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The Journal of Chemical Physics

Six-dimensional potential energy surface for NaK–NaK collisions: Gaussian process representation with correct asymptotic form

Arthur Christianen, Tijs Karman, Rodrigo A. Vargas–Hernández, Gerrit C. Groenenboom, Roman V. Krems

Published Feb 13, 2019• 51 citations
Publisher

Abstract

Constructing accurate global potential energy surfaces (PESs) describing chemically reactive molecule-molecule collisions of alkali metal dimers presents a major challenge. To be suitable for quantum scattering calculations, such PESs must represent accurately three- and four-body interactions, describe conical intersections, and have a proper asymptotic form at the long range. Here, we demonstrate that such global potentials can be obtained by Gaussian Process (GP) regression merged with the analytic asymptotic expansions at the long range. We propose an efficient sampling technique, which allows us to construct an accurate global PES accounting for different chemical arrangements with <2500 ab initio calculations. We apply this method to (NaK)2 and obtain the first global PES for a system of four alkali metal atoms. The resulting surface exhibits a complex landscape including a pair and a quartet of symmetrically equivalent local minima and a seam of conical intersections. The dissociation energy found from our ab initio calculations is 4534 cm−1. This result is reproduced by the GP models with an error of less than 3%. The GP models of the PES allow us to analyze the features of the global PES, representative of general alkali metal four-atom interactions. Understanding these interactions is of key importance in the field of ultracold chemistry.

