Large Internuclear Distances Research Articles

Temperature-Dependent Kinetics for the Reactions of Fen- (n = 2-17) and FexNiy- (x + y = 3-9) with O2: Comparison of Pure and Mixed Metal Clusters with Relevance to Meteor Radio Afterglows and Surface Oxidation.

Rate constants and product branching fractions were measured from 300-600 K for Fen- + O2 (n = 2-17) and for 300-500 K for FexNiy- + O2 (x + y = 3-9) using a selected-ion flow tube (SIFT) apparatus. Rate constants for 46 species are reported. All rate constants increased with increasing temperature, and several were in excess of the Langevin-Gioumousis-Stevenson (LGS) capture rate at elevated temperatures. As with previously studied transition metal anion oxidation reactions, the collision limit is treated as the sum of the LGS limit along with a hard-sphere contribution, allowing for determination of activation energies. These values are compared to each other along with previous results for Nin-. Measured rate constants for all three series (Fen-, Nin-, and FexNy-) vary over a relatively narrow range (1-5 × 10-10 cm3 s-1 at 300 K) being at least 15% of the collision rate constant. All reaction rate constants increase with temperature, described by small activation energies of 0.5-4 kJ mol-1. The data are consistent with an anticorrelation between the electron binding energy and rate constant, previously noted in other systems. The Fen- reaction produces a larger population of higher energy electrons than do the Nin- reactions, with FexNiy- producing an intermediate amount. The results suggest that the overall rate constant is limited by a small energetic barrier located at a large internuclear distance where electrostatic forces dominate, causing the potentials to be similar across systems, while the product formation is determined by the shorter-range, valence portion of the potential, which varies widely between systems.

Extrapolation properties of the Morse-Long Range potential at large internuclear distances

The accuracy of the potential energy curves for diatomic molecules determined from experimental data is confirmed empirically with numerous examples in the literature. Usually PECs are determined from a limited set of experimental data and this in turns limits the range of internuclear distances where the shape of the potential is unambiguously fixed. While the uncertainty for interpolation could be assessed, the extrapolation is usually questionable and needs careful analyses. The Morse/Long-Range potential (Le Roy and Henderson, 2007) has been reported to have a built in long-range asymptotic behavior and therefore it is plausible to expect that one can expect good extrapolation properties and even possibility to determine important molecular parameters like De or/and Cm from limited set of experimental data. In this contribution we undertake a systematic study which confirms these expectations in the case of Ca2 ground state.

Physical origins of complex interference structures in harmonic emission from molecular ions stretched to large internuclear distances

High-order harmonic generation (HHG) from the molecular ions stretched to large internuclear distances is studied numerically and analytically in this work. We focus on the fine structure of the HHG spectrum related to the contribution of short electron trajectory. In our numerically solving the time-dependent Schrodinger equation (TDSE), we use a trajectory-dependent filtering procedure to separate the short-trajectory contribution from other contributions of long trajectory and multiple returns. Our TDSE results reveal that the short-trajectory HHG spectra of molecular ion with larger internuclear distance show some complex interference structures characterized by some remarkable dips, and that the position of the dip is sensitive to the laser parameters. With a developed model arising from strong-field approximation (SFA), we are able to identify the physical origins of the complex interference structures. In this model considered is the charge-resonance effect which induces the strong coupling between the ground state and the first excited state of the molecular ion at large internuclear distance. In this model, the well-known effect of two-center interference occurs in the form of the canonical momentum instead of the momentum related to the instantaneous velocity of the electron in the general SFA. It is shown that some dips in TDSE results arise from two-center interference of the electronic wave between these two atomic cores of the molecule in the ionization process, while others come from that in the recombination process. These ionization and recombination dips alternately appear in the HHG spectra from the formed complex interference structures. The main differences between the interference effects in the ionization process and the recombination process are twofold. Firstly, in the ionization process, the destructive two-center interference strongly suppresses the forming of the continuum wavepacket, while in the recombination process, the recombination of the rescattering electron with other bound eigenstates with small weights can also contribute to HHG bedsides the recombination of the ground state with the first excited state with large weights. As a result, in TDSE results, the ionization dips are deeper and more remarkable than the recombination ones. Secondly, in the recombination process, the Coulomb acceleration remarkably changes the de Broglie wavelength of the rescattering electron and therefore changes the position of the interference-induced dip. While in the ionization process, the Coulomb potential plays a small role in the interference effect. As a result, the interference dips in the ionization process and the recombination process differ from each other.

Atomic autoionization in the photo-dissociation of super-excited deuterated water molecules fragmenting into D+ + O+ + D.

We present the relaxation dynamics of deuterated water molecules via autoionization, initiated by the absorption of a 61 eV photon, producing the very rare D+ + O+ + D breakup channel. We employ the COLd target recoil ion momentum spectroscopy method to measure the 3D momenta of the ionic fragments and emitted electrons from the dissociating molecule in coincidence. We interpret the results using the potential energy surfaces extracted from multi-reference configuration interaction calculations. The measured particle energy distributions can be related to a super-excited monocationic state located above the double ionization threshold of D2O. The autoionized electron energy shows a sharp distribution centered around 0.5 eV, which is a signature of the atomic oxygen autoionization occurring in the direct and sequential dissociation processes of D2O+* at a large internuclear distance. In this way, an O+ radical fragment and a low-energy electron are created, both of which can trigger secondary reactions in their environment.

Secondary Kinetic Peak in the Kohn-Sham Potential and Its Connection to the Response Step.

We consider a prototypical 1D model Hamiltonian for a stretched heteronuclear molecule and construct individual components of the corresponding KS potential, namely, the kinetic, the N - 1, and the conditional potentials. These components show very special features, such as peaks and steps, in regions where the density is drastically low. Some of these features are quite well-known, whereas others, such as a secondary peak in the kinetic potential or a second bump in the conditional potential, are less or not known at all. We discuss these features building on the analytical model treated in Giarrusso et al. J. Chem. Theory Comput. 2018, 14, 4151. In particular, we provide an explanation for the underlying mechanism which determines the appearance of both peaks in the kinetic potential and elucidate why these peaks delineate the region over which the plateau structure, due to the N - 1 potential, stretches. We assess the validity of the Heitler-London Ansatz at large but finite internuclear distance, showing that, if optimal orbitals are used, this model is an excellent approximation to the exact wave function. Notably, we find that the second natural orbital presents an extra node very far out on the side of the more electronegative atom.

Origins of complex interference structures in harmonic emission from stretched molecular ion with large internuclear distances

We study high-order harmonic generation (HHG) from stretched molecular ions with large internuclear distances numerically and analytically. We focus on the fine structure of the HHG spectrum related to the contributions of short electron trajectory. In our simulations through numerical solution of time-dependent Schrodinger equation (TDSE), we use a trajectory-dependent filtering procedure to separate the short-trajectory contributions from other contributions of long trajectory and multiple returns. Our TDSE results show that the short-trajectory HHG spectra of molecular ion with larger internuclear distances show some complex interference structures characterized by some remarkable dips and the positions of the dips are sensitive to the laser parameters. With a developed model arising from strong-field approximation (SFA), we are able to identify the physical origins of the complex interference structures. This model considers the charge-resonance effect which induces the strong coupling between the ground state and the first excited state of the molecular ion at large internuclear distance. In this model, the well-known effect of two-center interference occurs in terms of the canonical momentum instead of the momentum related to the instantaneous velocity of the electron in the general SFA. We show that some dips in TDSE results arise from two-center interference of the electronic wave between these two atomic cores of the molecule in the ionization process, while others come from that in the recombination process. These ionization and recombination dips alternately appear in the HHG spectra, with forming the complex interference structures. The main differences between the interference effects in the ionization and the recombination processes are twofold. Firstly, in the ionization process, the destructive two-center interference strongly suppresses the forming of the continuum wavepacket, while in the recombination process, the recombination of the rescattering electron to other bound eigenstates with small weights can also contribute to HHG bedsides the recombination to the ground state and the first excited state with large weights. As a result, in TDSE results, the ionization dips are deeper and more remarkable than the recombination ones. Secondly, in the recombination process, the Coulomb acceleration remarkably changes the de Broglie wavelength of the rescattering electron and therefore changes the position of the interference-induced dip, while in the ionization process, the Coulomb potential plays a small role in the interference effect. As a result, the interference dips in the ionization and the recombination processes differ from each other.

