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1s Slatertype function
A normalized 1s Slatertype function is a function which has the form
The parameter ζ is called the Slater orbital exponent. Related sets of functions can be used to construct STOnG basis sets which are used in quantum chemistry. Additional recommended knowledge
Applications for hydrogenlike atomic systemsA hydrogenlike 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 hydrogenlike atoms are twoparticle systems with an interaction depending only on the distance between the two particles, their (nonrelativistic) Schrödinger equation can be exactly solved in analytic form. The solutions are oneelectron functions and are referred to as hydrogenlike atomic orbitals.^{[2]}
The electonic Hamiltonian (in atomic units) of a Hydrogenic system is given by
Exact energy of a hydrogenlike atomThe 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 energyThe following energy values are thus calculated by using the expressions for energy and for the Slater exponent.
Relativistic energy of Hydrogenic atomic systemsHydrogenic 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

Notes
 ^ 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 "oneelectron function", i.e., a function of x, y, and z.