DOI
10.1063/1.5082740

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Constructing accurate global potential energy surfaces (PESs) describing chemically reactive molecule-molecule collisions of alkali metal dimers presents a major challenge. To be suitable for quantum scattering calculations, such PESs must represent accurately three- and four-body interactions, describe conical intersections, and have a proper asymptotic form at the long range. Here, we demonstrate that such global potentials can be obtained by Gaussian Process (GP) regression merged with the analytic asymptotic expansions at the long range. We propose an efficient sampling technique, which allows us to construct an accurate global PES accounting for different chemical arrangements with <2500 ab initio calculations. We apply this method to (NaK)2 and obtain the first global PES for a system of four alkali metal atoms. The resulting surface exhibits a complex landscape including a pair and a quartet of symmetrically equivalent local minima and a seam of conical intersections. The dissociation energy found from our ab initio calculations is 4534 cm−1. This result is reproduced by the GP models with an error of less than 3%. The GP models of the PES allow us to analyze the features of the global PES, representative of general alkali metal four-atom interactions. Understanding these interactions is of key importance in the field of ultracold chemistry.
The LiNa2 reactive system has recently received great attention in the experimental study of ultracold chemical reactions, but the corresponding theoretical calculations have not been carried out. Here, we report the first globally accurate ground-state LiNa2 potential energy surface (PES) using a Gaussian process model based on only 1776 actively selected high-level ab initio training points. The constructed PES had high precision and strong generalization capability. On the new PES, the quantum dynamics calculations on the Li(2S) + Na2(v = 0, j = 0) → LiNa + Na reaction were carried out in the 0.001–0.01 eV collision energy range using an improved time-dependent wave packet method. The calculated results indicate that this reaction is dominated by a complex-forming mechanism at low collision energies. The presented dynamics data provide guidance for experimental research, and the newly constructed PES could be further used for ultracold reaction dynamics calculations on this reactive system.
A full-dimensional global potential energy surface (PES) for the KRb + KRb → K 2 Rb 2 * → K 2 + Rb 2 reaction is reported based on high-level ab initio calculations. The short-range part of the PES is fit with the permutationally invariant polynomial-neural network method, while the long-range parts of the PES in both the reactant and product asymptotes are represented by an asymptotically correct form. The long- and short-range parts are connected with intermediate-range parts to make them smooth. Within a statistical quantum model, this PES reproduces both the measured loss rates of ultracold KRb molecules and the K 2 and Rb 2 product state distributions, underscoring the important role of tunneling in ultracold chemistry. The PES also correctly predicts the lifetime of the K 2 Rb 2 * intermediate complex within the Rice–Ramsperger–Kassel–Marcus limit. It thus provides a reliable platform for future dynamical studies of the prototypical reaction.
We derive a quasiclassical expression for the density of states (DOS) of an arbitrary, ultracold, NNN-atom collision complex, for a general potential energy surface (PES). We establish the accuracy of our quasiclassical method by comparing to exact quantum results for the ${\mathrm{K}}_{2}\text{\ensuremath{-}}\mathrm{Rb}$ and NaK-NaK systems, with isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to be 0.124 $\ensuremath{\mu}{\mathrm{K}}^{\ensuremath{-}1}$, with an associated Rice-Ramsperger-Kassel-Marcus sticking time of 6.0 $\ensuremath{\mu}\mathrm{s}$. We extrapolate the DOS and sticking times to all other polar bialkali-bialkali collision complexes by scaling with atomic masses, equilibrium bond lengths, dissociation energies, and dispersion coefficients. The sticking times calculated here are two to three orders of magnitude shorter than those reported by Mayle et al. [Phys. Rev. A 85, 062712 (2012)]. We estimate dispersion coefficients and collision rates between molecules and complexes. We find that the sticking-amplified three-body loss mechanism is not likely the cause of the losses observed in the experiments.
This thesis describes four types of cold molecular collision systems with increasing complexity: from simple atom-diatomic molecule to complicated polyatomic molecule-polyatomic molecule. The early thesis work is concerned with three open questions pertaining to collision dynamics of cold molecules. We demonstrate the possibility of controlling collisional decoherence of ultracold molecules by tuning an external magnetic field. We then provide insight into the feasibility of evaporative cooling of molecules, and for the first time incorporate the uncertainty analysis of the potential energy surface (PES) into scattering calculations. In addition, we use classical trajectory methods to study the effects of the interaction strength and the geometry of rigid polyatomic molecules on the formation of long-lived collision complexes at low collision energies. The second half of the thesis work is focused on combining statistical methodology and scattering calculations to address two major problems in molecular dynamics calculations: increasing computational complexity and uncertainties due to inaccuracies of PES. Using a small number of scattering calculations, we show that we can build a Gaussian Process (GP) model to statistically approximate collision outcomes for complex molecules, and then perform the uncertainty analysis and the sensitivity analysis. We also demonstrate that trained by a combination of classical and quantum calculations, a GP model can provide an accurate description of the quantum scattering cross sections, even near scattering resonances.
A full-dimensional global potential energy surface (PES) for the reaction 23 Na 87 Rb + 23 Na 87 Rb → 23 Na 2 + 87 Rb 2 was constructed based on high-level ab initio calculations. The short-range part was expressed as a permutation invariant polynomial-neural network (PIP-NN) fit of 22 003 ab initio points calculated using a coupled cluster method with the one-electron basis 5 s 5 p 5 d 2 f plus effective core potentials and core polarizability potentials, while the long-range part was represented in an asymptotically correct form based on multipole expansion. The formation rate of the 23 Na 2 87 Rb 2 complex calculated using a quantum statistical method is in good agreement with experiment, while the estimated 19.20 μs lifetime of the complex from Rice–Ramsperger–Kassel–Marcus (RRKM) theory is significantly shorter than the measured millisecond decay rate, signaling either the inadequacy of RRKM theory or a yet unresolved loss mechanism.
A faithful description of chemical processes requires exploring extended regions of the molecular potential energy surface (PES), which remains challenging for strongly correlated systems. Transferable deep-learning variational Monte Carlo (VMC) offers a promising route by efficiently solving the electronic Schrödinger equation jointly across molecular geometries at consistently high accuracy, yet its stochastic nature renders direct exploration of molecular configuration space nontrivial. Here, we present a framework for highly accurate ab initio exploration of PESs that combines transferable deep-learning VMC with a cost-effective estimation of energies, forces, and Hessians. By continuously sampling nuclear configurations during VMC optimization of electronic wave functions, we obtain transferable descriptions that achieve zero-shot chemical accuracy within chemically relevant distributions of molecular geometries. Throughout the subsequent characterization of molecular configuration space, the PES is evaluated only sparsely, with local approximations constructed by estimating VMC energies and forces at sampled geometries and aggregating the resulting noisy data using Gaussian process regression. Our method enables accurate and efficient exploration of complex PES landscapes, including structure relaxation, transition-state searches, and minimum-energy pathways, for both ground and excited states. This opens the door to studying bond breaking, formation, and large structural rearrangements in systems with pronounced multi-reference character.