Computation of molecular integrals over Slater type orbitals. II. Calculation of electric multipole moment integrals using translation formulas

Guseinov, I. I.; Rzaeva, A.M.; Мамедов, Б. А.; Orbay, Metin; Özdoğan, Telhat; Öner, F.

doi:10.1016/s0166-1280(98)00130-4

Cited by 12 publications

(16 citation statements)

References 8 publications

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“…It is seen from the values in Table 1 that the computer results for electric multipole moment integrals over integer n-STOs are in best agreement with the literature. 20,21,22 The computer results for multicenter electric multipole moment integrals over noninteger n-STOs are presented in Table 2 with no comparison due to the scarcity of the literature. But also we have tested the limit of a noninteger case with an integer case and at least 10-decimal digit accuracy is obtained.…”

Section: Computational Results and Discussionmentioning

confidence: 99%

Evaluation of Multicenter Electric Multipole Moment Integrals over Integer and Noninteger n‐STOs

Özdoğan

2004

J Chinese Chemical Soc

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Multicenter electric multipole moment integrals over Slater type orbitals with integer and noninteger principal quantum numbers are expressed in terms of overlap integrals. The computer results for the integer case agree best with the prior literature. The accuracy of the computer results for noninteger case is not compared with the literature due to the lack of relevant literature, but the limit of the noninteger case is compared with the integer case and good agreement is achieved for wide changes in the relevant molecular parameters.

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Section: Computational Results and Discussionmentioning

confidence: 99%

Evaluation of Multicenter Electric Multipole Moment Integrals over Integer and Noninteger n‐STOs

Özdoğan

2004

J Chinese Chemical Soc

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“…In recent years, Guseinov and his coworkers made an industry out of one-range addition theorems of exponentially decaying functions. They published -in addition to several other articles on different topics -a very long list of articles on the derivation and application of one-range addition theorems [23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,63,69], that are often remarkably similar and that do not give due credit to the previous work of others.…”

Section: Introductionmentioning

confidence: 99%

Extended Comment on "One-Range Addition Theorems for Coulomb Interaction Potential and Its Derivatives" by I. I. Guseinov (Chem. Phys. Vol. 309 (2005), pp. 209 - 213)

Weniger

2007

Preprint

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Addition theorems are principal tools that express a function f (r ± r ′ ) in terms of products of other functions that only depend on either r or r ′ . The best known example of such an addition theorem is the Laplace expansion of the Coulomb potential which possesses a characteristic two-range form. Guseinov [Chem. Phys. 309, 209 -213 (2005)] derived one-range addition theorems for the Coulomb potential via the limit β → 0 in previously derived one-range addition theorems for the Yukawa potential exp `−β|r − r ′ | ´/|r − r ′ |. At first sight, this looks like a remarkable achievement, but from a mathematical point of view, Guseinov's work is at best questionable and in some cases fundamentally flawed. One-range addition theorems are expansions in terms of functions that are complete and orthonormal in a given Hilbert space, but Guseinov replaced the complete and orthonormal functions by nonorthogonal Slater-type functions and rearranged the resulting expansions. This is a dangerous operation whose validity must be checked. It is shown that the one-center limit r ′ = 0 of Guseinov's rearranged Yukawa addition theorems as well as of several other addition theorems does not exist. Moreover, the Coulomb potential does not belong to any of the Hilbert spaces implicitly used by Guseinov. Accordingly, one-range addition theorems for the Coulomb potential diverge in the mean. Instead, these one-range addition theorems have to interpreted as expansions of generalized functions in the sense of Schwartz that converge weakly in suitable functionals.

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“…( 7) of Ref. [10]). In the calculation of electric multipole moment integrals, Guseinov [3] used the formula for overlap integrals presented in Ref.…”

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confidence: 99%

Response to “Comment on ‘Electric Multipole Moments for Some First-Row Diatomic Hydride Molecules’ [Commun. Theor. Phys. 38 (2002) 256]”

Orbay¹,

Özdoğan²

2003

Commun. Theor. Phys.

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The comment of Guseinov is irrelevant and also unjust. In contrast to his comment, we show that the obtained electric multipole moment values for some first-row diatomic molecules are original and better than his values (I.I. Guseinov, E. Akin, and A.M. Rzaeva, J. Mol. Struct. (Theochem) 453 (1998) 163) with respect to Hartree-Fock values. Moreover, it must be noted that all the formulas are cited in our paper (M. Orbay and T. Ozdogan, Commun. Theor. Phys. (Beijing, China) 35 (2001) 585) and corrigendum (M. Orbay and T. Ozdogan, Commun. Theor. Phys. (Beijing, China) 37 (2002) 768).

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Computation of molecular integrals over Slater type orbitals. II. Calculation of electric multipole moment integrals using translation formulas

Cited by 12 publications

References 8 publications

Evaluation of Multicenter Electric Multipole Moment Integrals over Integer and Noninteger n‐STOs

Evaluation of Multicenter Electric Multipole Moment Integrals over Integer and Noninteger n‐STOs

Extended Comment on "One-Range Addition Theorems for Coulomb Interaction Potential and Its Derivatives" by I. I. Guseinov (Chem. Phys. Vol. 309 (2005), pp. 209 - 213)

Response to “Comment on ‘Electric Multipole Moments for Some First-Row Diatomic Hydride Molecules’ [Commun. Theor. Phys. 38 (2002) 256]”

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