Internuclear Distance Research Articles

Interference effects in the photoelectron spectrum of the NeKr dimer and vibrationally selected interatomic Coulombic decay

In our work we study the interatomic Coulombic decay (ICD) in the NeKr dimer, where after $2s$ ionization of the Ne, the system relaxes and the excess energy is utilized to ionize the Kr. The temporal evolution of the ICD process in NeKr has been recently measured and theoretically explained by Trinter et al. [Chem. Sci. 13, 1789 (2022)]. Here we focus on two other main goals. The first goal regards the found interference effects in the photoemission (PE) spectrum, which are unusual phenomena in noble gas dimers. They result from the coherently excited vibrational energy levels and substantial dependence of the large ICD decay width on the internuclear distance. The PE spectrum reacts sensitively to changes in the potential energy curve (PEC) of the $2s$ ionized state, and we modified the available ab initio PEC in such a way that satisfactory agreement between theoretical and experimental data is achieved. The impact of isotope masses on the PE spectrum is briefly discussed and used in the determination of the PEC. Our second main goal concerns the nuclear motion during the ICD process. Here we investigate the impact of different vibrationally excited states of the electronic ground state on the ICD-electron and kinetic energy release (KER) spectra. To transfer our vibrationally selected ICD model to a realizable experiment, we also present the impact of temperature on the ICD-electron spectrum. Finally, our studies are complemented by comparing the directly computed KER spectrum to the mirror image of the ICD-electron spectrum, which coincide under certain conditions.

Integrated Assessment of the Structure and Dynamics of Solid Proteins.

Understanding macromolecular function, interactions, and stability hinges on detailed assessment of conformational ensembles. For solid proteins, accurate elucidation of the spatial aspects of dynamics at physiological temperatures is limited by the qualitative character or low abundance of solid-state nuclear magnetic resonance internuclear distance information. Here, we demonstrate access to abundant proton-proton internuclear distances for integrated structural biology and chemistry with unprecedented accuracy. Apart from highest-resolution single-state structures, the exact distances enable molecular dynamics (MD) ensemble simulations orchestrated by a dense network of experimental interproton distance boundaries gathered in the context of their physical lattices. This direct embedding of experimental ensemble distances into MD will provide access to representative, atomic-level spatial details of conformational dynamics in supramolecular assemblies, crystalline and lipid-embedded proteins, and beyond.

Laser-induced Coulomb explosion imaging of alkali-metal dimers on helium nanodroplets

Alkali dimers, $\mathrm{Ak}_2$, residing on the surface of He nanodroplets are doubly ionized due to multiphoton absorption from an intense, 50-fs laser pulse leading to fragmentation into a pair of alkali cations. Based on the measured kinetic energy distributions, $P(E_{\text{kin}})$, of the $\mathrm{Ak}^+$ fragment ions, we retrieve the distribution of internuclear distances, $P(R)$, via the $\mathrm{Ak}_2^{2+}$ potential curve. Results are obtained for $\mathrm{{Na}_2}$, $\mathrm{K}_2$, $\mathrm{Rb}_2$, and $\mathrm{Cs}_2$ in both the 1 $^1\Sigma_{g}^+$ ground state and in the lowest-lying triplet state 1 $^3\Sigma_{u}^+$, and for $\mathrm{Li}_2$ in the 1 $^3\Sigma_{u}^+$ state. For $\mathrm{Li}_2$, $\mathrm{K}_2$, and $\mathrm{Rb}_2$, the center of the measured $P(R)$'s is close to the center of the wave function, $\Psi(R)$, of the vibrational ground state in the 1 $^1\Sigma_{g}^+$ and 1 $^3\Sigma_{u}^+$ states, whereas for $\mathrm{{Na}_2}$ and $\mathrm{{Cs}_2}$ small shifts are observed. For all the $\mathrm{{Ak}_2}$, the width of the measured $P(R)$ is broader than $|\Psi(R)|^2$ by a factor of 2-4. We discuss that resonance effects in the multiphoton ionization and interaction of the $\mathrm{Ak}^+$ ion with the He droplet give rise to the observed deviations of $P(R)$ from $|\Psi(R)|^2$. Despite these deviations, we deem that timed Coulomb explosion will allow imaging of vibrational wave packets in alkali dimers on He droplets surfaces.

