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Atomic Data and Nuclear Data Tables

Matrix elements for spin-orbit couplings in KRb

Patryk Jasik, Dariusz Kędziera, J. E. Sienkiewicz

Published Oct 28, 2024• 2 citations
Publisher

Abstract

In response to the need to investigate and create a reliable dataset of spin-orbit coupling matrix elements, we have extended our recent work in which we presented results for the potential energy curves and permanent and transition dipole moments in KRb. This paper presents 190 allowed spin-orbit couplings between 30 singlet and triplet Σ + , Π , and Δ electronic states of the KRb molecule. These results are crucial for accurately interpreting spectroscopic data, especially for the deperturbation analysis challenges. 23 tables and 21 graphs present the L S X , L S Y , and L S Z components of reported spin-orbit couplings. Using the MOLPRO code, we performed MRCI calculations using the large-core pseudopotentials and core polarization potentials with reoptimized cutoff parameters. The spin-orbit parameters of the potassium pseudopotential were deduced and optimized from scratch. The Gaussian basis sets used in our calculations were appropriately selected, augmented, and optimized. We compare some of our data with available theoretical and experimental results.

DOI
10.1016/j.adt.2024.101698

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In response to the need to investigate and create a reliable dataset of spin-orbit coupling matrix elements, we have extended our recent work in which we presented results for the potential energy curves and permanent and transition dipole moments in KRb. This paper presents 190 allowed spin-orbit couplings between 30 singlet and triplet Σ + , Π , and Δ electronic states of the KRb molecule. These results are crucial for accurately interpreting spectroscopic data, especially for the deperturbation analysis challenges. 23 tables and 21 graphs present the L S X , L S Y , and L S Z components of reported spin-orbit couplings. Using the MOLPRO code, we performed MRCI calculations using the large-core pseudopotentials and core polarization potentials with reoptimized cutoff parameters. The spin-orbit parameters of the potassium pseudopotential were deduced and optimized from scratch. The Gaussian basis sets used in our calculations were appropriately selected, augmented, and optimized. We compare some of our data with available theoretical and experimental results.
The relativistic configuration interaction valence-bond method has been used to calculate permanent and transition electric dipole moments of the KRb heteronuclear molecule as a function of internuclear separation. The permanent dipole moment of the ground-state $X{}^{1}{\ensuremath{\Sigma}}^{+}$ potential is found to be 0.30(2) ea0{\mathrm{ea}}_{0}ea0​ at the equilibrium internuclear separation with excess negative charge on the potassium atom. For the $a{}^{3}{\ensuremath{\Sigma}}^{+}$ potential the dipole moment is an order of smaller magnitude (1 ${\mathrm{ea}}_{0}=8.47835{10}^{\ensuremath{-}30}\mathrm{Cm}).$ In addition, we calculate transition dipole moments between the two ground-state and excited-state potentials that dissociate to the K(4s)+Rb(5p)\mathrm{K}(4s)+\mathrm{Rb}(5p)K(4s)+Rb(5p) limits. Using this data we propose a way to produce singlet $X{}^{1}{\ensuremath{\Sigma}}^{+}$ KRb molecules by a two-photon Raman process starting from an ultracold mixture of doubly spin-polarized ground state K and Rb atoms. This Raman process is only allowed due to relativistic spin-orbit couplings and the absence of gerade-ungerade selection rules in heteronuclear dimers.
We present a deperturbation analysis of the spin-orbit-coupled $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ and $b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{{0}^{+}}$ states of LiRb based on the rovibrational energy levels observed previously by photoassociation spectroscopy in the bosonic 7Li85Rb^{7}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}^{85}\mathrm{Rb}7Li85Rb molecule. Using the genetic algorithm (GA), we optimize the pointwise ab initio potential energy curves of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state and the $b{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}}$ state based on spectroscopic data. Then we fit the pointwise potentials obtained by the GA and the ab initio spin-orbit-coupling term with the expanded Morse oscillator (EMO) function. Finally, we optimize the parameters of the EMO function using the sequential least-squares quadratic programming algorithm with the guidance of the experimental data and pointwise potentials obtained by the GA. From the fitted results, we calculate the transition dipole moment matrix elements for transitions from the rovibrational levels of the coupled $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}\text{--}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{{0}^{+}}$ state to the Feshbach state and the absolute rovibrational ground state for the fermionic 6Li87Rb^{6}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}^{87}\mathrm{Rb}6Li87Rb molecule. Based on the calculated transition dipole moment matrix elements, several levels of the coupled $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}\text{--}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{{0}^{+}}$ state are predicted to be suitable as the intermediate state for stimulated Raman adiabatic passage transfer from the Feshbach state to the absolute rovibrational ground state. In addition, we also provide a similar estimation for the $B{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}\text{--}c{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{1}^{+}\text{--}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{1}$ state based on available ab initio interaction potentials.
The spin-forbidden cooling of the LiRb molecule is investigated based on ab initio quantum chemistry calculations. The multireference configuration interaction method is used to generate the potential energy curves (PECs) of the ground state X(1)Σ(+) and the low-lying excited states a(3)Σ(+), B(1)Π, and b(3)Π. The spin-orbit coupling effects for the PECs and the transition dipole moments (TDMs) between the X(1)Σ(+), b(3)Π and a(3)Σ(+) states are also calculated. The analytical functions for the PECs are deduced. The rovibrational energy levels, the spectroscopic parameters and the Franck-Condon factors (FCF) are determined by solving the Schrödinger equation of nuclear movement with the obtained analytical functions. The b(3)Π0 ↔ X(1)Σ(+) and b(3)Π1 ↔ X(1)Σ(+) transitions have highly diagonal distributed FCFs and non-zero TDMs, demonstrating that the LiRb molecule could be a very promising candidate for laser cooling. Therefore, a three-cycle laser cooling scheme for the molecule has been proposed based on these two spin-forbidden transitions. Using the radiative lifetime and linewidth calculated from the obtained TDM functions, we present further analysis of the cooling of LiRb and the corresponding KRb molecule. The transition b(3)Π0 ↔ X(1)Σ(+) is found to be a practical transition to cool the LiRb molecule, and a sub-microkelvin cool temperature could be reached for the KRb molecule using a similar laser cooling scheme.
Obtaining ultracold samples of dipolar molecules is a current challenge which requires an accurate knowledge of their electronic properties to guide the ongoing experiments. In this paper, we calculate permanent dipole moments and transition dipole moments for excited states for alkali dimers NaK, NaRb and NaCs using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective terms for core polarization effects. We provide an extensive set of data concerning transitions among the first seven molecular states of each symmetry 1Σ+, 3Σ+, 1Π, 3Π. The accuracy of our results is generally improved compared to previous similar calculations on NaK, while they are found to be in good agreement with the few NaRb states calculated with other methods. Results for NaCs transition dipole moments are given here for the first time.
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.
Abstract Systematic quantum chemical calculations were performed for the ground and a number of low-lying electronically excited doublet and quartet states of the rubidium trimer molecule. The obtained potential energy surfaces (PES), spin-orbit couplings (SOC) and electronic transition dipole moments (ETDM) can be useful for optimizing paths for laser synthesis, cooling and manipulation of stable ensembles of Rb3 molecules at ultralow temperatures. Ab initio calculations of the electronic structure of the homonuclear Rb3 molecule, in linear, isosceles triangle and equilateral triangle geometries, were performed using the multi-reference configuration interaction method, taking into account single and double excitations (M-R‑CISD) and with explicit dynamic correlation of only the three valence electrons. The structure of each atom was approximated using a nine-electron effective core potential (ECP28MDF), and molecular orbitals (MOs) were optimized using the spin averaged (over doublet and quartet states) multi-configuration self-consistent field (SA-CASSCF) method. Core–valence correlations between twenty-four subvalence electrons located on doubly occupied MOs and three valence electrons were implicitly taken into account using a one-electron angular momentum-independent Müller–Mayer core polarization potential (CPP). As a result of topological investigations at over 35 000 points, two dimensional PES, SOC, and ETDM functions were obtained and the geometric parameters Rb3 were found at which the most intense vertical transitions and the maximum influence of the SOC are expected.