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Multipole-moment integrals

Coulomb term involves products of multipole moment integrals (up to octopole) with the multipoles on the EFP fragments ... [Pg.163]

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... [Pg.344]

Having considered the simple overlap integrals in Section 9.3.1, let us now consider the slightly more complicated multipole-moment integrals of the form... [Pg.346]

Like the overlap integrals, the multipole-moment integrals are invariant to an overall translation of the coordinate system. The sum of the derivatives of the integral (9.3.13) with respect to A, and C. must therefore be zero ... [Pg.346]

THE McMURCHIE-DAVIDSON SCHEME FOR MULTIPOLE-MOMENT INTEGRALS... [Pg.356]

Let us consider again the x component of the Cartesian multipole-moment integrals (9.3.11) ... [Pg.356]

Consider the evaluation of the multipole-moment integrals of the type... [Pg.361]

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. [Pg.361]

The two-center two-electron repulsion integrals ( AV Arr) represents the energy of interaction between the charge distributions at atom Aand at atom B. Classically, they are equal to the sum over all interactions between the multipole moments of the two charge contributions, where the subscripts I and m specify the order and orientation of the multipole. MNDO uses the classical model in calculating these two-center two-electron interactions. [Pg.286]

The first and second terms are the contributions of the atomic nuclei and the electrons, respectively. The calculation of the multipole integrals in the second term is simpler and faster than that of the potential integrals. After rearrangement of Eq. (12) a molecular multipole moment can be expressed as a sum of the atomic contributions (ukvlwm i ... [Pg.62]

If we extend the integration volume Va to the full R3 space we will get the multipole moment of the monomer A in the coordinate system located at the site a. [Pg.46]

The multipole expansion has already been used in certain quantum chemical calculations [59-65]. As localized orbitals are concentrated in certain spatial region, they can also be represented by their multipole moments. In the following we investigate whether the Coulomb integrals in terms of localized orbitals can be substituted by the multipole expansion of electric moments. [Pg.71]

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