Optical, structural and physical properties of fluoride doped bioactive glasses

Glasses of composition (60–x)NaPO3-25B2O3-xCaF2-15MgO, where x = 2.5, 5, 7.5, 10 and 12.5 mol% were synthesized by melt quench method at 1100 °C. The X ray diffractogram (XRD) of glass samples reveals their amorphous nature. Density of synthesized samples was found to increase when CaF2 composition varied from 2.5 to 12.5 mol%. UV visible absorption spectra of the samples show broad absorption band at nearly about 215 nm. The optical band gaps were estimated from the optical absorption spectra by using Tauc plots. An increase of band gap energies was observed due to the creation of ionic cross-links within the glass structure. The various other parameters like calcium ion concentration, polaron radius, internuclear distance and optical basicity values were calculated using the refractive index and density of glasses. For in vitro studies, the glasses were soaked in Simulated Body Fluid (SBF) solution for 14 days. The XRD and Infrared (IR) studies carried out on samples post immersion in SBF solution for 14 days have revealed the formation of hydroxyapatite layer.

Backward scattering impact on the photoionization time delay of asymmetric molecules

The time delays in photoionization of asymmetric diatomic molecules are numerically investigated using the technique of reconstruction of attosecond beating by interference of two-photon transitions (RABBITTs). Our results show that two different oscillatory structures appear in the molecular photoionization time delays as the photoelectron energy changes, and the contribution of these two oscillations to the time delays varies with the nuclear distance. By using an analytical interference model, we demonstrate that one oscillation is traced back to the two-center interference and the other originates from the photoelectrons backward scattering. With the increases of internuclear distance, the backward scattering impact on the time delays is gradually distinct in a particular direction of the photoionization. The amplitude of the backward scattering induced oscillation decreases when the photoelectron energy increases. Furthermore, the stereo RABBITT time delays display a distinct downshift as the increases of asymmetry degree of molecule, which is attributed to the increasing depth of the additional Coulomb potential experienced by the ionized electron.

PESPIP: Software to fit complex molecular and many-body potential energy surfaces with permutationally invariant polynomials.

We wish to describe a potential energy surface by using a basis of permutationally invariant polynomials whose coefficients will be determined by numerical regression so as to smoothly fit a dataset of electronic energies as well as, perhaps, gradients. The polynomials will be powers of transformed internuclear distances, usually either Morse variables, exp(-ri,j/λ), where λ is a constant range hyperparameter, or reciprocals of the distances, 1/ri,j. The question we address is how to create the most efficient basis, including (a) which polynomials to keep or discard, (b) how many polynomials will be needed, (c) how to make sure the polynomials correctly reproduce the zero interaction at a large distance, (d) how to ensure special symmetries, and (e) how to calculate gradients efficiently. This article discusses how these questions can be answered by using a set of programs to choose and manipulate the polynomials as well as to write efficient Fortran programs for the calculation of energies and gradients. A user-friendly interface for access to monomial symmetrization approach results is also described. The software for these programs is now publicly available.

Internuclear distance measurements between 1H and 14N in multi-component rigid solids at fast MAS

1H-14N internuclear distances are readily and accurately measured using the symmetry-based phase-modulated resonance-echo saturation-pulse double-resonance (PM-S-RESPDOR) method in rigid solids. The fraction curve, (S0 – S’)/S0, is represented by a single variable of a 1H-14N heteronuclear dipolar coupling, where S0 and S’ are the PM-S-RESPDOR signal intensity with and without 14N PM saturation pulse, respectively. Analytical equation of the fraction curve easily provides 1H-14N couplings. This treatment is only applicable when NH proton resonance is well separated from the other proton peaks. With the limited 1H resolution even at fast MAS > 60 kHz, unfortunately, this condition is not necessarily satisfied especially in multi-component systems which often appear in pharmaceutical applications. To overcome this problem, T-HMQC filtering is applied to suppress the 1H signals other than NH proton prior to the PM-S-RESPDOR experiments. The method is well demonstrated on two components acetaminophen-oxalic acid (APAP-OXA) systems. Further analysis of orientation dependence of T-HMQC and PM-S-RESPDOR shows that the analytical equation can be safely applied in the analysis of T-HMQC filtered PM-S-RESPDOR experiments.

