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The term "atomic orbital" is used in at least two senses in quantum chemistry.
In the quantum-chemical treatment of atoms, the one-electron wavefunctions arising from
the solution of the Schrödinger equation are referred to
as atomic orbitals.
In the quantum-chemical treatment of molecules, it is usually necessary to
express the solutions as linear combinations of one-electron
functions which are centered on the nuclei of the constituent atoms of
the molecule. These functions are referred to as atomic orbitals even though they may not actually be solutions of the
Schrödinger equation for those atoms taken in isolation. This method is referred to as the linear combination of atomic orbitals molecular orbital
method (LCAO MO method).
The orbitals used in the LCAO method are usually either exponentially decreasing from the atomic center (radial component of
the form r=e-kx, referred to as Slater-type
orbitals) or decreasing as a Gaussian function from the
atomic center (radial component of the form r=e-kx2, referred to as Gaussian orbitals), though other forms have been used.
(see also Electron configuration.)
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