Accurate Abinitio Potential Energy Curves and Spectroscopic Properties of the Four Lowest

Accurate abinitio potential energy curves and spectroscopic properties of the four lowest singlet states of C2

Jeffery S. Boschen,Daniel Theis, Klaus Ruedenberg, and Theresa L. Windus

Department of Chemistry and Ames Laboratory (USDOE), Iowa State University, Ames, Iowa 50011, United States

Corresponding Author:

Major determinant contributions (obtained from CASSCF(8,8) calculations with the cc-pVQZ basis) for each state at the experimental equilibrium bond distance for the state. Singly occupied orbitals with(out) bars represent β(α) electrons.

DeterminantCoefficient

X1Σ+gR = 1.24244Å

0.833

0.367

A1ΠuR = 1.318311Å

0.671

0.671

B1ΔgR = 1.38548 Å

0.676

-0.676

B'1Σ+gR = 1.37735Å

0.648

0.648

-0.245

Table S1. Summary of contributions to ab initio PECsof each state (Energies in hartree)

X1Σ+g
R (Å) / Referencea / Valenceb / Core corr.c / DKd / SOe / Total
0.9 / -75.252973 / -0.198252 / -0.096758 / -0.030220 / 0.000000 / -75.578203
0.95 / -75.383355 / -0.195183 / -0.095960 / -0.030069 / 0.000000 / -75.704567
1 / -75.476734 / -0.192583 / -0.095242 / -0.029950 / 0.000000 / -75.794510
1.05 / -75.541707 / -0.190262 / -0.094606 / -0.029858 / 0.000000 / -75.856433
1.1 / -75.584969 / -0.188155 / -0.094047 / -0.029787 / 0.000000 / -75.896957
1.15 / -75.611684 / -0.186198 / -0.093556 / -0.029733 / 0.000000 / -75.921171
1.2 / -75.625846 / -0.184444 / -0.093123 / -0.029693 / 0.000000 / -75.933105
1.24244 / -75.630356 / -0.182997 / -0.092795 / -0.029667 / 0.000000 / -75.935813
1.25 / -75.630566 / -0.182785 / -0.092739 / -0.029663 / 0.000000 / -75.935752
1.3 / -75.628286 / -0.181427 / -0.092396 / -0.029643 / 0.000000 / -75.931751
1.35 / -75.620926 / -0.180288 / -0.092085 / -0.029632 / 0.000000 / -75.922932
1.4 / -75.609999 / -0.179530 / -0.091800 / -0.029631 / 0.000000 / -75.910959
1.45 / -75.596708 / -0.179215 / -0.091533 / -0.029635 / 0.000000 / -75.897091
1.5 / -75.582017 / -0.179374 / -0.091275 / -0.029646 / 0.000000 / -75.882312
1.55 / -75.566736 / -0.180277 / -0.091016 / -0.029665 / 0.000000 / -75.867693
1.6 / -75.551615 / -0.182123 / -0.090754 / -0.029697 / 0.000000 / -75.854188
1.65 / -75.537461 / -0.184289 / -0.090512 / -0.029747 / 0.000000 / -75.842010
1.7 / -75.524968 / -0.185763 / -0.090311 / -0.029805 / 0.000000 / -75.830847
1.75 / -75.514034 / -0.186317 / -0.090147 / -0.029847 / 0.000000 / -75.820346
1.8 / -75.504062 / -0.186329 / -0.090009 / -0.029872 / 0.000000 / -75.810272
1.85 / -75.494705 / -0.186160 / -0.089890 / -0.029889 / 0.000000 / -75.800644
1.9 / -75.485862 / -0.185876 / -0.089786 / -0.029902 / 0.000000 / -75.791427
1.95 / -75.477531 / -0.185609 / -0.089696 / -0.029913 / 0.000001 / -75.782749
2 / -75.469732 / -0.185238 / -0.089619 / -0.029922 / 0.000001 / -75.774511
2.05 / -75.462497 / -0.184872 / -0.089555 / -0.029931 / 0.000001 / -75.766854
2.1 / -75.455848 / -0.184336 / -0.089503 / -0.029938 / 0.000001 / -75.759625