ARSENY: A program for computing inelastic transitions via hidden crossings in one-electron atomic ion–ion collisions with classical description of nuclear motion

The ARSENY program is intended to compute cross-sections of inelastic transitions via hidden crossings upon slow one-electron atomic ion–ion collisions using the approximation of classical description of nuclear motion in the collision energy region E<20 KeV/nucleon. Particular attention is paid to the calculation of the analytical properties of adiabatic potential energy curves of the two-center Coulomb problem for complex values of the internuclear distance. Complex branch points and hidden crossings are calculated and their significance for the dynamics of one-electron collisional systems is revealed. Benchmark calculations of cross sections for charge exchange, excitation, and ionization in slow He2++H(1s) collisions are presented and compared with experimental data. Program summaryProgram Title: ARSENYCPC Library link to program files:https://doi.org/10.17632/n43srxwdnm.1Licensing provisions: CC By 4.0Programming language: FORTRAN 90/95. Compilers: Intel(R) Visual Fortran Compiler 19.0.4.245 [IA-32]Nature of problem: The processes of charge exchange, excitation, and ionization in one-electron atomic ion–ion collisions in a low-temperature plasma are actively studied in astrophysics and tokamak Charge-eXchange Recombination Spectroscopy (CXRS) Edge diagnostics in ITER [1–7]. Numerical calculations of cross sections for charge exchange, excitation, and ionization for slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion have been conventionally implemented, in particular, by the electron-nuclear dynamics approach [8] and the close-coupled channel method using basis functions of the two-center Coulomb problem (see, e.g., [9–13]). However, with real-valued internuclear distance these approaches did not allow for the dynamical structure of discrete-discrete and discrete-continuous transitions in the two-center Coulomb problem. This disadvantage manifests itself in the disagreement between the theoretical and experimental cross-sections at small velocity of ions [13–15]. In a number of papers [1,14,16–20] the dynamical structure of the transitions is considered in terms of hidden crossing of potential curves, when using the analytic continuation to a complex plane of the internuclear distance. This approach is implemented in the ARSENY program aimed at computing cross sections of inelastic discrete-discrete and discrete-continuous transitions via hidden crossings for slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion announced in [1]. Benchmark calculations of cross sections for charge exchange, excitation, and ionization in slow He2++H(1s) collisions are presented and compared with experimental data.Solution method: The potential energy curves E=E(R) and the separation constant λ=λ(R) depending on the real-valued and complex-valued parameter R of the two-center Coulomb problem are calculated from the minimization condition for a quadratic functional corresponding to a pair of nonlinear equations with respect to a pair of unknowns E(R) and λ(R) by iterating three-term recurrent relations [21,22] using a mean least square method [23]. These equations are obtained from the known recurrent relations for the expansion coefficients of quasiradial and quasiangular spheroidal Coulomb functions. The series of branching points Rc sought for in the complex plane of internuclear distance R and the hidden crossings of complex potential energy curves E(R) are calculated by an iterative method using the known analytical behavior in the form of a square root of difference E(R)−E(Rc) in the vicinity of the unknown branch points Rc. Calculations of cross-sections of inelastic transitions via hidden crossings for the slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion are carried out by integration over the impact parameter of the nonadiabatic transition probability expressed in terms of the Stückelberg parameter determined integral of difference of imaginary parts of each pair of complex potential energy curves E(R) by a contour around the branching point Rc [18,19].Additional comments including restrictions and unusual features: In calculations of cross sections and required branch points, about 220 adiabatic states of the lower part of the discrete spectrum of the two-center problem are used.

