A normalized 1s Slater-type function is a function which is used in the descriptions of atoms and in a broader way in the description of atoms in molecules. It is particularly important as the accurate quantum theory description of the smallest free atom, hydrogen. It has the form
Contents
- Applications for hydrogen like atomic systems
- Exact energy of a hydrogen like atom
- Non relativistic energy
- Relativistic energy of Hydrogenic atomic systems
- References
It is a particular case of a Slater-type orbital (STO) in which the principal quantum number n is 1. The parameter
Applications for hydrogen-like atomic systems
A hydrogen-like atom or a hydrogenic atom is an atom with one electron. Except for the hydrogen atom itself (which is neutral) these atoms carry positive charge
Exact energy of a hydrogen-like atom
The energy of a hydrogenic system can be exactly calculated analytically as follows :
The optimum value for
Non relativistic energy
The following energy values are thus calculated by using the expressions for energy and for the Slater exponent.
Hydrogen : H
Gold : Au(78+)
Relativistic energy of Hydrogenic atomic systems
Hydrogenic atomic systems are suitable models to demonstrate the relativistic effects in atomic systems in a simple way. The energy expectation value can calculated by using the Slater orbitals with or without considering the relativistic correction for the Slater exponent
The relativistic energy of an electron in 1s orbital of a hydrogenic atomic systems is obtained by solving the Dirac equation.
Following table illustrates the relativistic corrections in energy and it can be seen how the relativistic correction scales with the atomic number of the system.