Rabi-flopping signatures in below-threshold harmonic generation from the stretched H2 and N2 molecules in intense laser fields

We theoretically study the spectral and temporal fine subpeak structures in the below-threshold harmonic (BTH) spectra of the stretched H2 and N2 molecules by solving the one-electron time-dependent Schrödinger equation (TDSE) in conjunction with the wavelet time-frequency analysis. We identify such fine subpeaks come from the Rabi-flopping between the ground state and the first excited state using the simple two-state model. We also confirm that these subpeak structures in BTH spectra are common for molecules at large internuclear distances if two molecular states are strongly coupled. Furthermore, the spacing between the adjacent subpeaks in BTH spectra can be determined approximately by analyzing the induced dipole moment in the time domain.

Electron angular correlation in nonsequential double ionization of molecules by counter-rotating two-color circularly polarized fields.

Electron correlation in nonsequential double ionization (NSDI) of molecules by counter-rotating two-color circularly polarized (TCCP) fields is investigated with a three-dimensional classical ensemble model. Numerical results indicate that the two electrons from NSDI of molecules in counter-rotating TCCP fields show strong angular correlation and the angular correlation behavior sensitively depends on the internuclear distance. With the internuclear distance increasing, the dominant behavior of electron pairs evolves from correlation to anti-correlation. It leaves a clear imprint on the ion momentum distributions, which exhibit an inverted Y-shape distribution at a small internuclear distance and a triangle-shape distribution at a large internuclear distance. Back analysis indicates that the asymmetric electron energy sharing by soft recollision and longer time delay of double ionization are responsible for more anti-correlated emissions at large internuclear distances.

Long-Range Atom–Ion Rydberg Molecule: A Novel Molecular Binding Mechanism

We present a novel binding mechanism where a neutral Rydberg atom and an atomic ion form a molecular bound state at a large internuclear distance. The binding mechanism is based on Stark shifts and level crossings that are induced in the Rydberg atom due to the electric field of the ion. At particular internuclear distances between the Rydberg atom and the ion, potential wells occur that can hold atom–ion molecular bound states. Apart from the binding mechanism, we describe important properties of the long-range atom–ion Rydberg molecule, such as its lifetime and decay paths, its vibrational and rotational structure, and its large dipole moment. Furthermore, we discuss methods of how to produce and detect it. The unusual properties of the long-range atom–ion Rydberg molecule give rise to interesting prospects for studies of wave packet dynamics in engineered potential energy landscapes.

Electric-field-induced wave-packet dynamics and geometrical rearrangement of trilobite Rydberg molecules

We investigate the quantum dynamics of ultra-long-range trilobite molecules exposed to homogeneous electric fields. A trilobite molecule consists of a Rydberg atom and a ground-state atom, which is trapped at large internuclear distances in an oscillatory potential due to scattering of the Rydberg electron off the ground-state atom. Within the Born-Oppenheimer approximation, we derive an analytic expression for the two-dimensional adiabatic electronic potential energy surface in weak electric fields valid up to 500 V/m. This is used to unravel the molecular quantum dynamics employing the Multi-Configurational Time-Dependent Hartree method. Quenches of the electric field are performed to trigger the wave packet dynamics including the case of field inversion. Depending on the initial wave packet, we observe radial intra-well and inter-well oscillations as well as angular oscillations and rotations of the respective one-body probability densities. Opportunities to control the molecular configuration are identified, a specific example being the possibility to superimpose different molecular bond lengths by a series of periodic quenches of the electric field.

Theoretical study of the Coriolis effect in LiNa, LiK, and LiRb molecules.

The non-adiabatic electronic matrix elements, LΠΣ(R), that arise from the spin-conserving electron-rotational interactions between all mΣ+ and mΠ states, where multiplicity m = 1, 3, converging to the lowest three dissociation limits of Li-containing alkali diatomics, LiM (M = Na, K, Rb), were calculated ab initio up to large internuclear distances, R. The required electronic wavefunctions were obtained within the framework of the multi-reference configuration interaction treatment of the two-valence-electron problem constructed using small-core scalar-relativistic effective core potentials and l-independent core-polarization potentials. A least squares analysis of the ab initio functions at large internuclear distances in conjunction with long-range perturbation theory (LRPT) revealed three different asymptotic behaviors of the LΠΣ(R → +∞)-functions: const. + β[n]/Rn, characterized by n = -1, 3 and 6. The asymptotic coefficients β[n], extracted from the point-wise ab initio data, were found to be in agreement with their LRPT counterparts, which were evaluated analytically using the relevant atomic parameters. The mass dependence of the LΠΣ matrix elements was investigated analytically and numerically. To confirm the reliability of the LΠΣ(R)-functions and interatomic potentials at small and intermediate distances, the empirical q-factors available for the D1Π-states of all LiM molecules studied were compared with their theoretical counterparts derived from the present ab initio data.

