Supplementary tables to the paper Nonadiabatic Energies of the a^3 Sigma _g State of the Hydrogen Molecule. by L. Wolniewicz Molec. Phys. 105,1497, 2007 Table 1. Non relativistic upper bounds to the total energies, E_vJ, of the a-Sigma_g levels in atomic units. v is the a-state vibrational quantum number. The global quantum number is given for each level below the energy. (The entries correspond to 101 coupled equations) v J = 0 1 2 3 4 5 6 7 8 9 10 0 -0.73082520 -0.73052141 -0.72991622 -0.72901438 -0.72782283 -0.72635057 -0.72460840 -0.72260870 -0.72036514 -0.71789244 -0.71520607 0 0 0 0 0 0 0 0 0 0 0 1 -0.71932375 -0.71903481 -0.71845924 -0.71760159 -0.71646854 -0.71506874 -0.71341258 -0.71151193 -0.70937993 -0.70703069 -0.70447908 1 1 1 1 1 1 1 1 1 1 1 2 -0.70844213 -0.70816758 -0.70762070 -0.70680587 -0.70572953 -0.70439999 -0.70282725 -0.70102272 -0.69899905 -0.69676980 -0.69434927 2 2 2 2 2 2 2 2 2 2 2 3 -0.69816264 -0.69790210 -0.69738317 -0.69661008 -0.69558902 -0.69432800 -0.69283665 -0.69112599 -0.68920818 -0.68709630 -0.68480412 3 3 3 3 3 3 3 3 3 3 3 4 -0.68847193 -0.68822514 -0.68773363 -0.68700148 -0.68603468 -0.68484097 -0.68342962 -0.68181128 -0.67999771 -0.67800155 -0.67583609 4 4 4 4 4 4 4 4 4 4 4 5 -0.67936150 -0.67912830 -0.67866392 -0.67797228 -0.67705920 -0.67593214 -0.67460013 -0.67307344 -0.67136349 -0.66948253 -0.66744351 5 5 5 5 5 5 5 5 5 5 5 6 -0.67082849 -0.67060887 -0.67017158 -0.66952044 -0.66866109 -0.66760080 -0.66634831 -0.66491366 -0.66330795 -0.66154315 -0.65963191 6 6 6 6 6 6 6 6 6 6 6 7 -0.66287691 -0.66267102 -0.66226115 -0.66165103 -0.66084615 -0.65985363 -0.65868203 -0.65734116 -0.65584195 -0.65419617 -0.65241634 7 7 7 7 7 7 7 7 7 7 7 8 -0.65551958 -0.65532782 -0.65494617 -0.65437830 -0.65362963 -0.65270715 -0.65161933 -0.65037590 -0.64898771 -0.64746653 -0.64582497 8 8 8 8 8 8 8 8 8 8 8 9 -0.64878125 -0.64860434 -0.64825237 -0.64772901 -0.64703964 -0.64619127 -0.64519239 -0.64405280 -0.64278350 -0.64139656 -0.63990496 11 11 11 11 11 11 11 11 10 10 10 10 -0.64270340 -0.64254254 -0.64222269 -0.64174758 -0.64112269 -0.64035517 -0.63945375 -0.63842860 -0.63729123 -0.63605446 -0.63473233 13 13 13 13 13 13 12 12 12 12 12 11 -0.63735167 -0.63720879 -0.63692499 -0.63650416 -0.63595207 -0.63527629 -0.63448614 -0.63359264 -0.63260848 -0.63154811 -0.63042784 15 15 15 15 15 15 15 15 15 14 14 12 -0.63282642 -0.63270457 -0.63246300 -0.63210598 -0.63163985 -0.63107307 -0.63041617 -0.62968189 -0.62888528 -0.62804410 -0.62717946 17 17 17 17 17 17 17 16 16 16 16 13 -0.62927252 -0.62917624 -0.62898613 -0.62870711 -0.62834655 -0.62791445 -0.62742349 -0.62688938 -0.62633138 -0.62577339 -0.62524645 19 19 19 19 19 19 18 18 18 18 17 14 -0.62685956 -0.62679412 -0.62666605 -0.62648100 -0.62624749 -0.62597704 -0.62568441 -0.62538803 -0.62511143 -0.62488701 -0.62474364 21 21 21 21 20 20 20 19 19 19 18 15 -0.62562041 -0.62558555 -0.62551842 -0.62542413 -0.62531020 -0.62518630 -0.62506321 -0.62494953 -0.62484626 -0.62474480 22 22 22 22 22 21 21 21 20 20 16 -0.62516752 -0.62515050 -0.62511761 -0.62507081 -0.62501237 -0.62494416 -0.62486787 -0.62478729 -0.62471177 23 23 23 23 23 22 22 22 21 17 -0.62494738 -0.62493479 -0.62491026 -0.62487517 -0.62483181 -0.62478343 -0.62473419 -0.62468893 24 24 24 24 24 24 23 23 18 -0.62479644 -0.62478837 -0.62477290 -0.62475134 -0.62472570 -0.62469872 -0.62467393 25 25 25 25 25 25 24 19 -0.62471539 -0.62471082 -0.62470226 -0.62469073 -0.62467759 -0.62466380 26 26 26 26 26 26 20 -0.62467709 -0.62467438 -0.62466907 -0.62466120 27 27 27 27 Table 3. Pi symmetry contribution to the nonadiabatic corrections in cm-1 v J = 1 2 3 4 5 6 7 8 9 10 0 -0.003 -0.010 -0.020 -0.033 -0.049 -0.068 -0.091 -0.117 -0.145 -0.177 1 -0.003 -0.010 -0.020 -0.033 -0.049 -0.068 -0.091 -0.116 -0.145 -0.177 2 -0.003 -0.010 -0.019 -0.032 -0.049 -0.068 -0.091 -0.116 -0.145 -0.177 3 -0.003 -0.010 -0.019 -0.032 -0.049 -0.068 -0.091 -0.117 -0.146 -0.178 4 -0.003 -0.010 -0.020 -0.033 -0.049 -0.069 -0.092 -0.118 -0.147 -0.180 5 -0.003 -0.010 -0.020 -0.033 -0.050 -0.069 -0.093 -0.119 -0.149 -0.183 6 -0.003 -0.010 -0.020 -0.034 -0.050 -0.071 -0.094 -0.121 -0.152 -0.186 7 -0.003 -0.010 -0.021 -0.034 -0.051 -0.072 -0.097 -0.125 -0.156 -0.192 8 -0.004 -0.011 -0.021 -0.035 -0.053 -0.075 -0.100 -0.129 -0.163 -0.200 9 -0.004 -0.011 -0.022 -0.037 -0.056 -0.078 -0.105 -0.136 -0.172 -0.213 10 -0.004 -0.012 -0.023 -0.039 -0.059 -0.084 -0.113 -0.147 -0.187 -0.233 11 -0.004 -0.013 -0.026 -0.043 -0.065 -0.092 -0.125 -0.164 -0.210 -0.263 12 -0.005 -0.014 -0.029 -0.048 -0.074 -0.105 -0.143 -0.188 -0.242 -0.303 13 -0.005 -0.016 -0.033 -0.055 -0.084 -0.119 -0.160 -0.208 -0.260 -0.315 14 -0.006 -0.017 -0.035 -0.057 -0.086 -0.119 -0.156 -0.196 -0.235 -0.237 15 -0.005 -0.016 -0.033 -0.054 -0.080 -0.110 -0.136 -0.150 -0.151 -0.125 16 -0.005 -0.015 -0.028 -0.044 -0.060 -0.075 -0.088 -0.091 -0.064 17 -0.003 -0.010 -0.019 -0.030 -0.039 -0.046 -0.045 -0.032 18 -0.002 -0.006 -0.012 -0.017 -0.020 -0.020 -0.012 19 -0.001 -0.003 -0.006 -0.008 20 -0.001 0.000 -0.002 0.000 Table 4. Relativistic corrections included in the final term values (in cm-1) 0 -1.76 -1.76 -1.76 -1.75 -1.74 -1.73 -1.72 -1.71 -1.70 -1.68 -1.67 1 -1.73 -1.73 -1.73 -1.72 -1.71 -1.70 -1.69 -1.68 -1.67 -1.66 -1.64 2 -1.70 -1.70 -1.70 -1.69 -1.68 -1.68 -1.67 -1.66 -1.64 -1.63 -1.62 3 -1.67 -1.67 -1.67 -1.67 -1.66 -1.65 -1.64 -1.63 -1.62 -1.61 -1.60 4 -1.65 -1.65 -1.65 -1.64 -1.64 -1.63 -1.62 -1.61 -1.60 -1.59 -1.58 5 -1.63 -1.63 -1.62 -1.62 -1.61 -1.61 -1.60 -1.59 -1.58 -1.57 -1.56 6 -1.61 -1.61 -1.60 -1.60 -1.60 -1.59 -1.58 -1.57 -1.57 -1.56 -1.55 7 -1.59 -1.59 -1.59 -1.58 -1.58 -1.57 -1.57 -1.56 -1.55 -1.54 -1.53 8 -1.57 -1.57 -1.57 -1.57 -1.56 -1.56 -1.55 -1.55 -1.54 -1.53 -1.52 9 -1.56 -1.56 -1.56 -1.55 -1.55 -1.54 -1.54 -1.53 -1.53 -1.52 -1.51 10 -1.55 -1.55 -1.54 -1.54 -1.54 -1.53 -1.53 -1.52 -1.52 -1.51 -1.51 11 -1.54 -1.53 -1.53 -1.53 -1.53 -1.52 -1.52 -1.52 -1.51 -1.51 -1.50 12 -1.53 -1.53 -1.53 -1.52 -1.52 -1.52 -1.52 -1.51 -1.51 -1.51 -1.51 13 -1.53 -1.53 -1.53 -1.52 -1.52 -1.52 -1.52 -1.53 -1.53 -1.53 -1.54 14 -1.54 -1.54 -1.54 -1.54 -1.54 -1.55 -1.55 -1.56 -1.57 -1.59 -1.60 15 -1.57 -1.57 -1.58 -1.58 -1.58 -1.59 -1.59 -1.60 -1.60 -1.60 -1.61 16 -1.60 -1.60 -1.60 -1.60 -1.60 -1.60 -1.60 -1.60 -1.61 -1.61 17 -1.60 -1.60 -1.60 -1.60 -1.60 -1.61 -1.61 -1.61 -1.61 18 -1.61 -1.61 -1.61 -1.61 -1.61 -1.61 -1.61 19 -1.61 -1.61 -1.61 -1.61 -1.61 -1.61 20 -1.61 -1.61 -1.61 -1.61 Table 5. Recommended theoretical term values for the a-state in cm-1 v J = 0 1 2 3 4 5 6 7 8 9 10 0 95076.26 95142.93 95275.75 95473.68 95735.19 96058.31 96440.66 96879.53 97371.92 97914.60 98504.18 1 97600.57 97663.98 97790.30 97978.53 98227.20 98534.41 98897.89 99315.02 99782.93 100298.51 100858.51 2 99988.84 100049.09 100169.12 100347.94 100584.17 100875.96 101221.13 101617.16 102061.29 102550.54 103081.77 3 102244.95 102302.13 102416.02 102585.69 102809.78 103086.53 103413.83 103789.27 104210.16 104673.65 105176.71 4 104371.84 104426.00 104533.87 104694.55 104906.74 105168.72 105478.46 105833.63 106231.65 106669.74 107144.98 5 106371.37 106422.55 106524.47 106676.26 106876.65 107124.00 107416.33 107751.38 108126.66 108539.46 108986.95 6 108244.17 108292.37 108388.34 108531.24 108719.84 108952.53 109227.41 109542.26 109894.66 110281.97 110701.41 7 109989.36 110034.54 110124.49 110258.39 110435.03 110652.86 110909.98 111204.25 111533.27 111894.45 112285.05 8 111604.12 111646.20 111729.96 111854.59 112018.89 112221.34 112460.07 112732.96 113037.61 113371.44 113731.69 9 113083.03 113121.85 113199.10 113313.95 113465.24 113651.42 113870.63 114120.72 114399.28 114703.65 115030.98 10 114416.97 114452.28 114522.47 114626.73 114763.87 114932.30 115130.12 115355.10 115604.69 115876.10 116166.23 11 115591.55 115622.91 115685.19 115777.54 115898.70 116046.99 116220.39 116416.46 116632.42 116865.11 117110.93 12 116584.74 116611.48 116664.49 116742.83 116845.12 116969.49 117113.63 117274.76 117449.55 117634.11 117823.82 13 117364.73 117385.86 117427.57 117488.80 117567.90 117662.71 117770.43 117887.61 118010.03 118132.43 118248.02 14 117894.30 117908.66 117936.75 117977.35 118028.57 118087.90 118152.08 118217.09 118277.74 118326.94 118358.39 15 118166.23 118173.87 118188.60 118209.27 118234.25 118261.41 118288.39 118313.31 118335.96 118358.22 16 118265.60 118269.33 118276.54 118286.80 118299.61 118314.56 118331.29 118348.96 118365.53 17 118313.91 118316.67 118322.05 118329.74 118339.25 118349.85 118360.65 118370.59 18 118347.04 118348.81 118352.20 118356.92 118362.55 118368.46 118373.90 19 118364.83 118365.83 118367.70 118370.23 118373.11 118376.15 20 118373.23 118373.82 118374.99 118376.71