Atomic orbitals radial behaviour

A wavefunction ipis mathematical function that contains detailed information about the behaviour of an electron. An atomic wavefunction ip consists of a radial component, R r), and an angular component, A 9, p>). The region of space defined by a wavefunction is called an atomic orbital. 

The situation is quite similar in chemistry. Due to decades of experience with Hartree-Fock and Cl calculations much is known about the construction of basis functions that are suitable for molecules. Almost all of this continues to hold in DFT — a fact that has greatly contributed to the recent popularity of DFT in chemistry. Chemical basis functions are classified with respect to their behaviour as a function of the radial coordinate into Slater type orbitals (STOs), which decay exponentially far from the origin, and Gaussian type orbitals (GTOs), which have a gaussian behaviour. STOs more closely resemble the true behaviour of atomic wave functions [in particular the cusp condition of Eq. (19)], but GTOs are easier to handle numerically because the product of two GTOs located at different atoms is another GTO located in between, whereas the product of two STOs is not an STO. The so-called contracted basis functions , in which STO basis functions are reexpanded in... 

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