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Dissociation of Benzene Molecule in a
Strong Laser Field
M. E. Sukharev
General Physics Institute of RAS
117942, Moscow, Russia
Dissociation of benzene molecule in a strong lowfrequency linearly polarized laser field is considered theoretically under the conditions of recent experiments. Analogy with the dissociation of diatomic molecules has been found. The dissociation probability of benzene molecule has been derived as a function of time. The threephoton dissociate process is shown to be realized in experiments.
1. Introduction.
The number of articles devoted to the interaction of molecules with a strong laser field increased considerably in recent years. The main features of interaction between diatomic molecules and a laser radiation were considered in a great number of experimental [15] and theoretical [69] papers. Classical and quantum investigations of spatial alignment of diatomic molecules and their molecular ions in a strong laser field, as well as ionization and dissociation of these molecules and their molecular ions account for physical pictures of all processes.
However, when considering complex organic molecules, we observe physical phenomena to be richer, and they are not thoroughly investigated. Most of results obtained for diatomic molecules can be generalized to the multiatomic molecules. This short paper contains the results of theoretical derivations for dissociation of benzene molecule C_{6}H_{6} in the field of linearly polarized Ti:Sapphire laser. Data were taken from experimental 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 molecule C_{6}H_{6 }in the field of Ti:Sapphire laser with the wavelength l=400 nm, pulse length t=300 fs and maximum intensity I_{max}=2´10^{14} W/cm^{2}. According to Ref. [4] first electron is ejected from this neutral molecule and then the dissociation of C_{6}H_{6}^{+}ion occurs.
The most probable channel for decay of this ion is the separation into the equal parts :
Of course, there is another channel for decay of C_{6}H_{6}^{+}ion which includes the ejection of the second electron and subsequent Coulomb explosion of the C_{6}H_{6}^{++}ion. We do not consider the latter process.
The channel (1) is seen to be similar to the dissociation of the hydrogen molecular ion considered in Ref. [2]. Indeed, the model scheme of energy levels for C_{6}H_{6}^{+}ion (see Ref. [4]) reminds the model scheme of energy levels for H_{2}^{+} [2] containing only two lowlying electronic levels: 1s_{g} (even) and 1s_{u} (odd).
Therefore we consider the dissociation process of C_{6}H_{6}^{+}ion analogously to that for H_{2}^{+}ion (see Fig. 1). The benzene molecular ion has the large reduced mass with respect to division into equal parts. Hence, its wave function is well localized in space (see Fig. 2) and therefore we can apply classical mechanics for description of the dissociation process (1). However, the solution of Newton equation with the effective potential (see below) does not produce any dissociation, since laser pulse length is too small for such large inertial system. In addition to, effective potential barrier exists during the whole laser pulse and tunneling of the molecular fragment is impossible due to its large mass ( see Fig. 2). Thus, we should solve the dissociation problem in the frames of quantum mechanics.
Where the strength envelope of the laser radiation is chosen in the simple Gaussian form F(t)=F_{0}exp(t^{2}/2t^{2}) and R internuclear separation between the fragments C_{3}H_{3}^{+} and C_{3}H_{3}, w is the laser frequency and t is the laser pulse length. The value½sinwt½ takes into account the repulsion between the involved ground even electronic term and the first excited odd repulsive electronic term.
Thus, the Hamiltonian of the concerned system
is
Where R_{e} is the equilibrium internuclear separation. When calculating we make use of R_{e}=1.39 A.
The time dependent Schrodinger equation
with Hamiltonian (3) has been solved
numerically by the splitoperator
method. The wave function
has been derived by the iteration procedure according to formula
The initial wave function Y(R,0) was chosen as the solution of the unperturbed problem for a particle in the ground state of Morse potential.
The dissociation
probability has been derived as a function
of time according to formula W(t)=
3. Results.
The quantity W(t) is seen from Fig. 4
increase exponentially with time and it is equal to 0.11 after the end of laser
pulse. It should be noted that the dissociation process can not be considered
as a tunneling of a fragment through the effective potential barrier (see Fi.
2). Indeed, the
tunneling
probability is on the order of magnitude of
Where V_{eff} is substituted for maximum value of the field strength and the integral is derived over the classically forbidden region under the effective potential barrier. The tunneling effect is seen to be negligibly small due to large reduced mass of the molecular fragment m>>1. The Keldysh parameter g=w(2mE)^{1/2}/F>>1. Thus, the dissociation is the pure multiphoton process. The frequency of laser field is w µ 2.7 эВ, while the dissociation potential is D_{e}=6 eV. Hence, threephoton process of dissociation takes place. The dissociation rate of threephoton process is proportional to m^{1/2}. The total dissociation probability is obtained by means of multiplying of this rate by the pulse length t. Therefore the probability of threephoton process can be large, unlike the tunneling probability. This is the explanation of large dissociation probability W»0.11 obtained in the calculations.
4. Conclusions.
Derivations given above of dissociation of benzene molecule show that approximately 11% of all C_{3}H_{3}^{+}ions decay on fragments C_{3}H_{3} and C_{3}H_{3}^{+} under the conditions of Ref. [4]. The absorption of three photons occurs in this process.
Author is grateful to N. B. Delone, V. P. Krainov, M. V. Fedorov and S. P. Goreslavsky for stimulating discussions of this problem. This work was supported by Russian Foundation Investigations (grant N 960218299).
References
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Figure captions
Fig. 1. Scheme of dissociation for benzene molecular ion C_{6}H_{6}^{+}.
Fig. 2. The Morse potential (a), the effective potential (b) for maximum value of the field strength (a.u.), and the square of the wave function of the ground state for benzene molecular ion (c) as functions of the nuclear separation R (a.u.) between the fragments C_{3}H_{3} and C_{3}H_{3}^{+}.
Fig. 3. Envelope of laser pulse as a function of time (fs).
Fig. 4. The dissociation probability of benzene molecular ion C_{6}H_{6}^{+} as a function of time (fs).
e^{} 
Fig. 1
Morse potential (a) (a.u.),
effective potential for max. field (b) (a.u),



R, a.u.
Fig. 2
t, fs
Fig. 3

W(t)
t, fs
Fig. 4
Dissociation of Benzene Molecule in a Strong Laser Field M. E. Sukharev General Physics Institute of RAS 117942, Moscow, Russia Dissociation of benzene molecule in a strong lowfrequency linearly polarized laser field is considered theo
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