Linking the Interatomic Exchange-Correlation Energy to ExperimentalJ-Coupling Constants

The main aim of the current work is to find an experimental connection to the interatomic exchange-correlation energy as defined by the energy decomposition method Interacting Quantum Atoms (IQA). A suitable candidate as (essentially) experimental quantity is the nuclear magnetic resonance (NMR) J-coupling constant denoted 3J(H,H'), which a number of previous studies showed to correlate well with QTAIM's delocalization index (DI), which is essentially a bond order. Inspired by Karplus equations, here, we investigate correlations between 3J(H,H') and a relevant dihedral angle in six simple initial compounds of the shape H3C-YHn (Y = C, N, O, Si, P, and S), N-methylacetamide (as prototype of the peptide bond), and five peptide-capped amino acids (Gly, Ala, Val, Ile, and Leu) because of the protein direction of the force field FFLUX. In conclusion, except for methanol, the inter-hydrogen exchange-correlation energy Vxc(H,H') makes the best contact with experiment, through 3J(H,H'), when multiplied with the internuclear distance RHH'.

Ellipticity properties of symmetric molecules &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ {\text{H}}_{\text{2}}^ + $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221946_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221946_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; in strong and short-wavelength laser fields

Ellipticity properties of high-order harmonic generation (HHG) from symmetric molecules &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$ {\text{H}}_{\text{2}}^ + $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221946_M6.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221946_M6.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; in strong and short wavelength (less than 800nm) laser fields are numerically investigated. In this study, the ellipticity of harmonic is compared with the corresponding harmonic spectrum and dipole, and the calculation results are analyzed and the results obtained at different laser intensities, different laser wavelengths, different internuclear distances and different orientation angles are compared with each other. Our numerical simulations show that the influences of laser intensity, laser wavelength, internuclear distance and orientation angle on the ellipticity of harmonic are different. Especially in a two-center interference region, the excited state plays an important role in the HHG, but the effects of the excited state on the ellipticity of harmonic are different at different orientation angles. Further analysis shows that these different effects are due to the influence of the excited state on the harmonic yield. Using the numerical scheme, it is determined that in the two-center interference region, the excited state plays an important role in the parallel harmonic spectrum, while the effects of the excited state on the perpendicular harmonics at different angles are all very small, which results in different phase differences between the accurate harmonic spectrum and the harmonic spectrum only returning to the ground state. Overall, the relative yields of the accurate perpendicular harmonics are lower (higher) than those of the accurate parallel harmonics, but the intensities of the perpendicular harmonics, which only return to the ground state, are comparable to (or farther away from) those of the parallel harmonics which are only to return to ground state in the two-center interference regions. Therefore, the small (large) intensity ratio between the accurate perpendicular harmonic and accurate parallel harmonic can be attributed to the contributions of the excited state to harmonics. Then we can conclude that the harmonic spectra that only go back to the ground state show high (small) ellipticity, whereas the accurate harmonic spectra show small (high) ellipticity, resulting in a strong angle dependence of the influence of the excited state on the ellipticity of harmonic. In addition, in the high-order harmonic plateau region, the relative yields of harmonics can be well predicted by the corresponding dipoles, indicating the applicability of tunneling pictures and plane wave approximation in the strong and short-wave laser fields. When the ellipticity of harmonic occurs in the interference region due to the two-center characteristics of the symmetric potential, the results show that the polarization measurement can also be used to detect the structures of symmetric molecules and track the dynamic behaviors of excited states.

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.

