Molecular integral evaluation Boys function

To speed up molecular integral evaluation. Boys proposed in 1950 the use of Gaussian-type functions (GTFs) instead of STOs for the atomic orbitals in an LCAO wave function. A Cartesian Gaussian centered on atom b is defined as... 

In Section 9.7, we found that the electrostatics of spherical Gaussian charge distributions are determined by the Boys function F ix). Since this function plays such an important role in the evaluation of molecular integrals over Gaussian functions, we shall in this section discuss its properties and evaluation in more detail. 

McWeeny [8] and, independently, Boys [9] introduced the Gaussian basis function, which held the key to practical applications to arbitrary polyatomic molecules because of the ease and accuracy with which the associated molecular integrals could be evaluated. The (cartesian) Gaussian basis functions have the form... 

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