2.15 / -75.449802 / -0.183788 / -0.089463 / -0.029944 / 0.000001 / -75.752998
2.2 / -75.444364 / -0.183211 / -0.089436 / -0.029950 / 0.000001 / -75.746960
2.25 / -75.439530 / -0.182515 / -0.089421 / -0.029955 / 0.000001 / -75.741420
2.3 / -75.435283 / -0.181769 / -0.089416 / -0.029959 / 0.000002 / -75.736427
2.35 / -75.431595 / -0.180990 / -0.089422 / -0.029963 / 0.000002 / -75.731967
2.4 / -75.428427 / -0.180106 / -0.089436 / -0.029966 / 0.000003 / -75.727930
2.5 / -75.423466 / -0.178490 / -0.089482 / -0.029970 / 0.000015 / -75.721392
2.6 / -75.419992 / -0.176852 / -0.089541 / -0.029972 / -0.000013 / -75.716369
2.7 / -75.417608 / -0.175415 / -0.089602 / -0.029972 / -0.000007 / -75.712605
2.8 / -75.415985 / -0.174096 / -0.089658 / -0.029972 / -0.000007 / -75.709717
2.9 / -75.414873 / -0.173026 / -0.089706 / -0.029971 / -0.000008 / -75.707584
3 / -75.414103 / -0.172172 / -0.089745 / -0.029970 / -0.000010 / -75.705999
3.1 / -75.413559 / -0.171535 / -0.089776 / -0.029969 / -0.000013 / -75.704852
3.2 / -75.413169 / -0.170986 / -0.089800 / -0.029968 / -0.000016 / -75.703940
4 / -75.412121 / -0.169211 / -0.089872 / -0.029966 / -0.000110 / -75.701280
5 / -75.411980 / -0.168900 / -0.089885 / -0.029965 / -0.000154 / -75.700885
6 / -75.411947 / -0.168843 / -0.089888 / -0.029965 / -0.000253 / -75.700897
20 / -75.411962 / -0.168809 / -0.089888 / -0.029966 / -0.000246 / -75.700871
A1Πu
R (Å) / Referencea / Valenceb / Core corr.c / DKd / SOe / Total
0.9 / -75.086026 / -0.211173 / -0.095857 / -0.030502 / 0.000000 / -75.423558
0.95 / -75.238692 / -0.208259 / -0.095144 / -0.030339 / 0.000000 / -75.572433
1 / -75.351818 / -0.205582 / -0.094507 / -0.030207 / 0.000000 / -75.682114
1.05 / -75.434257 / -0.203038 / -0.093937 / -0.030102 / 0.000000 / -75.761334
1.1 / -75.492938 / -0.200672 / -0.093427 / -0.030020 / 0.000000 / -75.817057
1.15 / -75.533280 / -0.198532 / -0.092971 / -0.029956 / 0.000000 / -75.854739
1.2 / -75.559523 / -0.196551 / -0.092563 / -0.029909 / 0.000000 / -75.878546
1.24244 / -75.573233 / -0.195010 / -0.092250 / -0.029879 / 0.000000 / -75.890371
1.25 / -75.574990 / -0.194748 / -0.092197 / -0.029874 / 0.000000 / -75.891809
1.3 / -75.582286 / -0.193125 / -0.091870 / -0.029850 / 0.000000 / -75.897131
1.35 / -75.583456 / -0.191577 / -0.091577 / -0.029835 / 0.000000 / -75.896445
1.4 / -75.580105 / -0.190260 / -0.091314 / -0.029827 / 0.000000 / -75.891505
1.45 / -75.573490 / -0.189053 / -0.091077 / -0.029824 / 0.000000 / -75.883444
1.5 / -75.564595 / -0.187983 / -0.090863 / -0.029826 / 0.000000 / -75.873267
1.55 / -75.554189 / -0.187100 / -0.090669 / -0.029831 / 0.000000 / -75.861789
1.6 / -75.542865 / -0.186344 / -0.090494 / -0.029839 / 0.000000 / -75.849542
1.65 / -75.531086 / -0.185659 / -0.090334 / -0.029848 / 0.000000 / -75.836927
1.7 / -75.519206 / -0.185109 / -0.090189 / -0.029858 / 0.000000 / -75.824362
1.75 / -75.507497 / -0.184643 / -0.090058 / -0.029869 / 0.000000 / -75.812066
