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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 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.
2.
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 lowlying 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.
The ground
even electronic term of C6H6+ion is presented
here in the form of the wellknown Morse potential with parameters b=2k and De=6.2
ýÂ, where k is approximated by the elastic constant of CC coupling in the C6H6molecule
and De is the dissociation potential for the C2molecule. 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 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)=<Y(R,0)Y(R,t)>2 . In Fig. 3
envelope of laser pulse is depicted and the dissociation probability W(t) is
shown in Fig. 4.
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 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 ýÂ, while the
dissociation potential is De=6
eV. Hence, threephoton process of
dissociation takes place. The dissociation rate of threephoton process is
proportional to m1/2. 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 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 960218299).
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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. 4. The dissociation probability of benzene
molecular ion C6H6+ as a function of time
(fs).
Fig. 1
Morse potential (a)
(a.u.),
effective potential for max. field (b) (a.u), c b a
square of the wave function of the ground
state for benzene molecular ion
(c)
R, a.u.
Fig. 2
t, fs
Fig. 3 b
W(t)
t, fs
Fig. 4
