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The Journal of Chemical Physics

Ab initio long-range interaction and adiabatic channel capture model for ultracold reactions between the KRb molecules

Alexei A. Buchachenko, A. V. Stolyarov, Małgorzata M. Szczęśniak, Grzegorz Chałasiński

Published Sep 19, 2012• 17 citations
Publisher

Abstract

The coefficients at the lowest-order electrostatic, induction, and dispersion terms of the anisotropic long-range potential between the two KRb((1)Σ(+)) molecules are evaluated through the static and dynamic molecular properties using the ab initio coupled cluster techniques. Adiabatic channel potentials for the ground-state molecules are obtained and used for the numerical quantum capture probability calculations in the spirit of the statistical adiabatic channel models. Capture rate coefficients for indistinguishable (polarized) and distinguishable (unpolarized) molecules at temperatures below 10 μK agree well with those computed with the simple isotropic dispersion R(-6) potential, but underestimate the measured ones [Ospelkaus et al., Science 327, 853 (2010)] up to a factor of 3. Preliminary assessment of the effects of higher-order long-range terms, retardation of dispersion forces, and magnetic dipole-dipole interaction does not offer any clear perspectives for drastic improvement of the capture approximation for the reactions studied.

DOI
10.1063/1.4752740

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The coefficients at the lowest-order electrostatic, induction, and dispersion terms of the anisotropic long-range potential between the two KRb((1)Σ(+)) molecules are evaluated through the static and dynamic molecular properties using the ab initio coupled cluster techniques. Adiabatic channel potentials for the ground-state molecules are obtained and used for the numerical quantum capture probability calculations in the spirit of the statistical adiabatic channel models. Capture rate coefficients for indistinguishable (polarized) and distinguishable (unpolarized) molecules at temperatures below 10 μK agree well with those computed with the simple isotropic dispersion R(-6) potential, but underestimate the measured ones [Ospelkaus et al., Science 327, 853 (2010)] up to a factor of 3. Preliminary assessment of the effects of higher-order long-range terms, retardation of dispersion forces, and magnetic dipole-dipole interaction does not offer any clear perspectives for drastic improvement of the capture approximation for the reactions studied.
Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultralow collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of the reactive scattering mechanism. Here, we report on the ab initio calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters, we then develop a single-channel scattering model with flexible boundary conditions. Our calculations show that, at low temperatures (and in the absence of an external electric field), the reaction rates between molecules or between molecules and atoms have a resonant character as a function of the short-range parameters. We also find that both the isotropic and anisotropic van der Waals coefficients have significant contributions from dipole coupling to excited electronic states. Their values can differ dramatically from those solely obtained from the permanent dipole moment. A comparison with recently obtained reaction rates of fermionic 40 K 87 Rb shows that the experimental data cannot be explained by a model where the short-range scattering parameters are independent of the relative orbital angular momentum or partial wave.
We use quantum and classical adiabatic capture theories to study the chemical reaction Li + CaH LiH + Ca. Using a recently developed ab initio potential energy surface, which provides an accurate representation of long-range interactions in the entrance reaction channel, we calculate the adiabatic channel potentials by diagonalizing the Li-CaH Hamiltonian as a function of the atom-molecule separation. The resulting adiabatic channel potentials are used to calculate both the classical and quantum capture probabilities as a function of collision energy, as well as the temperature dependencies of the partial and total reaction rates. The calculated reaction rate agrees well with the measured value at 1 K (V Singh et al 2012 Phys. Rev. Lett. 108 203201), suggesting that the title reaction proceeds without an activation barrier. The calculated classical adiabatic capture rate agrees well with the quantum result in the multiple-partial-wave regime of relevance to the experiment. Significant differences are found only in the ultracold limit ( mK), demonstrating that adiabatic capture theories can predict the reaction rates with nearly quantitative accuracy in the multiple-partial-wave regime.
A general and rigorous quantum method is proposed for studying capture dynamics between two diatomic molecules in full dimensionality. By solving the time-independent Schrödinger equation with proper boundary conditions, this method is ideally suited for studying quantum dynamics of cold and ultracold reactions. To illustrate its applicability, the capture dynamics between ultracold KRb molecules is characterized in full six dimensions for the first time using a first-principles based long-range interaction potential. The calculated capture rates for collisions involving distinguishable and indistinguishable 40K87Rb molecules are in good agreement with the experiment and exhibit clear Wigner threshold behaviors. Predictions for ultracold collisions between internally excited 40K87Rb suggest minor changes in the loss rate, consistent with experimental observations in similar systems.
A general and rigorous quantum method is proposed for studying capture dynamics between two diatomic molecules in full dimensionality. By solving the time-independent Schrodinger equation with proper boundary conditions, this method is ideally suited for studying quantum dynamics of cold and ultracold reactions. To illustrate its applicability, the capture dynamics between ultracold KRb molecules is characterized in full six dimensions for the first time using a first-principles based long-range interaction potential. The calculated capture rates for collisions involving distinguishable and indistinguishable 40K87Rb molecules are in good agreement with the experiment and exhibit clear Wigner threshold behaviors. Predictions for ultracold collisions between internally excited 40K87Rb suggest minor changes in the loss rate, consistent with experimental observations in similar systems.
Alkali bromides NaBr and KBr possess permanent electric dipole moments of approximately 9.1 and 10.5 D, among the largest of any diatomic molecule, making them exceptional candidates for dipolar quantum science and electric-field-controlled ultracold collisions. We report a systematic ab initio investigation of all two-body reaction channels for NaBr + NaBr, KBr + KBr, and NaBr + KBr collisions using CCSD(T)/aug-cc-pVQZ potential-energy curves validated against experimental spectroscopic constants, supplemented by phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) benchmarks. All bond-swap channels are endoergic by 38,000–43,000 cm−1 (109–122 kcal mol−1) and all atom-abstraction channels by 21,000–25,000 cm−1 (60–71 kcal mol−1), thermodynamically forbidding reactive product formation at ultracold collision energies. DLPNO-CCSD(T) approach potentials, validated against canonical CCSD(T), are purely attractive for all three collision pairs, with no entrance barriers. The NaBr + KBr system additionally supports a deep alternating NaKBr2 short-range complex (well depth −47.9 kcal mol−1 at the CCSD(T)/aug-cc-pVQZ level, −42.8 counterpoise-corrected; −50.3 ± 0.3 kcal mol−1 at the ph-AFQMC level), a rectangular rock-salt intermediate analogous to the M2X2 minimum characterized for calcium monofluoride (CaF + CaF) collisions. Owing to the large permanent dipoles, the isotropic long-range interaction is dominated by the rotational dispersion term, giving total C6 ≈ 4×107–1.3×108 a.u. and universal s-wave loss rates of ≈6–8 × 10−10 cm3 s−1, at or above the KRb value. Suppressing these losses requires electric-field shielding with the molecules prepared in their first rotationally excited state; the resonant mechanism is predicted to be highly effective, with critical fields of ≈1.6–3.4 kV cm−1, comparable to those for strongly dipolar bialkali molecules such as RbCs and within an order of magnitude of KRb (∼12 kV cm−1). These results establish alkali bromides as thermodynamically stable against exchange chemistry while identifying complex-mediated (“sticky”) loss and resonant electric-field shielding as the dominant processes governing ultracold NaBr and KBr collisions.
Abstract A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanokelvin. Here we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. We map out an accurate ab initio ground-state potential energy surface of the K 2 Rb complex in full dimensionality and report numerically-exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysis of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome.