Nuclear attraction integrals three center

For example, three center nuclear attraction integrals (AB C) will reduce to an expression involving two center integrals of (AA C) and (BB C) type. 

Because of the many center nature of the fourth integral case, a detailed analysis of three center nuclear attraction integral problem is given. Using the ideas developed in Sections 4 and 5, it is described how the three center integrals become expressible in terms of one and tv/o center ones. An example involving s-type WO-CETO functions is presented as a test of the developed theory of the preceding chapters. 

Variation of the Three Center Nuclear Attraction Integrals with L . 

Figure 6.1 Variation of the three center Nuclear Attraction integral <1Sa1Sb C> value.

Figure 6.1 shows the three center nuclear attraction integral variation using the same Eab covering of Figure 5.1, and the same... 

Table 7.1 shows how repulsion integrals over CETO functions can be constructed with reliable accuracy, as three center nuclear attraction integrals were computed. 

One of the authors (R.C.) wants to thank Prof. S. Fraga for the challenging proposal made to him in 1969, concerning computation of three center STO nuclear attraction integrals. The interest of Prof. S. Huzinaga on the possible use of STO s in the same manner as GTO s, and the test atomic calculations made by him in 1977 on the second and third rows of the periodic table [73] are also deeply acknowledged. 

Second-neighbor interactions (namely = — 2, — 1,0,1,2) have been included with a correct, electrostatistically balanced cutoff. This means that the two-electron repulsion integrals have been neglected in a way that balances the neglect of the electron-nuclear attraction integrals. Therefore, some of the two-electron integrals containing centers three units apart from one other had to be retained. 

Four-center integrals in the p basis are neglected. All one- and two-center nuclear attraction integrals are evaluated analytically, while three-center integrals are approximated by Gaussian expansion techniques. 

Therefore, in order to obtain Va (r) at point r, it is sufficient to calculate the distances of the point from any of the nuclei (trivial) as well as the one-electron integrals, which appear after inserting into Eq. (14.34) Pa(/) = 2 I a./C ) - Within the LCAO MO approximation, the electron density distribution pa represents the sum of products of two atomic orbitals (in general centered at two different points). As a result, the task reduces to calculating typical one-electron three-center integrals of the nuclear attraction type (cf.. Chapter 8 and Appendix P available at booksite.elsevier.com/978-0-444-59436-5), because the third center corresponds to the point r (Fig. 14.14). There is no computational problem with this for contemporary quantum chemistry. 

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