Table 2.
Summary of the computational schemes of B II, C I−IV, Al I−II, Si I−IV, P II, S II, Cl III, Ar IV, Ca I, Ti II, Zr III, and Sn II.
| Configurations | MR-RCI | Core orbitals | Correlation | AS | NNCFs |
|---|---|---|---|---|---|
| B II (1), Nlevels = 100 | |||||
| 2s2,2p2, | 2s2,2p2, | 1s | VV + CV | {11s,11p,11d,11f, | e: 777 325 |
| {2s,2p}nl (n ≤ 6, l ≤ 5) | {2s,2p}nl (n ≤ 6, l ≤ 5) | + CC (1s) | 11g,11h,11i,11k} | o: 800 410 | |
| C I, Nlevels = 100 | |||||
| 2s2p3 | 2s2p3 | 1s | VV + CV (1s) | {11s,10p,10d,9f, | e: 14 941 842 |
| 2s22p{n1s,n2p,n3d,4f} | 2s22p{n1s,n2p,n3d,4f} | 7g,6h} | o: 15 572 953 | ||
| (3 ≤ n1 ≤ 6, 2 ≤ n2 ≤ 5, 3 ≤ n3 ≤ 5) | (3 ≤ n1 ≤ 6, 2 ≤ n2 ≤ 6, 3 ≤ n3 ≤ 5) | ||||
| 2p3{n1s,n2p,n3d} | |||||
| (3 ≤ n1 ≤ 6, 3 ≤ n2 ≤ 5, 3 ≤ n3 ≤ 6) | |||||
| 2s2p2{3s,3p,4p,6p,6d,7s} | |||||
| 2s2p{n1s,n2p,n3d,4f}6d | |||||
| (3 ≤ n1 ≤ 6, 3 ≤ n2 ≤ 5, 3 ≤ n3 ≤ 5) | |||||
| C II, Nlevels = 69 | |||||
| 2s2nl(n ≤ 6, l ≤ 4) | 2s2p2, 2s2{n1s,n2p,n3d,n4f,n5g} | 1s | VV + CV (1s) | {13s,13p,13d,13f, | e: 6 623 511 |
| 2s27l(l ≤ 3) | (3 ≤ n1 ≤ 7, 2 ≤ n2 ≤ 8, 3 ≤ n3 ≤ 7 | 10g,8h} | o: 4 768 481 | ||
| 2s2p2, 2p3, | 4 ≤ n4 ≤ 7, 5 ≤ n5 ≤ 6) | ||||
| 2s2p3s, 2s2p3p | 2p3, 2p2{n1s,n2p,n3d,n4f,n5g} | ||||
| (3 ≤ n1 ≤ 7, 4 ≤ n2 ≤ 7, 3 ≤ n3 ≤ 7 | |||||
| 4 ≤ n4 ≤ 7, 5 ≤ n5 ≤ 6) | |||||
| 2s2p{3s,4s,8s,3p,3d,4d,5d,6d,8d} | |||||
| 2s3s{3p,8p} | |||||
| C III (2), Nlevels = 114 | |||||
| 2snl(n ≤ 7, l ≤ 4) | 2snl (n ≤ 7, l ≤ 4) | 1s | VV + CV (1s) | {12s,12p,12d,12f, | e: 1 578 620 |
| 2p2, 2p{3s,3p,3d} | 2p2, 2p{3s,3p,3d} | 11g,8h} | o: 1 274 147 | ||
| C IV (2), Nlevels = 53 | |||||
| 1s2nl (n ≤ 8, l ≤ 4) | 1s2nl (n ≤ 8, l ≤ 4) | 1s | CV + CC (1s) | {14s,14p,14d,12f,12g, | e: 1 077 872 |
| 1s26h | 1s26h | 8h,7i} | o: 1 287 706 | ||
| Al I (3), Nlevels = 28 | |||||
| 3s3p2, 3s2{n1s,n2p,n3d,n4f,5g} | 3s3p2, {3s2,3p2}{n1s,n2p,n3d,n4f,5g} | 1s,2s,2p | VV + CV (2p) | {12s,12p,12d,11f, | e: 4 362 628 |
