Supporting Information. Study of the Valence and Rydberg States of a Lithium Dimer by the Multi-reference Configuration-interaction Method

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1 Study of Excited States of Li 2 by the MRCI Method Bull. Korean Chem. Soc. 2014, Vol. 35, No Supporting Information Study of the Valence and Rydberg States of a Lithium Dimer by the Multi-reference Configuration-interaction Method Chun-Woo Lee Department of Chemistry, Ajou University, Woncheon-Dong, Yeongtong-Gu, Suwon , Korea * Received December 30, 2013, Accepted January 21, 2014 Comparison of potential energy curves of states obtained by the all-electron ab initio calculations with experimental ones Π g state Figures 1-5 show the comparison of the potential energy curves (PECs) of this work with those reported in Ref. [13] and the experimental PECs for the cases where other allelectron ab initio results are available. The effective core potential/core polarization potential (ECP/CPP) results are also compared together if they are available. 1. F(4) 1 Σ g state Figure 2. Comparison of the experimental and theoretical PECs of the 2 3 Π g state. Yiannopoulou et al. and Li et al. refer to Refs. [3] and [4], respectively. The line style and color for the experimental PECs and theoretical PECs of this work and others follow those of Fig. 1. Figure 1. Experimental and theoretical PECs of the F(4) 1 Σ g state are compared in (a). Qi et al. and Pashov et al. in the legend of (a) refer to the curves reported in Refs. [1] and [2], respectively. The line style and color convention of (b) follow those of (a).

2 2 Bull. Korean Chem. Soc. 2014, Vol. 35, No. 5 Chun-Woo Lee Σ g state Π g state Figure 3. Comparison of the experimental and theoretical PECs of the 5 1 Σ g state. Song et al. refers to Ref. [5]. The line style and color for the experimental PECs and theoretical PECs of this work and others follow those of Fig. 1. Figure 5. Comparison of the experimental and theoretical PECs of the 3 3 Π g state. Yiannopoulou et al. and Ivanov et al. refer to Refs. [3] and [6], respectively. The line style and color for the experimental PECs and theoretical PECs of this work and others follow that of Fig Σ g state Figure 4. Comparison of the experimental and theoretical PECs of the 6 1 Σ g state. Song et al. refers to Ref. [5]. The line style and color for the experimental PECs and theoretical PECs of this work and others follow that of Fig. 1.

3 Study of Excited States of Li 2 by the MRCI Method Bull. Korean Chem. Soc. 2014, Vol. 35, No. 5 3 The matching basis set for effective core potential ECP2SDF 1. Stoll's CC-PV5Z (4s4p4d3f2g) s: , , , p: , , , , d: , , , f: , , g: , Jasik and Sienkiewicz's basis set (JS) Stoll5s5p4d (9s9p8d3f2g) s : , , (core) , (diffused) p : , , (core) , (diffused) d : ,1.9783, , (core) (diffused) 3. Gadea basis set (GA) (27s17p14d6f2g) s,li,5000.,3000.,2000.,1000.,500.,300.,200.,100.,50.,30.,20.,10.,5.,3.,2.,1.; s,li,.5,.25,.1,.05,.03,.02,.01,.005,.003,.002,.001; p,li,100.,50.,30.,20.,10.,5.,3.,2.,1.; p,li,.6004,.1838,.06625,.02707,.01125, , , ; d,li,50.,30.,20.,10.,5.,3.,2.,1.; d,li,.3913,.09734,.03306,.01346, , ; f,li,10.,5.,1.; f,li,0.019,0.0066,0.0027; g,li,10.,1.; 4. Jasik and Sienkiewicz's extended basis set (JS extended) (12s12p12d10f2g) s,li, , , , , , s,li, , , , , , , p,li, , , , , , p.li , , , , , , d,li, , , ,1.9783, , d,li, , , , , , , f,li, , , , , , f,li, , , , , g,li, , JSGA set (10s, 10p, 10d, 5f, 2g) s,li, , , , , , , , ,,0.003,.002,.001 p,li, , , , ,0.1838,.06625,.02707,.01125, , , d,li, ,1.9783, , , , , , ,.01346, , f,li, , , ,0.019,0.0066, g,li, , Comparison of experimental atomic level energies with ones obtained by the ECP/CPP method using various basis sets

