Ab initio potential curves for the X 2 R þ u ,A 2 P u and B 2 R þ g states of Ca þ 2 Sandipan Banerjee ⇑ , John A. Montgomery Jr., Jason N. Byrd, H. Harvey Michels, Robin Côté Department of Physics, University of Connecticut, Storrs, CT 06269-3046, USA article info Article history: Received 22 March 2012 In final form 6 June 2012 Available online 14 June 2012 abstract We report ab initio calculations of the X 2 R þ u , A 2 P u and B 2 R þ g states of the Ca þ 2 dimer. All electron CAS + MRCI calculations are performed for the X 2 R þ u and B 2 R þ g states, while valence CAS + MRCI calcu- lations using an effective core potential are used to describe the A 2 P u state. A double well is found in the B 2 R þ g state. Spectroscopic constants, vibrational levels, transition moments and radiative lifetimes are calculated for the most abundant isotope of calcium ( 40 Ca). The static dipole and quadrupole polarizabil- ities, and the leading order van der Waals coefficients are also calculated for all three states. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction The presence of near degeneracies in the constituent atoms of diatomic molecules can lead to a rich structure in the resulting interaction potentials. In our recent work on the Be þ 2 dimer [1], we showed that the nearly degenerate 2s–2p state of beryllium leads to a complex set of low lying molecular curves, including a double minima in the lowest 2 R þ g state. In this Letter, we present new computational results on the Ca þ 2 dimer, and demonstrate that this system also exhibits a rich manifold of low-lying molecular states. Both Be and Ca represent group 2A elements in the periodic table, with their valence electronic structures (2s) 2 and (4s) 2 , respectively. Thus, some similarities between Be þ 2 and Ca þ 2 may be expected. The calculations presented here should help guide experimental efforts on cold molecular ions. The last few years have seen significant interest in ultracold atom–ion scattering [2,3] in the atomic, molecular and optical physics community. The experimental realization of Bose–Einstein condensation (BEC) has led to numerous applications involving charged atomic and molecular species. The cooling and trapping [4] of charged gases at sub-kelvin (ultracold) temperatures is a to- pic of growing interest. The phenomena of charge transport like resonant charge transfer [5] and charge mobility [6] at ultracold temperatures have also been studied in detail. Other emerging fields of interest include ultracold plasmas [7], ultracold Rydberg gases [8] and systems involving ions in a BEC [9,10]. In this Letter, we begin by describing the methods used in our calculations, and follow with a discussion of the results, which in- clude the potential curves of the X 2 R þ u , B 2 R þ g and A 2 P u states and their spectroscopic constants. We also calculate electric dipole transition moments for the X 2 R þ u $ B 2 R þ g and the B 2 R þ g $ A 2 P u transitions. Bound vibrational levels are computed for all the states along with Franck–Condon overlaps and radiative lifetimes for the most abundant calcium isotope ( 40 Ca 96:94%). We conclude with an analysis of long range behavior, calculation of static atomic dipole and quadrupole polarizabilities and deter- mination of the van der Waals dispersion coefficient C 6 . 2. Methods We can express the total energy of the Ca þ 2 dimer at any inter- atomic separation R as E total ¼ E valence þ DE core-valence þ DE scalar-relativistic : ð1Þ For calculation of the ground X 2 R þ u and B 2 R þ g states in Ca þ 2 , the valence contribution to the total energy is calculated by a multi-reference configuration interaction (MRCI) method using an 18 orbital complete active space (CAS) wavefunction as a reference. The active space was chosen to include molecular counterparts of nearly degenerate 4s, 4p and 3d orbitals of Ca. The state-averaged CAS includes all doublet states correlated to Ca þ ð 2 DÞþðCað 1 SÞ and Ca þ ð 2 SÞþðCað 1 SÞ asymptotes with equal weights. We have used the augmented correlation consistent polarized valence quintuple zeta (aug-cc-pV5Z) basis set of Peter- son [11,12]. In order to assess the quality of MRCI, we do a com- parison with a full CI calculation with aug-cc-pVTZ basis, and find out that the difference in total energy at the equilibrium separation of 7.3 bohrs for the X 2 R þ u state of Ca þ 2 is 4.5 microhar- trees. At large separation (1000 bohrs), this difference further reduces to 1.5 microhartrees. The second term in Eq. (1), the correction from the core-valence contribution is estimated by, DE core-valence ¼½E RIV  E Val  R ½E RIV  E Val  R1 : ð2Þ The core-valence correction DE core-valence is the difference of energies from a valence only (Ar core) and a restricted inner va- lence (RIV, Ne core) CCSDT calculation. For this purpose we have 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2012.06.011 ⇑ Corresponding author. Fax: +1 860 486 3346. E-mail address: banerjee@phys.uconn.edu (S. Banerjee). Chemical Physics Letters 542 (2012) 138–142 Contents lists available at SciVerse ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett