Theoretical Calculation of Ground and Electronically Excited States of MgRb+ and SrRb+ Molecular Ions: Electronic Structure and Prospects of Photo-Association
Mohamed Farjallah, Hela Ladjimi, Wissem Zrafi, Hamid Berriche
In this work, a comprehensive theoretical investigation is carried out to explore the electronic and spectroscopic properties of selected diatomic molecular ions MgRb+ and SrRb+. Using high-level ab initio calculations based on a pseudopotential approach, along with large Gaussian basis sets and full valence configuration interaction (FCI), we accurately determine adiabatic potential energy curves, spectroscopic constants, transition dipole moments (TDMs), and permanent electric dipole moments (PDMs). To deepen our understanding of these systems, we calculate radiative lifetimes for vibrational levels in both ground and low-lying excited electronic states. This includes evaluating spontaneous and stimulated emission rates, as well as the effects of blackbody radiation. We also compute Franck–Condon factors and analyze photoassociation processes for both ions. Furthermore, to explore low-energy collisional dynamics, we investigate elastic scattering in the first excited states (21Σ+) describing the collision between the Ra atom and Mg+ or Sr+ ions. Our findings provide detailed insights into the theoretical electronic structure of these molecular ions, paving the way for future experimental studies in the field of cold and ultracold molecular ion physics.
In this work, a comprehensive theoretical investigation is carried out to explore the electronic and spectroscopic properties of selected diatomic molecular ions MgRb+ and SrRb+. Using high-level ab initio calculations based on a pseudopotential approach, along with large Gaussian basis sets and full valence configuration interaction (FCI), we accurately determine adiabatic potential energy curves, spectroscopic constants, transition dipole moments (TDMs), and permanent electric dipole moments (PDMs). To deepen our understanding of these systems, we calculate radiative lifetimes for vibrational levels in both ground and low-lying excited electronic states. This includes evaluating spontaneous and stimulated emission rates, as well as the effects of blackbody radiation. We also compute Franck–Condon factors and analyze photoassociation processes for both ions. Furthermore, to explore low-energy collisional dynamics, we investigate elastic scattering in the first excited states (21Σ+) describing the collision between the Ra atom and Mg+ or Sr+ ions. Our findings provide detailed insights into the theoretical electronic structure of these molecular ions, paving the way for future experimental studies in the field of cold and ultracold molecular ion physics.
The adiabatic potential energy curves, permanent and transition dipole moments (TDMs) of the highly-excited states of the MgK + molecular ion have been computed as a function of the inter-nuclear distance R. The results are obtained by an ab initio approach involving a non-empirical pseudo-potential for the Mg and K cores, correlation treatment for core valence through an effective core polarisation potential, and full valence configuration interaction. The molecule is thus treated as a two electron system. Ab initio electronic TDM functions are calculated for all dipole-allowed transitions among the 42 states of MgK + . Many of these moment functions exhibit interesting behaviour due to charge transfer or ion-atom pair correlations. The positions of a number of satellite bands are predicted from the potential energy difference curves. We verified our results by performing complete active space self-consistent field calculations followed by a multireference configuration interaction and including Davidson correction. We observe a rather good agreement for most of them especially for the ground and lower excited states. We investigate ion-atom cold collisions at quantum regime. Furthermore, we explore ion-atom elastic collisions at low temperatures, predicting the formation of translationally and rotationally cold molecular ion MgK + in the ground state electronic potential by stimulated Raman type process. Our results are important in the perspective of upcoming experiments aiming at merging cold alkali atom and alkaline-earth ion in a hybrid trap for the creation of cold molecular ions by photoassociation.
In this paper, we extensively study the electronic structure, interactions, and dynamics of the (MgCs)+ molecular ion. The exchanges between the alkaline atom and the low-energy cationic alkaline earths, which are important in the field of cold and ultracold quantum chemistry, are studied. We use an ab initio approach based on the formalism of non-empirical pseudo-potential for Mg2+ and Cs+ cores, large Gaussian basis sets, and full-valence configuration interaction. In this context, the (MgCs)+ cation is treated as an effective two-electron system. Adiabatic potential energy curves and their spectroscopic constants for the ground and the first 20 excited states of 1,3Σ+ symmetries are determined. Furthermore, we identify the avoided crossings between the electronic states of 1,3Σ+ symmetries. These crossings are related to the charge transfer process between the two ionic limits, Mg/Cs+ and Mg+/Cs. Therefore, vibrational-level spacings and the transition and permanent dipole moments are presented and analyzed. Using the produced potential energy data, the ground-state scattering wave functions and elastic cross-sections are calculated for a wide range of energies. In addition, we predict the formation of a translationally and rotationally cold molecular ion (MgCs)+ in the ground-state electronic potential energy through a stimulated Raman-type process aided by ion–atom cold collision. In the low-energy limit (<1 mK), elastic scattering cross-sections exhibit Wigner law threshold behavior, while in the high-energy limit, the cross-sections act as a function of energy E go as E−1/3. A qualitative discussion about the possibilities of forming cold (MgCs)+ molecular ions by photoassociative spectroscopy is presented.
Electronic structure, spectroscopy, cold ion-atom elastic collision properties and photoassociation formation prediction of (MgCs)+ molecular ion
Studies on the interactions between an alkali atom and an alkaline earth ion at low energy are important in the field of cold chemistry. In this paper we, extensively, study the structure, interactions, and dynamics of (MgCs)+ molecular ion. We use an ab initio approach based on the formalism of non-empirical pseudo-potential for Mg2+ and Cs+ cores, large Gaussian basis sets and full valence configuration interaction. In this context, the (MgCs)+ cation is treated as an effective two-electron system. Potential energy curves and their spectroscopic constants for the ground and the first 41 excited states of 1,3Σ+, 1,3Π and 1,3Δ symmetries are determined. Furthermore, we identify the avoided crossings between the electronic states of 1,3Σ+ and 1,3Π symmetries. These crossings are related to the charge transfer process between the two ionic limits Mg/Cs+ and Mg+/Cs. In addition, vibrational-level spacings, the transition and permanent dipole moments are presented and analysed. Using the produced potential energy data, the ground-state scattering wave functions and elastic cross sections for a wide range of energies are performed. Furthermore, we predict the formation of translationally and rotationally cold molecular ion (MgCs) + in the ground state electronic potential energy by stimulated Raman type process aided by ion-atom cold collision. In the low energy limit (< 1 mK), elastic scattering cross sections exhibit Wigner law threshold behaviour; while in the high energy limit the cross sections as a function of energy E go as E−1/3. A qualitative discussion about the possibilities of forming the cold (MgCs)+ molecular ions by photoassociative spectroscopy is presented.
Abstract Molecular ions formed in cold hybrid ion-atom experiments may find interesting applications ranging from precision measurements to controlled chemical reactions. Here, we investigate electronic structure of the Sr2 + molecular ion, which may be produced by photoassociation of laser-cooled Sr+ ions immersed into an ultracold gas of Sr atoms or by ionization of ultracold Sr2 molecules. Using ab initio electronic structure methods, such as the coupled cluster and configuration interaction ones with small-core relativistic energy-consistent pseudopotentials and large Gaussian basis sets, we calculate potential energy curves for the ground and 41 excited electronic states, and electric dipole transition moments between them. We show that alkaline-earth molecular ions despite of their apparently simple structure with three valence electrons only are challenging for state-of-the-art quantum chemistry methods due to their multireference nature and high density of states. Finally, we calculate and analyze Franck-Condon factors governing the photoionization of ground-state Sr2 molecules into 2Σu + and 2Σg + states of Sr2 + molecular ions. The present results may be useful for studying and guiding formation and spectroscopy of cold Sr2 + molecular ions.
Abstract Molecular ions formed in cold hybrid ion–atom experiments may find interesting applications ranging from precision measurements to controlled chemical reactions. Here, we investigate the electronic structure of the Sr 2 + molecular ion, which may be produced by photoassociation of laser-cooled Sr+ ions immersed in an ultracold gas of Sr atoms or by ionization of ultracold Sr2 molecules. Using ab initio electronic structure methods, such as the coupled cluster and configuration interaction ones with small-core relativistic energy-consistent pseudopotentials and large Gaussian basis sets, we calculate potential energy curves for the ground and 41 excited electronic states, and electric dipole transition moments between them. We show that alkaline-earth molecular ions, despite their apparently simple structure with only three valence electrons, are challenging for state-of-the-art quantum chemistry methods due to their multireference nature and high density of states. Finally, we calculate and analyze Franck–Condon factors governing the photoionization of ground-state Sr2 molecules into Σ u + 2 and Σ g + 2 states of Sr 2 + molecular ions. The present results may be useful for studying and guiding the formation and spectroscopy of cold Sr 2 + molecular ions.
Abstract Alkaline-earth and alkali-metal mixtures have an electronic structure that is perfect for laser cooling. This makes them highly attractive for trapping and laser cooling experiments, allowing the formation of cold molecules. For this object, potential-energy curves and relevant spectroscopic parameters of the low-lying electronic excited states of 1,3Σ+, 1,3Π, and 1,3Δ symmetries of molecular-ion systems composed of alkaline-earth-ion and Francium alkali-metal-atom: ALKE-Fr+ (ALKE = Be, Mg, Ca and Sr), are determined using advanced theoretical technique in quantum chemistry, including a non-empirical pseudopotential, core-valence correlation, large Gaussian basis sets and Full Configuration Interaction (FCI). In order to obtain a more accurate understanding of the electronic structure of these systems, we also determined transition and permanent dipole moments and vibrational properties. Thereafter, the spontaneous and the black-body stimulated transition rates were determined and were employed to calculate lifetimes for all vibrational states of the ground electronic states 11Σ+ of molecular-ions under consideration. For the first and the second excited states, radiative lifetimes were investigated via the Franck–Condon approximation including bound-bound and bound-free transitions. High diagonal structure and large Franck Condon Factor (FCF) values f 00 = 0.987, f 11 = 0.959 and f 22 = 0.919 were obtained for the 11Π (v′ = 0, 1, 2)→ 11Σ+ (v = 0, 1, 2) transition making the BeFr+ system a good candidate for laser cooling. Furthermore, the current results could be used to investigate elastic scattering properties in cold-ion-atom collisions for the first excited states and may help the experimentalists for possible formation, spectroscopy, and photoassociation of cold ion-atom mixtures.