Аналітичні та експериментальні дослідження властивостей шлаків та шлакоутворюючих сумішей сталеплавильного виробництва

The aim of the study is to analyze and generalize the properties of slags within the CaO-SiO2-Al2O3-MgO-CaF2 system in different ratios of components and their concentrations, which is the basis of refining slags in modern steelmaking. To ensure the technological functions, the slag melt should have a set of optimal values of physical and chemical properties, in particular: viscosity, surface tension, electrical conductivity, melting temperature (beginning and end), enthalpy, density and others, which significantly affect the kinetics of heat and mass transfer processes in the "metal-slag" system. The information resource of researches is provided by own experimental data and data of databases "Slag" and "SFM" containing information about technological properties of melts of slag and oxide systems. The analysis of the data on the dependence of the properties of oxide systems on their chemical composition and temperature was performed. Oxide systems within the chemical composition CaO-SiO2-Al2O3-MgO-CaF2 are considered. The connection of the chemical composition of slag systems with the properties of their melts from the point of view of the concept of directed chemical bonding using integral parameters is established: ρ is the stoichiometry index; ∆e is the average number of electrons localized in the direction of the cation-anion (K-A) bond; d is the average inter-nuclear distance K-A; tgα is the change in the electron density in the direction of the K-A bond; ZA(A-A), ZK(K-A), ZK(K-K) are the weighted average values of cation and anion charges in the A-A, K-A, K-K bonds. Based on the results of experimental and analytical studies, predictive models of the properties of the considered oxide systems were obtained, namely for the calculation of viscosity, electrical conductivity, crystallization temperature and density of slag melts in the range of their temperatures from 1200°C to 1800°C. The presented method of predicting the properties of refining slags can be used to evaluate the use of slags of different composition in the ladle, for example, in ladle-furnace installations.

A local point of view of the Cu(100) → NiTPP charge transfer at the NiTPP/Cu(100) interface.

A precise understanding, at the molecular level, of the massive substrate → adsorbate charge transfer at the NiTPP/Cu(100) interface has been gained through the application of elementary symmetry arguments to the structural determination of the NiTPP adsorption site by photoelectron diffraction (PED) measurements and Amsterdam density functional calculations of the free D4h NiTPP electronic structure. In particular, the PED analysis precisely determines that, among the diverse NiTPP chemisorption sites herein considered (fourfold hollow, atop, and bridge), the fourfold hollow one is the most favorable, with the Ni atom located at 1.93 Å from the surface and at an internuclear distance of 2.66 Å from the nearest-neighbors of the substrate. The use of elementary symmetry considerations enabled us to provide a convincing modeling of the NiTPP-Cu(100) anchoring configuration and an atomistic view of the previously revealed interfacial charge transfer through the unambiguous identification of the adsorbate π* and σ* low-lying virtual orbitals, of the substrate surface atoms, and of the linear combinations of the Cu 4s atomic orbitals involved in the substrate → adsorbate charge transfer. In addition, the same considerations revealed that the experimentally reported Ni(II) → Ni(I) reduction at the interface corresponds to the fingerprint of the chemisorption site of the NiTPP on Cu(100).

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.

Calculation of One- and Two-Center Overlap Like Quantum Similarity Integrals over ψ^((α)) Exponential Type Functions

One- and two-center overlap like quantum similarity integrals over ψ^((α)) functions are evaluated using the one-center expansion method. These integrals are expressed through expansion coefficients and usual two-center overlap integrals. The expressions derived in this work have no restrictions for the values of orbital parameters, quantum numbers and internuclear distances. Since these integrals of ψ^((α)) functions are calculated for the first time, the comparison is made with literature values obtained from Slater type functions. The computation results are in good agreement with literature values. The algorithm presented in this study could be useful when exponential type functions are employed in quantum similarity measures of atomic and molecular systems.

Mechanisms of non-adiabatic charge-exchange transitions in slow collisions of W ions with He, Ar and Kr atoms

The study of slow collisions of heavy particles is a challenging task from both experimental and theoretical points of view. A powerful tool for the theoretical description of these collisions is the adiabatic theory of transitions in slow collisions developed by Solov’ev (1989), which is applied here to study low-energy charge exchange between tungsten ions and inert-gas atoms at 0.01–1 keV/u. It is found that the main mechanism of charge-exchange transitions in collisions of W+ ions with Ar and Kr atoms at energies below 1 keV/u is the rotational coupling associated with internuclear axis rotation in close collisions, while charge exchange between W8+ ions and He atoms is mainly due to the radial Landau–Zener type transitions. For all cases, potential curves as a function of the internuclear distance are calculated together with the charge-exchange cross sections. The cross sections obtained are compared with experimental data, showing good agreement and explaining the mechanisms of the transitions.

