Computational Chemistry - Safouhi, Hassan; Bouferguene, Ahmed (Scientific Data Mining and Knowledge Discovery, 2010)
It is well known that in any ab initio molecular orbital (MO) calculation, the major task involves the computation of the so–called molecular multi–center in–tegrals, namely overlap, two–, three–center nuclear attraction; hybrid, two– three– and four–center two–electron Coulomb; and exchange integrals. A great number of these integrals is required for molecular calculations based on the linear combi– nation of atomic orbitals–molecular orbitals approximation (LCAO–MO) [1]. As the molecular system gets larger, computation of these integrals becomes one of the most difficult and time consuming steps in molecular systems calculation. Improvement of the computational methods for molecular integrals would be in– dispensable to a further development in computational studies of large molecular systems. In ab initio calculations using the LCAO-MO approximation, molecular orbitals are built from a linear combination of atomic orbitals. Thus, the choice of reliable basis functions is of prime importance [2]. Agood atomic orbital basis should satisfy the cusp at the origin [3] and the exponential decay at infinity [4, 5]. The most popular functions used in ab initio calculations are the so-called Gaussian type functions (GTFs) [6,7].With GTFs, the numerous molecular integrals can be evaluated rather easily. Unfortunately, these GTF basis functions fail to satisfy the above mathematical conditions for atomic electronic distributions. A large number of GTFs have to be used in order to achieve acceptable accuracy and this increases the computational cost.