Equilibrium Internuclear Distance Research Articles

Viscous Current-Induced Forces.

We study the motion (translational, vibrational, and rotational) of a diatomic impurity immersed in an electron liquid and exposed to electronic current. An approach based on the linear response time-dependent density functional theory combined with the Ehrenfest dynamics leads to a system of linear algebraic equations, which account for the competing and counteracting effects of the current-induced force (electron wind) and the electronic friction. We find and emphasize the coupling between the center of mass motion and that of the nuclei relative to each other, the feature due to the mediation of the two-body interaction by the environment. The current-induced forces, by means of the dynamic exchange-correlation (xc) kernel f_{xc}(r,r^{'},ω), include the electronic viscosity contribution. Starting from the ground state at the equilibrium internuclear distance and applying a current pulse, we observe three phases of the motion: (i)acceleration due to the prevalence of the current-induced force, (ii)stabilization upon balancing of the two forces, and (iii)deceleration due to the friction after the end of the pulse. At lower, but still metallic, electron densities, the dynamic xc contribution to the force significantly affects the acceleration (deceleration) at the first (third) phase of the process. For the Cs density (r_{s}≈6 a.u.), this correction amounts up to 40% in the rotation regime.

Relativistic coupled cluster study on the spectroscopic and radiative properties of the KFr molecule and modeling of the transport properties of potassium–francium dilute gas medium

The KFr diatomic molecule represents a promising candidate for photoassociation and indirect laser cooling. It has not yet been investigated experimentally and remains the only representative of the family of alkali-metal diatomics, which is scarcely researched theoretically. The potential energy curves of the states belonging to the three lowest dissociation limits of the KFr molecule are calculated using the Fock-space relativistic coupled cluster theory for the first time. Properties and parameters, such as 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. We analyzed and evaluated the probabilities of the two-step schemes (optical cycles) for the transfer process of the KFr molecules from excited vibronic states to the ground vibronic state. The transport properties (diffusion, viscosity, and thermal conductivity coefficients) of two-component dilute gas media of potassium and francium atoms as functions of the translation temperature up to 3000 K are also calculated. The data obtained would be useful for laser cooling and spectral experiments with KFr molecules.

Interference effects in Compton scattering of keV photons at H 2+ : a nonrelativistic analytical approach

In this paper we study interference effects in Compton scattering at molecule by keV photons. As a test case we investigate the molecular system H 2+ at the equilibrium internuclear distance and in the dissociative channel. The initial molecular wavefunction is described as a linear combination of atomic orbitals centered on each nucleus. The final continuum state is a two-centre continuum Coulomb wavefunction. Using these approximations, we obtain an analytical form for the Compton scattering fully differential cross section. We investigate the molecular effects at various internuclear distance for an incident photon energy close to 2.1 keV. The relative contribution of the A⋅P and A 2 coupling terms in the Compton scattering magnitude is discussed (where P is the electron momentum operator and A the vector potential of the field). We focus on Cohen-Fano type interference effects, as the ones observed in the photoionization of molecules.

An ab initio diabatic study of rovibronic spectra of CN.

An ab initio study of the rovibronic spectra for the cyano radical (CN) based on a diabatic representation is presented. This work considers 17 electronic states, 59 dipole moment curves, 88 spin-orbit coupling curves, and 30 electronic angular momentum coupling curves, which are obtained using the internally contracted multireference configuration interaction method including the Davidson correction (icMRCI + Q) with the aug-cc-pwCV5Z-DK basis set. The diabatic transformations are performed based on a property-based diabatization method to remove the avoided crossings for the D2Π-H2Π and b4Π-24Π pairs. Ab initio potential energy curves of the X2Σ+, B2Σ+, E2Σ+, A2Π, D2Π, H2Π, F2Δ and J2Δ electronic states are shifted to match the experimental electronic excitation energies and the equilibrium internuclear distances. The coupled nuclear motion Schrödinger equations are then solved to obtain the rovibronic spectra of CN for wavenumbers from 0 to 80 000 cm-1. At wavenumbers of 0-30 000 cm-1, our absorption cross sections agree well with available theoretical data. For wavenumbers above 30 000 cm-1, our cross sections are larger than previous data in view of the fact that the transitions involving high-lying electronic states are considered. This work provides an overall prediction of the rovibronic spectrum of CN. Our results are suitable for temperatures below 8000 K and could be useful for the investigations of planetary exploration.

