A half-numeric algorithm for the evaluation of effective core potential integrals over Cartesian Gaussian functions is described. Local and semilocal integrals are separated into two-dimensional angular and one-dimensional radial integrals. The angular integrals are evaluated analytically using a general approach that has no limitation for the l-quantum number. The radial integrals are calculated by an adaptive one-dimensional numerical quadrature. For the semilocal radial part a pretabulation scheme is used. This pretabulation simplifies the handling of radial integrals, makes their calculation much faster, and allows their easy reuse for different integrals within a given shell combination. The implementation of this new algorithm is described and its performance is analyzed.
A study of the reduced density gradient s together with the density of s, g(s), for atoms across the periodic table (Li through Xe), following the work of Zupan et al. (Int. J. Quantum Chem. 1997, 61, 835), is presented. The results indicate that the reduced density gradient has maxima and minima related with the shell structure, and that these critical points are associated to the maxima in g(s). The behavior of the critical points in s, of the maxima in g(s) and of the average s calculated through g(s) across the rows and the columns of the periodic table is analyzed.
The relationship between the chemical structure and biological activity (log IC) of 40 derivatives of 1,4-dihydropyridines (DHPs) was studied using density functional theory (DFT) and multiple linear regression analysis methods. With the aim of improving the quantitative structure-activity relationship (QSAR) model, the reduced density gradient s( r) of the optimized equilibrium geometries was used as a descriptor to include weak non-covalent interactions. The QSAR model highlights the correlation between the log IC with highest molecular orbital energy (E ), molecular volume (V), partition coefficient (log P), non-covalent interactions NCI(H4-G) and the dual descriptor [Δf(r)]. The model yielded values of R=79.57 and Q =69.67 that were validated with the next four internal analytical validations DK=0.076, DQ=-0.006, R =0.056, and R =0.000, and the external validation Q=64.26. The QSAR model found can be used to estimate biological activity with high reliability in new compounds based on a DHP series. Graphical abstract The good correlation between the log IC with the NCI (H4-G) estimated by the reduced density gradient approach of the DHP derivatives.
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