Partition functions for ions and now some molecules. Ionization potentials and 5040 and 10,080 K logarithmic partition functions (in rows 3 and 4 for each element) are from Allen (3rd ed.), except the Ba III ionization potential comes from Serafin et al. (Vol. 5). There are only only the ground state statistical weights above ionization state 2. Abundances from Cameron in Barnes et al, Essays in Nucl. Ap., EXCEPT He abundance corresponds to Y=0.25 and F, Cl, Cu, Zn, Ga, Ge from Allen The abundances are NOT to be used. 999.999 or 9999.999 means unknown or nonexistent ionization energy; see Yb 70 0. for the statisical weight means unknown; a lot of the heavies are this way. Y 39 has an uncertainty about its statistical weights for V and VI. Se 34 has an uncertainty about its partition function for the second ionization stage. Actually, one should use this table only to A=38 Sr, until it's been verified/improved. What of the hydrogen anion (H-)? https://en.wikipedia.org/wiki/Hydrogen_anion : Not very complete. https://www.researchgate.net/post/What_is_statistical_weight_of_hydrogen_anion This says statistical weight is 1 for ground state. https://www.researchgate.net/publication/225589030_The_negative_ion_of_hydrogen A fairly complete reference. Says the ground state is the only bound state. Is it OK in the Saha solver to treat the H anion as effectively ionization state 0 and H neutral as effectively once ionized? If one did, a pure H gas at T=0 would be negatively charged which is unphysical since there must be overall neutrality. However, for finite temperature, the Saha solver always solves for n_e > 0 and as n_e goes to zero ionization increases. So I think a Saha solver can handle H-, but one would have to treat Hydrogen as a special case with a negative, zero, and positive contribution to n_e. Now the H- is an important opacity source for solar and cooler stars, but its abundance is probably always low (Mihalas-102). So perhaps it should be treated just as perturbation. But on the other hand, it's not so hard to treat in the Saha solver and after all one would like to know what the H- abundance is. So let's do it. One can check the data from NIST NIST Atomic Spectra Database Ionization Energies Form https://physics.nist.gov/PhysRefData/ASD/ionEnergy.html and this should be done as time allows. See also https://en.wikipedia.org/wiki/Ionization_energies_of_the_elements_(data_page) END: !23456789a123456789b123456789c123456789d123456789e123456789f123456789g123456789h123456789i123456789j H 1 1. 12.00 0.754 13.598 9999.999 9999.999 9999.999 9999.999 9999.999 0. 