1.8 / -75.496168 / -0.184259 / -0.089939 / -0.029880 / 0.000000 / -75.800246
1.85 / -75.485378 / -0.183926 / -0.089834 / -0.029891 / 0.000000 / -75.789029
1.9 / -75.475248 / -0.183604 / -0.089741 / -0.029902 / 0.000000 / -75.778494
1.95 / -75.465869 / -0.183241 / -0.089662 / -0.029912 / 0.000000 / -75.768683
2 / -75.457309 / -0.182874 / -0.089596 / -0.029921 / 0.000000 / -75.759701
2.05 / -75.449613 / -0.182455 / -0.089545 / -0.029930 / 0.000000 / -75.751543
2.1 / -75.442805 / -0.181904 / -0.089509 / -0.029938 / 0.000000 / -75.744156
2.15 / -75.436887 / -0.181288 / -0.089487 / -0.029945 / 0.000000 / -75.737608
2.2 / -75.431839 / -0.180615 / -0.089478 / -0.029952 / -0.000001 / -75.731885
2.25 / -75.427615 / -0.179845 / -0.089482 / -0.029957 / -0.000001 / -75.726900
2.3 / -75.424149 / -0.179048 / -0.089496 / -0.029961 / -0.000001 / -75.722655
2.35 / -75.421356 / -0.178215 / -0.089517 / -0.029965 / -0.000002 / -75.719055
2.4 / -75.419143 / -0.177342 / -0.089544 / -0.029967 / -0.000003 / -75.716000
2.5 / -75.416089 / -0.175725 / -0.089604 / -0.029970 / -0.000007 / -75.711395
2.6 / -75.414318 / -0.174299 / -0.089662 / -0.029971 / -0.000011 / -75.708261
2.7 / -75.413329 / -0.173111 / -0.089711 / -0.029971 / -0.000017 / -75.706140
2.8 / -75.412796 / -0.172146 / -0.089751 / -0.029971 / -0.000025 / -75.704688
2.9 / -75.412519 / -0.171402 / -0.089781 / -0.029970 / -0.000034 / -75.703707
3 / -75.412380 / -0.170823 / -0.089804 / -0.029969 / -0.000045 / -75.703022
3.1 / -75.412315 / -0.170371 / -0.089822 / -0.029969 / -0.000056 / -75.702532
3.2 / -75.412286 / -0.170016 / -0.089834 / -0.029968 / -0.000067 / -75.702172
4 / -75.412258 / -0.168962 / -0.089872 / -0.029966 / -0.000138 / -75.701196
5 / -75.412231 / -0.168750 / -0.089882 / -0.029966 / -0.000229 / -75.701059
6 / -75.412224 / -0.168690 / -0.089885 / -0.029966 / -0.000189 / -75.700954
20 / -75.412222 / -0.168544 / -0.089885 / -0.029966 / -0.000185 / -75.700801
B1Δg
R (Å) / Referencea / Valenceb / Core corr.c / DKd / SOe / Total
0.9 / -74.955965 / -0.222085 / -0.095915 / -0.030575 / 0.000000 / -75.304541
0.95 / -75.128926 / -0.217863 / -0.095186 / -0.030406 / 0.000000 / -75.472380
1 / -75.259223 / -0.213972 / -0.094524 / -0.030271 / 0.000000 / -75.597991
1.05 / -75.356334 / -0.210426 / -0.093931 / -0.030161 / 0.000000 / -75.690852
1.1 / -75.427557 / -0.207499 / -0.093402 / -0.030072 / 0.000000 / -75.758531
1.15 / -75.478681 / -0.204934 / -0.092928 / -0.030003 / 0.000000 / -75.806546
1.2 / -75.514309 / -0.202831 / -0.092503 / -0.029951 / 0.000000 / -75.839595
1.24244 / -75.535095 / -0.201176 / -0.092178 / -0.029918 / 0.000000 / -75.858367
1.25 / -75.538039 / -0.200916 / -0.092123 / -0.029913 / 0.000000 / -75.860991
1.3 / -75.552669 / -0.199117 / -0.091783 / -0.029888 / 0.000000 / -75.873457
1.35 / -75.560386 / -0.197601 / -0.091479 / -0.029871 / 0.000000 / -75.879336
1.4 / -75.562900 / -0.196265 / -0.091207 / -0.029860 / 0.000000 / -75.880231
1.45 / -75.561540 / -0.195145 / -0.090964 / -0.029856 / 0.000000 / -75.877506
1.5 / -75.557352 / -0.194048 / -0.090747 / -0.029856 / 0.000000 / -75.872004
1.55 / -75.551146 / -0.193047 / -0.090553 / -0.029860 / 0.000000 / -75.864606
1.6 / -75.543555 / -0.192165 / -0.090379 / -0.029867 / 0.000000 / -75.855965
1.65 / -75.535072 / -0.191369 / -0.090223 / -0.029873 / 0.000000 / -75.846537
1.7 / -75.526070 / -0.190648 / -0.090083 / -0.029882 / 0.000000 / -75.836684
1.75 / -75.516836 / -0.189991 / -0.089959 / -0.029891 / 0.000000 / -75.826678
1.8 / -75.507594 / -0.189371 / -0.089847 / -0.029901 / 0.000000 / -75.816712
1.85 / -75.498510 / -0.188791 / -0.089748 / -0.029911 / 0.000000 / -75.806960
1.9 / -75.489710 / -0.188198 / -0.089661 / -0.029919 / 0.000000 / -75.797488
1.95 / -75.481292 / -0.187670 / -0.089584 / -0.029928 / 0.000000 / -75.788474
2 / -75.473324 / -0.187044 / -0.089519 / -0.029934 / 0.000000 / -75.779821
2.05 / -75.465867 / -0.186482 / -0.089465 / -0.029940 / 0.000000 / -75.771754
2.1 / -75.458960 / -0.185757 / -0.089422 / -0.029946 / 0.000000 / -75.764085
2.15 / -75.452633 / -0.185043 / -0.089390 / -0.029951 / 0.000000 / -75.757016
2.2 / -75.446901 / -0.184325 / -0.089369 / -0.029955 / 0.000000 / -75.750551
2.25 / -75.441772 / -0.183517 / -0.089360 / -0.029959 / 0.000000 / -75.744608
2.3 / -75.437236 / -0.182653 / -0.089361 / -0.029963 / 0.000000 / -75.739213
2.35 / -75.433271 / -0.181782 / -0.089371 / -0.029965 / 0.000000 / -75.734390
2.4 / -75.429847 / -0.180836 / -0.089390 / -0.029967 / 0.000000 / -75.730041
2.5 / -75.424443 / -0.179035 / -0.089445 / -0.029970 / 0.000000 / -75.722894
2.6 / -75.420629 / -0.177277 / -0.089512 / -0.029972 / -0.000001 / -75.717391
2.7 / -75.417997 / -0.175739 / -0.089580 / -0.029972 / -0.000001 / -75.713289
2.8 / -75.416197 / -0.174379 / -0.089641 / -0.029972 / -0.000001 / -75.710190
2.9 / -75.414966 / -0.173232 / -0.089693 / -0.029971 / -0.000001 / -75.707864
3 / -75.414115 / -0.172342 / -0.089735 / -0.029970 / -0.000002 / -75.706164
3.1 / -75.413519 / -0.171691 / -0.089768 / -0.029969 / -0.000003 / -75.704951
3.2 / -75.413095 / -0.171131 / -0.089794 / -0.029969 / -0.000004 / -75.703993
4 / -75.412032 / -0.169380 / -0.089871 / -0.029966 / -0.000054 / -75.701303
5 / -75.411941 / -0.169012 / -0.089885 / -0.029965 / -0.000105 / -75.700908
6 / -75.411930 / -0.168912 / -0.089888 / -0.029965 / -0.000149 / -75.700844
20 / -75.411962 / -0.168809 / -0.089888 / -0.029965 / -0.000123 / -75.700747
B'1Σ+g
R (Å) / Referencea / Valenceb / Core corr.c / DKd / SOe / Total
0.9 / -75.056184 / -0.213959 / -0.097104 / -0.030129 / 0.000000 / -75.397376
0.95 / -75.193490 / -0.208448 / -0.096317 / -0.030008 / 0.000000 / -75.528262
1 / -75.297594 / -0.203863 / -0.095518 / -0.029942 / 0.000000 / -75.626916
1.05 / -75.377059 / -0.200193 / -0.094743 / -0.029911 / 0.000000 / -75.701906
1.1 / -75.437244 / -0.197532 / -0.094053 / -0.029890 / 0.000000 / -75.758718
1.15 / -75.481651 / -0.195429 / -0.093467 / -0.029868 / 0.000000 / -75.800415