Ab initio potential energy surfaces and spectroscopic and radiative properties of the low-lying states of the radium monohydroxide RaOH radical

Herein, we present the state-of-the-art ab initio studies of the lower states of radium monohydroxide RaOH radical and its deuterated RaOD isotopologue. The potential energy surfaces of the ground and five low-lying excited states are calculated using the Fock-space relativistic coupled cluster method. The vibrational energy levels and all the fundamental frequencies are calculated for the first time using the potential energy surfaces and taking into account the interaction of the modes. Spectroscopic parameters such as electronic term energies, equilibrium internuclear distances, transition and permanent dipole moments, Franck–Condon factors, and radiative lifetimes are predicted. The probable vibrational laser cooling schemes are also proposed.

Stability and bonding nature of positronic lithium molecular dianion.

We studied the stability of a system consisting of a positron (e+) and two lithium anions, [Li-; e+; Li-], using first-principles quantum Monte Carlo calculations combined with the multi-component molecular orbital method. While diatomic lithium molecular dianions Li22- are unstable, we found that its positronic complex can form a bound state with respect to the lowest energy decay into the dissociation channel Li2- and a positronium (Ps). The [Li-; e+; Li-] system has the minimum energy at the internuclear distance of ∼3 Å, which is close to the equilibrium internuclear distance of Li2-. At the minimum energy structure both an excess electron and a positron are delocalized as orbiting around the Li2- molecular anion core. A dominant feature of such a positron bonding structure is described as the Ps fraction bound to Li2-, unlike the covalent positron bonding scheme for the electronically isovalent [H-; e+; H-] complex.

Alignment sensitivity of molecular-frame photoelectron momentum and angular distribution of by XUV attosecond pulses

In this work, we investigate the molecular-frame photoelectron momentum and angular distributions (MF-PMD and MF-PAD) of in the presence of XUV Attosecond Pulses. We present the alignment-sensitive effect of MF-PMDs and MF-PADs when the laser field polarization and the molecular axis are close to parallel geometry. Our results show that the MF-PADs and MF-PMDs of single-photon ionization of ion vary drastically when the alignment slightly shifts from parallel geometry to a small alignment angle (e.g. 4°) between the laser polarization direction and the molecular axis at the equilibrium inter-nuclear distance of R c = 2 atomic units. As R c increases to 4 atomic units, such sensitivity is decreased. The R c -dependent transition cross-sections in different channels are found to be the origin of such sensitivity.

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.

Ab-initio study of the electronic structure of LaF including spin-orbit coupling.

Spectroscopic investigation of lanthanum monofluoride molecule LaF is carried out by ab-initio methods and all the observed band systems are predicted through the fine structure of LaH. This structure consisted of 67 Ω(±) states is calculated by taking into account the spin-orbit coupling effect of lanthanum. Therefore, these Ω(±) states are degenerated from 33 low-lying 1,3Λ(±) states below 33,200cm-1. The potential energy curves (PECs) of 1,3Λ(±) and Ω(±) states are displayed in the range of internuclear distance from 1.40 to 3.00Å and their spectroscopic constants ([Formula: see text],[Formula: see text], [Formula: see text], [Formula: see text]) are reported. Moreover, the permanent and the transition dipole moments are plotted as a function of internuclear distance. Furthermore, the composition of the Ω(±) state-wave functions in terms of Λ-S parent states is calculated at the equilibrium internuclear distance of the ground state. Furthermore, through calculating the splitting energy between the spin-orbit components of a 3Λ(±) state, Hund's case of many states involved in the observed band systems is determined.

Ab initio study on the spectroscopic and radiative properties of the low-lying states of the radium monoiodide RaI molecule

The main focus of this study is the radium monoiodide RaI molecule, which is a promising candidate for direct laser cooling. To support this statement we calculated the potential energy curves of the ground and five low-lying excited states using the Fock-space relativistic coupled cluster theory. Calculations of spectroscopic properties including electronic term energies, equilibrium internuclear distances, transition and permanent dipole moments, vibrational energies and harmonic vibrational frequencies, Frank–Condon factors and radiative lifetimes were also performed. Based on the results we conclude that RaI molecule can be used for direct laser cooling and propose the probable laser cooling scheme. This work continues the series of research of radium monohalides and includes the comparison of results with previously studied RaCl, RaF and RaBr molecules. It can provide an understanding of trends in spectroscopic and radiative properties of this alkaline earth metal monohalides series.

Laser-induced fluorescence experimental spectroscopy and theoretical calculations of uranium monoxide

As a model molecule of actinide chemistry, UO molecule plays an important role in understanding the electronic structure and chemical bonding of actinide-containing species. We report a study of the laser-induced fluorescence spectra of the U16O and U18O using two-dimensional spectroscopy. Several rotationally resolved excitation spectra were investigated. Accurate molecular rotational constants and equilibrium internuclear distances were reported. Low-lying electronic states information was extracted from high resolution dispersed fluorescence spectra and analyzed by the ligand field theory model. The configuration of the ground state was determined as U2+(5f37s)O2−. The branching ratios, and the vibrational harmonic and anharmonic parameters were also obtained. Radiative lifetimes were determined by recording the time-resolved fluorescence spectroscopy. Transition dipole moments were calculated using the branching ratios and the radiative lifetimes. These findings were elucidated by using quantum-chemical calculations, and the chemical bonding was also analyzed. The findings presented in this work will enrich our understanding of actinide-containing molecules.

