Graduate Thesis Or Dissertation
 

A configuration-interaction calculation of wave functions for certain states of lithium

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  • A configuration-interaction determination of wave functions has been made for the ²S and ²P states of lithium, and for the ¹S and ³S states of the lithium ion. Two 1s, one 2s, one 3s, and two 2p functions served as starting functions for all four states. Results of the total energy calculations (and percent error) were as follows: Li atom, ²S (19 configurations) -7.467 315 a.u. (0.15%) Li atom, ²P (22 configurations) -7.395 851 a.u. (0.20%) Li⁺ ion, ¹S (13 configurations) -7.265 950 a.u. (0.2004) Li⁺ ion, ³S ( 7 configurations) -5.040 783 a.u. (1.38%) The calculated ionization energy, 0.201 365 a.u., is 1.6204 high. The ²P calculation is believed to be the first configuration-interaction treatment of this state, and the resulting energy is the most accurate yet achieved. (The energies of the other states have previously been computed to a high accuracy, but only with considerably longer expansions.) The larger error of the ³S calculation is probably due to the inadequacy of the description with only seven configurations available. Energies of four excited states of the same symmetries as the ones above are also presented for the first time; their accuracy, however, is somewhat poorer. Methods are discussed for obtaining a good representation of an atomic wave function with as few configurations as possible. Suggestions are made for testing the accuracy of the wave functions in describing other atomic properties. All the calculations were done on a desk calculator, with the exception of the matrix eigenvalue problem which was run on an IBM 709 using a standard routine. Thus this work demonstrates the feasibility of configuration interaction calculations for light atoms by investigators with limited computer facilities.
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