1.2 / -75.513136 / -0.193736 / -0.092968 / -0.029847 / 0.000000 / -75.829687
1.24244 / -75.531630 / -0.192391 / -0.092600 / -0.029832 / 0.000000 / -75.846452
1.25 / -75.534248 / -0.192180 / -0.092539 / -0.029829 / 0.000000 / -75.848796
1.3 / -75.547187 / -0.190762 / -0.092165 / -0.029817 / 0.000000 / -75.859930
1.35 / -75.553789 / -0.189464 / -0.091838 / -0.029809 / 0.000000 / -75.864900
1.4 / -75.555543 / -0.188224 / -0.091552 / -0.029804 / 0.000000 / -75.865124
1.45 / -75.553631 / -0.187008 / -0.091305 / -0.029803 / 0.000000 / -75.861746
1.5 / -75.548967 / -0.185509 / -0.091097 / -0.029803 / 0.000000 / -75.855375
1.55 / -75.542220 / -0.183487 / -0.090930 / -0.029801 / 0.000000 / -75.846438
1.6 / -75.533792 / -0.180914 / -0.090802 / -0.029792 / 0.000000 / -75.835299
1.65 / -75.523772 / -0.178234 / -0.090685 / -0.029770 / 0.000000 / -75.822461
1.7 / -75.512174 / -0.176359 / -0.090557 / -0.029743 / 0.000000 / -75.808833
1.75 / -75.499639 / -0.175684 / -0.090420 / -0.029734 / 0.000000 / -75.795477
1.8 / -75.487158 / -0.175633 / -0.090285 / -0.029743 / 0.000000 / -75.782819
1.85 / -75.475379 / -0.175811 / -0.090160 / -0.029760 / 0.000000 / -75.771110
1.9 / -75.464626 / -0.176013 / -0.090049 / -0.029782 / 0.000000 / -75.760470
1.95 / -75.455047 / -0.176226 / -0.089954 / -0.029805 / 0.000000 / -75.751032
2 / -75.446704 / -0.176356 / -0.089878 / -0.029831 / -0.000001 / -75.742769
2.05 / -75.439583 / -0.176367 / -0.089820 / -0.029853 / -0.000001 / -75.735624
2.1 / -75.433626 / -0.176184 / -0.089779 / -0.029873 / -0.000001 / -75.729463
2.15 / -75.428731 / -0.175931 / -0.089754 / -0.029892 / -0.000002 / -75.724309
2.2 / -75.424775 / -0.175581 / -0.089741 / -0.029907 / -0.000003 / -75.720006
2.25 / -75.421618 / -0.175158 / -0.089738 / -0.029920 / -0.000004 / -75.716438
2.3 / -75.419125 / -0.174682 / -0.089740 / -0.029930 / -0.000007 / -75.713485
2.35 / -75.417173 / -0.174211 / -0.089748 / -0.029939 / -0.000014 / -75.711085
2.4 / -75.415651 / -0.173679 / -0.089757 / -0.029945 / -0.000039 / -75.709072
2.5 / -75.413555 / -0.172919 / -0.089778 / -0.029954 / 0.000011 / -75.706194
2.6 / -75.412307 / -0.172211 / -0.089797 / -0.029959 / 0.000006 / -75.704267
2.7 / -75.411579 / -0.171650 / -0.089813 / -0.029961 / 0.000004 / -75.702998
2.8 / -75.411170 / -0.171148 / -0.089826 / -0.029963 / 0.000004 / -75.702103
2.9 / -75.410958 / -0.170788 / -0.089836 / -0.029964 / 0.000004 / -75.701542
3 / -75.410867 / -0.170449 / -0.089845 / -0.029964 / 0.000004 / -75.701121
3.1 / -75.410851 / -0.170131 / -0.089851 / -0.029965 / 0.000004 / -75.700794
3.2 / -75.410878 / -0.169917 / -0.089857 / -0.029965 / 0.000004 / -75.700613
4 / -75.411392 / -0.169379 / -0.089879 / -0.029965 / 0.000008 / -75.700607
5 / -75.411746 / -0.169052 / -0.089887 / -0.029965 / 0.000020 / -75.700630
6 / -75.411855 / -0.168953 / -0.089889 / -0.029965 / -0.000056 / -75.700718
20 / -75.411962 / -0.168809 / -0.089889 / -0.029966 / -0.000062 / -75.700686

