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Detailed mechanism of trans-cis photoisomerization of azobenzene studied bysemiclassical dynamics simulationYusheng Dou ab; Yun Hu a; Shuai Yuan ac; Weifeng Wu a; Hong Tang a

a Institute of Computational Chemistry, Chongqing University of Posts and Telecommunications, Chongqing400065, China b Department of Physical Sciences, Nicholls State University, Thibodaux, LA 70310, USA c

Department of Chemistry, Northwest University, Xi'an, Shaanxi 710069, China

Online Publication Date: 01 January 2009

To cite this Article Dou, Yusheng, Hu, Yun, Yuan, Shuai, Wu, Weifeng and Tang, Hong(2009)'Detailed mechanism of trans-cisphotoisomerization of azobenzene studied by semiclassical dynamics simulation',Molecular Physics,107:2,181 — 190

To link to this Article: DOI: 10.1080/00268970902769497

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Molecular Physics

Vol. 107, No. 2, 20 January 2009, 181–190

RESEARCH ARTICLE

Detailed mechanism of trans–cis photoisomerization of azobenzene studied by semiclassical

dynamics simulation

Yusheng Douab*, Yun Hua, Shuai Yuanac, Weifeng Wua and Hong Tanga

aInstitute of Computational Chemistry, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;bDepartment of Physical Sciences, Nicholls State University, PO Box 2022, Thibodaux, LA 70310, USA; cDepartment of

Chemistry, Northwest University, Xi’an, Shaanxi 710069, China

(Received 6 December 2008; final version received 21 January 2009)

A realistic dynamics simulation study is reported for the trans–cis photoisomerization of azobenzene. Thesimulation follows both n�* and ��* excitations and each excitation is induced by a 50 fs (FWHM) laser pulse.The simulation results show that, for both excitations, the reaction path is predominated by the rotationcoordinate of the NN bond. The simulation finds that the CNN inversion angles expand as soon as the rotationstarts. The expansion of the CNN bond angles permits the molecule to rotate efficiently. It is therefore suggestedthat the photoisomerization of trans-azobenzene follows an inversion-assisted rotation path. These simulationresults are significant for understanding the mechanism of this important process.

Keywords: ab initio; electronic structure; quantum chemistry; computational

1. Introduction

Azobenzene undergoes trans— cis isomerizationwhen subject to ultraviolet or visible radiation. Thisproperty makes azobenzene and its derivatives goodcandidates for many applications [1–3], includingmolecular switches, image storage devices, as well asthe recently designed light-driven molecular shuttle [4].For this reason, the photochemical and photophy-sical features of azobenzene have attracted extensiveresearch interest.

One of the main challenges in the field is the inter-pretation of the dependence of the azobenzene iso-merization quantum yield on the excitation energy [5].For example, in hexane, a non-polar solvent, the trans–cis quantum yield is 0.56 for n�* excitation (S1 state)and 0.27 for ��* excitation (S2 state) [3,6], whereasthe cis–trans quantum yield is 0.25 for the S1 state and0.11 for the S2 state [7]. In polar solvents such asethanol the quantum yield ratio for trans! cis overcis! trans is significantly different from that inhexane. However, the ratio between the two excita-tions remains about the same: the quantum yieldfor n�* excitation is about two times greater than thatfor ��* excitation. Clearly, azobenzene isomeriza-tion provides a case of violation of the Kasha rulewhereby the quantum yield is independent of theexcitation energy.

To understand this unusual feature of azobenzenephotoisomerization, it has been suggested that thereaction proceeds differently for different excitations:the azobenzene molecule takes the inversion pathfrom the reactant to the product for n�* excitationand the rotation path for ��* excitation [5,8], as shownin Figure 1. Using this mechanism, Rau rationalizedthe experimentally observed energy dependence of theisomerization quantum yield for the free azobenzenemolecule. Since then, this mechanism has been widelyused to interpret experimental observations [9–14].In addition, the model has attracted considerable theo-retical interest [5]. However, recent high-level quan-tum chemical calculations, including first-principlesconstrained density-functional calculations [15] andCASSCF level calculations [16–18], predict that therotation path is the preferred candidate for azobenzeneisomerization. Moreover, recent experimental observa-tions do not support the inversion path for the S(n�*)state [19]: fluorescence anisotropy measurements inhexane clearly demonstrate that photoisomerizationin the S(n�*) state follows the NN torsion path.Clearly, the mechanism of azobenzene photoisomeri-zation is still open to debate. Although theoreticalquantum calculations are fundamentally important inunderstanding the main features of the mechanism,static calculations alone cannot provide detailed

*Corresponding author. Email: [email protected]

ISSN 0026–8976 print/ISSN 1362–3028 online

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information on the mechanism because they areincapable of describing the time-dependent process ofphotoisomerization.

