Laser Control of Atom-Molecule Reaction: Application to Li +CH 4 Reaction

Transcription

1 Adv. Studies Theor. Phys., Vol. 3, 2009, no. 11, Laser Control of Atom-Molecule Reaction: Application to Li +CH 4 Reaction Hassan Talaat Physics Dept., Faculty of Science, Ain Shams University, Cairo, Egypt El-Wallid S. Sedik and M. Tag El-Din Kamal Theoretical Physics Dept., National Research Center, Dokki, Giza, Egypt wsedik@yahoo.com Abstract Laser atom molecule reaction interaction through dipole moments leads to barrier reshaping in atom molecule reaction (Li+CH 4 ). We will show here by using gauge representation (electric field gauge) that we can reshape the barrier height (increase/decrease) the height by changing the laser phase for Li+CH 4 Li H + CH 3 where dipole moment changes sign in the transition state region. Keywords: Intense laser fields; polarizability; dipole moment; reaction path; coherent control 1. Intoduction Laser control and manipulation of reaction paths in molecular systems can lead to coherent control of the reaction path as a function of the absolute phase of an incident laser field through inclusion of dipole moments along the reaction path, thus leading to the potential surfaces crossings along the reaction path. Molecular systems have permanent dipole moments which will interact with laser fields creating surface crossings. Infrared (IR) laser-induced chemical reactions were examined earlier by classical models where it was found that intense lasers will lower activation energies. 1 A quantum mechanical approach was used to show that barrier suppression 2 and modification of non adiabatic effects 3 is a general phenomenon in the presence of intense IR laser fields.

2 440 H. Talaat, El-Wallid S. Sedik and M. Tag El-Din Kamal Crossing of potential energy surfaces is important in ion-molecule reactions as well as in charge transfer processes, also barrier reshaping is important in atom molecule reactions. In the present work we focus on the Li + CH 4 atom molecule reaction with the goal of studying the effect of an intense laser field on the permanent dipole moment of this and other similar systems. 4 Using ab-initio methods, we calculate the energy of the reaction path, and the permanent dipole moment along the reaction path. We find that the permanent dipole moment for the ion reaction is linear with the reaction path and this moment can vanish at critical distances while for the atom molecule reaction the dipole moment changes sign in the transition state region. This result implies maximum electron delocalization at this point along the reaction path. Electric field gauge is used to obtain the influence of the laser field on the potential surfaces of ion/atommolecule systems this leads to barrier reshaping, figs.(3-4). We restrict ourselves to a 1-D model using the electric field gauge representation of laser molecule interactions. This allows to incorporate the laser interaction directly into the potential surface, thus leading to simple analytic formulae to describe the laserreaction path interactions. 2. Laser Dressed Potentials The standard description of laser-particle interaction starts from the classical electric-field particle interaction which by successive unitary transformations on the molecular time-dependent Schrödinger equation, TDSE, leads to various representations (gauges), where particle -radiative couplings have different frequency dependencies. 5 Since we shall consider 1-D reaction paths with coordinates - s, the corresponding TDSE with linear dipole moment μ(s)= μ o s can be written as: 2 ψ ( st, ) ˆ p s i = Hψ ( s, t) = + V ( s) + μo ( s) ε ( t) ψ ( s, t), (1) t 2ms ψ(s,t) is the wavefunction for propagation of the relative motion of a nuclear wavepacket as a function of time along the reaction coordinate s which defines a potential V(s) to be calculated by ab-initio methods. The system under investigation will be the ion-molecule reaction 6,9 and / or the reverse, 24,25,26,27 Li + CH 4 Li H + CH 3 (2) Thus in the center of mass system the reduced mass M s will be nearly constant due to the much smaller mass of the transferred proton. The ab-initio calculations below will show that the dipole moment of reaction (2) is indeed linear with s in case of ion-molecule so that equation (1) with M s constant will be an excellent approximation to represent the motion along the reaction path s in the presence of a laser field ε () t = Eo cosωt, with amplitude E o and frequency ω. The laserparticle interaction in (1) is written in the dipole approximation (s/λ <<1), i.e., the long wavelength approximation. As an example current intense near IR lasers operate at 800nm whereas our simulations will be in the range s 1 nm.