aCBS extrapolated MCSCF reference energy

b CBS extrapolated CEEIS valence correlation energy

cCore-valence correlation correction

d Douglas-Kroll (DK3) scalar relativistic correction

e Spin orbit correction

Note: Tables S2 and S3 provide the vibrational levels for the four lowest singlet states of C2 from the ab initio PECs of this work. In S2 the levels are calculated using the VIBROT module of MOLCAS [1]. A limitation in the software prevented the calculation of the vibrational levels all the way to dissociation (could only calculate to v = 39). To provide values for the vibrational levels up to dissociation, the program LEVEL [2] was also used. Table S3 contains the results from the LEVEL calculations. Both programs employed cubic spline fits to the ab initio energies and used Numerov's method to solve the nuclear Schrödinger equation for the ro-vibrational levels. The two programs have good agreement at low values of v, but the deviations accumulate at higher levels.

Table S4 reports the vibrational levels (from MOLCAS) of the four states relative to the same zero energy (X1Σ+g state PEC minimum) in order to provide some information on the overlap of the vibrational manifolds of these states.
Table S2. Theoretical vibrational levels of C2 singlet states up to v = 39 (Energies in

cm-1, relative to thev = 0 level of each state, calculated using VIBROT)

v / X1Σ+g / A1Πu / B1Δg / B'1Σ+g
0 / 0.00 / 0.00 / 0.00 / 0.00
1 / 1830.36 / 1588.34 / 1381.87 / 1409.45
2 / 3636.49 / 3153.00 / 2746.41 / 2820.18
3 / 5410.95 / 4693.26 / 4086.49 / 4229.91
4 / 7152.49 / 6208.29 / 5405.04 / 5638.05
5 / 8862.59 / 7697.74 / 6701.39 / 7042.23
6 / 10539.43 / 9162.06 / 7974.97 / 8440.05
7 / 12180.87 / 10601.86 / 9225.33 / 9828.77
8 / 13783.33 / 12017.23 / 10452.66 / 11205.12
9 / 15342.32 / 13407.75 / 11657.34 / 12565.14
10 / 16853.78 / 14772.62 / 12839.60 / 13904.83
11 / 18315.28 / 16111.60 / 13999.30 / 15221.06
12 / 19726.68 / 17424.89 / 15136.20 / 16512.30
13 / 21089.61 / 18712.39 / 16250.35 / 17777.37
14 / 22407.36 / 19973.69 / 17342.06 / 19014.59
15 / 23683.73 / 21208.50 / 18411.06 / 20222.51
16 / 24922.42 / 22416.73 / 19456.73 / 21399.90
17 / 26127.04 / 23598.23 / 20479.51 / 22545.46
18 / 27299.93 / 24752.83 / 21480.43 / 23657.43
19 / 28442.54 / 25880.39 / 22458.92 / 24733.88
20 / 29556.05 / 26980.78 / 23413.58 / 25773.29
21 / 30642.09 / 28053.56 / 24345.17 / 26774.34
22 / 31701.20 / 29097.93 / 25255.23 / 27735.38
23 / 32733.21 / 30113.08 / 26142.60 / 28654.88
24 / 33738.96 / 31098.66 / 27005.09 / 29531.35
25 / 34719.81 / 32054.53 / 27842.63 / 30361.63
26 / 35675.64 / 32980.24 / 28655.86 / 31141.79
27 / 36605.74 / 33874.69 / 29444.55 / 31869.95
28 / 37511.31 / 34736.03 / 30208.20 / 32543.65
29 / 38393.38 / 35562.63 / 30945.70 / 33159.09
30 / 39250.42 / 36353.48 / 31656.06 / 33713.08
31 / 40080.87 / 37107.06 / 32339.08 / 34201.52
32 / 40885.31 / 37820.86 / 32994.11 / 34617.40
33 / 41664.31 / 38492.09 / 33619.05 / 34960.39
34 / 42417.50 / 39119.18 / 34212.25 / 35227.83
35 / 43143.89 / 39699.14 / 34774.17
36 / 43842.31 / 40226.77 / 35303.40
37 / 44512.82 / 40698.75 / 35797.64
38 / 45155.21 / 41112.25 / 36255.55
39 / 45766.99 / 41463.36 / 36677.28

