Imaging of the Structure of the Argon and Neon Dimer, Trimer, and Tetramer

Structure determination of alkali trimers on helium nanodroplets through laser-induced Coulomb explosion

Alkali trimers, Ak3, located on the surface of He nanodroplets are triply ionized following multiphoton absorption from an intense femtosecond laser pulse, leading to fragmentation into three correlated Ak+ ions. Combining the information from threefold covariance analysis of the emission direction of the fragment ions and their kinetic energy distributions P(Ekin), we find that Na3, K3, and Rb3 have an equilateral triangular structure, corresponding to that of the lowest lying quartet state A2'4, and determine the equilibrium bond distance Req(Na3) = 4.65 ± 0.15 Å, Req(K3) = 5.03 ± 0.18 Å, and Req(Rb3) = 5.45 ± 0.22 Å. For K3 and Rb3, these values agree well with existing theoretical calculations, while for Na3, the value is 0.2-0.3 Å larger than the existing theoretical results. The discrepancy is ascribed to a minor internuclear motion of Na3 during the ionization process. In addition, we determine the distribution of internuclear distances P(R) under the assumption of fixed bond angles. The results are compared to the square of the internuclear wave function |Ψ(R)|2.

Electron transfer in strong-field three-body fragmentation of ArKr2 trimers

We experimentally studied the three-body fragmentation dynamics of a noble gas cluster (ArKr₂) upon its multiple ionization by an intense femtosecond laser pulse. The three-dimensional momentum vectors of correlated fragmental ions were measured in coincidence for each fragmentation event. A novel comet-like structure was observed in the Newton diagram of the quadruple-ionization-induced breakup channel of ArKr₂ ⁴⁺→ Ar⁺ + Kr⁺ + Kr²⁺. The concentrated head part of the structure mainly originates from the direct Coulomb explosion process, while the broader tail part of the structure stems from a three-body fragmentation process involving electron transfer between the distant Kr⁺ and Kr²⁺ ion fragments. Due to the field-driven electron transfer, the Coulomb repulsive force of the Kr²⁺ and Kr⁺ ions with respect to the Ar⁺ ion undergoes exchange, leading to changes in the ion emission geometry in the Newton plot. An energy sharing among the separating Kr²⁺ and Kr⁺ entities was observed. Our study indicates a promising approach for investigating the strong-field-driven intersystem electron transfer dynamics by using the Coulomb explosion imaging of an isosceles triangle van der Waals cluster system.

Femtosecond Time-Resolved Neighbor Roles in the Fragmentation Dynamics of Molecules in a Dimer

How the neighbor effect plays its role in the fragmentation of molecular clusters attracts great attention for physicists and chemists. Here, we study this effect in the fragmentation of N_{2}O dimer by performing three-body coincidence measurements on the femtosecond timescale. Rotations of bound N_{2}O^{+} triggered by neutral or ionic neighbors are tracked. The forbidden dissociation path between B^{2}Π and ^{4}Π is opened by the spin-exchange effect due to the existence of neighbor ions, leading to a new channel of N_{2}O^{+}→NO+N^{+} originating from B^{2}Π. The formation and dissociation of the metastable product N_{3}O_{2}^{+} from two ion-molecule reaction channels are tracked in real time, and the corresponding trajectories are captured. Our results demonstrate a significant and promising step towards the understanding of neighbor roles in the reactions within clusters.

Van der Waals five-body size-energy universality

A universal relationship between scaled size and scaled energy is explored in five-body self-bound quantum systems. The ground-state binding energy and structure properties are obtained by means of the diffusion Monte Carlo method. We use pure estimators to eliminate any residual bias in the estimation of the cluster size. Strengthening the inter-particle interaction, we extend the exploration from the halo region to classical systems. Universal scaled size-scaled energy line, which does not depend on the short-range potential details and binding strength, is found for homogeneous pentamers with interaction potentials decaying at long range predominantly as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r^{-6}$$\end{document}r-6. For mixed pentamers, we discuss under which conditions the universal line can approximately describe the size-energy ratio. Our data is compatible with generalized Tjon lines, which assume a linear dependence between the binding energy of the pentamers and the one of tetramers, when both are divided by the trimer energies.

