Hindawi Publishing Corporation International Journal of Photoenergy Volume 2014, Article ID 874102, 11 pages http://dx.doi.org/10.1155/2014/874102 Research Article Mechanisms of Laser-Induced Reactions of Stacked Benzene Molecules: A Semiclassical Dynamics Simulation and CASSCF Calculation Kunxian Shu,1 Jie Zhao,1 Shuai Yuan,1 Yusheng Dou,2 and Glenn V. Lo2 1 Institute of Bioinformatics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China 2 Department of Physical Sciences, Nicholls State University, P.O. Box 2022, Thibodaux, LA 70310, USA Correspondence should be addressed to Shuai Yuan; [email protected] and Yusheng Dou; [email protected] Received 8 May 2014; Accepted 27 June 2014; Published 27 October 2014 Academic Editor: Fuli Li Copyright © 2014 Kunxian Shu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The response to ultrashort laser pulses of two stacked benzene molecules has been studied by semiclassical dynamics simulation; two typical pathways were found following excitation of one of the benzene molecules by a 25 fs (FWHM), 4.7 eV photon. With a 2 fluence of 40.49 J/m , the stacked molecules form a cyclobutane benzene dimer; the formation of the two covalent bonds linking 2 two benzenes occurs asynchronously after the excimer decays to electronic ground state. With a fluence of 43.26 J/m , only one bond is formed, which breaks about 50 fs after formation, followed by separation into the two molecules. The deformation of benzene ring is found to play an important role in the bond cleavage. 1. Introduction interpreted as being due to (i) charge transfer processes, (ii) nonconcerted mechanism, and (iii) excitation to the 2 The photocycloaddition reactions of unsaturated double state.Cliffordetal.found[13]thatforthebenzeneplus bond complexes are of theoretical interest because these reactions are involved in DNA photodamage [1–4]and ethylene system cycloadditions could take place from 1 state organic synthesis [5, 6]. The best known examples are the without barrier through a conical intersection (CI), which is [2 + 2] photocycloaddition (forming either cyclobutanes or common to all three cycloadducts. This low energy CI results four-membered heterocycles) and excited state [4 + 4] cyclo- from the formation of one C–C bond between benzene and ethylene. Their subsequent studies [14]suggestthatCIseam additions that produce cyclooctadiene compounds. Although quite (thermally) stable, benzene molecules between 1 and 0 could control chemical selectivity in the can become quite reactive when being photoexcited; they photocycloaddition of benzene and ethylene. can be transformed to benzvalene [7, 8]andfulvenewhen Cycloadditions, [4 + 2] and [4 + 4], are also observed being excited to the first singlet (1) excited state or to between polycondensed aromatic compounds such as naph- Dewar benzene [9, 10] when being excited to the second thalene, anthracene, and their derivatives. The [4 + 2] singlet (2) excited state. Benzene can be involved in a cycloaddition (photo-Diels-Alder reaction) [15–18]isfre- photocycloaddition reaction with an alkene molecule. The quently observed with naphthalene derivatives. [4 + 4] reactions can be classified into three categories [5, 6]: [2 photocycloadditions are often observed in two-arene systems +2](orortho), [3 + 2] (or meta), and [4 + 2] (or para) whichareconnectedbyasaturatedbridge(suchas–CH2– photocycloadditions. Photocycloadditions of benzene and an CH2–CH2–or–CH2–O–CH2–). These bridge aromatic sys- alkene are usually triggered by the photoexcitation of the tems can undergo intramolecular [4 + 4] photocycloadditions benzene molecule. If the 1 state of benzene is involved, to form “biplanemers,”in which the two systems are stacked only meta addition is allowed to occur in a concerted face-to-face [19]. fashion according to molecular orbital symmetry rules [11, Todate,themechanismofcycloadditionamongaro- 12]. The formation of ortho- and para-cycloadducts can be matic ring compounds has not been clearly characterized. 