1. 2. 1. 5040. 0. 0.30 1. 10080. 0. 0.30 1. He 2 4. 10.92 24.587 54.416 9999.999 9999.999 9999.999 9999.999 0. 1. 2. 1. 5040. 0.00 0.30 1. 10080. 0.00 0.30 1. Li 3 7. 3.35 5.392 75.638 122.451 9999.999 9999.999 9999.999 0. 2. 1. 2. 1. 5040. 0.32 0.00 1. 10080. 0.49 0.00 1. Be 4 9. 0. 9.322 18.211 153.893 217.713 9999.999 9999.999 0. 1. 2. 1. 2. 1. Be IV must be hydrogenic and have g_0=2. 5040. 0.01 0.30 1. 10080. 0.13 0.30 1. B 5 11. 0. 8.298 25.155 37.930 259.366 340.22 9999.999 0. 6. 1. 2. 1. 2. 1. B V must be hydrogenic and have g_0=2 5040. 0.78 0.00 10080. 0.78 0.00 C 6 12. 8.62 11.260 24.383 47.887 64.492 392.08 489.98 9999.999 0. 9. 6. 1. 2. 1. 2. 1. C VI must be hydrogenic and have g_0=2 5040. 0.97 0.78 10080. 1.00 0.78 N 7 14. 7.94 14.534 29.601 47.448 77.472 97.89 552.06 0. 4. 9. 6. 1. 2. 1. 5040. 0.61 0.95 10080. 0.66 0.97 O 8 16. 8.84 13.618 35.117 54.934 77.413 113.90 138.12 0. 9. 4. 9. 6. 1. 2. 5040. 0.94 0.60 10080. 0.97 0.61 F 9 19. 4.6 17.422 34.970 62.707 87.138 114.24 157.16 0. 6. 9. 4. 9. 6. 1. 5040. 0.75 0.92 10080. 0.77 0.94 Ne 10 20. 7.99 21.564 40.962 63.45 97.11 126.21 157.93 0. 1. 6. 9. 4. 9. 6. 5040. 0. 0.73 10080. 0. 0.75 Na 11 23. 6.35 5.139 47.286 71.64 98.91 138.40 172.15 0. 2. 1. 6. 9. 4. 9. 5040. 0.31 0.00 10080. 0.60 0.00 Mg 12 24. 7.60 7.646 15.035 80.143 109.31 141.27 186.51 0. 1. 2. 1. 6. 9. 4. 5040. 0.01 0.31 10080. 0.15 0.31 Al 13 27. 6.50 5.986 18.826 28.448 119.99 153.75 190.47 0. 6. 1. 2. 1. 6. 9. 5040. 0.77 0.00 10080. 0.81 0.01 Si 14 28. 7.58 8.151 16.345 33.492 45.141 166.77 205.08 0. 9. 6. 1. 2. 1. 6. 5040. 0.98 0.76 10080. 1.04 0.77 P 15 31. 5.39 10.486 19.725 30.18 51.42 65.02 220.45 0. 4. 9. 6. 1. 2. 1. 5040. 0.65 0.91 10080. 0.79 0.94 S 16 32. 7.27 10.360 23.33 34.83 47.30 72.68 88.05 0. 9. 4. 9. 6. 1. 2. 5040. 0.91 0.62 10080. 0.94 0.72 Cl 17 35. 5.6 12.967 23.61 39.61 53.46 67.7 97.03 0. 6. 9. 4. 9. 6. 1. 5040. 0.72 0.89 10080. 0.75 0.92 Ar 18 40. 6.60 15.759 27.629 40.74 59.81 75.04 91.01 0. 1. 6. 9. 4. 9. 6. 5040. 0.00 0.69 10080. 0.00 0.71 K 19 39. 5.12 4.341 31.63 45.72 60.92 86.66 99.9 0. 2. 1. 6. 9. 4. 9. 5040. 0.34 0.00 10080. 0.60 0.00 Ca 20 40. 6.37 6.113 11.871 50.91 67.15 84.43 108.78 0. 1. 2. 1. 6. 9. 4. 5040. 0.07 0.34 10080. 0.55 0.54 Sc 21 45. 3.07 6.54 12.80 24.76 73.7 91.7 111.1 0. 10. 15. 10. 1. 6. 9. 4. 5040. 1.08 1.36 10080. 1.49 1.52 Ti 22 48. 4.94 6.82 13.58 27.49 43.26 99.4 119.36 0. 21. 28. 21. 10. 1. 6. 9. 5040. 1.48 1.75 10080. 1.88 1.92 V 23 51. 3.98 6.74 14.65 29.31 46.71 65.23 128.6 0. 28. 25. 28. 21. 10. 1. 6. 5040. 1.62 1.64 10080. 2.03 1.89 Cr 24 52. 