling and gauge invari-ance in the empirical tight-binding method, Phys. Rev. B 63 (2001) 245314–245330.

[25] B.R. Torralva, T.A. Niehaus, M. Elstner, et al., Response of C60 and Cn to ultrashortlaser pulses, Phys. Rev. B 64 (2001) 153105–153108.

[26] D. Porezag, T. Frauenheim, T. Kohler, D. Seifert, R. Kaschner, Construction of tight-binding-like potentials on the basis of density-functional theory: application tocarbon, Phys. Rev. B 51 (1995) 12947–12957.

[27] W.C. Swope, H.C. Andersen, P.H. Berens, K.R. Wilson, A computer simulationmethod for the calculation of equilibrium constants for the formation of physicalclusters of molecules: applications to small water clusters, J. Chem. Phys. 76(1982) 637–649.

[28] G. Karlstrom, R. Lindh, P.A. Malmqvist, et al., MOLCAS: a program package forcomputational chemistry, Comput. Matl. Sci. 28 (2003) 222–239.