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arXiv:1207.3546 · Physical Review A

Long-range forces between polar alkali-metal diatoms aligned by external electric fields

Jason N. Byrd, John A. Jr. Montgomery, Robin Côté

Published Sep 25, 2012• 19 citations
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Abstract

Long-range electrostatic, induction, and dispersion coefficients including terms of order ${R}^{\ensuremath{-}8}$ have been calculated by the sum over states method using time-dependent density-functional theory. We also computed electrostatic moments and static polarizabilities of the individual diatoms up to the octopole order using coupled-cluster and density-functional theory. The laboratory-frame transformed electrostatic moments and van der Waals coefficients corresponding to the alignment of the diatomic molecules were found. We use this transformation to obtain the coupling induced by an external dc electric field and present values for all $XY$ combinations of like polar alkali-metal diatomic molecules with atoms from Li to Cs. Analytic solutions to the dressed-state laboratory-frame electrostatic moments and long-range intermolecular potentials are also given for the dc low-field limit.

DOI
10.1103/physreva.86.032711

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Long-range electrostatic, induction, and dispersion coefficients including terms of order R\ensuremath−8{R}^{\ensuremath{-}8}R\ensuremath−8 have been calculated by the sum over states method using time-dependent density-functional theory. We also computed electrostatic moments and static polarizabilities of the individual diatoms up to the octopole order using coupled-cluster and density-functional theory. The laboratory-frame transformed electrostatic moments and van der Waals coefficients corresponding to the alignment of the diatomic molecules were found. We use this transformation to obtain the coupling induced by an external dc electric field and present values for all XYXYXY combinations of like polar alkali-metal diatomic molecules with atoms from Li to Cs. Analytic solutions to the dressed-state laboratory-frame electrostatic moments and long-range intermolecular potentials are also given for the dc low-field limit.
We computed the long-range interactions between two identical polar bialkali molecules in their rovibronic ground level for all ten species involving Li, Na, K, Rb, and Cs, using accurate quantum chemistry results combined with available spectroscopic data. A huge van der Waals interaction is found for eight species in free space. The competition of the van der Waals interaction with the dipole-dipole interaction induced by an external electric field parallel or perpendicular to the intermolecular axis is investigated by varying the electric-field magnitude and the intermolecular distance. Our calculations predict a regime with the mutual orientation of the two molecules but with no preferential direction in the laboratory frame. A mechanism for the stimulated one-photon radiative association of a pair of ultracold polar molecules into ultracold tetramers is proposed, which would open the way towards the optical manipulation of ultracold polyatomic molecules.
We have calculated the isotropic C6 coefficients characterizing the long-range van der Waals interaction between two identical heteronuclear alkali-metal diatomic molecules in the same arbitrary vibrational level of their ground electronic state X(1)Σ(+). We consider the ten species made up of (7)Li, (23)Na, (39)K, (87)Rb, and (133)Cs. Following our previous work [Lepers et al., Phys. Rev. A 88, 032709 (2013)], we use the sum-over-state formula inherent to the second-order perturbation theory, composed of the contributions from the transitions within the ground state levels, from the transition between ground-state and excited state levels, and from a crossed term. These calculations involve a combination of experimental and quantum-chemical data for potential energy curves and transition dipole moments. We also investigate the case where the two molecules are in different vibrational levels and we show that the Moelwyn-Hughes approximation is valid provided that it is applied for each of the three contributions to the sum-over-state formula. Our results are particularly relevant in the context of inelastic and reactive collisions between ultracold bialkali molecules in deeply bound or in Feshbach levels.
Knowledge of the long-range interaction between atoms and molecules is of fundamental importance for low-energy and low-temperature collisions. The electronic interaction between the charge distributions of two ground-state alkali-metal atoms can be expanded in inverse powers of R, the internuclear distance. The coefficients C6{\mathit{C}}_{6}C6​, C8{\mathit{C}}_{8}C8​, and C10{\mathit{C}}_{10}C10​ of, respectively, the ${\mathit{R}}^{\mathrm{\ensuremath{-}}6}$, ${\mathit{R}}^{\mathrm{\ensuremath{-}}8}$, and ${\mathit{R}}^{\mathrm{\ensuremath{-}}10}$ terms are calculated by integrating the products of the dynamic electric multipole polarizabilities of the individual atoms at imaginary frequencies, which are in turn obtained by solving two coupled inhomogeneous differential equations. Precise one-electron model potentials are developed to represent the motion of the valence electron in the field of the closed alkali-metal positive-ion core. The numerical results for the static multipole polarizabilities for the alkali-metal atoms and the coefficients C6{\mathit{C}}_{6}C6​, C8{\mathit{C}}_{8}C8​, and C10{\mathit{C}}_{10}C10​ for homonuclear and heteronuclear alkali-metal diatoms are compared with other calculations.
We theoretically investigate the properties of highly polar diatomic molecules containing 2S^{2}S2S-state transition-metal atoms. We calculate potential energy curves, permanent electric dipole moments, spectroscopic constants, and leading long-range dispersion-interaction coefficients for molecules consisting of either a Cu or Ag atom interacting with an alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atom. We use ab initio electronic structure methods, such as the coupled cluster and configuration interaction ones, with large Gaussian basis sets and small-core relativistic-energy-consistent pseudopotentials. We predict that the studied molecules in the ground electronic state are strongly bound with highly polarized covalent or ionic bonds resulting in very large permanent electric dipole moments. We find that highly excited vibrational levels have maximal electric dipole moments, e.g., exceeding 13 D for CsAg and 6 D for BaAg. Results for Cu2,Ag2{\mathrm{Cu}}_{2}, {\mathrm{Ag}}_{2}Cu2​,Ag2​, and CuAg are also reported. The studied molecules may find application in ultracold dipolar many-body physics, controlled chemistry, or precision measurement experiments.
A systematic study of the leading isotropic van der Waals coefficients for the alkali-metal atom+molecule and molecule+molecule systems is presented. Dipole moments and static and dynamic dipole polarizabilities are calculated employing high-level quantum chemistry calculations. The dispersion, induction, and rotational parts of the isotropic van der Waals coefficient are evaluated. The known van der Waals coefficients are then used to derive characteristics essential for simple models of the collisions involving the corresponding ultracold polar molecules.
Ultracold diatomic molecules find application in quantum studies ranging from controlled chemistry and precision measurement physics to quantum many-body simulation and potentially quantum computing. Accurate knowledge of molecular properties is required to guide and explain ongoing experiments. Here, in an extensive and comparative study, we theoretically investigate the electronic properties of the ground-state diatomic molecules composed of alkali-metal (Li, Na, K, Rb, Cs, Fr) and alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atoms. We study 78 heteronuclear and homonuclear diatomic combinations, including 21 alkali-metal molecules in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ and ${a}^{3}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic states, 36 alkali-metal--alkaline-earth-metal molecules in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state, and 21 alkaline-earth-metal molecules in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state. We calculate potential energy curves, permanent electric dipole moments, and polarizabilities using the hierarchy of coupled-cluster methods up to CCSDTQ with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials. We collect and analyze corresponding spectroscopic constants. We estimate computational uncertainties and compare the present values with previous experimental and theoretical data to establish a different theoretical benchmark. The presented results should be useful for further application of the studied molecules in modern ultracold physics and chemistry experiments.