Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett Research paper The S 2 Rydberg series of the lithium atom. Calculations with all-electron explicitly correlated Gaussian functions Amir Bralin a , Sergiy Bubin a , Monika Stanke b , Ludwik Adamowicz c,d, ⁎ a Department of Physics, School of Science and Technology, Nazarbayev University, Astana 010000, Kazakhstan b Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, ul. Grudzia¸dzka 5, Toruń PL 87-100, Poland c Department of Chemistry and Biochemistry and Department of Physics, University of Arizona, Tucson, AZ 85721, USA d Interdisciplinary Center for Modern Technologies, Nicolaus Copernicus University, ul. Wileńska 4, Toruń PL 87-100, Poland HIGHLIGHTS • High-accuracy calculations for the 12 2 S Rydberg states of Li. • Finite-nuclear-mass approach is used. • Isotope shifts of the transition energies are calculated. • All-electron explicitly correlated Gaussian functions are used. • The non-linear parameters of the Gaussians are optimized. • Analytical energy gradient is used in the optimization. • For the 10s, 11s, 12s, and 13s states the present calculations are the first ever. ABSTRACT In this work we report very accurate variational calculations of the twelve lowest S 2 Rydberg states of the lithium atom performed with the finite-nuclear-mass (FNM) approach and with all-electron explicitly correlated Gaussian functions. The FNM non-relativistic variational energies of the states are augmented with the leading relativistic and QED corrections. The calculated transition energies are compared with the previous works (only eight states of the series were calculated before) and with the available experimental results. Density distributions of the electrons and the nucleus in the center-of-mass frame are also shown. 1. Introduction One of the major challenges of the quantum theory of atoms is to determine the energy levels corresponding to bound ground and excited states and the frequencies of the transitions between these levels with the spectroscopic accuracy (i.e. below 1 cm -1 ). As such determination involves the calculation of the corresponding wave functions re- presenting the computed states, various properties of the states can also be determined. That involves, for example, the transition intensities, the average distances of the electrons to the nucleus and between the electrons, etc. As the amount of computations required grows very ra- pidly with the number of electrons (this growth is proportional to the factorial of the number of electrons) even for atoms with a few electrons this becomes a computationally very demanding task. Thus, in under- taking such calculations the accuracy one aims to achieve needs to be balanced with the computational resources the calculations are expected to use. One of the many challenges involved in atomic calculations is to target not only a few lowest lying states but to extend the calculations to a wider spectrum of states. For the lithium atom calculations exist where excited-state energies and the corresponding wave functions were determined with high accuracy using various approaches such as: multi-reference self-consistent-field, full configuration interaction, Hylleraas-configuration-interaction, etc. [1–8]. Particularly relevant to the present work are the most recent calculations performed by Drake and Yan, Wang et al., and Puchalski et al. [2,7,8]. For the beryllium atoms only the lowest five S 1 states [9] and one P 1 state [10] were calculated. Recently, very accurate calculations were also performed for the lowest four S 2 states of the boron atom [11]. Capabilities now exist to extend the calculations of Rydberg states of small atoms to ten states and beyond. In this work such calculations are reported for two iso- topologues of the lithium atom ( 6 Li and 7 Li). The S 2 Rydberg series is https://doi.org/10.1016/j.cplett.2019.06.051 Received 24 April 2019; Received in revised form 17 June 2019; Accepted 18 June 2019 ⁎ Corresponding author. E-mail addresses: amir.bralin@nu.edu.kz (A. Bralin), sergiy.bubin@nu.edu.kz (S. Bubin), monika@fizyka.umk.pl (M. Stanke), ludwik@email.arizona.edu (L. Adamowicz). Chemical Physics Letters 730 (2019) 497–505 Available online 19 June 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved. T