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ELECTRONIC STRUCTURE OF THE X 1_+ ION CORE OF CaF RYDBERG STATES

Stephen L. Coy

Published Jan 5, 2016• 0 citations
OpenAlex

Abstract

We use ab-initio calculations to examine the electronic structure of CaF${^+}$,making comparison to the available experimental data and effective potential models. An electron-density-difference plot comparing isolated Ca${^{+2}}$ and F${^-}$ ions with the CaF${^+}$ ab-initio density shows s-d mixing at Ca, and maintenance of near spherical symmetry at F. This unexpected result is interpreted in terms of the electronic states of Ca${^+}$. Calculation of the effective charge on F spanning the region of the transition from ionic to dissociating Ca${^+}$ F${^0}$ locates the transition very near the crossing of the Ca${^{+2}}$ F${^-}$ and Ca${^+}$ F${^0}$ curves and additionally determines the width of the ionic-bonding transition region. An accurate non-relativistic long or intermediate range effective potential for the CaF Rydberg electron is obtained by choice of origin at the center of polarizability, with inclusion of multipoles through octopole and the use of anisotropic polarizability. The estimates of CaF${^+}$ polarizability from ab-initio and effective potential models predict high anisotropy, with the parallel dipole polarizability, where the atomic dipoles are mutually enhancing, predicted to be about double the perpendicular polarizability, where the atomic dipoles are mutually antagonistic.