Structural analysis of the ro-vibrational states of screened hydrogen molecular ion in the regime of Borromean binding

A detailed analysis on the structural properties of first three ro-vibrational (J = 0, ν = 0, 1, 2; J and ν being the rotational and vibrational quantum numbers, respectively) states of ion bound via screened Coulomb interaction has been reported. Generalized Hylleraas type basis set has been considered to construct the trial wave function under the Ritz variational framework. In order to incorporate the localized relative motion of the protons (or nuclei), we have used high powers of the interprotonic (or internuclear) distance in the basis set. The Borromean binding regime or the Borromean window (BW) has been identified for the said three states of ion. The energy components contributing to the total energy are estimated as a parametric function of the screening parameter. Different geometrical entities e.g. radial moments (p = − 1, 1 and 2), angular moments [(i) = (1) or (12)], expectation value of the delta function as well as the one-particle density are determined to get a clear view of the structural behaviour of ion in its ground state as well as in the excited states, specially within the BW.

Relativistic ab initio study on the spectroscopic and radiative properties of the lowest states and modeling of the optical cycles for the LiFr molecule

The LiFr diatomic represents a promising candidate for indirect laser cooling that has not yet been investigated not theoretically or experimentally. The potential energy curves of the ground and low-lying excited states of the LiFr heteronuclear alkali metal dimer are calculated using the Fock-space relativistic coupled cluster theory for the first time. A number of properties such as the electronic term energies, equilibrium internuclear distances, transition and permanent dipole moments, sequences of vibrational energies, harmonic vibrational frequencies, Franck–Condon factors, and radiative lifetimes (including bound and free transitions) are predicted. The probabilities of the two-step schemes (optical cycles) for the transfer process of the LiFr molecules from high excited vibrational states to the ground vibronic state are also predicted. The data obtained would be useful for laser cooling and spectral experiments with LiFr molecules.

A simple quantum model for solving two-electron diatomics approximately

Analytical expressions are obtained for the total energy of two-electron heteronuclear diatomics using a minimal basis set consisting of a 1S-Gaussian orbital centered on each atom and a Heitler-London trial wavefunction. The equations are applied to the recently discovered helium hydride cation (2019, Nature 568, 357–9) to understand its stability. Special attention was given to the fulfillment of the virial theorem and the different limiting cases (homonuclear diatomics, short and long internuclear distances). The correctness of equations and numerical results was confirmed via a brute-force Metropolis Monte Carlo integration. Expressions for the moments of the electron density (including the dipole moments) were obtained. The effect of the spin state on the dipole moment is discussed and the model agrees qualitatively with results from more advanced ab initio calculations. I also applied the model to study the metastable helium dimer dication () and the predicted bond length (0.7359 Å) is in good agreement with the experimental value (0.75 ± 0.02 Å). The advantages and limitations of this simple quantum model are discussed.

Generation of ellipticity-tunable isolated attosecond pulses from diatomic molecules in intense laser fields

We theoretically investigate the high-order harmonic generation (HHG) and the isolated attosecond pulse (IAP) with tunable ellipticity from the aligned molecule. It is found that the ellipticity of harmonic depends on the internuclear distance R. Further analysis presents that the nonzero ellipticity of harmonic generated at R=6a.u. is attributed to the 2pσu state of H2+. The 2pσu state with nonvanishing angular momentum originates from a resonant transition from the 1sσg state induced by the fundamental pulse. With specific intensity of the orthogonally polarized two-color (OTC) laser fields, an IAP with high ellipticity can be obtained. To further illustrate the origin of the high ellipticity, we present the electron trajectories and electron currents induced by the electron wavepackets of H2+, which shows a clear picture of the dynamic process of HHG. Moreover, the polarization of the IAP varies from left to right elliptical polarization by synthesizing the harmonic spectrum with different orders. Such an IAP may serve as a potential tool for probing and manipulating the ultrafast magnetic and chiral dynamics.