Молекула Бензола в сильном лазерном поле
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 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.
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. . We use the
atomic system of units throughout the paper.
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.  first electron is ejected from
this neutral molecule and then the dissociation of C6H6+-ion
The most probable channel for decay of this ion is the separation into
the equal parts :
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. . Indeed, the model scheme of
energy levels for C6H6+-ion (see Ref. ) reminds the
model scheme of energy levels for H2+  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
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. )
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
Thus, the Hamiltonian of the concerned system
The kinetic energy operator being of the form
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
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.
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).
tunneling probability is on the order of
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.
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. . The absorption of three photons occurs in
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
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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
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).
potential (a) (a.u.),
potential for max. field (b) (a.u),
square of the wave function of the ground state
for benzene molecular ion (c)