2 International Journal of Photoenergy Rogachev and coworkers [20] performed a series of calcula- In this technique, forces acting on nucleus or ions are tions involving benzene dimers in the ground state, but no computed by the Ehrenfest equation studies have been made on the photochemical dimerization 2 of benzene. In this paper, we studied photoinduced [2 + 2 2] cycloaddition of two-benzene system by semiclassical dynamic simulation. The simulation results provide detailed 1 H 1 S =− ∑ Ψ+ ⋅( −ℏ ⋅ )⋅Ψ − rep , dynamics features for this process from photon excitation to 2 2 the formation of product. The geometry at the conical inter- section (CI) between the first singlet (1) excited state and (3) ground state (0) was optimized by using completed active where is effective nuclear-nuclear repulsive potential and space self-consistent field (CASSCF) method to compare with rep =⟨̂ ⟩ other theoretical results. is the expectation value of the time-dependent Heisenberg operator for the coordinate of the nucleus labeled by (with = ,,). Equation (3)isobtainedby 2. Methodology neglecting the second and higher order terms of the quantum −⟨̂ ̂ ⟩ 2.1. Semiclassical Dynamics Simulation. We carried out fluctuations in the exact Ehrenfest theorem. the dynamics simulations using the semiclassical electron- The present “Ehrenfest” principle is complementary to radiation-ion dynamics (SERID) method. In this approach, other methods based on different approximations, such as the valence electrons are calculated by the time-dependent the full multiple spawning model developed by the Ben- Schrodinger¨ equation while both the radiation field and the Nun and Mart´ınez [25]. The limitation of this method is motion of the nuclei are treated by the classical approxi- that the simulation trajectory moves along a path dominated mation. A detailed description of this technique has been by averaging over all the terms in the Born-Oppenheimer published elsewhere [21, 22]andonlyabriefreviewis expansion [26, 27], given here. The one-electron states are updated by solving Ψtotal ( , ,)=∑Ψ ( ,)Ψ ( , ), (4) the time-dependent Schrodinger¨ equation at each time step (typically 0.05 femtoseconds in duration) in a nonorthogonal basis, rather than following the time evolution of a single potential energy surface, which is approximately decoupled from all the Ψ −1 others [26–29]. (Here and represent the sets of nuclear ℏ = S ⋅ H ⋅Ψ, (1) and electronic coordinates resp., and the Ψ are eigenstates of the electronic Hamiltonian at fixed .) The strengths S where is the overlap matrix for the atomic orbitals. The of the present approach include retention of all of the 3 A laser pulse is characterized by the vector potential ,which nuclear degrees of freedom and the incorporation of the laser is coupled to the Hamiltonian via the time-dependent Peierls excitation as well as the subsequent deexcitation at an avoided substitution crossing near a conical intersection. (X − X) =0 (X − X) ( A ⋅ (X − X)) ; exp ℏ 2.2. CASSCF. Multiconfigurational self-consistent field (2) (MCSCF) is a method in quantum chemistry used to gene- rate qualitatively correct reference states of molecules in here (X − X ) is the Hamiltonian matrix element for basis cases where Hartree-Fock (HF) and DFT are not adequate functions and on atoms at X and X ,respectively,and= (e.g., for molecular ground states which are quasidegenerate − is the charge of the electron. with low lying excited states or in bond breaking situations). The Hamiltonian matrix elements, overlap matrix ele- It uses a linear combination of configuration state functions ments, and repulsive energy are calculated with the density- (CSF) or configuration determinants to approximate the functional based tight bonding (DFTB) method. The DFTB exact electronic wavefunction of an atom or molecule. In an method does have essentially the same strengths and lim- MCSCFcalculation,thesetofcoefficientsofboththeCSFs itations as time-dependent density-functional theory (TD- or determinants and the basis functions in the molecular DFT). In particularly, the bonding is well described but orbitals are varied to obtain the total electronic wavefunction theexcitedstateenergiesaretypicallytoolow.Forthis with the lowest possible energy. This method can be consi- reason, we matched the effective central photon energy of dered a combination of configuration interaction (where the the laser pulse to the relevant density-functional (rather than molecular orbitals are not varied but the expansion of the experimental) excitation energy and this should not adversely wave function are varied) and Hartree-Fock (where there is affect the interpretation of the results. This model has been only one determinant but the molecular orbitals are varied). used in biologically relevant studies such as photoinduced A particularly important MCSCF approach is the CASSCF, dimerization of thymine [23] and cytosine [24]via[2+2] where the linear combination of CSFs includes all that arise photocycloaddition reaction. All the results were found to be from a particular number of electrons in a particular number consistent with experimental observations. The formation of of orbitals [30, 31]. cyclobutane pyrimidine dimer may provide good references In this research, the CASSCF