arXiv:1508.07184v1 [physics.chem-ph] 28 Aug 2015 State of the art for ab initio vs empirical potentials for predicting 6e - excited state molecular energies: Application to Li 2 (b, 1 3 Π u ) Nikesh S. Dattani, 1,2,3, ∗ 1 Quantum Chemistry Laboratory, Department of Chemistry, Kyoto University, 606-8502, Kyoto, Japan, 2 School of Materials Science and Engineering, Nanyang Technological University, 639798, Singapore, and 3 Fukui Institute for Fundamental Chemistry, 606-8103, Kyoto, Japan, Robert J. Le Roy, 3, † 4 Guelph-Waterloo Centre for Graduate Work in Chemistry and Biochemistry, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada. We build the first analytic empirical potential for the most deeply bound Li2 state: b ( 1 3 Πu ) . Our potential is based on experimental energy transitions covering v =0 - 34, and very high precision theoretical long-range constants. It provides high accuracy predictions up to v = 100 which pave the way for high-precision long-range measurements, and hopefully an eventual resolution of the age old discrepancy between experiment and theory for the Li ( 2 2 S ) + Li ( 2 2 P ) C3 value. State of the art ab initio calculations predict vibrational energy spacings that are all in at most 0.8 cm -1 disagreement with the empirical potential. PACS numbers: 02.60.Ed , 31.50.Bc , 82.80.-d , 31.15.ac, 33.20.-t, , 82.90.+j, 97, , 98.38.-j , 95.30.Ky There is currently a rather large discrepancy between the best atomic 3e − ab initio calculation [1], and the most current empirical value [2, 3], for the leading long- range Li(2 2 S) − Li(2 2 P ) interaction constant (C 3 ), de- spite the latter being the most precise experimentally determined oscillator strength for any system, by an or- der of magnitude [4]. Li 2 (b, 1 3 Π u ) is one of the molecular states that dissociates to Li(2 2 S)+Li(2 2 P ), and therefore its long-range potential has this C 3 interaction constant. This “b-state” is also the deepest Li 2 potential, and out of the five lowest Li 2 states, the b-state is the only one for which an analytic empirical potential has never been made. Since the highest 2000 cm −1 worth of vibrational levels of the b-state still have not been observed, and part of this region is now accessible by current ultra-high preci- sion PA (photoassociation) technology [2, 5], an analytic potential would be very useful for making predictions to assist in observing the missing levels. The b-state also mixes strongly with the A(1 1 Σ u )-state , which has by far the most precisely determined excited molecular state po- tential in all of chemistry, yet still has a rather large gap of missing data in the middle of its energy range [2, 3]. Finally, the b(1 3 Π u )-state has been a key doorway to the triplet manifold, and was directly involved in the measurements for a vast number of other triplet states such as 2 3 Δ g [6], 3 3 Π g [7], 3 3 Σ + g [7–9], 2 3 Σ + g [7, 10], 2 3 Π g [7–9, 11], 1 3 Δ g [8, 9, 11–14], 1 3 Σ − g , and other un- determined 3 Λ states [15, 16]. Some of these more highly excited triplet states (namely 3 3 Σ + g , 2 3 Σ + g , 2 3 Π g , and 1 3 Δ g ) are so thoroughly covered by these spectroscopic * dattani.nike@gmail.com † rleroy@uwaterloo.ca measurements, that global empirical potentials can be built for them too. For this, an analytic potential for the b-state would be used as a base. In this work we will build analytic empirical potentials for the b-states of all stable homonuclear isotopologues of Li 2 . Previous work has shown that analytic empirical potentials for the c(1 3 Σ g )-state were able to predict en- ergies correctly to about 1 cm −1 , in the middle of a gap of > 5000 cm −1 where data were unavailable [5, 17], and this was much better agreement than was obtained with the most sophisticated Li 2 ab initio calculations of the time [18]. It was recently shown that the best ground-state rota- tionless ab initio potentials for the 5e − molecules BeH, BeD, and BeT, were able to predict vibrational energy spacings to within 1 cm −1 for all measured energy levels except one. The b-state of Li 2 might be expected to be more challenging ab initio because it (1) is an excited state, (2) has one more e − , and (3) involves many more vibrational energies. We will therefore compare our an- alytic empirical potentials for the b-state of 6,6 Li 2 and 7,7 Li 2 with the most state-of-the-art ab initio calcula- tions, which were published recently in [19]. Table I summarizes all experiments we could find which provided information on rovibrational levels of the b-state . Unfortunately attempts to recover the data from [9, 15, 20–22] were unsuccessful, but we were still able to include all data from the other experiments in our study. Furthermore, it is noted that the b-state was also involved in various other studies [6–8, 23, 24] but these just made use of rovibrational levels that were already determined in the studies listed in Table I, in order to access levels of other electronic states.