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.

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

yA, 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 yA, 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

1. Peter Dietrich, Donna T. Strickland, Michel Laberge and Paul B.

Corkum, Phys. Rev. A, 47, N3, 2305 (1993). M. Ivanov, T. Siedeman, P.

Corkum, Phys. Rev. A, 54, N2, 1541 (1996).

2. F. A. Ilkov, T. D. G. Walsh, S. Turgeon and S. L. Chin, Phys. Rev. A,

51, N4, R2695 (1995). F. A. Ilkov, T. D. G. Walsh, S. Turgeon and S. L.

Chin, Chem. Phys. Lett 247 (1995).

3. S. L. Chin, Y. Liang, J. E. Decker, F. A. Ilkov, M. V. Amosov, J.

Phys. B: At. Mol. Opt. Phys. 25 (1992), L249.

4. A. Talebpour, S. Larochelle and S. L. Chin, in press.

5. D. Normand, S. Dobosz, M. Lezius, P. D’Oliveira and M. Schmidt: in

Multiphoton Processes, 1996, Conf., Garmish-Partenkirchen, Germany,

Inst. Phys. Ser. No 154 (IOPP, Bristol 1997), p. 287.

6. A. Giusti-Suzor, F. H. Mies, L. F. DiMauro, E. Charon and B. Yang, J.

Phys. B: At. Mol. Opt. Phys. 28 (1995) 309-339.

7. P. Dietrich, M. Yu. Ivanov, F. A. Ilkov and P. B. Corkum, Phys. Rev.

Lett. 76, 1996.

8. S. Chelkowski, Tao Zuo, A. D. Bandrauk, Phys. Rev. A, 46, N9, R5342

(1992)

9. M. E. Sukharev, V. P. Krainov, JETP, 83, 457,1996. M. E. Sukharev, V.

P. Krainov, Laser Physics, 7, No3, 803, 1997. M. E. Sukharev, V. P.

Krainov, JETP, 113, No2, 573, 1998. M. E. Sukharev, V. P. Krainov, JOSA

B, in press.

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

Нашли опечатку? Выделите и нажмите CTRL+Enter

## Оставить комментарий