| (4 ≤ n1 ≤ 6, 3 ≤ n2 ≤ 6, 3 ≤ n3 ≤ 6, | (4 ≤ n1 ≤ 6, 3 ≤ n2 ≤ 6, 3 ≤ n3 ≤ 6, | 11g,10h} | o: 2 889 385 | ||
| 4 ≤ n4 ≤ 5) | 4 ≤ n4 ≤ 5) | ||||
| Al II (3), Nlevels = 78 | |||||
| 3s2, 3p2, 3s6h, 3p3d | 3s2, 3p2, 3s6h, 3p3d | 1s,2s,2p | VV + CV (2s,2p) | {13s,13p,12d,12f,12g, | e: 911 795 |
| 3s{n1s,n2p,n3d,n4f} | 3s{n1s,n2p,n3d,n4f} | 8h,7i} | o: 1 269 797 | ||
| (4 ≤ n1 ≤ 7, 3 ≤ n2 ≤ 7, 3 ≤ n3 ≤ 6, | (4 ≤ n1 ≤ 7, 3 ≤ n2 ≤ 7, 3 ≤ n3 ≤ 6, | ||||
| 4 ≤ n4 ≤ 6) | 4 ≤ n4 ≤ 6) | ||||
| Si I (4), Nlevels = 168 | |||||
| 3s23p2, 3s3p3, 3s23p5g | 3s23p2, 3s3p3, 3p4, 3s23p5g, 3s3p23d, | 1s,2s,2p | VV + CV (2s,2p) | {13s,12p,12d,11f,10g, | e: 8 789 575 |
| 3s23p{n1s,n2p,n3d,n4f} | 3p37d, 3s3p7d2, 3s23p3d, 3p35g, | 9h,7i} for VV | o: 9 097 389 | ||
| (4 ≤ n1 ≤ 8, 4 ≤ n2 ≤ 7, 3 ≤ n3 ≤ 6, | {3s23p,3p3,3s3p3d}{n1s,n2p,n3d,n4f} | {9p,7d,6f,5g} for CV | |||
| 4 ≤ n4 ≤ 6) | (4 ≤ n1 ≤ 8, 4 ≤ n2 ≤ 7, 3 ≤ n3 ≤ 6 | ||||
| 4 ≤ n4 ≤ 6), 3s3p3d5g | |||||
| Si II (4), Nlevels = 56 | |||||
| 3s3p2, 3s3p3d, 3s3p4s, 3s2{5g,6g} | 3s3p2, 3s3p3d, 3s3p4s, 3s2{5g,6g} | 1s,2s,2p | VV + CV (2s,2p) | {13s,12p,12d,11f,10g, | e: 5 267 943 |
| 3s2{n1s,n2p,n3d,n4f} | 3s2{n1s,n2p,n3d,n4f4} | 9h,7i} for VV | o: 6 582 233 | ||
| (4 ≤ n1 ≤ 8, 3 ≤ n2 ≤ 7, 3 ≤ n3 ≤ 7, | (4 ≤ n1 ≤ 8, 3 ≤ n2 ≤ 7, 3 ≤ n3 ≤ 7, | {9p,7d,6f,5g} for CV | |||
| 4 ≤ n4 ≤ 7) | 4 ≤ n4 ≤ 7) | ||||
| Si III (5), Nlevels = 106 | |||||
| 3s2, 3p2, 3p4s, 3p4p, | 3s2, 3p2, 3p4s, 3p4p, | 1s,2s,2p | VV + CV (2s,2p) | {13s,13p,12d,12f,12g, | e:1 401 150 |
| 3s{n1s,n2p,n3d,n4f,n5g} | 3s{n1s,n2p,n3d,n4f,n5g} | 9h} | o: 1 760 209 | ||
| (4 ≤ n1 ≤ 7, 3 ≤ n2 ≤ 7, 3 ≤ n3 ≤ 7, | (4 ≤ n1 ≤ 9, 3 ≤ n2 ≤ 9, 3 ≤ n3 ≤ 8, | ||||
| 4 ≤ n4 ≤ 7, 5 ≤ n5 ≤ 7) | 4 ≤ n4 ≤ 8, 5 ≤ n5 ≤ 8) | ||||
| 3pnd (3 ≤ n2 ≤ 4) | 3pnd (3 ≤ n2 ≤ 4) | ||||
| Si IV (5), Nlevels = 45 | |||||
| 2s22p6nl (n ≤ 7, l ≤ 6) | 2s22p6nl (n ≤ 9, l ≤ 6) | 1s,2s,2p | CV + CC (2s,2p) | {13s,13p,13d,12f,12g, | e: 995 020 |