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We use ab-initio calculations to examine the electronic structure of CaF+{^+}+,making comparison to the available experimental data and effective potential models. An electron-density-difference plot comparing isolated Ca+2{^{+2}}+2 and F−{^-}− ions with the CaF+{^+}+ ab-initio density shows s-d mixing at Ca, and maintenance of near spherical symmetry at F. This unexpected result is interpreted in terms of the electronic states of Ca+{^+}+. Calculation of the effective charge on F spanning the region of the transition from ionic to dissociating Ca+{^+}+ F0{^0}0 locates the transition very near the crossing of the Ca+2{^{+2}}+2 F−{^-}− and Ca+{^+}+ F0{^0}0 curves and additionally determines the width of the ionic-bonding transition region. An accurate non-relativistic long or intermediate range effective potential for the CaF Rydberg electron is obtained by choice of origin at the center of polarizability, with inclusion of multipoles through octopole and the use of anisotropic polarizability. The estimates of CaF+{^+}+ polarizability from ab-initio and effective potential models predict high anisotropy, with the parallel dipole polarizability, where the atomic dipoles are mutually enhancing, predicted to be about double the perpendicular polarizability, where the atomic dipoles are mutually antagonistic.
The main electronic properties, namely potential energy curves, permanent and transition dipole moments, static dipole polarizabilities, of the alkaline-earth hydride ion SrH + , as well as of CaH + and BaH + are computed through a full configuration interaction performed in a two-valence electronic configuration space build from a large Gaussian basis set. The doubly charged ionic core of the alkaline-earth atoms is modelled by an effective core potential including core polarization effects. Our study confirms that the properties of these series of molecular ions have very similar patterns, while it is predicted that the major electronic transition between the electronic ground state and the lowest excited state in BaH + is significantly weaker than the one in CaH + and SrH + . Such a study represents a first step towards the modelling of reactive collisions between cold and trapped alkaline-earth ions and H 2 , as well as for precision measurements based on overtone transitions using cold molecular ions.
Rydberg states of atoms or molecules for which the inner turning point of the Rydberg electron on the radial plus centrifugal potential lies outside the bulk of the ion core electron density are known as core-non-penetrating states. Interpretation of Rydberg spectroscopic data for polar molecules makes use of effective potentials that include ionic bonding and polarizability in order to represent electric properties of the ion core. We examine the accuracy and convergence properties of single-center polarization potentials and show that the center of charge representation, for which the core dipole moment is zero so that first-order l-mixing can be neglected, is excluded by the convergence sphere for use with l-states that can be treated by an expansion about the center or mass, the center of dipole or a newly-defined center of polarizability. The potential expansion converges only outside a sphere enclosing the charge distribution, and the sphere is much larger when the center of charge is used. For higher l-states of the rotating molecule (turning points defined in center of mass), the sphere required for convergence is much smaller for an origin within the charge distribution, so that lower l states are modeled correctly.
We compute the Rydberg spectrum of a single Ca+{\mathrm{Ca}}^{+}Ca+ ion in a Paul trap by incorporating various internal and external coupling terms of the ion to the trap in the Hamiltonian. The coupling terms include spin-orbit coupling in Ca+{\mathrm{Ca}}^{+}Ca+, charge (electron and ionic core) coupling to the radio frequency and static fields, ion-electron coupling in the Paul trap, and ion center-of-mass coupling. The electronic Rydberg states are precisely described by a one-electron model potential for ${e}^{\ensuremath{-}}+{\mathrm{Ca}}^{2+}$, and accurate eigenenergies, quantum defect parameters, and static and tensor polarizabilities for a number of excited Rydberg states are obtained. The time-periodic rf Hamiltonian is expanded in the Floquet basis, and the trapping-field-broadened Rydberg lines are compared with recent observations of Ca+(23P){\mathrm{Ca}}^{+}(23P)Ca+(23P) and Ca+(52F){\mathrm{Ca}}^{+}(52F)Ca+(52F) Rydberg lines.
Accurate ab initio potential energy surfaces are essential to understand and predict collisional outcomes in ultracold molecular systems. In this study, we explore the intermolecular interactions between two laser-cooled CaF molecules, in both their ground and excited electronic states, aiming to understand the mechanisms behind the observed collisional losses on the nonreactive, spin-polarized surface of the CaF+CaF\mathrm{CaF}+\mathrm{CaF}CaF+CaF system. Using state-of-the-art ab initio methods, we compute 12 electronic states of the Ca2F2{\mathrm{Ca}}_{2}{\mathrm{F}}_{2}Ca2​F2​ complex within the rigid rotor approximation applied to CaF. Calculating the potential energy surfaces for the excited electronic states of Ca2F2{\mathrm{Ca}}_{2}{\mathrm{F}}_{2}Ca2​F2​ is challenging and computationally expensive. Our approach employs the multireference configuration interaction method, restricted to single and double excitations, along with a reasonably large active space to ensure the convergence in the excited states. We also compute the spin-orbit coupling between the ground state and the lowest spin-polarized triplet state, as well as the spin-spin coupling within the lowest triplet state (1) $^{3}{\mathrm{A}}^{\ensuremath{'}}$. Additionally, we determine the electric transition dipole moments for the (1) $^{3}{\mathrm{A}}^{\ensuremath{'}}$--(2) $^{3}{\mathrm{A}}^{\ensuremath{'}}$ and (1) $^{3}{\mathrm{A}}^{\ensuremath{'}}$--(1) $^{3}{\mathrm{A}}^{\ensuremath{''}}$ transitions. Notably, we find that the lowest spin-polarized state (1) $^{3}{\mathrm{A}}^{\ensuremath{'}}$, shifted by 1064 nm of laser light from the optical dipole trap, intersects several electronically excited states. Finally, by analyzing the potential energy surfaces, we discuss two plausible pathways that may account for the observed collisional losses on the spin-polarized surface of the CaF+CaF\mathrm{CaF}+\mathrm{CaF}CaF+CaF system.
Alkaline-earth dimers are now been used, as new grounds for, testing fundamental physics laws, precision measurements and quantum computation. As a starting point for such experiments, one needs a very good knowledge of the electronic structure, energetics and long-range behavior of these molecular ions. We perform accurate ab initio calculations for the ground and low-lying excited states of Be2+, Mg2+, Ca2+ and Sr2+ molecular ions. We have also calculated the spectroscopic constants, electronic transition dipole moments, polarizabilities and long-range dispersion coefficients for the various alkaline-earth ionic dimers. We have extended our calculations to study heteronuclear species of alkaline-earth molecular ions, like BeCa+, and also mixed alkali alkaline-earth species like NaCa+. We calculated photoassociation (PA) pathways for formation of cold molecular ions and also studied corrections to the Born-Oppenheimer Hamiltonian: non-adiabatic couplings and hyperfine structure due to nuclear spins and electric quadrupoles. We believe, this work would lay foundation, not only for new experiments in ultracold physics and chemistry, but would also provide valuable starting point for theoretical calculations involving low temperature scattering and resonant charge transfer.