Two-center Molecules Research Articles

Probing the interplay between geometric and electronic-structure features via high-harmonic spectroscopy.

We present molecular-frame measurements of the recombination dipole matrix element (RDME) in CO2, N2O, and carbonyl sulfide (OCS) molecules using high-harmonic spectroscopy. Both the amplitudes and phases of the RDMEs exhibit clear imprints of a two-center interference minimum, which moves in energy with the molecular alignment angle relative to the laser polarization. We find that whereas the angle dependence of this minimum is consistent with the molecular geometry in CO2 and N2O, it behaves very differently in OCS; in particular, the phase shift which accompanies the two-center minimum changes sign for different alignment angles. Our results suggest that two interfering structural features contribute to the OCS RDME, namely, (i) the geometrical two-center minimum and (ii) a Cooper-like, electronic-structure minimum associated with the sulfur end of the molecule. We compare our results to ab initio calculations using time-dependent density functional theory and present an empirical model that captures both the two-center and the Cooper-like interferences. We also show that the yield from unaligned samples of two-center molecules is, in general, reduced at high photon energies compared to aligned samples, due to the destructive interference between molecules with different alignments.

Atomic few-body systems with muonium

Properties of some few-body systems which include one positively charged muon and two electrons are discussed. In particular, we consider the negatively charged muonium ion Mu (or ) and four-body MuPs (or ) systems, each of which has only one stable bound (ground) state. The problem of annihilation of the electron–positron pair(s) in the MuPs system is investigated. The hyperfine structure splitting of the ground state in the MuPs system evaluated with our expectation value of the muon-positron delta-function is 23.05758 MHz. Another group of interesting four-body neutral systems investigated in this study includes the and ‘quasi-molecules’. These quasi-molecules are formed in large numbers when positively charged muons slow down in liquid hydrogen, or in liquid deuterium and/or tritium. The properties of these systems are unique, since they occupy an intermediate position between actual two-center molecules and one-center atoms.

Orbital geometry determined by orthogonal high-order harmonic polarization components

We study the polarization state of high-order harmonics produced by linearly polarized light interacting with two-center molecules. By generating high-harmonic ``polarization maps'' from Radon transformations of excited electronic wave functions, we show that the polarization of the harmonic radiation can be linked to the geometry of the molecular orbital. While in the Radon transformation the plane-wave approximation for the rescattered electron is implicitly assumed, numerical solutions of the two-dimensional time-dependent Schr$\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$dinger equation, in which this approximation is not made, confirm the validity of this topological connection. We also find that measuring two orthogonal amplitude components of the harmonics provides a method for quantum tomography that substantially improves the quality of reconstructed molecular states.

Quantum path interferences of electron trajectories in two-center molecules

We report a new quantum path interference effect of electron trajectories in high-order harmonic generation (HHG) from two-center molecules, in which the interference minima are mainly located in the high-energy portion of HHG spectrum. The quantum calculations of the time-frequency analyses and the classical results of the electron trajectories demonstrate very good agreement and reveal that the positions of the interference minima are associated with the cutoff of various kinds of molecular electron trajectories. The interference fringes within a half optical cycle can be clearly seen in the time-frequency analysis spectrum. Moreover, the characteristics of both the HHG in frequency domain and the corresponding attosecond pulse generation in time domain permit tracing back the interference information of these electron trajectories. These interference phenomena offer new possibilities for getting insight into the attosecond electronic dynamics in molecules.

Mechanisms of ultrahigh-order harmonic generation

We analyze mechanisms of high-order harmonic generation from two-center molecules at large internuclear separations in linearly polarized laser fields. Since laser-driven electrons acquire instantaneous kinetic energies of up to 8 times the ponderomotive potential ${U}_{\mathrm{p}}$, recombination at an appropriately placed nucleus leads to ultrahigh-order harmonic emission [P. Moreno, L. Plaja, and L. Roso, Phys. Rev. A 55, R1593 (1997)]. By solving the time-dependent Schr\"odinger equation for model systems, we show that this mechanism is only efficient if the single-particle orbital of the electron is coherently delocalized over the two potential wells. This is realized in the ground state of a one-electron molecular ion. In a neutral molecule or in a molecular ion created by ionization of a neutral molecule at large internuclear distance, the coherence is destroyed by electron-electron correlation.