Rotational spectroscopy of the argon dimer by time-resolved Coulomb explosion imaging of rotational wave packets

We report time-domain rotational spectroscopy of the argon dimer, Ar₂, by implementing time-resolved Coulomb explosion imaging of rotational wave packets. The rotational wave packets are created in Ar₂ with a linearly polarized, nonresonant, ultrashort laser pulse, and their spatiotemporal evolution is fully characterized by measuring angular distribution of the fragmented Ar⁺ promptly ejected from Ar₂²⁺ generated by the more intense probe pulse. The pump-probe measurements have been carried out up to a delay time of 16 ns. The alignment parameters, derived from the observed images, exhibit periodic oscillation lasting for more than 15 ns. The pure rotational spectrum of Ar₂ is obtained by Fourier transformation of the time traces of the alignment parameters. The frequency resolution in the spectrum is about 90 MHz, the highest ever achieved for Ar₂. The rotational constant and the centrifugal distortion constant are determined with much improved precision than the previous experimental results: B₀ = 1.72713 ± 0.00009 GHz and D₀ = 0.0310 ± 0.0005 MHz. The present B₀ value does not match within the quoted experimental uncertainty with that from the VUV spectroscopy, so far accepted as an experimental reference to assess theories. The present improved constants would stand as new references to calibrate state-of-the-art theoretical investigations and an indispensable experimental source for the construction of an accurate empirical intermolecular potential.

Three-electron correlations in strong laser field ionization

Strong field processes involving several active electrons reveal unambiguous dynamical signatures of the Pauli principle importance even in the nonrelativistic regime. We exemplify this statement studying three active electrons model atoms interacting with strong pulsed radiation, using an ab-initio time-dependent Schrödinger equation on a grid. In our restricted dimensionality model we are able to analyze momenta correlations of the three outgoing electrons using Dalitz plots. The different symmetries of the electronic wavefunctions, directly related to the initial state spin components, appear clearly visible.

Laser-Induced Electron Transfer in the Dissociative Multiple Ionization of Argon Dimers

We report on an experimental and theoretical study of the ionization-fragmentation dynamics of argon dimers in intense few-cycle laser pulses with a tagged carrier-envelope phase. We find that a field-driven electron transfer process from one argon atom across the system boundary to the other argon atom triggers subcycle electron-electron interaction dynamics in the neighboring atom. This attosecond electron-transfer process between distant entities and its implications manifests itself as a distinct phase-shift between the measured asymmetry of electron emission curves of the Ar^{+}+Ar^{2+} and Ar^{2+}+Ar^{2+} fragmentation channels. This letter discloses a strong-field route to controlling the dynamics in molecular compounds through the excitation of electronic dynamics on a distant molecule by driving intermolecular electron-transfer processes.

Visualizing the Geometry of Hydrogen Dimers

The simplest molecular dimer, H₂-H₂, poses a challenge to both experiment and theory as a system with a multidimensional energy surface that supports only a single weakly bound quantum state. Here, we provide a direct experimental image of the structure of hydrogen dimers [(H₂)₂, H₂-D₂, and (D₂)₂] obtained via femtosecond laser-induced Coulomb explosion imaging. Our results indicate that hydrogen dimers are not restricted to a particular geometry but rather occur as a mixture of all possible configurations. The measured intermolecular distance distributions were used to deduce the isotropic intermolecular potential as well as the binding energies of the dimers.

In search of molecular ions for optical cycling: a difficult road

Optical cycling, a continuous photon scattering off atoms or molecules, is the key tool in quantum information science.

Exact bound rovibrational spectra of the neon tetramer

Exact quantum dynamics calculations are performed for the bound rovibrational states of the neon tetramer (Ne₄) in its ground electronic state, using pair-wise Lennard-Jones potentials and the ScalIT suite of parallel codes. The vibrational states separate into a low-lying group mostly localized to a single potential well and a higher-energy delocalized group lying above the isomerization threshold-with such a structure serving as a testament to the "intermediate" quantum nature of the Ne₄ system. To accurately and efficiently represent both groups of states, the phase-space optimized discrete variable representation (PSO-DVR) approach was used, as implemented in the ScalIT code. The resultant 1D PSO effective potentials also shed significant light on the quantum dynamics of the system. All vibrational states were computed well up into the isomerization band and labeled up to the classical isomerization threshold-defined as the addition of the classical energy of a single bond, ϵ = 24.7 cm^-1, to the quantum ground state energy. Rovibrational energy levels for all total angular momentum values in the range J = 1-5 were also computed, treating all Coriolis coupling exactly.