Ultrafast manipulation of the weakly bound helium dimer

Controlling the interactions between atoms with external fields opened up new branches in physics ranging from strongly correlated atomic systems to ideal Bose and Fermi gases and Efimov physics. Such control usually prepares samples that are stationary or evolve adiabatically in time. On the other hand, in molecular physics external ultrashort laser fields are employed to create anisotropic potentials that launch ultrafast rotational wave packets and align molecules in free space. Here we combine these two regimes of ultrafast times and low energies. We apply a short laser pulse to the helium dimer, a weakly bound and highly delocalized single bound state quantum system. The laser field locally tunes the interaction between two helium atoms, imparting an angular momentum of $2\hbar$ and evoking an initially confined dissociative wave packet. We record a movie of the density and phase of this wave packet as it evolves from the inside out. At large internuclear distances, where the interaction between the two helium atoms is negligible, the wave packet is essentially free. This work paves the way for future tomography of wave packet dynamics and provides the technique for studying exotic and otherwise hardly accessible quantum systems such as halo and Efimov states.

A cautionary tale: Problems in the valence-CASSCF description of the ground state (X1Σ+) of BF.

In the full optimized reaction space and valence-complete active space self-consistent field (vCAS) methods, a set of active orbitals is defined as the union of the valence orbitals on the atoms, all possible configurations involving the active orbitals are generated, and the orbitals and configuration coefficients are self-consistently optimized. Such wave functions have tremendous flexibility, which makes these methods incredibly powerful but can also lead to inconsistencies in the description of the electronic structure of molecules. In this paper, the problems that can arise in vCAS calculations are illustrated by calculations on the BH and BF molecules. BH is well described by the full vCAS wave function, which accounts for molecular dissociation and 2s-2p near-degeneracy in the boron atom. The same is not true for the full vCAS wave function for BF. There is mixing of core and active orbitals at short internuclear distances and swapping of core and active orbitals at large internuclear distances. In addition, the virtual 2π orbitals, which were included in the active space to account for the 2s-2p near degeneracy effect, are used instead to describe radial correlation of the electrons in the F2pπ-like pairs. Although the above changes lead to lower vCAS energies, they lead to higher vCAS+1+2 energies as well as irregularities and/or discontinuities in the potential energy curves. All of the above problems can be addressed by using the spin-coupled generalized valence bond-inspired vCAS wave function for BF, which includes only a subset of the atomic valence orbitals in the active space.

Long-range asymptotics of exchange energy in the hydrogen molecule

The exchange energy, i.e., the splitting ΔE between gerade and ungerade states in the hydrogen molecule, has proven very difficult in numerical calculation at large internuclear distances R, while the known results are sparse and highly inaccurate. On the other hand, there are conflicting analytical results in the literature concerning its asymptotics. In this work, we develop a flexible and efficient numerical approach using explicitly correlated exponential functions and demonstrate highly accurate exchange energies for internuclear distances as large as 57.5 a.u. This approach may find further applications in calculations of inter-atomic interactions. In particular, our results support the asymptotics form ΔE ∼ R5/2e-2R, but with the leading coefficient being 2σ away from the analytically derived value.

Asymptotic solution of a Coulomb multichannel scattering problem with a nonadiabatic channel coupling

We develop a well-posed multiparticle Coulomb scattering problem based on asymptotic solutions of a Coulomb multichannel scattering problem constructed in the adiabatic representation. A key feature of the studied problem is that the nonadiabatic channel coupling matrix is nontrivial at large internuclear distances. We consider the scattering problem in the case with an arbitrary momentum value and study solutions for small channel coupling matrix values in detail, constructing explicit representations for the asymptotic solution of the scattering problem.

An effective Xe+–Xe interaction potential for electric propulsion systems

An effective Xe+–Xe interaction potential for electric propulsion systems is proposed based on both spin–orbit free interaction potentials and the screened-Coulomb potential. The model not only conforms with the potential obtained by an ab initio method at large internuclear distances but also matches well with the potential derived from experimental scattering data at short internuclear distances. The scattering angles and differential cross sections computed by the effective potential are in good agreement with those obtained by the Morse potential in low-energy regions and those via two screened-Coulomb potentials (the Ziegler–Biersack–Littmark and Zinoviev potential) in high-energy regions, respectively. To further validate the effective potential, a particle-in-cell method with a Monte Carlo collisions technique, coupled with a direct method for solving the scattering equation, was applied to simulate the collisions of 1500-eV and 7000-eV single-charged xenon ions with background xenon atoms in a test cell. The simulated currents on the inner cylinder, exit plate, exit orifice, and front plate are calculated by different potentials. Results show that the effective potential can give a good prediction of the Xe+–Xe elastic collisions in the wider energy region compared with the Morse, Ziegler–Biersack–Littmark, and Zinoviev potentials.

