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1s Slater-type function
A normalized 1s Slater-type function is a function which has the form
Additional recommended knowledge
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 , where is the atomic number of the atom. Because hydrogen-like atoms are two-particle systems with an interaction depending only on the distance between the two particles, their (non-relativistic) Schrödinger equation can be exactly solved in analytic form. The solutions are one-electron functions and are referred to as hydrogen-like atomic orbitals.
The electonic Hamiltonian (in atomic units) of a Hydrogenic system is given by
Exact energy of a hydrogen-like atom
The energy of a hydrogenic system can be exactly calculated analytically as follows :
Integrals needed when 'n' is even. when 'n' is odd.
The optimum value for is obtained by equating the differential of the energy with respect to as zero.
Non relativistic energy
The following energy values are thus calculated by using the expressions for energy and for the Slater exponent.
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 relativistically corrected Slater exponent is given as
- ^ Attila Szabo and Neil S. Ostlund (1996). Modern Quantum Chemistry - Introduction to Advanced Electronic Structure Theory. Dover Publications Inc., 153. ISBN 0486691861.
- ^ In quantum chemistry an orbital is synonymous with "one-electron function", i.e., a function of x, y, and z.