Electronic transition dipole moment function of the f' 0+ (1D2) – X1Σ+ transition of ICl

The transition dipole moment (TDM) function of the f′ 0+ (1D2) – X1Σ+ transition of ICl is determined in the range 2.76 – 3.49 Å from analyses of fluorescence spectra and data on the f′ 0+ (1D2) state lifetime. The TDM function in the specified range shows non-monotonic dependence with a maximum at R ≈ 2.9 Å. Ab initio calculations carried out using the complete active space self-consistent field method followed by calculations that take into account the dynamic electron correlations and spin–orbit interaction reproduce reasonably well the shape of the experimental TDM function. It is shown that the f′ 0+ (1D2) state near its equilibrium internuclear distance (Re = 3.226 Å) consists mainly of the ls-state 3 1Σ+ which is optically coupled with the ls-state 1 1Σ+, the dominant component of the X1Σ+ state in this R-region. The non-monotonic behavior of the f′ 0+ (1D2) – X1Σ+ TDM function at shorter distances is mainly due to spin-orbit interaction between the ls-states 3 1Σ+ and 3 3Π. The potentials of these ls-states cross at R ≈ 2.6 Å that leads to decrease in the weight of 3 1Σ+in f′ 0+ (1D2) and, as a consequence, to a non-monotonic TDM function of the f′ 0+ (1D2) – X1Σ+ transition. The TDM functions of the transitions from f′ 0+ (1D2) to other 0+ valence states were also calculated. The behavior of these TDM functions is qualitatively interpreted in terms of the R-dependence of the weights of the optically coupled ls-states.

A new theoretical study of the deformed unequal scalar and vector Hellmann plus modified Kratzer potentials within the deformed Klein–Gordon equation in RNCQM symmetries

In this paper, within the framework of relativistic quantum mechanics and using the improved approximation scheme to the centrifugal term for any [Formula: see text]states via Bopp’s shift method and standard perturbation theory, we have obtained the modified energy eigenvalues of a newly proposed modified unequal vector and scalar Hellmann plus modified Kratzer potentials (DUVSHMK-Ps) for some diatomic N2, I2, CO, NO, O2 and HCl molecules. This study includes corrections of the first-order in noncommutativity parameters [Formula: see text]. This potential is a superposition of the attractive Coulomb Yukawa potential plus the Kratzer potential and new central terms appear as a result of the effects of noncommutativity properties of space–space. The obtained energy eigenvalues appear as a function of noncommutativity parameters, the strength parameters [Formula: see text] and [Formula: see text] of the (scalar vector) Hellmann potential, the screening range parameter [Formula: see text], the dissociation energy of the vector, and scalar potential [Formula: see text], the equilibrium inter-nuclear distance [Formula: see text] in addition to the atomic quantum numbers [Formula: see text]. Furthermore, we obtained the corresponding modified energy of DUVSHMK-Ps in the symmetries of non-relativistic noncommutative quantum mechanics (NRNCQM). In both relativistic and non-relativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM.

Fock-space relativistic coupled cluster study on the spectroscopic properties of the low-lying states of the radium monobromide RaBr molecule

The potential energy curves of the ground and five low-lying excited states of the RaBr molecule 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 are predicted. The results of this study show that RaBr molecules can be used for the direct laser cooling. The comparison to the previous theoretical studies of the RaF and RaCl molecules is also provided.

Highly Accurate Potential Energy Curves for the Hydrogen Molecular Ion

AbstractPotential energy curves of the hydrogen molecular ion in the Born‐Oppenheimer approximation are computed by means of the Riccati‐Padé method (RPM). The convergence properties of the method are analysed for different states. The equilibrium internuclear distance, as well as the corresponding electronic plus nuclear energy, and the associated separation constants, are computed to 40 digits of accuracy for several bound states. For the ground state the same parameters are computed with more than 100 digits of accuracy. Additional benchmark values of the electronic energy at different internuclear distances are given for several additional states. The software implementation of the RPM is given under a free software license. The results obtained in the present work are the most accurate available so far, and further additional benchmarks are made available through the software provided.

