Gaussian-type orbitals Cartesian GTOs

Cartesian Gaussian-type orbitals (GTOs) Jfa.i.f( ( characterized by the quantum numbers a, b and c, which detail the angular shape and direction of the orbital, and the exponent a which governs the radial size . 

Boys (1950) proposed an alternative to the use of STOs. All that is required for there to be an analytical solution of the general four-index integral formed from such functions is that the radial decay of the STOs be changed from e to e. That is, the AO-like functions are chosen to have the form of a Gaussian function. The general functional form of a normalized Gaussian-type orbital (GTO) in atom-centered Cartesian coordinates is... 

The nonorthogonal basis functions Xx( )are referred to as atomic orbitals (AOs) and are often taken to be Cartesian Gaussian-type orbitals (GTOs) of the (unnormalized) form ... 

Cartesian Gaussian-type orbitals (GTOs) characterized by the... 

The use of Cartesian Gaussian-type orbitals (GTOs) in ab initio work may come as a surprise to anyone who recalls the functional form of the hydrogen atom orbitals, hydrogen exp( - Ir). Cartesian GTO s have the form ... 

Gaussian-type orbitals (GTOs), usually represented in their Cartesian form, have been proposed (i +j + k = I determines the type of the orbital (s, p, etc.)). 

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