3 Laser control of atom-molecule reaction 441 We describe the laser-molecule Hamiltonian by retaining only the dipole μ(s) along the reaction path s, following, 7,8,9,10,16 H ˆ ( ) ( ) cos L = μ s ε t θ, (3) Assuming ε () t = ε o cos( ωt+ φ) (as shown later μ (s) will dominate at the transition state s = 0 ), we can re-write Eq.(3) as: 11,12,13,14,15,17 Hˆ = μ( s) cos( ωt + φ). (4) L ε o Thus, the parameters μ(s)ε o determine the relative amplitude in the present case and φ remains the relative phase in Eq.(4). This creates periodic but nonsymmetric electric fields which induce asymmetric concomitant dissociation and ionization. In the present work we will examine the effect of the laser fields on the reaction path based on Eq.(4) which will be dominant in the transition state region. It is to be noted immediately that for negative dipoles μ, destructive interferences will occur at some phase φ. The effective potential along the reaction path is defined as: 18,19,20,21 V = V ( s) μ( s) εo cos( φ). (5) The parameters μ(s) are next calculated by ab-initio methods in order to illustrate the laser-molecule interaction along the reaction path, based on (Eq. 5) and this will be shown to be the dominant interaction in the transition state region. 3. Computational Methods All calculations were carried out using the unrestricted second-order Møller-Plesset perturbation theory 22 including excitations from inner shell electrons and using a large polarized basis set supplemented with diffuse functions on all atoms [UMP2(full)/ G(2d,2p)]. All geometry optimizations, potential energy scans, and reaction path tracings, were also carried out at the same computational level. Geometry optimizations carried out in this work are full unconstrained energy minimizations with respect to all geometric parameters. Electronic structure calculations were performed using the Gaussian 98 program. 23 Very tight convergence criteria for both the selfconsistent field (SCF) calculation as well as for geometry optimizations were set in all calculations. The spin contamination was found to be negligible along the reaction paths. 4. Results and Discussions An inverted repulsive Morse potential was fitted to the ab-initio potential Fig.1a and V(s) was obtained by ab-initio quantum chemical calculations using configuration interaction at the level of MP2 which is described in the previous section. In Fig.1.a shows the reaction path for Li + CH 4 LiH + CH 3, reactants Li + CH 4 at a.u. and products LiH + CH 3 at s = 4

4 442 H. Talaat, El-Wallid S. Sedik and M. Tag El-Din Kamal a.u. Fig.2. shows the 2D inverted Morse in which the cationic system lacks transition state. Fig.1b. Illustrates the ab-initio permanent dipole moment μ(s) of the reactions (2) along the reaction coordinate s. The dipole moment for Li + CH 4 reaction changes sign at the transition state. The present study shows as in Figures 3-4 the effect of the laser phase on molecules. The thick curve is the potential energy surface in the absence of the laser field while the thin curve is the potential energy surface in the presence of the laser field. Li + CH 4 LiH +CH 3 in the intensity of W/cm 2. The surface barrier decreases gradually in height at θ =0 and it continues its decrease at θ = π/4, π/3. Continuous variation of the laser phase leads to lowering and reshaping of the barrier at θ = 2π/3, π. In the intensity of W/cm 2. The surface barrier decreases gradually in height at θ =0 and it continues its decrease at θ = π/4, π/3. Continuous variation of the laser phase leads to lowering and reshaping of the barrier at θ = 2π/3, π. Figure Captions 1. a) Plot of the potential energy surface of the Li+CH 4 Li H + CH 3 reaction reactants Li+CH 4 at -6.5 a.u. and products Li H + CH 3 at 4.a.u. b)the dipole moment for Li+CH 4 changes sign at the transition state region. 2. 2D potential energy surface of the Li-H + CH 3 + Li + + CH 4 reaction. The cationic system lacks transition state 3. Snapshots of the energy profile along the reaction coordinate plus Inclusion of only the Dipole moment for Li+CH 4 Li H + CH 3. I = W/cm 2. a) θ = π/3, b) θ = 2π/3. c) θ = π. 4. Snapshots of the energy profile along the reaction coordinate plus inclusion of only the Dipole moment for Li+CH 4 Li H + CH 3. I = W/cm 2. a) θ = π/3, b) θ = 2π/3. c) θ = π.

5 Laser control of atom-molecule reaction 443 1a) b) μ Ζ (a.u.) s(a.u.)

6 444 H. Talaat, El-Wallid S. Sedik and M. Tag El-Din Kamal 2)

7 Laser control of atom-molecule reaction 445 3a) V(s) b) Reaction coordinate (s) V(s) Reaction coordinate (s)

8 446 H. Talaat, El-Wallid S. Sedik and M. Tag El-Din Kamal c) V(s) Reaction coordinate (s)

9 Laser control of atom-molecule reaction 447 4a) V(s) b) Reaction coordinate (s) V(s) Reaction coordinate (s)

10 448 H. Talaat, El-Wallid S. Sedik and M. Tag El-Din Kamal c) V(s) Reaction coordinate (s) References 1. A. D. Bandrauk and H. Kono, in Advances in Multiphoton Processes and Spectroscopy, edit. S. H. Lin, Vol. 15, World Scientific, Singapore, (2003), M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular Processes,Wiley, Interscience, NY, (2003). 3. G. Paulus et al., Phys. Rev. Lett. 91, (2003), V. S. Yakovlev et al., Appl. Phys. B76, (2003), S. Chelkowski and A. D. Bandrauk, Phys. Rev. A65, (2002), A. E. Orel and W. H. Miller, Chem. Phys. Lett 57, (1978), 362; J. Chem. Phys. 73, (1980), 241.

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12 450 H. Talaat, El-Wallid S. Sedik and M. Tag El-Din Kamal 26. J. C. Corchado and J. Espinosa-García, J. Chem. Phys. 105, (1996), J.C.Corchado, D.G.Truhlar, and J.Espinosa Garcia, J. Chem. Phys. 112, (2000), Received: March, 2009