Atomic energy states, semi-empirical

The energy levels and eigenfunctions, obtained in one or other semi-empirical approach, may be successfully used further on to find fairly accurate values of the oscillator strengths, electron transition probabilities, lifetimes of excited states, etc., of atoms and ions [18, 141-144]. 

Similar expressions are used for (ss r), etc. Except for the integral F°, evaluated from Slater orbitals, semi-empirical values are used for G1 and F2 chosen to give the best fit with atomic spectra. At this level Pople thus expresses the energy of the average state associated with the configuration (2s)m (2p)n as... 

The energy level diagram for Ti3+ in fig. 3.4 shows the manner by which the 2D spectroscopic term is resolved into two different levels, or crystal field states, when the cation is situated in an octahedral crystal field produced by surrounding ligands. In a similar manner the spectroscopic terms for each 3d" configuration become separated into one or more crystal field states when the transition metal ion is located in a coordination site in a crystal structure. The extent to which each spectroscopic term is split into crystal field states can be obtained by semi-empirical calculations based on the interelectronic repulsion Racah B and C parameters derived from atomic spectra (Lever, 1984, p. 126). 

Depending on the type of interaction between an adsorbed particle and a solid state surface there are cases, where adsorption enthalpies can be calculated using empirical and semi-empirical relations. In the case of atoms with a noble-gas like ground-state configuration and of symmetrical molecules the binding energy (EB) to a solid surface can be calculated as a function of the polarizability (a), the ionization potential (IP), the distance (R) between the adsorbed atom or molecule and the surface, and the relative dielectric constants (e) (Method 9) [58-61] ... 

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