Hydrogen waves levels

The Self-Consistent-Field (SCF) procedure can be initiated with hydrogenic wave functions and Thomas-Fermi potentials. It leads to a set of solutions w(fj), each with k nodes between 0 and oo, with zero nodes for the lowest energy and increasing by one for each higher energy level. The quantum number n can now be defined asn = / + l + A to give rise to Is, 2s, 2p, etc. orbitals. 

The polarographic behavior of 1,10-phenanthroline,150-152 1,7-phenanthroline,153 and 4,7-phenanthroline154 has been studied in aqueous solution, but the interpretation of the reduction waves is not always certain because of complications due to adsorption and catalytic hydrogen waves. Some substituted 1,10-phenanthrolines have also been investigated in this way.151,155 Two clear reduction waves were obtained with 1,10-phenanthroline in dimethylformamide,156 however, and an attempt was made to correlate the reduction potentials with the energy levels of the molecule. Other studies in nonaqueous solvents with 1,10-, 1,7-, and 4,7-phenanthrolines also gave distinct waves.151,157... 

Waerden, 1968) and can be used to rederive the Bohr formula for the energy levels. Corresponding to each energy level a unirrep of so(4) is obtained. The basis functions for each such unirrep are just the hydrogenic wave functions belonging to the energy level. 

The hydrogen-like atomic energy levels are given in equation (6.48). If n and 2 are the principal quantum numbers of the energy levels E and E2, respectively, then the wave number of the spectral line is... 

For the hydrogen bonded complexes (FH)2, (HC1)2, (H20)2, FH-CO, FH -OC, FH -NH3, CIH- NH3, OH2-NH3, and H30+—H20, with binding energies ranging from 1.7 kcal/mol (FH-CO) to 32.9 kcal/mol (H30+—H20), Tuma, Boese, and Handy, 1999, compared results of several density functional methods with high level conventional wave function based data. With the exception of the HCTH functional, all functionals were found to over-... 

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