Double-slit effect on laser induced electron diffraction of dimers

We theoretically study strong-field ionization of dimers with large internuclear distance in linearly and circularly polarized light fields. By numerically solving the time-dependent Schrödinger equation (TDSE), we show that the double-slit interference effect plays a significant role in the laser-induced electron diffraction of dimers. And the prominent double-slit interference structures are sensitive to the symmetry and orientation of the orbitals of dimers. We then develop a semi-classical trajectory model including the double-slit effect by coherently summing up the contributions of two separated atoms. This model explains the interference fringes of TDSE simulations. And the effect of long-range potential on the double-slit interference is discussed. This work provides intuitive physical insights into how dimers being ionized in strong laser fields and has implications to extract ultrafast dynamics of polyatomic molecules from strong-field photoelectron spectroscopy.

Hidden-crossing explanation of frozen-planet resonances in antiprotonic helium; their positions and widths

The existence of the frozen-planet states in antiprotonic helium pHe+, characterized by an excited electron and strongly localized antiproton in a potential well at large internuclear distance between p and He+, was predicted in 1991 (K. Richter, J.M. Rost, R. Thurwachter, J.C. Briggs, D. Wintgen, E.A. Solov’ev, Phys. Rev. Lett. 66, 149 (1991)) in an analysis of the adiabatic Born-Oppenheimer potentials. However, no explanation for appearance of this well and no data for positions and widths of these states were given. Here we show that the formation of an outer well is due to the hidden-crossings of S-type. We also calculate positions and widths of these resonances.There are two adiabatic mechanisms that explain decay of the frozen planet states into the inner well: (i) tunneling of antiproton through the barrier and (ii) transition via S-type of hidden-crossings. The third competing mechanism that determines the lifetime of the frozen planet states is the radiative decay of the excited electron.

Attosecond pulse generation from $H_2^ + $H2+ ions using a multicolor beam superposition method.

The behavior of the high-order harmonics and output attosecond pulses from hydrogen molecule ions with various internuclear distances that are exposed to high intensity incoming pulses are investigated. The incoming pulses that are spectrally wide yield from a superposition of monochromatic beams with a constant frequency distance. Our simulations show that the most intense and shortest attosecond pulses can result from hydrogen molecular ions with large internuclear distances which are exposed to irradiation of intense pulses with a frequency width greater than 0.03 a.u.

Inelastic processes in oxygen–hydrogen collisions

ABSTRACT New accurate theoretical rate coefficients for (de)-excitation and charge transfer in low-energy O + H, O+ + H− and O− + H+ collisions are reported. The calculations of cross-sections and rate coefficients are performed by means of the quantum probability current method, using full configuration interaction ab initio electronic structure calculations that provide a global description of all 43 lowest molecular states from short to asymptotic internuclear distances. Thus, both long- and short-range non-adiabatic regions are taken into account for the first time. All the doublet, quartet and sextet OH molecular states, with excitation energy asymptotes up to 12.07 eV, as well as the two lowest ionic states with the asymptotes O−H+ and O+H− are treated. Calculations are performed for the collision energy range 0.01–100eV and the temperature range 1 000–10 000 K. The mechanisms underlying the processes are analysed: it is shown that the largest rate coefficients, with values exceeding 10−8 cm3 s−1, are due to ionic–covalent interactions present at large internuclear distances, while short-range interactions play an important role for rates with moderate values involved in (de)-excitation processes. As a consequence, a comparison of the present data with previously published results shows that differences of up to several orders of magnitude exist for rate coefficients with moderate values. It is worth pointing out the relatively large rate coefficients for triplet–quintuplet oxygen transitions, as well as for transitions between the O$(\rm 2p^{3}3s\, ^{5}$So) and O$(\rm 2p^{3}3p\, ^{5}$P) levels of the oxygen triplet and H(n = 2) levels. The calculated data are important for modelling stellar spectra, leading to accurate oxygen abundances.