In this paper we present a realistic dynamicssimulation study of trans-azobenzene photoisomeri-zation by a semiclassical dynamics approach. Thesimulation follows both n�* and ��* excitationsinduced by two 50 fs (FWHM) laser pulses differentin photon energy, and we find that, for both exci-tations, the reaction path is predominated by therotation coordinate. However, the inversion anglesalso play an important role. The simulation resultsprovide complementary information for a detailedunderstanding of the mechanism of this importantphotochemical reaction.

2. Methodology

A semiclassical method is used for this study. In thisapproach, the state of the valence electrons iscalculated by the time-dependent Schrodinger equa-tion, but the radiation field and the motion of thenuclei are treated classically. According to time-dependent perturbation theory, such a semiclassicaltreatment effectively includes effective ‘n-photon’ and‘n-phonon’ processes in absorption and stimulatedemission. With this approximation, we are able toexamine non-trivial processes such as multi-electronand multi-photon excitations, the indirect excitation ofvibrational modes, intra-molecular vibrational energyredistribution, and interdependence of the variouselectronic and vibrational degrees of freedom.

A detailed description of this method has beenpublished elsewhere [20,21], so only a brief explanationis presented here. The one-electron states are obtainedat each time step by solving the time-dependentSchrodinger equation in a non-orthogonal basis,

i�h@)j

@t¼ S�1 �H �)j, ð1Þ

where S is the overlap matrix for the atomic orbitals.

The laser pulse is characterized by the vector potential

A, which is coupled to the Hamiltonian through the

time-dependent Peierls substitution [22]

HabðX�X0Þ ¼ H 0abðX�X0Þ exp

iq

�hcA � ðX�X0Þ

� �: ð2Þ

Here, HabðX� X0Þ is the Hamiltonian matrix element

for basis functions a and b on atoms at X and X0,

respectively, and q¼�e is the charge of the electron.The Hamiltonian matrix, overlap matrix, and

effective nuclear–nuclear repulsion are obtained usingthe density-functional-based tight-binding method [23].

In this approach, the electronic energy of the system

can be written as

Eelec ¼Xi¼occ

ni"i þX�4�

Urep

�jX� � X�j

�,

ð3Þ

where the first sum goes over the occupied orbitals, "i isthe eigenvalue of orbital i and is determined by solvingthe Kohn–Sham equations, and ni is the occupation

number of orbital i. The effective repulsion potential

Urep(jX��X�j) is a function of the inter-atom distance.In our previous investigations, this same model was

found to yield good descriptions of the molecularresponse to ultra-short laser pulses. For example, the

non-thermal fragmentation of C60 [24] is in good

agreement with experimental observations, the simula-

tion of the formation of the tetramethylene intermedi-ate diradical [25] is consistent with time-of-flight mass

spectrometry measurements, and the characterization

of the geometry changes at certain critical points [26] is

compatible with molecular mechanics valence bondcalculations.

The nuclear motion is solved using the Ehrenfest

equation of motion,

Mld2Xl�

dt2¼ �

1

2

Xj

)þj �@H

@Xl�� i�h

1

2

@S

@Xl��@

@t

� ��)j

� @Urep=@Xl �, ð4Þ

where Urep is the effective nuclear–nuclear repulsive

potential and Xl� ¼ hXl�i is the expectation value

of the time-dependent Heisenberg operator for the �coordinate of the nucleus labeled l (with �¼x, y, z).

Equation (4) is obtained by neglecting the terms of

second and higher order in the quantum fluctuations

X� hXl�i in the exact Ehrenfest theorem.The time-dependent Schrodinger Equation (1) is

solved using a unitary algorithm obtained from

the equation for the time evolution operator [27].

Equation (4) is numerically integrated with the velocity

Verlet algorithm (which preserves phase space). A time

Figure 1. Schematic diagram of the two reaction paths in thetrans! cis isomerization of azobenzene.

182 Y. Dou et al.


step of 50 attoseconds was used for this study. Thistime step was found to produce energy conservationbetter than 1 part in 106 in a 1 ps simulation.

The present ‘Ehrenfest’ approach is complementaryto other methods based on different approximations.The weakness of this method is that it amounts toaveraging over all the terms in the Born–Oppenheimerexpansion [28–32],

�totalðXn, xe, tÞ ¼Xi

�ni ðXn, tÞ�

ei ðxe,XnÞ, ð5Þ

rather than following the time evolution of a singleterm, i.e. a single potential energy surface, which isapproximately decoupled from all the others. (Here, Xn

and xe represent the sets of nuclear and electroniccoordinates, respectively, and � e

i are eigenstates of theelectronic Hamiltonian at fixed Xn.) The strengthsof the present approach are that it retains all ofthe 3N nuclear degrees of freedom and it includes boththe excitation due to the laser pulse and the sub-sequent de-excitation at an avoided crossing near aconical intersection [30–35], which we will discuss inthe next section.

3. Results and discussion

3.1. Equilibrated ground-state geometry

The ground-state geometry of trans-azobenzene wasobtained after 1000 fs simulation at room temperature.This temperature was achieved by scaling the velocityof each atom at each 50 as time step. The molecule hasa roughly planar structure with C2h symmetry at itsequilibrium configuration. The geometry parameters,including the bond lengths, bond angles, and dihedralangles, as well as energies are found to be in goodagreement with published results [36–39]. Three mole-cular orbitals, namely the HOMO-1, HOMO, andLUMO, are plotted in Figure 2 together with themolecular numbering used in this study. These mole-cular orbitals are significantly involved in the laserexcitations and excited state dynamics. As can be seenfrom Figure 2, each of these orbitals has a pronouncedfeature exhibited by the nature of the central NNdouble bond: HOMO-1 exhibits appreciable � bond-ing, the HOMO displays n non-bonding lone pairs, andthe LUMO shows apparent �* antibonding. The firstelectronically excited state, S(n�*), has Bg symmetryand mainly corresponds to the HOMO to LUMOexcitation. The second excited state, S(��*), with, Bu

symmetry, mainly results from HOMO-1 to LUMOexcitation. For the generation of the initial geometriesfor the dynamics simulation, the molecule was simu-lated for an additional 1000 fs in the ground state.

From this trajectory, 10 geometries taken at equal time

intervals were used as starting geometries.

3.2. np* Excitation

To produce an n�* excitation, a 50 fs (FWHM) laser

pulse was applied with an effective photon energy of

1.75 eV. It was found that this photon energy results in

an effective non-resonant n�* excitation. Simulationswere run for different fluences to select an appropriate

laser intensity for the isomerization of trans-azoben-

zene. It was found that a fluence of 0.459 kJm–2 leads

to isomerization without breaking any chemical

bonds. With this same set of laser parameters, different

starting geometries lead to multiple trajectories for

azobenzene photoisomerization that generally exhibit

no substantial differences. We will, therefore, only

discuss a representative trajectory.The variations with time of the energies of the

HOMO-1, HOMO and LUMO are plotted in Figure 3.

The energy gap between the HOMO and LUMO

decreases rapidly from about 2.2 to 1.6 eV immediately

after the laser pulse is applied. One finds three avoided

crossings between the HOMO and LUMO: one at

1518 fs, one at 2291 fs, and the other at 2800 fs. Soon

after 1550 fs, the energy gap expands to its initial

value and remains at this value for the remaining

simulation time.The time-dependent populations of the HOMO-1,

HOMO and LUMO are presented in Figure 4. The

laser pulse excites about 1.1 electrons from the HOMO

to the LUMO in 100 fs. This n�* excitation promotes

the molecule to the first electronically excited state.

Three electronic transitions from the LUMO to the

HOMO are observed at the times when the two

orbitals find avoided crossings. These electronic tran-

sitions eventually bring the molecule back into the

electronic ground state after 2800 fs.

Figure 2. (a) Atom labeling and the (b) HOMO-1,(c) HOMO, and (d) LUMO of trans-azobenzene at t¼ 0 fs.