5.68 6.766 16.50 30.96 49.1 70.2 90.57 0. 7. 6. 25. 28. 21. 10. 1. 5040. 1.02 0.86 10080. 1.51 1.22 Mn 25 55. 5.54 7.435 15.640 33.67 51.4 73.0 97. 0. 6. 7. 6. 25. 28. 21. 10. 5040. 0.81 0.89 10080. 1.16 1.13 Fe 26 56. 7.53 7.870 16.16 30.651 54.8 75.5 100. 0. 25. 30. 25. 6. 25. 28. 21. 5040. 1.43 1.63 10080. 1.74 1.80 Co 27 56. 4.92 7.86 17.06 33.50 51.3 79.5 103. 0. 28. 21. 28. 25. 6. 25. 28. 5040. 1.52 1.46 10080. 1.76 1.66 (4.92 solar) Ni 28 56. 6.24 7.635 18.168 35.17 54.9 75.5 108. 0. 21. 10. 21. 28. 25. 6. 25. 5040. 1.47 1.02 10080. 1.60 1.28 (6.24 solar) Cu 29 64. 4.5 7.726 20.292 36.83 55.2 79.9 103. 0. 2. 1. 10. 21. 28. 25. 6. the Cu VI g_0 is an extrapln 5040. 0.36 0.01 maybe for IV and V too 10080. 0.58 0.18 Zn 30 65. 4.2 9.394 17.964 39.72 59.4 82.6 108. 0. 1. 2. 1. 10. 21. 28. g_0 for V may be an extrapln. 5040. 0.00 0.30 g_0 for VI is an extrapln. 10080. 0.03 0.30 Ga 31 70. 2.4 5.999 20.51 30.71 64. 87. 116. g_0 for V may be an extrapln 0. 6. 1. 2. 1. 10. 21. g_0 for VI is an extrapln. 5040. 0.73 0.00 10080. 0.77 0.00 Ge 32 73. 2.9 7.899 15.934 34.22 45.71 93.5 112. 0. 9. 6. 1. 2. 1. 10. g_0 for VI is an extrapln. 5040. 0.91 0.64 10080. 1.01 0.70 As 33 75. 0. 9.81 18.633 28.351 50.13 62.63 127.6 147. 0. 4. 9. 6. 1. 2. 1. 5040. -10. -10. 10080. -10. -10. Se 34 79. 0. 9.752 21.19 30.820 42.944 68.3 81.7 155.4 0. 9. 4. 9. 6. 1. 2. 1. 5040. 0.83 0.60 10080. 0.89 0.60 Br 35 80. 0. 11.814 21.8 36. 47.3 59.7 88.6 103.0 0. 6. 9. 4. 9. 6. 1. 2. 5040. -10. -10. 10080. -10. -10. Kr 36 84. 0. 13.999 24.359 36.95 52.5 64.7 78.5 0. 1. 6. 9. 4. 9. 6. g_0 for V and VI are extraplns 5040. 0.00 0.62 10080. 0.00 0.66 Rb 37 85. 0. 4.177 27.28 40. 52.6 71.0 84.4 0. 2. 1. 6. 9. 4. 9. g_0 for IV, V and VI are extraplns. 5040. 0.36 0.00 10080. 0.7 0.00 Sr 38 88. 2.93 5.695 11.030 43.6 57. 71.6 90.8 0. 1. 2. 1. 6. 9. 4. g_0 for VI is an extrapln. 5040. 0.10 0.34 10080. 0.70 0.53 Y 39 89. 15.1 6.38 12.24 20.52 61.8 77.0 93. 0. 10. 1. 2. 1. 6. 9. g_0 for V, VI by isoelectonic extrapled: 15 means don't use 5040. 1.08 1.18 10080. 1.50 1.41 Zr 40 91. 15.1 6.84 13.13 22.99 34.34 81.5 99. 0. 21. 28. 21. 10. 6. g_0 for V can't be extrapled; VI extrapled: 15 means don't use 5040. 1.53 1.66 10080. 1.99 1.91 Nb 41 93. 0. 6.88 14.32 25.04 38.3 50.55 102.6 125. 0. 30. 25. 28. 21. 10. 1. 6. 5040. -10. -10. 10080. -10. -10. Mo 42 96. 15.1 7.99 16.15 27.16 46.4 61.2 68. 126.8 0. 7. 6. 25. 28. 5040. -10. -10. 10080. -10. -10. Ru 44 101. 15.1 7.37 16.76 28.47 50. 60. 92. -10. 0. 35. 28. 25. 6. 5040. -10. -10. 10080. -10. -10. Rh 45 103. 15.1 7.46 18.08 31.06 48. 65. 97. -10. 0. 28. 21. 