Dissociative ionization of neon clusters Ne(n), n=3 to 14: a realistic multisurface dynamical study

The molecular dynamics with quantum transitions (MDQT) method is applied to study the fragmentation dynamics of neon clusters following vertical ionization of neutral clusters with 3 to 14 atoms. The motion of the neon atoms is treated classically, while transitions between the adiabatic electronic states of the ionic clusters are treated quantum mechanically. The potential energy surfaces are described by the diatomics-in-molecules model in a minimal basis set consisting of the effective 2p orbitals on each neon atom for the missing electron. The fragmentation mechanism is found to be rather explosive, with a large number of events where several atoms simultaneously dissociate. This is in contrast with evaporative atom by atom fragmentation. The dynamics are highly nonadiabatic, especially at shorter times and for the larger clusters. Initial excitation of the neutral clusters does not affect the fragmentation pattern. The influence of spin-orbit coupling is also examined and found to be small, except for the smaller size systems for which the proportion of the Ne+ fragment is increased up to 43%. From the methodological point of view, most of the usual momentum adjustment methods at hopping events are shown to induce nonconservation of the total nuclear angular momentum because of the nonzero electronic to rotation coupling in these systems. A new method for separating out this coupling and enforcing the conservation of the total nuclear momentum is proposed. It is applied here to the MDQT method of Tully but it is very general and can be applied to other surface hopping methods.     

Modelization of the fragmentation dynamics of krypton clusters (Kr(n),n=2-11) following electron impact ionization

We present the first prediction for the fragmentation dynamics following electron impact ionization of neutral krypton clusters from 2 to 11 atoms. Fragment proportions and parent ion lifetimes are deduced from a molecular dynamics with quantum transitions study in which the nuclei are treated classically and the transitions between electronic states quantum mechanically. The potential-energy surfaces are derived from a diatomics-in-molecules model to which induced dipole-induced dipole and spin-orbit interactions are added. The results show surprisingly fast and extensive fragmentation for clusters of such a heavy atom, although not as extensive as in the case of neon clusters studied previously [D. Bonhommeau et al., J. Chem. Phys. 123, 54316 (2005)]. The parent ion lifetimes range from 2.8 to 0.7 ps, and the most abundant fragment is Kr(2) (+) for all studied sizes, followed by Kr(+) for sizes smaller than 7 atoms and by Kr(3) (+) for larger sizes. Trimer and larger fragments are found to originate from the lower electronic states of parent ions. The comparison with preliminary results from experiments on size-selected neutral clusters conducted by Steinbach et al. (private communication) reveal a good agreement on the extensive character of the fragmentation. It is checked that the additional internal energy brought by the helium scattering technique used for size selection does not affect the fragment proportions. In addition, the existence of long-lived trajectories is revealed, and they are found to be more and more important for larger cluster sizes and to favor the stabilization of larger fragments. The implications of this work for microsecond-scale dynamics of ionized rare-gas clusters are discussed. In particular, given the extent of fragmentation of the parent clusters and the fast kinetics of the whole process, the small cluster ions that exhibit a monomer loss in the microsecond time window must originate from much larger neutral precursors. The decay rate of the II(12)(u) state of the ionic dimer Kr(2) (+) by spin-orbit coupling is found to be of the order of 3 ps, in contrast to the expected tens of microseconds, but only reasonably faster than the corresponding state of HeNe(+). Finally, the spin-orbit interaction strongly affects both the Kr(+)Kr(2) (+) ratio and some of the characteristic times of the dynamics, especially for smaller sizes, but not the overall dependence of the fragment proportions as a function of cluster size.     

Fragmentation of ionized doped helium nanodroplets: theoretical evidence for a dopant ejection mechanism

We report a theoretical study of the effect induced by a helium nanodroplet environment on the fragmentation dynamics of a dopant. The dopant is an ionized neon cluster Ne(n) (+) (n=4-6) surrounded by a helium nanodroplet composed of 100 atoms. A newly designed mixed quantum/classical approach is used to take into account both the large helium cluster zero-point energy due to the light mass of the helium atoms and all the nonadiabatic couplings between the Ne(n) (+) potential-energy surfaces. The results reveal that the intermediate ionic dopant can be ejected from the droplet, possibly with some helium atoms still attached, thereby reducing the cooling power of the droplet. Energy relaxation by helium atom evaporation and dissociation, the other mechanism which has been used in most interpretations of doped helium cluster dynamics, also exhibits new features. The kinetic energy distribution of the neutral monomer fragments can be fitted to the sum of two Boltzmann distributions, one with a low kinetic energy and the other with a higher kinetic energy. This indicates that cooling by helium atom evaporation is more efficient than was believed so far, as suggested by recent experiments. The results also reveal the predominance of Ne(2) (+) and He(q)Ne(2) (+) fragments and the absence of bare Ne(+) fragments, in agreement with available experimental data (obtained for larger helium nanodroplets). Moreover, the abundance in fragments with a trimeric neon core is found to increase with the increase in dopant size. Most of the fragmentation is achieved within 10 ps and the only subsequent dynamical process is the relaxation of hot intermediate He(q)Ne(2) (+) species to Ne(2) (+) by helium atom evaporation. The dependence of the ionic fragment distribution on the parent ion electronic state reached by ionization is also investigated. It reveals that He(q)Ne(+) fragments are produced only from the highest electronic state, whereas He(q)Ne(2) (+) fragments originate from all the electronic states. Surprisingly, the highest electronic states also lead to fragments that still contain the original ionic dopant species. A mechanism is conjectured to explain this fragmentation inhibition.     

