Dissociation of Benzene Molecule in a Strong Laser Field
Dissociation of Benzene Molecule in a
Strong Laser Field
M. E. Sukharev, General Physics Institute
of RAS
Dissociation of benzene molecule in a
strong low-frequency 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 three-photon dissociate
process is shown to be realized in experiments.
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 [1-5] and
theoretical [6-9] 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 multi-atomic molecules. This short paper contains the
results of theoretical derivations for dissociation of benzene molecule C6H6 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.
Theoretical approach.
Let us consider the benzene molecule C6H6
in the field of Ti:Sapphire laser with the wavelength l=400 nm, pulse length t=300
fs and maximum intensity Imax=2´1014 W/cm2.
According to Ref. [4] first electron is ejected from this neutral molecule and
then the dissociation of C6H6+-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 C6H6+-ion which includes the ejection of the second electron and
subsequent Coulomb explosion of the C6H6++-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 C6H6+-ion (see Ref. [4]) reminds the
model scheme of energy levels for H2+ [2] containing only two low-lying
electronic levels: 1sg (even) and 1su (odd).
Therefore we consider the dissociation
process of C6H6+-ion analogously to that for H2+-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.
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The ground even electronic term of
C6H6+-ion is presented here in the form of the well-known Morse potential with
parameters b=2k and De=6.2 эВ,
where k is approximated by the elastic constant of C-C coupling in the
C6H6-molecule and De is the dissociation potential for the C2-molecule. The
interaction of the molecular ion with the laser field is given by expression
(see. Ref. [9])
Where the strength envelope of the laser
radiation is chosen in the simple Gaussian form F(t)=F0exp(-t2/2t2) and R internuclear separation between the fragments
C3H3+ and C3H3, 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
The kinetic energy operator being of
the form
Where Re is the equilibrium internuclear
separation. When calculating we make use of Re=1.39 A.
The time dependent Schrodinger
equation with Hamiltonian (3) has been solved numerically by the split-operator
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.
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 Veff 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 De=6
eV. Hence, three-photon process of dissociation takes place. The dissociation
rate of three-photon 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 three-photon
process can be large, unlike the tunneling probability. This is the explanation
of large dissociation probability W»0.11
obtained in the calculations.
Conclusions.
Derivations given above of dissociation of
benzene molecule show that approximately 11% of all
C3H3+-ions decay on fragments C3H3 and C3H3+ 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 96-02-18299).
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Figure captions
Fig. 1. Scheme of dissociation for benzene
molecular ion C6H6+.
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 C3H3 and
C3H3+.
Fig. 3. Envelope of laser pulse as a
function of time (fs).
Fig. 1
Morse potential (a) (a.u.),
effective potential for max. field (b)
(a.u),
square of the wave function of the
ground state for benzene molecular ion (c)
R, a.u.
Fig. 2
t, fs
Fig. 3
W(t)
Fig. 4
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