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Relaxation Dynamics of Photoexcited Calcium Deposited on Argon Clusters: Theoretical Simulation of Time-Resolved Photoelectron Spectra† Marie-Catherine Heitz,‡ Laurent Teixidor,‡ Nguyen-Thi Van-Oanh,§ and Fernand Spiegelman*,‡ Laboratoire de Chimie et de Physique Quantiques, IRSAMC, CNRS and UniVersite´ de Toulouse, UniVersite´ Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, Cedex, France, Laboratoire de Chimie Physique, CNRS and UniVersite´ Paris XI, 91405 Orsay, France ReceiVed: October 1, 2009; ReVised Manuscript ReceiVed: January 7, 2010
Relaxation dynamics following photoexcitation of a calcium atom deposited on an icosahedral-like argon cluster Arn (n ≈ 55) is investigated through theoretical simulations. Based on ab initio calculations of the CaAr molecule, a diatomics-in-molecules model is set up to efficiently describe the electronic excited states of the system. The excited state dynamics is studied using molecular dynamics with electronic transitions (Tully, J. C. J. Chem. Phys. 1990, 93, 1061). The signature of this dynamics in the time-resolved photoelectron spectra is investigated, to assess the possibility of detecting competing vibrational and electronic relaxations through pump-probe experiments. The vibrational relaxation, influenced by nonadiabatic transitions, can clearly be seen in the time-resolved photoelectron spectra. The details of the electronic relaxation, as well as the possible ejection of the chromophore, are found to be sensitive to the local environment of the calcium atom deposited on the argon cluster. I. Introduction The dynamics of atomic and molecular chromophores in a rare gas environment has attracted large interest from various aspects. One aspect is matrix isolation spectroscopy. The influence of the matrix may significantly change the absorption features, inducing line shifts, cutoff in the spectra, and changes in the oscillator strengths. It may also modify the postexcitation dynamics and relaxation, inducing differential behavior between valence and Rydberg states, caging and quenching of predissociation, matrix relaxation and the so-called electronic bubble formation in the excited electronic state, or change the luminescence spectra.1-10 Chromophores interacting with inert systems in the gas phase have also focused wide interest. Early investigations were concerned with van der Waals complexes.11 More recently, rare gas clusters have also received considerable attention. They can indeed be considered as model systems to understand solvation at the microscopic level.12-15 One important issue is naturally that of monitoring the structural properties at finite size and the formation and organization of the solvation shells as a precursor situation to actual bulk solvation. Absorption and emission spectroscopy can provide valuable information about the interaction of the chromophore with the neighboring rare gas atoms or the first solvation shell, either in the ground state or in the relaxed excited state. Rare gas clusters can also be considered as convenient finite size media to investigate reactivity, like in the so-called cluster induced chemical reaction (CICR) scheme.16,17 More recently, investigations have been involved in the study of guest species in helium nanodropolets.18 In the present work, we address the problem of the theoretical investigation of the relaxation dynamics following the photoexcitation of a calcium atom deposited on an argon cluster. In †
Part of the “Benoît Soep Festschrift”. * Corresponding author. Electronic address: fernand.spiegelman@ irsamc.ups-tlse.fr. ‡ CNRS and Universite´ de Toulouse, Universite´ Paul Sabatier. § CNRS and Universite´ Paris XI.
the past years, spectroscopic experiments have been performed concerning the photoexcitation of an alkaline-earth atom deposited on an argon cluster.19-22 The experiments consisted of exciting either a barium19-21 or a calcium atom22 in the vicinity of the atomic ns2 1S0 f nsnp 1P1 transition and investigating the relaxation processes through the recording of excitation and emission spectra. Electronic relaxation among the excited states issued from the nsnp configurations, and possibly desorption of the adsorbed atom, were observed. Theoretical simulations performed for the BaArn system have confirmed these observations.21 The scope of the work presented here is to unravel the relaxation mechanism of a Ca atom deposited on a middle size argon cluster with icosahedral shape and especially to assess to which extent time-resolved photoelectron spectroscopy can provide information. Time-resolved photoelectron spectroscopy has proven to be a very powerful tool to investigate complex dynamics (for recent reviews, see refs 23 and 24). Elementary processes constituting the reaction mechanisms can be detected, like vibrational motion25 or electronic relaxation through nonadiabatic transitions.26,27 This can also be achieved in the presence of a medium such as a cluster, allowing, for instance, highlight of the solvation of specific excited states of deposited molecules28 or to characterize the dynamics of electron solvation in molecular clusters.29 From the theoretical point of view, timeresolved photoelectron signals can be extracted from dynamical simulations on the basis of either a quantum framework30-32 or classical trajectories.33,34 For the CaArn system investigated in this work, details of the relaxation mechanism can be obtained through theoretical simulations allowing for the description of both the electronic relaxation of the chromophore and the vibrational energy redistribution to the inert cluster. This is done using the molecular dynamics with quantum transition (MDTQ) scheme proposed by Tully,35,36 together with a diatomic in molecules (DIM) model for the electronic structure. This methodology seems to us to be the most appropriate: the high
10.1021/jp909443p 2010 American Chemical Society Published on Web 02/01/2010
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Heitz et al.