Universality of size-energy ratio in four-body systems

Universal relationship of scaled size and scaled energy, which was previously established for two- and three-body systems in their ground state, is examined for four-body systems, using Quantum Monte Carlo simulations. We study in detail the halo region, in which systems are extremely weakly bound. Strengthening the interparticle interaction we extend the exploration all the way to classical systems. Universal size-energy law is found for homogeneous tetramers in the case of interaction potentials decaying predominantly as r⁻⁶. In the case of mixed tetramers, we also show under which conditions the universal line can approximately describe the size-energy ratio. The universal law can be used to extract ground-state energy from experimentally measurable structural characteristics, as well as for evaluation of theoretical interaction models.

Retrieving the excitation and polarization configurations in Coulomb explosion of a trimer driven by strong laser field

Ultrafast imaging and manipulating transient molecular structures in chemical reactions and photobiological processes is a fundamental but challenging goal for scientists. Theoretically, the challenge originates from the complex multiple-time-scale correlated electron dynamics and their coupling with the nuclei. Here, we employ classical polyatomic models for this kind of study and take the Coulomb explosion of argon and neon trimers in strong laser fields as an illuminating example. Our results demonstrate that the degree of asymmetry on the kinetic energy release (KER) spectrum, together with a Dalitz plot, constitutes a powerful tool for retrieving the ionization, excitation, and polarization configurations (femtosecond-to-attosecond time-scale electron dynamics) of trimers under strong-field radiation.

Dissociative Ionization of Argon Dimer by Intense Femtosecond Laser Pulses

We experimentally and theoretically studied dissociative ionization of argon dimer driven by intense femtosecond laser pulses. In the experiment, we measured the ion yield and the angular distribution of fragmental ions generated from the dissociative ionization channels of (1,1) (Ar₂²⁺ → Ar⁺ + Ar⁺) and (2,1) (Ar₂³⁺ → Ar²⁺ + Ar⁺) using a cold target recoil ion momentum spectroscopy. The channel ratio of (2,1)/(1,1) is 4.5-7.5 times of the yield ratio of double ionization to single ionization of argon monomer depending on the laser intensity. The measurement verified that the ionization of Ar⁺ is greatly enhanced if there exists a neighboring Ar⁺ separated by a critical distance. In addition, the fragmental ions exhibit an anisotropic angular distribution with the peak along the laser polarization direction and the full width at half maximum becomes broader with increasing laser intensity. Using a full three-dimensional classical ensemble model, we calculated the angle-dependent multiple ionization probability of argon dimer in intense laser fields. The results show that the experimentally observed anisotropic angular distribution of fragmental ions can be attributed to the angle-dependent enhanced ionization of the argon dimer in intense laser fields.

Quantum Halo States in Helium Tetramers

The universality of quantum halo states enables a comparison of systems from different fields of physics, as demonstrated in two- and three-body clusters. In the present work, we studied weakly bound helium tetramers in order to test whether some of these four-body realistic systems qualify as halos. Their ground-state binding energies and structural properties were thoroughly estimated using the diffusion Monte Carlo method with pure estimators. Helium tetramer properties proved to be less sensitive on the potential model than previously evaluated trimer properties. We predict the existence of realistic four-body halo ⁴He₂³He₂, whereas ⁴He₄ and ⁴He₃³He are close to the border and thus can be used as prototypes of quasi-halo systems. Our results could be tested by the experimental determination of the tetramers' structural properties using a setup similar to the one developed for the study of helium trimers.

Can dielectric spheres accurately model atomic-scale interactions?

We calculate the polarization portion of electrostatic interactions at the atomic scale using quantum mechanical methods such as density functional theories (DFT) and the coupled cluster approach, and using classical methods such as a surface charge method and a polarizable force field. The agreement among various methods is investigated. Using the coupled clusters method CCSD(T) with large basis sets as the reference, we find that for systems comprising two to six atoms and ions in S-states the classical surface charge method performs much better than commonly used DFT methods with moderate basis sets such as B3LYP/6-31G(d,p). The remarkable performance of the classical approach comes as a surprise. The present results indicate that the use of a rigorous formalism of classical electrostatics can be better justified for determining molecular interactions at intermediate distances than some of the widely used methods of quantum chemistry. PACS numbers: 41.20.Cv,32.10.Dk, 87.10.Tf.

