Multipole-moment integrals integral evaluation

Having discussed the Cartesian Gaussian functions and their overlap distributions, we are now ready to consider the evaluation of the simple one-electron integrals. By simple, we here mean the standard molecular integrals that do not involve the Coulomb interaction. In the present section, we thus discuss the evaluation of overlap integrals and multipole-moment integrals by the Obara-Saika scheme [5], based on the translational invariance of the integrals. We also... 

Consider the evaluation of the multipole-moment integrals of the type... 

Note that, in (9.6.26), the abscissae and weights are the same for all integrals of the same quantum number i + j + e. The Gauss-Hermite scheme for multipole-moment integrals may easily be extended to the evaluation of kinetic-energy integrals. 

Let us now consider an alternative procedure for the evaluation of the contracted multipole moments (9.13.36). First, we calculate - for each primitive overlap distribution contributing to the two-electron integral - local multipole moments of the type (9.13.20), each with origin at the centre of the primitive overlap distribution ... 

Some authors do not make use of AIM but air certain views about it in their papers or express an interest in applying it in the near future. For example, Abramov et al. report on the evaluation of molecular dipole moments firom multipole refinement of X-ray diffraction data. They promised that a further analysis would include integration of the basins obtained from the experimental electron density in order to obtain further information about the observed differences between theory and experiment. 

Moon and Oxtoby presented a general theory for collision-induced absorption, which occurs in the near- and far-infrared region of the spectrum, in molecules. Speeific results were presented for the case of symmetric linear Dooh) and tetrahedral (Tj) molecules. The authors subsequently applied their nonasymptotic theory of the pair dipole moment to the eal-culation of binary spectral integrals and the far-infrared speetrum for dinitrogen.The authors also evaluate the eontributions to the seeond-order multipole model (including the anisotropy of the polarizability, the hexadecapole moment and the dipole-oetopole polarizability). 

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