28. 25. 5040. -10. -10. 10080. -10. -10. Pd 46 106. 15.1 8.34 19.43 32.92 53. 62. 90. 110. 0. 1. 10. 21. 28. 5040. -10. -10. 10080. -10. -10. Ag 47 108. 15.1 7.576 21.49 34.83 56. 68. 89. 115. 0. 2. 1. 10. 21. 5040. -10. -10. 10080. -10. -10. Cd 48 112. 15.1 8.993 16.908 37.48 59. 72. 94. 15 means don't use 0. 1. 2. 1. 10. 5040. 0.00 0.30 10080. 0.02 0.30 In 49 115. 15.1 5.786 18.869 28.03 54.4 77. 98. 120. 0. 6. 1. 2. 1. 5040. -10. -10. 10080. -10. -10. Sn 50 119. 0. 7.344 14.632 30.502 40.734 72.28 103. 0. 9. 6. 1. 2. 1. 10. 5040. 0.73 0.52 10080. 0.88 0.61 Sb 51 122. 15.1 8.641 16.53 25.3 44.2 56. 108. 130. 0. 4. 9. 6. 1. 5040. -10. -10. 10080. -10. -10. Te 52 128. 15.1 9.009 18.6 27.96 37.41 58.75 70.7 137. 0. 9. 4. 9. 6. 5040. -10. -10. 10080. -10. -10. I 53 127. 15.1 10.541 19.131 33. 42. 66. 81. 100. 0. 6. 9. 4. 9. 5040. -10. -10. 10080. -10. -10. Xe 54 131. 15.1 12.130 21.21 32.1 46. 57. 82. 100. 0. 1. 6. 9. 4. 5040. -10. -10. 10080. -10. -10. Cs 55 133. 15.1 3.894 25.1 35. 46. 62. 74. 100. 0. 2. 1. 6. 9. 5040. -10. -10. 10080. -10. -10. Ba 56 137. 2.26 5.212 10.004 35. 49. 62. 80. 0. 1. 2. 1. 6. 9. 5040. 0.36 0.62 10080. 0.92 0.85 La 57 139. 15.1 5.577 11.06 19.175 52. 66. 80. 15 means don't use 0. 10. 21. 10. 1. 5040. 1.41 1.47 10080. 1.85 1.71 Ce 58 140. 15.1 5.47 10.87 20.20 36.72 70. 85. 100. 0. 9. 44. 33. 14. 5040. -10. -10. 10080. -10. -10. Yb 70 173. 15.1 6.254 12.17 25.2 -10. -10. -10. -10. 15 means don't use 0. 1. 2. 1. 14. 5040. 0.02 0.30 10080. 0.21 0.31 Ta 73 181. 15.1 7.89 16. 22. 33. 45. 9999.999 9999.99 0. 28. 35. 5040. -10. -10. 10080. -10. -10. W 74 184. 15.1 7.98 18. 24. 35. 48. 61. 9999.99 0. 25. 30. 5040. -10. -10. 10080. -10. -10. Ir 77 192. 15.1 9.1 17. 27. 39. 57. 72. 88. 0. 28. 35. 5040. -10. -10. 10080. -10. -10. Pt 78 195. 15.1 9.0 18.56 28. 41. 55. 75. 92. 0. 15. 10. 5040. -10. -10. 10080. -10. -10. Au 79 197. 15.1 9.225 20.5 30. 44. 58. 73. 96. 0. 2. 1. 10. 21. 5040. -10. -10. 10080. -10. -10. Hg 80 201. 15.1 10.437 18.756 34.2 46. 61. 77. 94. 0. 1. 2. 1. 10. 5040. -10. -10. 10080. -10. -10. Tl 81 204. 15.1 6.108 20.428 29.83 50.7 64. 81. 98. 0. 6. 1. 2. 5040. -10. -10. 10080. -10. -10. Pb 82 207. 0. 7.416 15.032 31.937 42.32 68.8 84. 0. 9. 6. 1. 2. 1. 1. g_0 for VI is set to 1 incorrectly. 5040. 0.26 0.32 10080. 0.54 0.40 Bi 83 209. 15.1 7.289 16.69 25.56 45.3 56.0 88.3 107. 0. 4. 9. 6. 1. 5040. -10. -10. 10080. -10. -10. Th 90 232. 15.1 6. 11.5 20.0 28.8 65. 80. 94. 0. 21. 28. 33. 14. 5040. -10. -10. 10080. -10. -10. U 92 238. 15.1 6. -10. -10. -10. -10. -10. 104. 0. 85. 52. 52. 5040. -10. -10. 10080. -10. -10.