High-order harmonic generation from two-center molecules: Time-profile analysis of nuclear contributions

We solve the exact three-dimensional time-dependent Schr\odinger equation for ${{\mathrm{H}}_{2}}^{+}$ (with fixed nuclei) interacting with an intense laser pulse with an arbitrary oriented linear polarization. We find that at equilibrium internuclear distance, the ionization probability of ${{\mathrm{H}}_{2}}^{+}$ is maximum for the parallel orientation of the molecule with respect to the laser polarization, and is minimum for the perpendicular orientation. The contribution of each nucleus to the harmonic spectrum is evaluated, so that interference effects between the two contributions are assessed unambiguously. We show that every half-cycle, high order harmonics are emitted by each nucleus when the electron wave packet returns for a recollision with both nuclei, and that the resulting harmonic emission is predominant for the nucleus that experiences the first recollision. In general, each nucleus emits both even and odd harmonics, but even harmonics are destroyed by interferences between contributions from each nucleus. In general, this destructive interference occurs over a large spread of harmonic orders, which depends on the angle between the molecular axis and the laser polarization.

Electron diffraction in above-threshold ionization of molecules

We calculate the spectra and angular distributions of electrons from ionization of two-center molecules in linearly polarized strong laser pulses. A fully numerical quantum-mechanical method is compared to a simple semiclassical model designed to describe the diffraction of electrons when they recollide with the two-center core. Within both approaches, clear signatures of diffraction are found in the angular distributions. We discuss the dependence of electron diffraction on the internuclear distance and on the molecular orientation.

Role of the Intramolecular Phase in High-Harmonic Generation

We study numerically the generation of high-order harmonics by two-center molecules for arbitrary angles between the molecular axis and the laser polarization axis. For fixed angle, the harmonic spectrum exhibits a minimum at a frequency which is independent of the laser parameters. The amplitude of each harmonic is strongly angle dependent, and a pronounced minimum is found at the same angle where a sudden jump in the harmonic phase occurs. By calculating the spatial dependence of the harmonic amplitudes and phases, we are able to explain these effects in terms of interfering contributions from various regions within the molecule.

Electronic Isomerism: Symmetry Breaking and Electronic Phase Diagrams for Diatomic Molecules at the Large-Dimension Limit

We present symmetry-breaking and electronic-structure phase diagrams for two-center molecules with one and two electrons in the limit of a space of large dimensions. For one electron, the phase diagram in the internuclear distance-nuclear charge (R-Z) plane has two different stable phases. One corresponds to the electron equidistant from the two nuclei; the other where the electron is localized on one of the nuclei. The phase diagram for two electrons with two equally charged centers shows three different stable phases corresponding to different electronic-structure configurations. This phase diagram is characterized by a bicritical point. When the charges are unequal, the phase diagram shows only two stable phases, covalent and ionic. This phase diagram is characterized by a tricritical point, where the first-order transition line meets with the second-order transition line. The role of the inter-electron Coulombic repulsion in giving rise to different electronic structures and the distinction between a continuous deformation of one structure into another versus a discontinuous, so-called first-order, transition, where two isomers can coexist, are emphasized. The connection to the spectroscopic notion of intersecting potential energy curves is discussed.

M-like X-ray transitions in superheavy quasi-molecules

The anisotropy of the molecular orbital X-ray emitted in heavy-ion collisions was investigated for 18 systems with combined atomic numbers between 104 and 184. Well defined anisotropy peaks were observed which may reflect M-like transitions in the corresponding superheavy two-center molecules.

On the definition of the atomic charge in a molecule

Atomic charges calculated by various methods for model two-center molecules have been compared with corresponding electron-count functions. Varying the overlap and polarity conditions in the model system, it could be found out under what conditions the individual definitions fail to predict physically reasonable values of atomic charges.