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

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.

Quasiclassical method for calculating the density of states of ultracold collision complexes

“…This is the same potential as used by Croft et al [20], except that we use for V K 2 the diatom potential constructed for our previous work in Ref. [24]. Just as in Ref.…”

“…The realistic potential energy surface of NaK-NaK consists of three parts [24]: two symmetrically equivalent NaK-NaK parts and one Na 2 -K 2 part. Although one set of Jacobi coordinates can in principle describe all arrangements, integrating over these Jacobi coordinates is very difficult, because an increasingly fine angular grid is needed when going further into an arrangement that does not match the chosen coordinates.…”

“…Because there are some overlapping parts of the grids in the center of the PES, we assign a geometry dependent weighting factor to the integrands for each arrangement. This weighting factor W (q) is based on the symmetrization function in our previous work [24].…”

“…For the isotropic PES, the NaK monomer potentials of Ref. [24] were used, together with a Lennard-Jones intermolecular potential with parameters C 6 = 8500 E h a 6 0 . and D e = 4534 cm −1 .…”

Photoinduced Two-Body Loss of Ultracold Molecules

“…Here, E is the total energy in the system, J is the total angular momentum quantum number, p is the parity and VðqÞ is the potential energy as a function of the Jacobi coordinates of the complex q ¼ ðR; r 1 ; r 2 ; θ 1 ; θ 2 ; ϕÞ: the intermolecular distance R, the bond lengths r 1 , r 2 , the polar angles, θ 1 , θ 2 , and the dihedral angle, ϕ (see Ref. [29]). The complex has D ¼ 6 internal degrees of freedom.…”