Fragmentation dynamics of argon clusters (Ar(n), n = 2 to 11) following electron-impact ionization: modeling and comparison with experiment

The fragmentation dynamics of argon clusters ionized by electron impact is investigated for initial cluster sizes up to n = 11 atoms. The dynamics of the argon atoms is modeled using a mixed quantum-classical method in which the nuclei are treated classically and the transitions between electronic states quantum mechanically. The potential-energy surfaces are derived from a diatomics-in-molecules model with the addition of the induced dipole-induced dipole and spin-orbit interactions. The results show extensive and fast fragmentation. The dimer is the most abundant ionic fragment, with a proportion increasing from 66% for n = 2 to a maximum of 95% for n = 6 and then decreasing down to 67% for n = 11. The next abundant fragment is the monomer for n < 7 and the trimer otherwise. The parent ion dissociation lifetimes are all in the range of 1 ps. Long-lived trajectories appear for initial cluster sizes of seven and higher, and favor the formation of the larger fragments (trimers and tetramers). Our results show quantitative agreement with available experimental results concerning the extensive character of the fragmentation: Ar+ and Ar2(+) are the only ionic fragments for sizes up to five atoms; their overall proportion is in quantitative agreement for all the studied sizes; Ar2(+) is the main fragment for all sizes; stable Ar3(+) fragments only appear for n > or = 5, and their proportion increases smoothly with cluster size from there. However, the individual ionic monomer and dimer fragment proportions differ. The experimental ones exhibit oscillations with initial cluster size, with a slight tendency to decrease on average for the monomer. In contrast our results show a monotonic, systematic evolution, similar to what was found in our earlier studies on neon and krypton clusters. Several hypotheses are discussed in order to find the origin of this discrepancy. Finally, the metastable II(1/2)u and II(1/2)g states of Ar2(+) are found to decay with a lifetime of 3.5 and 0.1 ps, respectively, due to spin-orbit coupling. The difference with the commonly accepted microsecond range value for rare-gas dimer ions could originate from the role of autoionizing states in the formation of the parent ions.     

Modeling the fragmentation dynamics of ionic clusters inside helium nanodroplets: the case of He100Ne4+

We present simulation results on the effect of a helium nanodroplet environment on the fragmentation dynamics of embedded molecular systems. The helium atoms are treated explicitly, with zero-point effects taken into account through an effective helium-helium interaction potential. The ionized neon tetramer is used as a model molecular system because, like all the small rare-gas clusters, it fragments extensively upon ionization. All the nonadiabatic effects between electronic states of the ionized neon cluster are taken into account. The results reveal a predominance of Ne2+ and HepNe2+ fragments and the absence of bare Ne+ fragments, in agreement with available experimental data. The neutral monomer fragments exhibit a rather wide kinetic energy distribution that can be fitted to the sum of two Boltzmann distributions, one with a low kinetic energy and the other with a higher kinetic energy. This indicates that cooling by helium atom evaporation is more efficient than was believed so far, as suggested by recent experimental results. Purely classical calculations are shown to strongly overestimate the amount of cage effect (cooling), clearly indicating the need to take into account zero-point effects.     

Optical absorption of small copper clusters in neon: Cu(n), (n = 1-9)

We present optical absorption spectra in the UV-visible range (1.6 eV < ?ω < 5.5 eV) of mass selected neutral copper clusters Cu(n)(n = 1-9) embedded in a solid neon matrix at 7 K. The atom and the dimer have already been measured in neon matrices, while the absorption spectra for sizes between Cu(3) and Cu(9) are entirely (n = 6-9) or in great part new. They show a higher complexity and a larger number of transitions distributed over the whole energy range compared to similar sizes of silver clusters. The experimental spectra are compared to the time dependent density functional theory (TD-DFT) implemented in the TURBOMOLE package. The analysis indicates that for energies larger than 3 eV the transitions are mainly issued from d-type states; however, the TD-DFT scheme does not reproduce well the detailed structure of the absorption spectra. Below 3 eV the agreement for transitions issued from s-type states is better.     

Small helium clusters formation

We investigated small helium clusters formation in nonequilibrium conditions using the non-Hermitian formalism. Helium is a simple enough system for analytical study while complicated enough to have a rich variety of quantum properties. In this article, we used a new formalism based on non-Hermitian quantum mechanics for describing the electronic excited states in clusters. This formalism enabled to estimate the decay time of excited states within a single scheme. Its implementation to helium shows the existence of new long-lived excited states in small helium clusters at the distance of 5.6 Bohr radii between atoms. Moreover, several helium excimers and exciplexes at the distances between helium atoms of 35.5, 22.8, 14.0, and 8.5 Bohr radii with the scaling factor of about 1.6 were found. It is related to the restructuring of the electronic structure caused by powerful external excitations. These results give a new insight on clustering processes providing more profound and complete understanding.     

Structure and stability of Ne+He(n): experiment and diffusion quantum Monte Carlo theory with "on the fly" electronic structure

New data are reported for the mass-spectrometry fragmentation patterns of helium clusters, either pure or containing a Ne or an Ar atom. The patterns for He(n)+ and Ar+He(n) show clear evidence of structure, while those of Ne+He(n) do not. To better understand the surprising result for the Ne+He(n) fragments, diffusion quantum Monte Carlo (DMC) calculations of the energies and structural properties of these ions were performed using a diatomics-in-molecule (DIM) parametrization of the potential energy. Using DIM for electronic energy evaluation allows us to sample 10(9) configurations even for a cluster as large as Ne+He14. The results of the DMC calculation are very surprising. For n > 7, the DMC random walkers rarely venture within 100 cm(-1) of the minimum potential energy. Analysis of the resulting particle density distributions shows that the zero-point energy does more than spread the wave function around the potential-energy minima, resulting in very diffuse wave functions. For some of the clusters the quantum effects nearly exclude the region of the potential minimum from the overall wave function. An important result of this effect is that the incremental bonding energy of the nth helium atom varies quite smoothly with n, for n > 5. This eliminates the expected shell structure and explains the lack of magic-number-type features in the data.     

Electronic excitation spectra of the [Ir(ppy)2(bpy)]+ photosensitizer bound to small silver clusters Ag(n) (n = 1-6)

The changes in nature and order of the excited electronic states of the photosensitizer [Ir(ppy)(2)(bpy)](+) upon binding to small silver clusters, Ag(n) (n = 1-6), were studied theoretically using the linear response TDDFT method with the range-separated LC-BLYP functional. Binding energies and localization of HOMO and LUMO orbitals are found to oscillate with the number of silver atoms. Special emphasis is put on the discussion of long-range charge transfer transitions between the photosensitizer and the silver cluster. The energies of these transitions were found to be only slightly dependent on the relative orientations of both fragments, but strongly dependent on the intermolecular distance. The absorption spectrum of the combined system does not show a systematic trend with respect to cluster size, but it is strongly modified by the charge transfer transitions. Possible photophysical processes of the systems containing larger clusters are discussed.     

Les orbitales de Slater à nombre quantique ≪n≫ non-entier

Slater-Orbitals of non-integral principal quantum number have been used to construct a ground-state wave function for atoms from helium to neon.     

Excess electron localization sites in neutral water clusters

We present approximate pseudopotential quantum-mechanical calculations of the excess electron states of equilibrated neutral water clusters sampled by classical molecular dynamics simulations. The internal energy of the clusters are representative of those present at temperatures of 200 and 300 K. Correlated electronic structure calculations are used to validate the pseudopotential for this purpose. We find that the neutral clusters support localized, bound excess electron ground states in about 50% of the configurations for the smallest cluster size studied (n = 20), and in almost all configurations for larger clusters (n > 66). The state is always exterior to the molecular frame, forming typically a diffuse surface state. Both cluster size and temperature dependence of energetic and structural properties of the clusters and the electron distribution are explored. We show that the stabilization of the electron is strongly correlated with the preexisting instantaneous dipole moment of the neutral clusters, and its ground state energy is reflected in the electronic radius. The findings are consistent with electron attachment via an initial surface state. The hypothetical spectral dynamics following such attachment is also discussed.     