Fock-space relativistic coupled cluster study on the RaF molecule promising for the laser cooling

The potential energy curves of the ground and five low-lying excited terms of the RaF molecule are calculated using the Fock-space relativistic coupled theory. 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 are predicted. The calculated spectroscopic constants are in good agreement with the available theoretical and experimental data. The scheme for the direct laser cooling involving the first excited A2П1/2 state is proposed. The data obtained in this study suggests the A2П1/2 → X2Σ+ channel in the RaF molecule is the almost ideal case for direct laser cooling. It is quite possible that the effective cooling scheme for the RaF molecule can be realized using only one pump laser.

New insight into the spectroscopy of LaH by ab-initio methods

By ab-initio methods, the spectroscopy of lanthanum hydride molecule LaH is predicted and the states involved in all the observed band systems are assigned. So, 34 low - lying 1,3Λ(±) states located below 31400 cm−1 are calculated and 67 Ω(±) states are generated by taking into account the spin–orbit coupling effect of lanthanum. For these states, the spectroscopic constants such as Re, Te, ωe and ωeχe are determined and the potential energy curves (PECs) are plotted in the range of internuclear distance from 1.00 Å to 3.00 Å. The calculated electronic configuration of 1,3Λ(±) states shows the ionic nature La+H- of this species. Moreover, the composition of the Ω(±) state-wave functions in term of Λ-S parent states are calculated at the equilibrium internuclear distance of the ground state. Indeed, this molecule belongs to Hund’s case (c) since the transition in many observed band systems only obeys the rule ΔΩ = 0, ±1.

Multi-reference perturbation theory study on the RaCl molecule promising for the laser cooling

The potential energy curves of the ground and eight low-lying excited atomic and ionic terms of the RaCl molecule are calculated for the first time using the multi-reference perturbation theory method at the CASSCF/XMCQDPT2 level of theory including the spin-orbit coupling. The electronic term energies, equilibrium internuclear distances, dissociation energies, transition dipole moments, sequences of vibrational energies, harmonic vibrational frequencies, Franck–Condon factors, and radiative lifetimes are predicted. The data obtained in this study suggests the possibility of the direct laser cooling of the RaCl molecules.

Ab Initio Study of Ion-Pair States of Halogen Molecules

The ion-pair states of IBr, ICl, and BrCl molecules correlating to the limits of dissociation X+(3P2,1,0, 1D2) + Y–(1S0) are studied using a complete active space self-consistent field (CASSCF), allowing for dynamic electronic correlations and spin–orbit interaction. Using experimental results, the calculated values of the equilibrium energy of the X+Y−(3P2) states correlating to the lowest ion state X+(3P2) are grouped in the range ΔTe ∼ 100 cm−1, with the error of their relative location also on the order of 100 cm−1. For most states, the difference between the experimental and calculated values of the equilibrium internuclear distance does not exceed $$R_{{\text{e}}}^{{\exp }}$$ – $$R_{{\text{e}}}^{{{\text{calc}}}}$$ = 0.02 A. A comparative analysis of structural features of the ion-pair states of homonuclear and heteronuclear halogen molecules is performed using results from recent ab initio calculations for the I2 molecule. We also discuss some issues concerning ion-pair states X−Y+ with inverted charge localization, which correlate to the limits of dissociation X– + Y+ and are coupled with the X+Y− states by two-electron transitions. It is noted that the structures with two stable localizations of two electrons, X+‒D‒Y− and X−‒D‒Y+, where X, Y are electron affinity centers (atoms, molecules, clusters) and D is a dielectric spacer, could be of interest for microelectronics.

Computational spectroscopy of diatomic tungsten carbide, WC

The bond length, electronic term symbols, bond dissociation energies (BDEs), and spectroscopic parameters of numerous low-lying electronic states of diatomic tungsten carbide (WC) have been calculated at a high level of theory. The calculations were done by using the Internally-Contracted multi-reference wave function IC-MRCI/aug-cc-pV5Z(-PP) approach. Davidson corrections were also included using the MRCI + Q method. Zero-point vibrational energy (ZPE) corrections, spin–orbit interactions, and relativistic effects are also included. The bond dissociation energy, equilibrium internuclear distance and the harmonic vibrational frequency of the ground electronic state WC(X3Δ) are computed to be D0 = 5.26 eV, Re = 1.714 Å and ωe = 979 cm−1, respectively. The energies of the lowest vibrational levels (v = 0, 1, 2 and 3) of WC(X3 Δ) are computed to be (0.00, 979.7, 1948.9, 2903.6 cm−1); their rotational constants, Bv, are also computed as (0.50717, 0.50966, 0.49990 and 0.49626 cm−1), respectively. Spectroscopic parameters (ωe, ωexe, Be and αe) and equilibrium bond lengths (Re) for several Λ-S and Ω bound states of WC are also provided in this work. These results are in excellent agreement with the available experimental data.