J. Phys. Chem. C 2007, 111, 17765-17772
17765
Interaction of the Charged Deuterium Cluster D3+ with Femtosecond Laser Pulses† M. Isla*,‡ and J. A. Alonso‡,§ Departamento de Fı´sica Teo´ rica, Ato´ mica y O Ä ptica, UniVersidad de Valladolid, 47005 Valladolid, Spain, and Donostia International Physics Center (DIPC), E-20018 San Sebastia´ n, Spain ReceiVed: January 27, 2007; In Final Form: March 31, 2007
A computational study of the dynamics of the charged deuterium trimer D3+ under irradiation by femtosecond laser pulses is presented. The computer simulations are carried out in the frame of a nonadiabatic, nonlinearized model of the coupled evolution of electrons and ions based on the time dependent density functional theory (TDDFT). Several laser field parameters such as intensity, frequency, and polarization have been varied, and their effects on the excitation of the cluster have been analyzed. A proper choice of the laser parameters can be used to lead the trimer across one of the several excitation output channels, from a perturbative regime at low intensities to a nonlinear domain with the occurrence of Coulomb explosion at high intensities.
I. Introduction technology,1
Motivated by advances in laser there is a great interest in the study of the interaction between matter and ultrafast lasers, that is, lasers with intensities higher than 1014 W/cm2 and pulse duration below 100 fs. The intensity of the currently available lasers can exceed the electric field created by an atomic nucleus (the atomic unit of intensity is I0 ) 3.5 × 1016 W/cm2) and the time scale of fs is also typical of the electron motion. This new research field allows for the exploration of the nonlinear response of atoms to intense laser pulses, leading to the observation of new processes, e.g., abovethreshold ionization (ATI),2 correlated double ionization,3-5 and high order harmonic generation (HHG).6 The theoretical understanding for the atomic case is nowadays well-known. The three time scales (laser, nuclear, and electronic) involved7 make the complete system nonseparable, and the superposition of the electronic and nuclear motion requires non-Born-Oppenheimer solutions of the equations giving the dynamics of the system. Numerical solutions are then required for a proper understanding of electron-nuclear dynamics in intense laser fields, for instance the ones based on the time-dependent Schro¨dinger equation,8 S-matrix theories,9 and even quasiclassical tunneling theories (ADK10 or the recollision model by Corkum11), which have provided quantitative agreement with experiment.12 The behavior of molecules and clusters under similar laser conditions offers a new challenge due to the existence of additional degrees of freedom, such as the nuclear motion or the presence of inter- and intramolecular forces. This leads to a distinction from atoms through the delocalization of electrons and the possible charge transfer between the constituents of the molecule or cluster, giving rise to a broad range of complex phenomena: above-threshold dissociation (ATD),13 bond softening14 and hardening,15 interatomic Coulombic decay (ICD) of excited molecules,16 and enhanced ionization.17 Some of these phenomena are followed by a Coulomb explosion. When molecules or clusters are multiply ionized by laser pulses of very short duration, the unbalanced positive charges are suf†
Part of the special issue “Richard E. Smalley Memorial Issue”. * To whom correspondence should be addressed. ‡ Universidad de Valladolid. § Donostia International Physics Center (DIPC).
ficiently close together to cause a repulsion-induced explosion of the nuclear skeleton.18 This is the basis for the Coulombexplosion imaging technology19 and for the nuclear fusion reactions observed by Ditmire and co-workers20 in beams of large deuterium clusters irradiated by femtosecond lasers. Another important application of lasers, pioneered by Smalley,21 is the production of cluster beams of even the most refractory materials. This method allowed for the discovery of the C60 fullerene.22 The interest in hydrogen and deuterium clusters is due to their peculiar properties.23-25 These are typical molecular clusters, with a strong intramolecular bonding and weak intermolecular forces. A lot of research has been carried out on ionized hydrogen clusters. Aggregates such as H3+ (H2)n, with n ) 1, 2, ..., are formed by a trimer cation H3+ solvated by neutral molecules forming shells around the trimer.26,27 Being charged makes them easier to handle experimentally.28 They are also active species in the nucleation phenomena in the stratosphere and interstellar clouds. The response of hydrogen clusters to intense laser pulses has been studied by several authors29-31 using theoretical methods, and a variety of phenomena has been revealed, ranging from a slow hydrodynamic expansion to an energetic Coulomb explosion. In a previous work,31 we presented results for the fragmentation of the deuterium cluster D3+ (D2)5, and the importance of the behavior of the central trimer became clear. When a neutral hydrogen cluster is ionized, the reaction
H2+ + H2 f H3+ + H
(1)
occurring in the interior of the cluster leads to a trimer carrying the positive charge, and a neutral atom is ejected from the cluster. The H3+ trimer becomes the core of those clusters as it is the stable unit around which the H2 molecules form shells. This trimer ion and its deuterated isotopomers have attracted attention because of their fundamental nature, astrophysical significance and dynamical richness. The experiments32,33 and ab initio simulations of Tennyson34,35 have shed light on the electronic structure, the infrared photodissociation spectrum, and the classical and quantal behavior of the molecule at its dissociation limit. The enhanced ionization mechanism has also
10.1021/jp070717+ CCC: $37.00 © 2007 American Chemical Society Published on Web 05/19/2007
17766 J. Phys. Chem. C, Vol. 111, No. 48, 2007
Isla and Alonso
been observed for this molecule.36 On the other hand, it is known that H3+ is the main agent responsible for the formation of complex molecules in the interstellar medium.37 H3+ is present in any environment where molecular hydrogen gas is ionized.38 It has been detected in the atmosphere of the giant planets,39-41 in the supernova SN1987A,42 and in interstellar clouds.43,44 The aim of this paper is to study the dynamical response of D3+ under irradiation by ultrashort laser pulses, using the time dependent density functional theory (TDDFT). We are not aware of previous theoretical or experimental studies of the properties of this trimer under intense ultrafast laser fields, except for a first exploration of H3+ by Ma et al.45 We then show and discuss the results of a comprehensive study of the behavior of the D3+ under such drastic conditions, by performing simulations for a variety of laser parameters, with the intention of motivating experimental studies of the interesting dynamical phenomena revealed by the simulations. II. Methodology Among the methods employed to approximate the Schro¨dinger equation to solve the many-electron problem, the most extended one is density functional theory (DFT);46 its extension to time-dependent problems treating interacting electrons in external fields is by now a well-established theory.47 Our calculations have been carried out with OCTOPUS,48 a recently developed TDDFT code where the time dependent Kohn-Sham equations giving the evolution of the orbitals are explicitly integrated in real space. The ground state structure of the fieldfree cluster is first calculated using the DFT formalism. The system is then perturbed by a classically treated laser pulse with a cosinoidal envelope
E(t) ) A0 cos
(
)
π t - 2τ0 - t0 sin(ωt) eˆ , |t - t0| < τ0 2 τ0
(2)
where ω is the frequency of the field and eˆ is the polarization vector; 2τ0 is the total pulse duration, t0 indicates the center (maximum), and A0 is the amplitude. The time-dependent Kohn-Sham equations are propagated in real time. For the exchange-correlation energy functional, we have chosen the time-dependent local-density approximation (TDLDA),49 with the Perdew-Wang parametrization,50 which has been tested as a robust tool for dynamical applications. The LDA has wellknown limitations,51 but for an off-equilibrium process like this, it is convenient to work with such a well tested approximation, which provides a good compromise between computational ease and accuracy. The nuclei are treated as classical point particles obeying Newton’s equations of motion. It is important to treat this aspect correctly, as the impact of ionic motion on the ionization rate is crucial.45,52 Therefore, the framework implemented in OCTOPUS to address the problem of the dynamical evolution of a system of interacting electrons and nuclei in excited states is that known as Ehrenfest path for nonadiabatic molecular dynamics (EP-NAMD). We have a coupled system, composed of (i) an electronic subsystem in a quantum state treated with TDDFT and (ii) a classical subsystem for the ions, whose Hamiltonian gives the expectation value path of the nuclei through the application of the Ehrenfest theorem. Both subsystems have to be evolved simultaneously. One of the most important features of this model is that it can deal either with adiabatic or nonadiabatic problems. The Lagrangian of the system is then53
L)
∑R
[
1
2
]
mRR4 R2 + ZRRR E(t) -
∑i
〈|
φi ip
∂ ∂t
∑ |R
R
