Promolecular atomic shell approximation PASA

Practical computation of the integral (1) becomes computationally expensive when the involved density functions correspond to large molecules or have been calculated at high computational levels. Even concrete applications of MQSM have been carried out at the ab initio level, when several molecules are studied simultaneously, as in QSAR studies, MQSM need to be computed several times, preventing their usage at these stages. In order to overcome this problem, the promolecular atomic shell approximation (PASA) [34-38] has been defined as a model of the true ab initio density, devised as a linear combination of 15 functions, and mathematically expressed as ... 

Clearly, the Hirshfeld promolecular electron density is not likely to simplify the integrals in Eq. [39]. The essential difference between the Hirshfeld and ASA promolecular densities is that in the ITirshfeld method, the isolated atom electron densities pa(r) are obtained in the same basis set as the one in the ab initio calculation of the true molecular electron density, whereas in the ASA approach, the isolated atom densities are obtained in the way as described below. In the ASA method, we use a slightly different promolecular atomic shell approximation (PASA) electron density, where the number of electrons Pa attached to each atom a is introduced. The total promolecular electron density for an N-atom molecule is given by... 

In their work related to the Promolecular Atom Shell Approximation (PASA), Amat and Carbo-Dorca used atomic Gaussian ED functions that were fitted on 6-31IG atomic basis set results [35]. In the PASA approach that is considered in the present work, a promolecular ED distribution Pa is represented analytically as a weighted summation over the nat atomic ED distributions p, which are described in terms of series of three squared Is Gaussian functions fitted from atomic basis set representations [36] ... 

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