Atomic orbital

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 isolution. 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.)