Molecular Physics 183


The variations of the three torsional angles withtime are plotted in Figure 5. The molecule starts torotate about its N–N bond after 800 fs. After 1600 fs,it attains a geometry in which the two phenyl ringsare almost perpendicular to each other. The CNNCdihedral angle fluctuates about this twisted structurefor the next 1000 fs and then increases to about 360�

after 3000 fs, indicating the formation of the cis isomer.The C2C1NN torsion shows a slight decrease after1500 fs. On the other hand, the C3C4NN torsion first

decreases to about 90� after 2400 fs and then increasesto 360� after 3500 fs. Figure 6 shows the variations ofthe two CNN bond angles with time. The CNN bondangles oscillate about their original value of 114� up to800 fs. Immediately after this time they expand withnon-symmetric distortion. Both bond angles return totheir initial values soon after 2100 fs. The bond lengthvariations of the NN and two NC bonds with timeare plotted in Figure 7. Following laser excitation, theN–N bond stretches from about 1.29 A to an averagelength of 1.4 A after 100 fs and remains at this length

Figure 4. Variation with time of the electronic populationsof the HOMO-1, HOMO, and LUMO following applicationof a 50 fs (FWHM) laser pulse with a fluence of 0.459 kJm–2

and photon energy of 1.75 eV.

Figure 3. Energy variation with time of the HOMO-1,HOMO and LUMO, following application of a 50 fs(FWHM) laser pulse with a fluence of 0.459 kJm–2 andphoton energy of 1.75 eV.

Figure 5. Changes in the three torsions of trans-azobenzenesubjected to excitation by a 50 fs (FWHM) laser pulse witha fluence of 0.459 kJm–2 and photon energy of 1.75 eV.

Figure 6. Variation with time of the C1NN and C3NN bondangles of trans-azobenzene subjected to excitation by a 50 fs(FWHM) laser pulse with a fluence of 0.459 kJm–2 andphoton energy of 1.75 eV.

184 Y. Dou et al.


until 800 fs. It then quickly shortens to about 1.34 A.The NN bond remains at this length up to 2800 fs andthen returns to its initial length. In contrast, the twoC–N bonds shorten to about 1.36 A after 100 fs andremain at this length, on average, up to 2200 fs. Theythen soon settle at an average length of 1.41 A andoscillate about this length until the end of the simu-lation. The fact that the stretching of the N–N bondand the compression of the C–N bonds immediatelyfollow laser irradiation suggests that the stretchingvibrations of the N–N and C–N bonds are responsiblefor the sharp shrinkage of the LUMO–HOMO gapobserved before 100 fs.

The variations of the CNNC torsion with timeclearly demonstrate that isomerization on n�* excita-tion follows the rotation path. Examining Figure 5,one can see that although one of the bond angles

becomes as large as 138�, no CNN angle attains

a linear arrangement, indicating that the reaction doesnot follow the inversion path. Comparing Figures 5and 6, one finds that the CNN bond angle begins to

widen when the excited molecule begins to rotate aboutthe NN bond. For example, the C1NN angle becomeswider when the molecule rotates away from its basicgeometry, and it becomes narrower when the molecule

approaches the twisted structure; it returns to approxi-mately its initial value after the molecule has adoptedthe geometry of the cis isomer. Expansion of the CNN

angles facilitates the rotation of the molecule about theNN bond. In conclusion, although the rotation pathis the predominant reaction coordinate, the inversioncoordinate is strongly involved and plays an important

role in trans! cis isomerization. In other words, n�*excitation eventually leads to an inversion-assistedrotation path for the trans! cis isomerization of trans-azobenzene.

3.3. pp* Excitation

A laser pulse of 50 fs (FWHM) with an effectivephoton energy of 2.15 eV was selected to producea non-resonant ��* excitation. The simulations wererun for various fluences, and a fluence of 0.125 kJm–2

was found to lead to isomerization without breakingany chemical bonds. Different starting geometries weresimulated for this set of laser parameters and no

substantial differences were found for these multipletrajectories. In the following discussion, one represen-tative trajectory will be presented.

The variations with time of the energies of theHOMO-1, HOMO and LUMO are plotted in Figure 8,

where (a) is an expanded scale from 0 to 100 fs of (b).The HOMO-1 is very close to the HOMO in energy atthe beginning of the simulation. The most pronouncedchange in the HOMO-1 and HOMO energies is at

30 fs, when two orbitals find an avoided crossing. Theenergy gap at this avoided crossing is 0.006 eV. Soonafter this crossing, the energy gap between these twoorbitals is about 0.7 eV and remains at this value for

the next 650 fs. The energy gap expands significantlyafter 670 fs due to the increase in the HOMO energy.It shrinks to a much smaller value after 1120 fs. A rapid

decrease in the energy gap between the HOMO andLUMO is evidenced before 100 fs, which is similar ton�* excitation. The gap remains constant up to about600 fs, but then changes remarkably after 600 fs

because of the increase in the HOMO energy. Fouravoided crossings between the HOMO and LUMOare found at about 730, 940, 1005, and 1057 fs, res-

pectively. The energy gap expands to its initial value

Figure 7. Changes with time of (a) the N–N and (b) the C–Nbonds of trans-azobenzene excited by a 50 fs (FWHM) laserpulse with a fluence of 0.459 kJm–2 and photon energy of1.75 eV.



shortly after 1100 fs and then no appreciable changesare observed until the end of the simulation.