Dynamics of charge-transfer-to-solvent precursor states in I- (water)n (n = 3-10) clusters studied with photoelectron imaging

The dynamics of charge-transfer-to-solvent states are studied in I- (H2O)(n=3-10) clusters and their deuterated counterparts using time-resolved photoelectron imaging. The photoelectron spectra for clusters with n > or = 5 reveal multiple time scales for dynamics after their electronic excitation. An increase in the vertical detachment energy (VDE) by several hundred millielectronvolts on a time scale of approximately 1 ps is attributed to stabilization of the excess electron, primarily through rearrangement of the solvent molecules, but a contribution to this stabilization from motion of the I atom cannot be ruled out. The VDE drops by approximately 50 meV on a time scale of tens of picoseconds; this is attributed to loss of the neutral iodine atom. Finally, the pump-probe signal decays with a time constant of 60 ps-3 ns, increasing with cluster size. This decay is commensurate with the growth of very slow electrons and is attributed to autodetachment. Smaller clusters (n = 3, 4) display simpler dynamics. Anisotropy parameters are reported for clusters n = 4-9.     

Nonadiabatic molecular dynamics of photoexcited Li2(+) Ne(n) clusters

We investigate the relaxation of photoexcited Li(2)(+) chromophores solvated in Ne(n) clusters (n = 2-22) by means of molecular dynamics with surface hopping. The simplicity of the electronic structure of these ideal systems is exploited to design an accurate and computationally efficient model. These systems present two series of conical intersections between the states correlated with the Li+Li(2s) and Li+Li(2p) dissociation limits of the Li(2)(+) molecule. Frank-Condon transition from the ground state to one of the three lowest excited states, hereafter indexed by ascending energy from 1 to 3, quickly drives the system toward the first series of conical intersections, which have a tremendous influence on the issue of the dynamics. The states 1 and 2, which originate in the Frank-Condon area from the degenerated nondissociative 1(2)Π(u) states of the bare Li(2)(+) molecule, relax mainly to Li+Li(2s) with a complete atomization of the clusters in the whole range of size n investigated here. The third state, which originates in the Frank-Condon area from the dissociative 1(2)Σ(u)(+) state of the bare Li(2)(+) molecule, exhibits a richer relaxation dynamics. Contrary to intuition, excitation into state 3 leads to less molecular dissociation, though the amount of energy deposited in the cluster by the excitation process is larger than for excitation into state 1 and 2. This extra amount of energy allows the system to reach the second series of conical intersections so that approximately 20% of the clusters are stabilized in the 2(2)Σ(g)(+) state potential well for cluster sizes n larger than 6.     

On the noble-gas-induced intersystem crossing for the CUO molecule: experimental and theoretical investigations of CUO(Ng)n (Ng = Ar, Kr, Xe; n = 1, 2, 3, 4) complexes in solid neon

Uranium atoms excited by laser ablation react with CO in excess neon to produce the novel CUO molecule, which forms distinct Ng complexes (Ng = Ar, Kr, Xe) when the heavier noble gases are added. The CUO(Ng) complexes are identified through CO isotopic and Ng substitution on the neon matrix infrared spectra and by comparison to DFT frequency calculations. The U-C and U-O stretching frequencies of CUO(Ng) complexes are slightly red-shifted from frequencies for the (1)Sigma(+) CUO ground state, which identifies singlet ground state CUO(Ng) complexes. In solid neon the CUO molecule is also a complex CUO(Ne)(n), and the CUO(Ne)(n-1)(Ng) complexes are likewise specified. The next singlet CUO(Ne)(x)(Ng)(2) complexes in excess neon follow in like manner. However, the higher CUO(Ne)(x)(Ng)(n) complex (n = 3, 4) stretching modes approach pure argon matrix CUO(Ar)(n) values and isotopic behavior, which are characterized as triplet ground state complexes by DFT frequency calculations. This work suggests that the singlet-triplet crossing occurs with 3 Ar, 3 Kr, or 4 Xe and a balance of Ne atoms coordinated to CUO in the neon matrix host.     

Electronic spectra of jet-cooled calix[4]arene and its van der Waals clusters: encapsulation of a neutral atom in a molecular bowl

The encapsulation of neutral guest has been studied for calix[4]arene (C4A) by forming van der Waals clusters with Ar and Ne in supersonic jets. The electronic transitions of these clusters suggest that the first Ar (Ne) is encapsulated inside the C4A cavity, while the next atoms are bound outside.     

First-principles study of electronic and magnetic properties of Co(n)Mn(m) and Co(n)V(m) (m + n < or = 6) clusters

The electronic and magnetic properties of small Co(n)Mn(m) and Co(n)V(m) (m + n < or = 6) clusters are systematically studied using density functional theory. The results show that Co and V atoms prefer to aggregate in Co-Mn and Co-V clusters, respectively. Significant magnetic moment enhancement in Co-Mn clusters with Mn doping and reduction in Co-V clusters with V doping are found, consistent with experiment results for larger clusters [Phys. Rev. Lett. 2007, 98, 113401]. The results are discussed by analyzing the magnetic coupling type and local magnetic moment on each atoms. Density of states and vertical ionization potentials are calculated and show cluster size dependent behavior.