| 12h,12i} | o: 993 501 | ||||
| P II (6), Nlevels = 106 | |||||
| 3s23p2, 3s3p23d, 3s3p3, | 3s23p2, 3s3p23d, 3s3p3, 3s23d2, 3p4, | 1s,2s,2p | VV + CV (2p) | {12s,11p,11d,10f,9g, | e: 5 954 032 |
| 3s23p{n1s,n2p,n3d,n4f} | 3s23d7d, 3s3p27d, 3s3p24p, 3p37d, | 7h,7i} | o: 4 815 663 | ||
| (4 ≤ n1 ≤ 6, 4 ≤ n2 ≤ 6, 3 ≤ n3 ≤ 5, | 3s23p{n1s,n2p,n3d,n4f} | ||||
| 4 ≤ n4 ≤ 5) | (4 ≤ n1 ≤ 7, 4 ≤ n2 ≤ 6, 3 ≤ n3 ≤ 7, | ||||
| 4 ≤ n4 ≤ 5) | |||||
| 3p3{n1s,n2p,n3d,n4f} (4 ≤ n1 ≤ 7, | |||||
| 4 ≤ n2 ≤ 6, 3 ≤ n3 ≤ 7, 4 ≤ n4 ≤ 5) | |||||
| S II (7), Nlevels = 134 | |||||
| 3s3p4, 3s23p3, 3s3p33d | 3s3p4, 3s23p3, 3s3p33d, 3p5 | 1s,2s,2p | VV + CV (2p) | {9s,9p,9d,8f,8g,8h,8i} | e: 6 220 422 |
| 3s23p2{n1s,n2p,n3d,n4f} | 3s23p2{n1s,n2p,n3d,n4f} | {6s,6p,5d,5f} for S | |||
| (4 ≤ n1 ≤ 5, 4 ≤ n2 ≤ 5 | (4 ≤ n1 ≤ 5, 4 ≤ n2 ≤ 5 | from 2p | |||
| 3 ≤ n3 ≤ 4, n4 = 4) | 3 ≤ n3 ≤ 5, n4 = 4) | ||||
| 3p4{3d,4s,4p,4d,4f,5s,5p} | |||||
| 3s3p23d{3d,4s,4p,4d,4f,5s,5p} | |||||
| Cl III (7), Nlevels = 87 | |||||
| 3s3p4, 3s23p3, 3s3p33d, 3p5 | 3s3p4, 3s23p3, 3s3p33d, 3p5 | 1s,2s,2p | VV + CV (2p) | {9s,9p,9d,8f,8g,8h,8i} | e: 6 466 816 |
| 3s23p2{3d,4s,4p,4d} | 3p4{3d,4p}, 3s3p34s, 3s3p23d2 | {6s,6p,5d,5f} for S | o: 4 111 005 | ||
| 3s3p23d{4s,4p,4d}, 3s23p3d2 | from 2p | ||||
| Ar IV (7), Nlevels = 103 | |||||
| 3s3p4, 3s23p3, 3s3p33d, 3p5 | 3s3p4, 3s23p3, 3s3p33d, 3p5 | 1s,2s,2p | VV + CV (2p) | {9s,9p,9d,8f,8g,8h,8i} | e: 4 946 496 |
| 3s23p2{3d,4s,4p} | 3s23p2{3d,4s,4p,4d,4f}, 3p43d | {7s,6p,6d,6f,5g} for S | o: 7 329 546 | ||
| 3s3p23d{3d,4s,4p}, 3s3d24s, 3s23d3 | from 2p | ||||
| 3s23p3d2, 3s3p34s, 3p44p, 3p33d2 | |||||
| Ca I, Nlevels = 45 | |||||
| 4s2, 4p2, 3d{4s,4p}, | 4s2, 4p2, 3d2 | 1s,2s,2p, | VV + CV | {10s, 10p, 8d, 8f, 8g, 6h} | e: 2 916 533 |
| 4s{4p,4d,4f,5s,5p,6s,6p} | 4s{5s,6s,4p,5p,6p,4d,5d,4f} | 3s,3p | + CC (3s,3p) | {10s,10p,8d} for CC | o: 3 021 057 |
| 4p{5p,7p,4d,5d} | |||||
| 3d{4s,5s,4p,5p,4d,5d} | |||||
| Ti II, Nlevels = 99 | |||||
| 3d2{4s,4p}, 3d3, 3d4s2 | 3d2{4s,4p,4d}, 3d3, 3d{4s2,4p2,4d2} | 1s,2s,2p, | VV + CV | {8s,8p,8d,8f,8g,8h,7i} | e: 14 089 101 |
| 3d4s4p | 3d4s{4p,4d,5s}, 4s2{4p,4d}, 4s{4p2,4d2} | 3s,3p | + CC (3s,3p) | {8s,8p,8d} for CC | o: 15 573 967 |
| 4s4p4d, 3d4s5p, 3d4p4d, 4p4d2 | |||||
| 3p4{3d44s,3d5,3d34s2,3d44p,3d34s4p} | |||||
| Zr III (8), Nlevels = 88 | |||||
| 4d2, 5s2, 5p2, 5s5p, | 4d2, 5s2, 5p2, 5p5d, 5s{5p,5d}, | 1s,2s,2p,3s, | VV + CV | {11s,11p,10d,9f,7g,7h} | e: 14 255 953 |
| 4d{4f,5s,5p,5d,6s,6p} | 4d{4f,5s,5p,5d,6s,6p,6d} | 3p,4s,4p | + CC (4s,4p) | o: 16 514 844 | |
| Sn II, Nlevels = 22 | |||||
| 5s2{4f,5p,5d,6s,6p,6d,7s,7p}, | 5s2{4f,5p,5d,6s,6p,6d,7s,7p, | 1s,2s,2p,3s, | VV + CV (4s, | {14s,14p,13d,10f,10g, | e: 1 329 994 |
| 5s5p2 | 7d,8s,8p}, 5s5p2 | 3p,4s,4p,4d | 4p,4d) | 8h,8i} | o: 674 998 |
Notes. Nlevels is the number of the targeted levels computed in this work. Configuration denotes the targeted configuration states. MR-RCI denotes multireference for relativistic configuration interaction calculations. Core orbitals denotes core orbitals defined in the calculations. Correlation denotes correlation effects included in the calculation. The orbitals included in the CV and CC correlation effects are shown in parentheses and the remaining core orbitals define an inactive closed core. AS denotes active set of orbitals; NCSFs is the number of generated configuration state functions for the relativistic configuration interaction calculations.
References. (1) Wang et al. (2018); (2) Papoulia et al. (2019a); (3) Papoulia et al. (2019b); (4) Pehlivan Rhodin et al. (2019); (5) Atalay et al. (2019); (6) Rynkun et al. (2019a); (7) Rynkun et al. (2019b); (8) Rynkun et al. (2020).
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