The time-dependent populations of the HOMO-1,HOMO and LUMO are presented in Figure 9, withFigure 9(a) being an expanded scale. The laser pulsepromotes about 1.6 electrons to the LUMO by 30 fsand leaves holes mainly in HOMO-1. A sharpelectronic population transfer from the HOMO toHOMO-1 is found at 30 fs. This electronic transition isinduced by the avoided crossing between these twoorbitals, as shown in Figure 8(a). Four electronictransitions from the LUMO to the HOMO areobserved at the times when the two orbitals findavoided crossings. These electronic transitions essen-tially bring the molecule from the electronically excitedstate to the ground state.

The variations of the three torsions with time areplotted in Figure 10. No obvious changes are observedin any dihedral angles before 600 fs. The CNNCtorsion first diverges from 180� and attains a value ofabout 138� at 730 fs. It remains at this value for thefollowing 170 fs and attains a value of 90� at 1050 fs.It is about 0� after 1200 fs when the molecule even-tually adopts the geometry of the cis isomer. On theother hand, the other two dihedral angles only showsmall variations with time. The fact that the HOMOenergy sharply increases when the molecule starts torotate about the N–N bond suggests that the CNNCtorsion plays a central role in the LUMO–HOMOband gap shrinkage.

Figure 8. Energy variation with time of the HOMO-1,HOMO and LUMO following application of a 50 fs(FWHM) laser pulse with a fluence of 0.124 kJm–2 andphoton energy of 2.15 eV. (a) is an expanded scale of (b) from0 to 100 fs.

Figure 9. Variation with time of the electronic populationsof the HOMO-1, HOMO, and LUMO following applicationof a 50 fs (FWHM) laser pulse with a fluence of 0.124 kJm–2

and photon energy of 2.15 eV. (a) is an expanded scale of (b)from 0 to 100 fs.

186 Y. Dou et al.


The variations of the two CNN bond angles withtime are presented in Figure 11. Both bond anglesoscillate about their initial value of 114� up to 660 fs.Immediately after 660 fs, they sharply increase to anaverage value of 125� and remain at this value up to1350 fs. They then quickly decrease to about theirinitial value and fluctuate about this value for theremaining simulation time.

The bond length variations of the N–N and twoN–C bonds with time are presented in Figure 12.Figure 12(a) shows that, after 40 fs of laser irradiation,

the N–N bond is stretched from 1.29 A to an averagelength of 1.45 A, a typical value for a single N–N bond.It remains at this length up to 600 fs. The N–N bondconstricts after 600 fs and returns to its initial valueafter 1100 fs. It remains at this length for the remainingsimulation time. In contrast, the two C–N bondsbecome shorter after the laser pulse is applied. From1000 fs, both C–N bonds increase to an average lengthof 1.41 A and oscillate about this length for theremaining simulation time. The strong variations inthe N–N and C–N bond lengths immediately followlaser irradiation and therefore are responsible for theHOMO–LUMO energy gap shrinkage and theHOMO–LUMO avoided crossing, both of which arefound before 50 fs.

The CNNC torsion variations show that, for ��*excitation, the isomerization process predominately

Figure 11. Variation with time of the C1NN and C3NNbond angles of trans-azobenzene subjected to excitation bya 50 fs (FWHM) laser pulse with a fluence of 0.124 kJm–2

and photon energy of 2.15 eV.

Figure 12. Changes with time of (a) the N–N and (b) theC–N bonds of trans-azobenzene excited by a 50 fs (FWHM)laser pulse with a fluence of 0.124 kJm–2 and photon energyof 2.15 eV.

Figure 10. Changes in the three torsions of trans-azobenzenesubjected to excitation by a 50 fs (FWHM) laser pulse witha fluence of 0.124 kJm–2 and photon energy of 2.15 eV.



Figure 13. Molecular geometries of azobenzene taken at (a) t¼ 1515 fs, (b) t¼ 2292 fs, and (c) t¼ 2788 fs in the simulationfor n–�* excitation.

Figure 14. Molecular geometries of azobenzene taken at (a) t¼ 30 fs, (b) t¼ 1005 fs, and (c) t¼ 1057 fs in the simulationfor �–�* excitation.

188 Y. Dou et al.


proceeds by the rotation path. Examining Figures 11and 12, one can see that the CNN bond angles increaseas soon as the molecule begins to rotate about the NNbond, and decrease to their initial values immediatelyafter the cis isomer is formed. This analysis suggeststhat ��* excitation leads to the inversion-assistedrotation path for trans–cis isomerization, similar ton�* excitation.

To compare the present study with potentialenergy surface calculations, we consider theHOMO!LUMO excitation as n�* excitation, theHOMO-1!LUMO excitation as ��* excitation,HOMO-1!HOMO hole excitation as S(��*) decay,and HOMO!LUMO double excitation as (�)2(�*)2

excitation [40]. These interpretations are based on thepredominant features of these frontier orbitals regard-ing the nature of the central NN double bond.

For n�* excitation, the laser pulse promotes trans-azobenzene to the S(n�*) state. The excited moleculefinds three S(n�*)/S0 decay channels. Although themolecule relaxes to the ground state basically throughthe channel at 2788 fs, the simulation demonstratesthat other relaxation paths to the ground state exist.The molecular geometries at these decay channels areshown in Figure 13. Each of these geometries has anapproximate twisted structure: CNNC¼ 85� for thegeometry at 1515 fs, 97� at 2292 fs, and 91� at 2788 fs.Quantum chemical calculations [41–45] have foundthat the conical intersection between the S(n�*) andS0 states exists at a CNNC torsion close to 90�. Themolecule decaying to the ground state in the twistedstructure either proceeds to form the product orreturns to the reactant, avoiding isomerization. Thelifetime of 2788 fs found is consistent with the experi-mental value of 2900 fs [46].

For ��* excitation, the laser pulse first excitestrans-azobenzene to the S(*) state. Electronic transferat about 30 fs is immediately followed by (�)2(�*)2

excitation. This brings the excited molecule from theS(��*) state to the S((�)2(�*)2) state. The decay timeof 30 fs for the S(��*) state is comparable to theexperimentally observed lifetime of less than 100 fs.The molecular geometry at 30 fs is presented inFigure 14(a). Experimentally, it is found [48] that,after relaxation from the S(��*) state, the molecule hasa planar structure, but the NN bond is significantlylengthened. Our simulation shows that, for the S(��*)/S((�)2(�*)2) channel, the NN bond is stretched and theCN bonds are compressed drastically. No appreciablechanges are found for the other geometrical param-eters. CASSCF/CASPT2 calculation [47] finds thatthe S((�)2(�*)2) MEP is essentially degenerated witha seam of the S(��*)/S(n�*) conical intersections andthat the decay of the molecule to the S(n�*) state is

essentially barrierless. We therefore assume that themolecule moves in the S(n�*) state soon after S(��*)/S((�)2(�*)2) decay. Since the CNNC torsion and theCNN bond bending angles after S(��*)/S((�)2(�*)2)decay are basically the same as the corresponding geo-metrical parameters of the S(n�*) state geometrygenerated in n�* excitation, the molecule follows thesame isomerization paths for both n�* and ��* exci-tation. For ��* excitation, the most remarkable decaysto the S0 state occur at about 1005 and 1057 fs. Thegeometrical parameters at these decays are presentedin Figures 14(b) and (c). The molecule shows a roughlytwisted structure at each of the two decays. In thetrajectory presented, the molecule returns to thereactant after moving to the ground state.

4. Conclusion

In this publication we have presented simulationresults for the trans–cis isomerization of azobenzenefollowing two different excitations: n�* and ��*excitations. Two ultra-short laser pulses are employedto generate the excitations. The simulation finds that,for both excitations, isomerization is achieved predo-minately through the inversion-assisted rotation path.This is different from the previous suggestion [5,15]that the reaction takes the rotation path for ��*excitation, but follows the inversion path for n�*excitation. In addition, the simulation results providedetailed information concerning laser excitation of themolecule and de-excitation of the excited moleculethrough non-adiabatic transitions. The simulationfinds that the torsional rotation, bond bending andbond stretching vibrations are all involved and eachof them plays a significant role in the trans–cisisomerization process.

Acknowledgements

The authors acknowledge support by the NationalNatural Science Foundation of China (grant 20773168), theResearch Fund of Chongqing University of Posts andTelecommunications (A2006-81) and also the AmericanChemical Society Petroleum Research Fund for support ofthis research at Nicholls State University.

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