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International Journal of Quantum Chemistry

Potential energy surface and bound states of the (X4Σ)KRb‐K complex

David López‐Durán, Néstor F. Aguirre, Gerardo Delgado-Barrio, Pablo Villarreal, Franco Antonio Gianturco, María Pilar de Lara‐Castells

Published Sep 11, 2014• 3 citations

Abstract

We present in this work a potential energy surface of the (X4Σ)KRb‐K complex for which high level ab initio calculations have been carried out at the RCCSD(T) level of theory, using ECP10MDF/ECP28MDF effective core potentials and basis sets for K/Rb, respectively, with the dimer at its lowest triplet state and fixed to the equilibrium distance. The interaction is shown to be very anisotropic, with one clear minimum at a T‐type geometry of the complex. The depth of the well is found to be 767.7 cm−1 located at in Jacobi coordinates from the center of mass of the diatomic partner. A variational (VAR) procedure and the Diffusion Monte Carlo technique have been applied to explore the bound states of the aggregate. Both descriptions provide similar features for the vibrational, nonrotating, ground‐state, with an energy of cm−1 and the maximum of the wavefunction peaked above the well of the surface. Excited states are also reported using the VAR treatment and angular and/or radial excitations are identified among the lower‐lying vibrational states. These results should already provide an initial step toward a more comprehensive study of the collisions at ultralow temperatures of K+KRb, important process in the field of ultracold molecular chemistry. © 2014 Wiley Periodicals, Inc.

DOI: 10.1002/qua.24759

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We present in this work a potential energy surface of the (X4Σ)KRb‐K complex for which high level ab initio calculations have been carried out at the RCCSD(T) level of theory, using ECP10MDF/ECP28MDF effective core potentials and basis sets for K/Rb, respectively, with the dimer at its lowest triplet state and fixed to the equilibrium distance. The interaction is shown to be very anisotropic, with one clear minimum at a T‐type geometry of the complex. The depth of the well is found to be 767.7 cm−1 located at in Jacobi coordinates from the center of mass of the diatomic partner. A variational (VAR) procedure and the Diffusion Monte Carlo technique have been applied to explore the bound states of the aggregate. Both descriptions provide similar features for the vibrational, nonrotating, ground‐state, with an energy of cm−1 and the maximum of the wavefunction peaked above the well of the surface. Excited states are also reported using the VAR treatment and angular and/or radial excitations are identified among the lower‐lying vibrational states. These results should already provide an initial step toward a more comprehensive study of the collisions at ultralow temperatures of K+KRb, important process in the field of ultracold molecular chemistry. © 2014 Wiley Periodicals, Inc.

Interaction energies for the lowest triplet state a (3)Sigma(+) of KRb are calculated using high level ab initio methods. The interaction energies are then morphed so that the resulting potential energy curve yields 32 bound states and the correct scattering length for (40)K(87)Rb. Calculated vibrational spacings are shown to be in very good agreement with the available experimental Fourier transform and photoassociation vibrational data, but a different numbering scheme has to be used for the experimental vibrational assignment.

The structure and energetics of (3,4)HeCs(2)((3)Sigma(u)) molecules are analyzed from first principles. Fixing the cesium dimer at its equilibrium distance, the electronic structure was determined through ab initio methods at the CCSD(T) level of theory using a large basis set to compute the interaction energies. At the T-shaped geometry, there is a shallow well with a depth of approximately 2 cm(-1) placed at R approximately 6.75 A, R being the distance from the center of mass of Cs(2) to He. That depth gradually decreases to approximately 0.75 cm(-1), while R increases to about 11.5 A at linear arrangements. A simple model of adding atom-atom Lennard-Jones potentials with well-depth and equilibrium distance parameters depending on the angular orientation was found to accurately reproduce the ab initio points. Using this analytical form, variational calculations at zero total angular momentum are performed, predicting a single bound level at approximately -0.106 (approximately -0.042) cm(-1) for the boson (fermion) species. Further calculations using Quantum Monte Carlo methods are carried out and found to be in good agreement with the variational ones. On the basis of the present results, such analytical expression could in turn be used to describe the structure and binding of larger complexes and therefore opens the possibility to further studies involving such aggregates.

We investigate atom-diatom reactive collisions, as a preliminary step,in order to assess the possibility of forming Rb(2) molecules in their lowest triplet electronic state by cold collisions of rubidium atoms on the surface of helium nanodroplets [corrected]. A simple model related to the well-known Rosen treatment of linear triatomic molecules [N. Rosen, J. Chem. Phys. 1, 319 (1933)] in relative coordinates is used, allowing to estimate reactive probabilities for different values of the total angular momentum. The best available full dimensional potential energy surface [Guillon et al., J. Chem. Phys. 136, 174307 (2012)] is employed through the calculations. Noticeable values of the probabilities in the ultracold regime, which numerically fulfill the Wigner threshold law, support the feasibility of the process. The rubidium dimer is mainly produced at high vibrational states, and the reactivity is more efficient for a bosonic helium partner than when the fermion species is considered.

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.

A new full-dimension potential energy surface of the three-body He-Rb₂(³Σ(u)(+)) complex and a quantum study of small (⁴He)(N)-Rb₂(³Σ(u)(+)) clusters, 1 ≤ N ≤ 4, are presented. We have accurately fitted the ab initio points of the interaction to an analytical form and addressed the dopant's vibration, which is found to be negligible. A Variational approach and a Diffusion Monte Carlo technique have been applied to yield energy and geometric properties of the selected species. Our quantum structure calculations show a transition in the arrangements of the helium atoms from N = 2, where they tend to be separated across the diatomic bond, to N = 4, in which a closer packing of the rare gas particles is reached, guided by the dominance of the He-He potential over the weaker interaction of the latter adatoms with the doping dimer. The deepest well of the He-Rb₂ interaction is placed at the T-shape configuration, a feature which causes the dopant to be located as parallel to the helium "minidroplet". Our results are shown to agree with previous findings on this and on similar systems.

We report analyses and comparison of three high quality ab initio KRb $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state potentials [Rousseau et al., J. Mol. Spectrosc. 203, 235 (2000); Park et al., Chem. Phys. 257, 135 (2000); Kotochigova et al., Phys. Rev. A 68, 011501 (2003)]. Eigenvalues for all vibrational levels and precision binding energies for high-lying levels (and corresponding triplet scattering lengths) are presented. By adjusting the inner wall of a potential, we show that we can reproduce measured scattering lengths of two isotopomers and predict scattering lengths of all isotopomers.