4 4 Bull. Korean Chem. Soc. 2014, Vol. 35, No. 5 Chun-Woo Lee Table 2. Comparison of the spectroscopic parameters R e (Å), D e, and T e (cm -1 ) of a lithium dimer obtained by ECP/CPP method, from the all-electron ab initio PECs of this work with those of experimental data. The values of experimental data are taken from Ref. [13] State ECP/CPP 13 All-electron (this work) Exp. R e D e T e R e D e T e R e D e T e 1 1 Σ g Σ g Σ g Σ g Σ g Σ u Σ u Σ u Σ u Σ u Σ u Σ u Σ u Σ u Σ u Σ u Σ g Σ g Π g Π g Π u Π u Π g Π u Π u Δ g Figure 3. Errors in the calculations of R e, D e, and T e by the ECP/ CPP and all-electron ab initio methods compared to the experimental data. The first (blue) and second (red) bars for each state denote the errors in the ECP/CPP and all-electron ab initio methods, respectively. Table 3. Percent electron correlation energies of the MRCI method in He and Li atoms. Hartree-Fock energies are obtained by the program developed by Fischer 49 Energy (a. u.) He 1s 2 1 S He 1s2p 3 P E HF E MRCI (AV6Z) E Exact % corr 99.4 Energy (a. u.) ΔE (cm 1 ) Li 1s 2 2s 2 S Li 1s 2 2p 2 P E HF E MRCI (AV5Z) E Exact % corr Experimental value 14903

5 Study of Excited States of Li 2 by the MRCI Method Bull. Korean Chem. Soc. 2014, Vol. 35, No. 5 5 Table 1. Comparison of experimental atomic energy levels with theoretical values obtained by the ECP/CPP method with various basis sets State Atomic level energies (cm -1 ) Exp. ECP/CPP MRCI Stoll JS JS extended GA JSGA 2s s d d s d d s p p p f f Table 2. Errors in the calculated atomic energy levels obtained by the ECP/CPP method with various basis sets compared to the experimental data State Errors in calculated atomic level energies (cm -1 ) Stoll JS JS extended GA JSGA 2s s d d s d d s p p p f f

6 6 Bull. Korean Chem. Soc. 2014, Vol. 35, No. 5 Chun-Woo Lee Kaufmann's basis set 1. (3p,4d,5f,3g) p, , , d, , , , f, , , , , g, , , (3p,4d,5f,2g) p, , , d, , , , f, , , , , g, , (3f) f, ,0.0066, (3p,4d,3f) p, , , d, , , , f, , , References 1. Qi, P.; Lazarov, G.; Marjatta Lyyra, A.; Jeung, G.-H. J. Mol. Spectrosc. 2008, 247, Pashov, A.; Jastrzebski, W.; Kowalczyk, P. J. Chem. Phys. 2000, 113, Yiannopoulou, A.; Urbanski, K.; Antonova, S.; Lyyra, A. M.; Li, L.; An, T.; Whang, T. J.; Ji, B.; Wang, X. T.; Stwalley, W. C.; Leininger, T.; Jeung, G. H. J. Chem. Phys. 1995, 103, Xie, X.; Field, R. W. J. Mol. Spectrosc. 1986, 117, Song, M.; Yi, P.; Dai, X.; Liu, Y.; Li, L.; Jeung, G. H. J. Mol. Spectrosc. 2002, 215, Ivanov, V. S.; Sovkov, V. B.; Li, L.; Lyyra, A. M.; Lazarov, G.; Huennekens, J. J. Mol. Spectrosc. 1999, 194, 147.