dimensionality of nuclear dynamics does not allow for a straightforward quantum wavepacket approach on a precalculated grid but requires on-the-fly methods. Furthermore, to obtain a large number of trajectories to get a significant statistical averaging, the calculation of the forces and nonadiabatic couplings needs to be extremely efficient. This combined strategy has been widely used in theoretical studies of photoexcitation of atoms or diatomic molecules deposited on or embedded in argon clusters, shedding light on various processes like electronic transitions,21 dissociation,37,38 recombination,39-41 spin nonconserving transitions,39 and on the factors influencing them like size and local environnement. The same approach has been applied for the computation of time-resolved photoelectron spectra for related systems.40,42 Furthermore, in the BaArn study mentioned above, this methodology was employed and gave results that confirmed experimental observations.21 The present work extends previous investigation of CaArn clusters,22,43 which were more concerned with the interplay between structural, dynamical, and thermodynamical behavior in the ground state and nanosecond scale absorption features. The structure of the article is the following. The methods used are detailed in section II. Section II.A introduces the DIM formalism used to represent the electronic structure of the excited states of CaArn system in the range of the 4s4p levels. Section II.B presents the methods used to compute the timeresolved photoelectron spectra, extracted from the nonadiabatic dynamics, simulated within the MDQT scheme.35,36 Section III is dedicated to the presentation and discussion of the results. II. Methods A. Electronic Calculations. 1. DIM Hamiltonian. The DIM model appears as very appealing in the case of a chromophoreinert cluster interaction since the size of the DIM Hamiltonian is constant with the inert cluster size, as long as the rare gas atoms remain in their ground state. The scope of the present paper is to investigate the relaxation dynamics of calcium excited in the vicinity of the resonant 4s4p 1P line. In previous investigations dealing with absorption spectroscopy, we used for the excited states a DIM model expressed in a basis including only the three adiabatic states dissociating in the latter asymptote.22,43 However, the low energy electronic spectrum of atomic calcium is featured by the embedding of the 4s3d configuration within the 4s4p triplet and singlet multiplets, due to a large 4s-4p atomic exchange integral. The experimental atomic transition energies (after removal of spin-orbit coupling) are 15 263, 20 356, 21 849, and 23 652 cm-1 for states 4s4p 3 P, 4s3d 3D, 4s3d 1D, and 4s4p 1P, respectively.44 To ensure a better transferability of the diatomic interactions to the cluster case, and to provide a better account of the 4s4p-4s3d electronic interconfigurational mixing in the cluster situation, and hence a better estimate of the gradient and nonadiabatic couplings, we have developed a DIM model for CaArn expressed in a valence-bond-like diabatic representation, involving all states related to the three configurations of interest, namely 4s2, 4s4p, and 4s3d. The Hamiltonian for CaArn systems is expressed under the general form
operator between the calcium atom (labeled A) and one argon atom (labeled B), whereas HBC is the Hamiltonian for an argon-argon pair interaction. The DIM scheme used here consists of expressing the above Hamiltonian in a basis of molecular valence-bond type configurations. Let the ground state of the system be described as a single Slater determinant Φ0 built up from the occupied orbitals of the constituting atoms Ar
Φ0 ) A [(1s1s¯...4s4s¯)A
∏ (1s1s¯...3px3p¯x3py3p¯y3pz3p¯z)B] B
(2) From this ground state determinant, one can generate the determinants or configurations spanning the lowest excited states of calcium, namely ζσ + Φlµ ) alµσ asζΦ0
(3)
where the operators asζ and a+lµR create an excitation on calcium, promoting an electron from occupied spin orbital 4sζ (ζ ) R, β) to excited spin orbital φlµσ (l ) 4p, 3d, µ ) x, y, z for 4p, µ ) x2 - y2, xy, xz, yz, 3z2 - r2 for 3d, and spin projection σ ) R, β). This determinantal basis set includes 33 determinants (1 for the ground state, 12 for the 4s4p excited states, and 20 for the 4s3d excited states, involving all space and spin arrangements Rβ, βR, RR, and ββ). The cluster excited states can be safely restricted to excitations on calcium. Indeed, the present excited states of atomic calcium are in the range 15 263-23 653 cm-1, whereras the lowest excitations on atomic argon lie above 93 144 cm-1.44 For each type of single excitation toward orbitals φlµ, the associated determinantal basis set can be readily mapped S into a configurational basis ΦSM lµ set, which are spin-eigenfunc00 Rβ βR 10 Rβ βR ) (Φlµ + Φlµ )/2, Φlµ ) (Φlµ - Φlµ )/ tions, namely, Φlµ 11 RR 1-1 ββ 2, Φlµ ) Φlµ and Φlµ ) Φlµ . The matrix size of singlet states is reduced to 9, independent of the number of inert atoms. In the following, we will assume the orthogonality of the DIM basis set. The energy of the ground state determinant Φ0 is given by Ar
〈Φ0 |H|Φ0〉 ) E0 +
∑
Ar
AB VCaAr +
B
BC ∑ VArAr
AB BC and VArAr are the CaAr and ArAr potential, where VCaAr respectively, taken at the geometries of the relevant pairs. Let us note that the VCaAr potential actually describes a diabatic interaction between a ground state calcium atom and an argon atom, since the basis set is formally kept frozen on calcium. The matrix elements for the other configurations are
Ar
SM BC )δµµ′δl,l′ + 〈ΦlµSM |H|Φl'µ′ 〉 ) (ESl + ∑ VArAr S
S
B
