Potential energy surfaces of the low-lying electronic

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Feb 3, 2018 - imental and theoretical studies on the heteronuclear and homonu- clear alkali trimers ... help to describe elastic and inelastic atom-molecule collisions. [10,11] ... diatomics-in-molecules (DIM) approximation and used empirically evaluated ..... Analysis of the potential energy surfaces has shown character-.
Chemical Physics Letters 695 (2018) 119–124

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Research paper

Potential energy surfaces of the low-lying electronic states of the Li + LiCs system P. Jasik a,⇑, T. Kilich a, J. Kozicki b, J.E. Sienkiewicz a,* a b

´ sk University of Technology, Gdan ´ sk, Poland Faculty of Applied Physics and Mathematics, Gdan ´ sk University of Technology, Gdan ´ sk, Poland Faculty of Civil and Environmental Engineering, Gdan

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 16 November 2017 In final form 1 February 2018 Available online 3 February 2018

Ab initio quantum chemistry calculations are performed for the mixed alkali triatomic system. Global minima of the ground and first excited doublet states of the trimer are found and Born-Oppenheimer potential energy surfaces of the Li atom interacting with the LiCs molecule were calculated for these states. The lithium atom is placed at various distances and bond angles from the lithium-caesium dimer. Three-body nonadditive forces of the Li2Cs molecule in the global minimum are investigated. Dimeratom interactions are found to be strongly attractive and may be important in the experiments, particularly involving cold alkali polar dimers. Ó 2018 Elsevier B.V. All rights reserved.

Keywords: Potential energy surfaces Li2Cs Triatomic system Atom-molecule collisions Three-body nonadditive forces

1. Introduction There is a growing demand for data concerning heteronuclear alkali-metal dimers interacting with an alkali-metal atom. The investigations are carried out in the three main streams: the electronic structure properties, the dissociation or fragmentation processes and the association processes. The very extensive experimental and theoretical studies on the heteronuclear and homonuclear alkali trimers were given by the group of Ernst [1–5], where alkali quartet trimers formed on helium nanodroplets are probed by one-color femtosecond photoionization spectroscopy. The observation of predissociation in the mixed alkali trimer clusters was reported by the experimental group of Wöste [6]. The same group presented the coherent control of alkali cluster fragmentation dynamics [7]. The polar dimer gas can be controlled in optical traps and eventually converted into the quantum degenerate ultracold dipolar gas [8]. Triatomic systems attract considerable attention in the context of experiments involving cold and ultracold molecules [9]. Efficient control of such three-body interactions requires detailed knowledge of low-lying interatomic potentials. Among other data, the potential energy surfaces (PESs) for a dimer interacting with an atom are of growing interest since they may help to describe elastic and inelastic atom-molecule collisions [10,11], particularly when experiments on magnetic tuning of ⇑ Corresponding authors. E-mail addresses: (J.E. Sienkiewicz).

[email protected]

(P.

https://doi.org/10.1016/j.cplett.2018.02.005 0009-2614/Ó 2018 Elsevier B.V. All rights reserved.

Jasik),

[email protected]

Feshbach resonances [12,13] and three-body recombination [14,15] are considered. In this paper, we study the interaction between the lithium atom and the lithium-caesium dimer. We also calculate the global minima of the ground (12 A0 ) and first excited (22 A0 ) doublet states of the Li2Cs trimer, as well as three-body nonadditive contribution for the minimum of the ground state. Until now, this system was very scarcely studied. To the authors’ knowledge the first study concerning this system was performed in 1982 by Richtsmeier et al. [16], where energies of the optimized geometries for the linear LiCsLi in D1h and CsLiLi in C1v symmetries, as well as nonlinear Li2Cs trimer in the C2v symmetry were presented. This study was carried out by means of the diatomics-in-molecules (DIM) approximation and used empirically _ evaluated integrals. In turn, Zuchowski and Hutson [11] modeled the reactions involving pairs of the alkali metal dimers. Using the multireference average-quadratic coupled-cluster method (AQCC), they found the global minima of mixed alkali-metal trimers, including Li2Cs.

2. Computational method In our calculations, Li + LiCs is considered as an effective threeelectron system. Each n-electron atom is replaced by one valence electron and the effective core consisting of a nuclei and n-1 electrons. Since our theoretical approach has been already presented in a few earlier papers (e.g. [17–21]), here we give only salient details

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concerning pseudopotentials and atomic basis sets which differ from those used in our earlier calculations involving lithium and caesium atoms [17,22]. The calculations are based on the multireference singles and doubles configuration interaction with Davidson correction (MRCISD + Q) method with atomic effective core potentials and core-polarization potentials, which enables us to treat only three valence electrons explicitly. The full configuration interaction (FCI) method is used to account for the correlation missing in MRCI calculations. An augmented atomic orbital basis allows to obtain reliable Born-Oppenheimer (BO) adiabatic potentials of several molecular states. All calculations of the BO adiabatic potential energy curves (PECs) and surfaces are performed by means of the MOLPRO program package [23,24]. The core electrons of the caesium atom are represented by the ECP54SDF pseudopotential [25] and core-polarization potential with the values of dipole polarizability and cut-off parameter taken as aD ¼ 15:1 a30 and q ¼ 0:17 a2 0 , respectively. In the case of s and p functions, we use the basis set for caesium which comes with the ECP54SDF pseudopotential. For the d and f functions, we use the def2-QZVPPD basis set [26]. Additionally, these basis sets are augmented by the six s functions with the given exponential coefficients of the Gaussian Type Orbitals (GTO) (2.055983, 1.188777, 0.687355, 0.009778, 0.005059, 0.002617), the four p functions (0.695867, 0.293629, 0.004186, 0.001830) and the two d functions (11.281944, 0.003919). In turn, for Li, the core electrons are represented by the ECP2SDF pseudopotential [27] with its respective core-polarization potential parameters (aD ¼ 0:1915 a30 and q ¼ 0:831 a2 0 ). Basis set constructed for this pseudopotential is augmented by the six s functions (392.169555, 77.676373, 15.385230, 0.010159, 0.003894, 0.001493) and the four p functions (19.845562, 4.076012, 0.007058, 0.002598). Additionally, for d and f functions we use the cc-pV5Z basis set [28] augmented by the two d functions (1.043103, 0.026579). We check the quality of our basis sets by performing the CI calculations for the ground states of lithium and caesium atoms as well as for the several excited states of both atoms. The potential energy surfaces for the interaction between the LiCs dimer and the Li atom were computed using the multiconfigurational self-consistent field/complete active space self-consistent field (MCSCF/CASSCF) method to generate the orbitals for the subsequent configuration interaction calculations. The corresponding active space involves the molecular orbitals build from the 6s and 6p valence orbitals of caesium as well as 2s and 2p valence orbitals of lithium. Altogether the active space consists of 5 states in A0 and 2 states in A00 irreducible representations. In order to determine the quality of our choice, we run dimer calculations for the aforementioned basis sets and pseudpotentials. Our calculated values of the LiCs dimers ground state dissociation energy (De = 6090.259 cm1) and bond length (Re = 3.6160 Å) are in good agreement with experimental [29] values (De = 5875.455 cm1 and Re = 3.6681 Å). In order to test the active space and amount of correlation energy that is missing in MRCISD + Q computations, we run FCI calculations, both for the atomization energy of the Li2Cs trimer and for minima. No difference between the MRCI and FCI results in the atomic limit was found, while the non-zero FCI corrections to atomization and dissociation energies are respectively specified in Tables 1 and 2. Following Soldan et al. [30], we decompose the three-atom interaction potential at the minimum of the ground state into a sum of additive (V dimer ) and nonadditive (V3) contributions. Such decomposition can be expressed as

V trimer ðr 12 ; r 13 ; r 23 Þ ¼

X V dimer ðrij Þ þ V 3 ðr 12 ; r 13 ; r 23 Þ: i