Electric field integrals for Slater‐type orbitals

Abstract

ABSTRACT:General algorithms for electric field integrals with Slater-type orbitals (STO) are reported, and the efficiency of the computational procedure based in these algorithms is analyzed. An accuracy of nine decimal places, at least, is estimated for the molecular electric field computed on any point. Timing was examined for calculations with STO basis sets ranging from 30 to 300 basis functions. Computational cost was moderate, even for the largest basis set.

Auxiliary functions for molecular integrals with Slater‐type orbitals. I. Translation methods

“…Expressions for some particular cases were derived some time ago by several investigators 8, 16, 17 and recently extended by Barnett 18. There is also a recent program for their computation based in algorithms obtained from ellipsoidal coordinates 5. Comparison with the results of this program, presented in Table I, again shows excellent agreement.…”

“…To give an idea of the cost, we report in Table II the computational time per integral calculated with this program. As a reference, we note that potential (nuclear attraction) integrals computed with SMILES 4 and electric field integrals computed with the previous program based in ellipsoidal coordinates 5 take ∼1 μs per integral.…”

“…In the case of STO, the algorithms for molecular integrals are much more involved, and general programs 1–4 for molecular calculation of polyatomics have not been developed until just a few years ago. Although these currently available programs are still quite rudimentary, they indicate that STOs perform more efficiently than GTOs in some applications, such as high‐level studies of electronic structure 4 or calculation of density‐dependent properties 5. This fact has quickened the search for improving the efficiency of the current programs and the development of new algorithms for the integrals required to test the capabilities of STOs in further applications.…”

Accuracy of the electrostatic theorem for high‐quality Slater and Gaussian basis sets

“…The energy derivatives were thus calculated by numerical methods, and the electrostatic forces were computed directly from the density—Eq. (9)—using our own programs 17.…”

Combining Slater-type orbitals and effective core potentials

“…Interestingly enough, there has been a significant progress on this issue in recent years. In fact, looking at only the past 15 years, there are many notable works of Bouferguene et al [10][11][12][13], Rico et al [14][15][16][17][18][19][20][21][22][23][24], Hoggan et al [25][26][27][28][29][30], Pachucki [31][32][33][34][35], and others [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. In particular, for the diatomic systems STOs can be now used routinely [51].…”