Table S3.Theoretical vibrational levels of C2 singlet states up to dissociation (Energies in cm-1, relative to thev = 0 level of each state, calculated using LEVEL)

v / X1Σ+g / A1Πu / B1Δg / B'1Σ+g
0 / 0.00 / 0.00 / 0.00 / 0.00
1 / 1830.52 / 1588.46 / 1381.95 / 1409.53
2 / 3636.87 / 3153.28 / 2746.61 / 2820.38
3 / 5411.65 / 4693.98 / 4086.98 / 4230.49
4 / 7153.96 / 6209.67 / 5406.10 / 5639.29
5 / 8865.37 / 7700.14 / 6703.29 / 7044.47
6 / 10544.02 / 9165.88 / 7978.00 / 8443.72
7 / 12187.85 / 10607.48 / 9229.84 / 9834.38
8 / 13793.04 / 12025.16 / 10459.03 / 11213.25
9 / 15355.13 / 13418.49 / 11666.01 / 12576.36
10 / 16870.02 / 14786.74 / 12851.01 / 13919.72
11 / 18335.23 / 16129.67 / 14013.87 / 15240.22
12 / 19750.59 / 17447.49 / 15154.37 / 16536.29
13 / 21117.85 / 18740.14 / 16272.57 / 17806.79
14 / 22440.27 / 20007.18 / 17368.78 / 19050.01
15 / 23721.76 / 21248.28 / 18442.72 / 20264.40
16 / 24966.00 / 22463.31 / 19493.78 / 21448.71
17 / 26176.66 / 23652.12 / 20522.36 / 22601.51
18 / 27356.06 / 24814.47 / 21529.50 / 23720.93
19 / 28505.60 / 25950.18 / 22514.54 / 24804.90
20 / 29626.49 / 27059.06 / 23476.06 / 25851.75
21 / 30720.27 / 28140.59 / 24414.89 / 26860.00
22 / 31787.45 / 29193.85 / 25332.49 / 27827.82
23 / 32827.79 / 30217.95 / 26227.47 / 28753.51
24 / 33842.16 / 31212.49 / 27097.53 / 29635.27
25 / 34831.85 / 32177.24 / 27942.72 / 30469.47
26 / 35796.54 / 33111.58 / 28763.61 / 31252.04
27 / 36735.56 / 34014.14 / 29559.81 / 31981.07
28 / 37650.23 / 34882.81 / 30330.64 / 32653.55
29 / 38541.28 / 35715.88 / 31074.80 / 33265.54
30 / 39406.79 / 36512.18 / 31791.29 / 33813.62
31 / 40245.34 / 37269.78 / 32479.86 / 34293.18
32 / 41057.68 / 37985.70 / 33139.46 / 34696.97
33 / 41844.18 / 38657.12 / 33767.56 / 35026.65
34 / 42604.15 / 39282.32 / 34362.88 / 35278.53
35 / 43336.36 / 39857.19 / 34925.74 / 35454.47
v / X1Σ+g / A1Πu / B1Δg / B'1Σ+g
36 / 44039.70 / 40376.36 / 35454.07
37 / 44714.40 / 40836.98 / 35945.55
38 / 45359.52 / 41235.63 / 36399.06
39 / 45971.77 / 41568.90 / 36814.98
40 / 46549.01 / 41834.44 / 37191.86
41 / 47092.68 / 42033.07 / 37527.01
42 / 47601.38 / 42173.83 / 37817.37
43 / 48072.71 / 42262.89 / 38064.08
44 / 48506.42 / 42296.71 / 38274.24
45 / 48902.98 / 42315.22 / 38445.85
46 / 49259.22 / 42330.02 / 38571.85
47 / 49572.89 / 42340.81 / 38642.63
48 / 49843.56 / 42348.15 / 38684.97
49 / 50073.36 / 42352.98
50 / 50268.63 / 42356.04
51 / 50425.69 / 42357.85
52 / 50537.74 / 42358.82
53 / 50601.60 / 42359.23
54 / 50642.79
55 / 50642.79
56 / 50644.38

