Dissociation of BenzeneMolecule in a
Strong Laser Field
M. E. Sukharev
General Physics Institute ofRAS
117942, Moscow, Russia
Dissociationof benzene molecule in a strong low-frequency linearly polarized laser field isconsidered theoretically under the conditions of recent experiments. Analogywith the dissociation of diatomic molecules has been found. The dissociationprobability of benzene molecule has been derived as a function of time. Thethree-photon dissociate process is shown to be realized in experiments.
1. Introduction.
The number of articles devoted to the interaction of molecules with astrong laser field increased considerably in recent years. The main features of interaction between diatomicmolecules and a laser radiation were considered in a great number ofexperimental [1-5] and theoretical [6-9] papers. Classical and quantuminvestigations of spatial alignment of diatomic molecules and their molecularions in a strong laser field, as well as ionization and dissociation of thesemolecules and their molecular ions account for physical pictures of allprocesses.
However, when considering complex organic molecules, we observe physicalphenomena to be richer, and they are not thoroughly investigated. Most of results obtained for diatomic molecules can begeneralized to the multi-atomic molecules. This short paper contains theresults of theoretical derivations for dissociation of benzene molecule C6H6in the field of linearly polarized Ti:Sapphire laser. Data were taken fromexperimental results by Chin’s group, Ref. [4].We use the atomic system of units throughout the paper.
2. Theoretical approach.
Let us consider the benzene moleculeC6H6 in the field of Ti:Sapphirelaser with the wavelengthl=400 nm,pulse lengtht=300 fs and maximumintensity Imax=2´1014 W/cm2.Accordingto Ref. [4] first electron is ejected from this neutral molecule and then thedissociation of C6H6+-ion occurs.
The most probable channel for decayof this ion is the separation into the equal parts:
Of course, there isanother channel for decay of C6H6+-ion whichincludes the ejection of the second electron and subsequent Coulomb explosionof the C6H6++-ion. We do not consider thelatter process.
The channel(1) is seen to be similar to the dissociation of the hydrogen molecular ionconsidered in Ref. [2]. Indeed, the model scheme of energy levels for C6H6+-ion(see Ref. [4])reminds the modelscheme of energy levels forH2+[2] containing only two low-lying electronic levels: 1sg(even) and1su(odd).
Therefore we consider the dissociationprocess of C6H6+-ion analogously to that for H2+-ion(see Fig. 1). The benzene molecular ion has the large reduced mass with respectto division into equal parts. Hence, its wave function is well localized inspace (see Fig. 2) and therefore we can apply classical mechanics fordescription of the dissociation process (1). However, the solution of Newtonequation with the effective potential (see below) does not produce anydissociation, since laser pulse length is too small for such large inertialsystem. In addition to, effective potential barrier exists during the wholelaser pulse and tunneling of the molecular fragment is impossible due to itslarge mass ( see Fig. 2). Thus, we should solve the dissociation problem in theframes of quantum mechanics.
The groundeven electronic term of C6H6+-ion is presentedhere in the form of the well-known Morse potential with parameters b=2k and De=6.2эВ, wherek is approximated by the elastic constant ofC-C coupling in the C6H6-moleculeand De is the dissociation potential for the C2-molecule. The interaction of the molecular ion with the laserfield is given by expression (see. Ref. [9])
Where the strengthenvelope of the laser radiation is chosen in the simple Gaussian formF(t)=F0exp(-t2/2t2) and R internuclear separation between thefragments C3H3+ and C3H3,wis the laserfrequency andtis the laser pulselength. The value½sinwt½takes into accountthe repulsionbetween theinvolved ground even electronic term and the first excited odd repulsiveelectronic term.
Thus, the Hamiltonian of the concerned systemis
The kineticenergy operator being of the form
Where Reis the equilibrium internuclear separation. When calculating we make use of Re=1.39A.
The time dependent Schrodinger equationwith Hamiltonian(3) has been solvednumerically by thesplit-operatormethod.The wave functionhas been derived by the iteration procedure according to formula
The initial wavefunction Y(R,0) was chosen asthe solution of the unperturbed problem for a particle in the ground state ofMorse potential.
The dissociationprobability has been derived as a function of time according to formula W(t)=|Y(R,0)|Y(R,t)>|2. In Fig. 3envelope of laser pulse is depicted and the dissociation probability W(t) isshown in Fig. 4.
3. Results.
The quantity W(t)is seen from Fig. 4increase exponentially with time and it is equal to 0.11 after the end of laserpulse. It should be noted thatthe dissociation process can not be consideredas a tunneling of a fragment through the effective potential barrier (see Fi.2). Indeed, the
tunnelingprobability is on the order of magnitude of
Where Veffis substituted for maximum value of the field strengthand the integral is derived over theclassically forbidden region under the effective potential barrier. Thetunneling effect is seen to be negligibly small due to large reduced mass ofthe molecular fragment m>>1. The Keldysh parameter g=w(2mE)1/2/F>>1. Thus, the dissociation is the pure multiphotonprocess. The frequency of laser field iswµ2.7 эВ, while thedissociation potential is De=6eV.Hence, three-photon process ofdissociation takes place. The dissociation rate of three-photon process isproportional to m-1/2. The totaldissociation probability is obtained by means of multiplying of this rate bythe pulse length t. Therefore theprobability of three-photon process can be large, unlike the tunnelingprobability. This is the explanation of large dissociation probability W»0.11 obtained inthe calculations.
4. Conclusions.
Derivations given above ofdissociation of benzene molecule show that approximately11%of allC3H3+-ionsdecay on fragments C3H3 and C3H3+under the conditions of Ref. [4]. The absorption of three photons occurs inthis process.
Author is grateful to N. B.Delone, V. P. Krainov, M. V. Fedorov and S. P. Goreslavsky for stimulatingdiscussions of this problem. This work was supported by Russian FoundationInvestigations (grant N96-02-18299).
References
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Figure captions
Fig. 1. Scheme of dissociation for benzene molecularion C6H6+.
Fig. 2. The Morse potential (a), the effectivepotential (b) for maximum value of the field strength (a.u.), and the square ofthe wave function of the ground state for benzene molecular ion (c) asfunctions of the nuclear separation R (a.u.) between the fragments C3H3and C3H3+.
Fig. 3. Envelope of laser pulse as a functionof time (fs).
Fig. 4. The dissociation probability of benzenemolecular ion C6H6+ as a function of time(fs).
e-
Fig. 1
Morsepotential (a) (a.u.),
effective potential for max. field (b) (a.u),
c
b
a
square of the wave function of the groundstate for benzene molecular ion(c)
R, a.u.
Fig. 2
t, fs
Fig. 3
b
W(t)
t, fs
Fig. 4