Absorption Spectroscopy, a Tool for Probing Local Structures and the Onset of Large-Amplitude Motions in Small KAr(n) Clusters at Increasing Temperatures

Photoabsorption spectra of KArn (n = 1-10) are simulated at temperatures ranging between 5 and 25 K. The calculations associate a Monte Carlo (MC) method to sample cluster geometries at temperature T, with a one-electron ab initio model to calculate the ground-state and excited-state energies of the cluster. The latter model replaces the K(+) core electrons and all the electrons of the Ar atoms by appropriate pseudopotentials, complemented by core polarization potentials. It also provides the necessary oscillator strengths to simulate the spectra. Global optimization by basin-hopping is used in combination with MC simulation at low temperature (5 K) to identify the most stable isomer and remarkable isomers of ground-state KArn clusters, which are stable with respect to deformations of the order of those expected with Zero Point Energy motions. The absorption spectra calculated for each of these isomers at 5 K suggest that absorption spectroscopy can probe sensitively the local environment of K atom: surface location of K with respect to a close-packed Ar moiety, number of Ar atom in close vicinity, and local symmetry about K. Simulation at increasing temperatures, up to the evaporation limit of K out of the cluster, shows the onset of large amplitude motions above 20 K, when the K atom experiences a variety of local environments.

Strong field multiple ionization as a route to electron dynamics in a van der Waals cluster

We study the order in which a strong laser field removes multiple electrons from a van der Waals (vdW) cluster. The N2Ar, with an equilibrium T-shaped geometry, contains both a covalent and a vdW bond and serves as a simple yet rich example. Interestingly, the fragmenting double and triple ionizations of N2Ar with vdW bond breaking are favored when the vdW bond is aligned along the laser field polarization vector. However, the orientation of the covalent bond with respect to the laser field rules the triple ionization when both the covalent and vdW bonds are simultaneously broken. Electron-localization-assisted enhanced ionization and molecular orbital profile-dominated, orientation-dependent ionization are discussed to reveal the order of electrons release from different sites of N2Ar.

ROVIBRATIONAL BOUND STATES OF THE Ar2Ne COMPLEX

We report exact quantum dynamics calculations of the eigenstate energy levels for the bound rovibrational states of the Ar2Ne complex, across the range of J values for which such states are observed (J = 0–35). All calculations have been carried out using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phase-space optimized discrete variable representation, optimal separable basis, and preconditioned inexact spectral transform (PIST) methods, together with an effective massive parallelization scheme. The Ar2Ne energy levels were computed using a pair-wise Aziz potential plus a three-body correction, in Jacobi co-ordinates. Effective potentials for the radial co-ordinates are constructed, which reveal important physical insight into the two distinct dissociation pathways, Ar2Ne → NeAr + Ar and Ar2Ne → Ar2 + Ne . A calculation of the bound vibrational (J = 0) levels, computed using the Tang–Toennies potential, is also performed for comparison with results from the previous literature.

What is the shape of the helium trimer? A comparison with the neon and argon trimers

Despite its apparent simplicity and extensive theoretical investigations, the issue of what is the shape of the helium trimer is still debated in the literature. After reviewing previous conflicting interpretations of computational studies, we introduce the angle-angle distribution function as a tool to discuss in a simple way the shape of any trimer. We compute this function along with many different geometrical distributions using variational and diffusion Monte Carlo methods. We compare them with the corresponding ones for the neon and argon trimers. Our analysis shows that while Ne(3) and Ar(3) fluctuate around an equilibrium structure that is an equilateral triangle, (4)He(3) shows an extremely broad angle-angle distribution function, and all kinds of three-atom configurations must be taken into account in its description. Classifying (4)He(3) as either equilateral or linear or any other particular shape, as was done in the past, is not sensible, because in this case the intuitive notion of equilibrium structure is ill defined. Our results could help the interpretation of future experiments aimed at measuring the geometrical properties of the helium trimer.