Table S4.Theoretical vibrational energy levels of C2singlet states relative to ground state potential minimum (Energies in cm-1, levels calculated using VIBROT)

v / X1Σ+g / A1Πu / B1Δg / B'1Σ+g
0 / 919.49 / 9220.64 / 12862.20 / 16132.82
1 / 2749.85 / 10808.98 / 14244.07 / 17542.27
2 / 4555.98 / 12373.64 / 15608.61 / 18953.00
3 / 6330.44 / 13913.90 / 16948.69 / 20362.73
4 / 8071.98 / 15428.93 / 18267.24 / 21770.87
5 / 9782.08 / 16918.38 / 19563.59 / 23175.05
6 / 11458.92 / 18382.70 / 20837.17 / 24572.87
7 / 13100.36 / 19822.50 / 22087.53 / 25961.59
8 / 14702.82 / 21237.87 / 23314.86 / 27337.94
9 / 16261.81 / 22628.39 / 24519.54 / 28697.96
10 / 17773.27 / 23993.26 / 25701.80 / 30037.65
11 / 19234.77 / 25332.24 / 26861.50 / 31353.88
12 / 20646.17 / 26645.53 / 27998.40 / 32645.12
13 / 22009.10 / 27933.03 / 29112.55 / 33910.19
14 / 23326.85 / 29194.33 / 30204.26 / 35147.41
15 / 24603.22 / 30429.14 / 31273.26 / 36355.33
16 / 25841.91 / 31637.37 / 32318.93 / 37532.72
17 / 27046.53 / 32818.87 / 33341.71 / 38678.28
18 / 28219.42 / 33973.47 / 34342.63 / 39790.25
19 / 29362.03 / 35101.03 / 35321.12 / 40866.70
20 / 30475.54 / 36201.42 / 36275.78 / 41906.11
21 / 31561.58 / 37274.20 / 37207.37 / 42907.16
22 / 32620.69 / 38318.57 / 38117.43 / 43868.20
23 / 33652.70 / 39333.72 / 39004.80 / 44787.70
24 / 34658.45 / 40319.30 / 39867.29 / 45664.17
25 / 35639.3 / 41275.17 / 40704.83 / 46494.45
26 / 36595.13 / 42200.88 / 41518.06 / 47274.61
27 / 37525.23 / 43095.33 / 42306.75 / 48002.77
28 / 38430.8 / 43956.67 / 43070.40 / 48676.47
29 / 39312.87 / 44783.27 / 43807.90 / 49291.91
30 / 40169.91 / 45574.12 / 44518.26 / 49845.90
31 / 41000.36 / 46327.70 / 45201.28 / 50334.34
32 / 41804.8 / 47041.50 / 45856.31 / 50750.22
33 / 42583.8 / 47712.73 / 46481.25 / 51093.21
34 / 43336.99 / 48339.82 / 47074.45 / 51360.65
35 / 44063.38 / 48919.78 / 47636.37
36 / 44761.8 / 49447.41 / 48165.60
37 / 45432.31 / 49919.39 / 48659.84
38 / 46074.7 / 50332.89 / 49117.75
39 / 46686.48 / 50684.00 / 49539.48

References

1. Aquilante F, De Vico L, Ferre N, Ghigo G, Malmqvist P-A, Neogrady P, Pedersen TB, Pitonak M, Reiher M, Roos BO, Serrano-Andres L, Urban M, Veryazov V, Lindh R (2010) J Comput Chem 31 (1):224-247

2.Le Roy RJ (2007) LEVEL 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels. University of Waterloo Chemical Physics Research Report CP-663; see