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Journal of Physics B Atomic Molecular and Optical Physics

Accurate analytical potential energy curves for the a 3 Σ + state of LiK, LiRb and LiCs

Dongying Li, Xiaowei Sheng

Published Jul 14, 2026• 0 citations
Publisher

Abstract

Abstract Heteronuclear lithium-containing alkali dimers in their ground triplet state offer both electric and magnetic dipole moments, which arise from their unpaired electron distributions and make them suitable for exploring many-body quantum phenomena. Currently, no simple yet accurate analytical form exists to model the triplet interaction potentials of heavier Li-alkali pairs such as LiK, LiRb and LiCs. The Sheng-Tang–Toennies(STT) potential, containing merely two fitting parameters, has earlier successfully reproduced the lowest triplet potential curve of Li 2 and LiNa. In this work, we extend its application to predict the a 3 Σ + state interactions for the three dimers LiK, LiRb, and LiCs. The derived analytical potentials agree closely with high-level a b i n i t i o benchmarks and existing spectroscopic measurements over the complete range of internuclear separations. Our findings verify the robustness and portability of the STT model for representing triplet state potentials across heteronuclear alkali dimers that include lithium.

DOI
10.1088/1361-6455/ae8a96

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Abstract Heteronuclear lithium-containing alkali dimers in their ground triplet state offer both electric and magnetic dipole moments, which arise from their unpaired electron distributions and make them suitable for exploring many-body quantum phenomena. Currently, no simple yet accurate analytical form exists to model the triplet interaction potentials of heavier Li-alkali pairs such as LiK, LiRb and LiCs. The Sheng-Tang–Toennies(STT) potential, containing merely two fitting parameters, has earlier successfully reproduced the lowest triplet potential curve of Li 2 and LiNa. In this work, we extend its application to predict the a 3 Σ + state interactions for the three dimers LiK, LiRb, and LiCs. The derived analytical potentials agree closely with high-level a b i n i t i o benchmarks and existing spectroscopic measurements over the complete range of internuclear separations. Our findings verify the robustness and portability of the STT model for representing triplet state potentials across heteronuclear alkali dimers that include lithium.
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 systematically investigate the ground state and the lowest triplet state of mixed alkali dimers (involving Li, Na, K, Rb, Cs) using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective terms for core polarization effects. We emphasize on the convergence of the results for permanent dipole moments regarding the size of the Gaussian basis set, and we discuss their predicted accuracy by comparing to other theoretical calculations or available experimental values. We also revisit the difficulty to compare computed potential curves among published papers, due to the differences in the modelization of core-core interaction.
A modified semi-empirical Tang-Toennies potential model is used to describe the a3Σu+ potentials of the alkali dimers. These potentials are currently of interest in connection with the laser manipulation of the ultracold alkali gases. The fully analytical model is based on three experimental parameters, the well depth De, well location Re, and the harmonic vibrational frequency ωe of which the latter is only slightly optimized within the range of the literature values. Comparison with the latest spectroscopic data shows good agreement for Na2, K2, Rb2, and Cs2, comparable to that found with published potential models with up to 55 parameters. The differences between the reduced potential of Li2 and the conformal reduced potentials of the heavier dimers are analyzed together with why the model describes Li2 less accurately. The new model potential provides a test of the principle of corresponding states and an excellent first order approximation for further optimization to improve the fits to the spectroscopic data and describe the scattering lengths and Feshbach resonances at ultra-low temperatures.
A new four parameter Tang-Toennies type potential model is described for the a 3Σu+ triplet state of the alkali dimers Na2, K2, Rb2, and Cs2. Compared to an earlier three parameter semi-empirical model based on the experimental well depth, De, well location, Re, and the harmonic vibrational frequency, ωe [Lau et al., J. Chem. Phys. 145, 194308 (2016)], the new model is also adjusted to be consistent with the scattering length. The results are shown to have a similar good agreement with the spectroscopic term values as the earlier model with the advantage that the scattering length is properly described. The deviations from recent potentials for Cs2 are discussed.
The rapid development of experimental techniques to produce ultracold alkali molecules opens the ways to manipulate them and to control their dynamics using external electric fields. A prerequisite quantity for such studies is the knowledge of their static dipole polarizability. In this paper, we computed the variations with internuclear distance and with vibrational index of the static dipole polarizability components of all homonuclear alkali dimers including Fr(2), and of all heteronuclear alkali dimers involving Li to Cs, in their electronic ground state and in their lowest triplet state. We use the same quantum chemistry approach as in our work on dipole moments [Aymar and Dulieu, J. Chem. Phys. 122, 204302 (2005)], based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective potentials for core polarization. Polarizabilities are extracted from electronic energies using the finite-field method. For the heaviest species Rb(2), Cs(2), and Fr(2) and for all heteronuclear alkali dimers, such results are presented for the first time. The accuracy of our results on atomic and molecular static dipole polarizabilities is discussed by comparing our values with the few available experimental data and elaborate calculations. We found that for all alkali pairs, the parallel and perpendicular components of the ground state polarizabilities at the equilibrium distance R(e) scale as (R(e))(3), which can be related to a simple electrostatic model of an ellipsoidal charge distribution. Prospects for possible alignment and orientation effects with these molecules in forthcoming experiments are discussed.
We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure (n2Lj{n}^{2}{L}_{j}n2Lj​; $L\ensuremath{\le}2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X^{1}\mathrm{\ensuremath{\Sigma}}^{+}$; v=0,J=0v=0, J=0v=0,J=0). We compute the associated C6{C}_{6}C6​ dispersion coefficients of atom-molecule pairs involving 133Cs^{133}\mathrm{Cs}133Cs and 85Rb^{85}\mathrm{Rb}85Rb atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial O(n7)O({n}^{7})O(n7) over the range of principal quantum numbers $40\ensuremath{\le}n\ensuremath{\le}150$. For all atom-molecule pairs considered, Rydberg states n2Sjn^{2}S_{j}n2Sj​ and n2Pjn^{2}P_{j}n2Pj​ result in attractive 1/R61/{R}^{6}1/R6 potentials. In contrast, n2Djn^{2}D_{j}n2Dj​ states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as ${n}^{\ensuremath{-}5}$ for n>40n>40n>40. For intermediate values of $n\ensuremath{\lesssim}40$, both repulsive and attractive interaction energies of the order of 10--$1000\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ can be achieved with specific atomic and molecular species. The accuracy of the reported C6{C}_{6}C6​ coefficients is limited by the quality of the atomic quantum defects, with relative errors $\mathrm{\ensuremath{\Delta}}{C}_{6}/{C}_{6}$ estimated to be no greater than 1% on average.