Dissociation of Benzene Molecule

in a Strong Laser Field

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 [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.

2. Theoretical approach.

Let us consider the benzene molecule C6H6 in the field of Ti:Sapphire
laser with the wavelength =400 nm, pulse length =300 fs and maximum
intensity Imax=21014 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: 1g (even) and 1u (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 well-known Morse potential with parameters =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(-t2/22) and R internuclear separation
between the fragments C3H3+ and C3H3, is the laser frequency and is
the laser pulse length. The valuesint 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 (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)=<(R,0)(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 1.
The Keldysh parameter =(2E)1/2/F>>1. Thus, the dissociation is the pure
multiphoton process. The frequency of laser field is 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 -1/2. The total dissociation probability is obtained
by means of multiplying of this rate by the pulse length . Therefore the
probability of three-photon process can be large, unlike the tunneling
probability. This is the explanation of large dissociation probability
W0.11 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
96-02-18299).

References

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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),

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)

t, fs

Fig. 4

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