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Molecular Integrals (molecular + integral)
Selected AbstractsEvaluation of one-electron molecular integrals over complete orthonormal sets of ,, -ETO using auxiliary functionsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 10 2010Israfil I. Guseinov Abstract By the use of expansion and one-range addition theorems, the one-electron molecular integrals over complete orthonormal sets of ,, -exponential type orbitals arising in Hartree,Fock,Roothaan equations for molecules are evaluated. These integrals are expressed through the auxiliary functions in ellipsoidal coordinates. The comparison is made using Slater-, Coulomb-Sturmian-, and Lambda-type basis functions. Computation results are in good agreement with those obtained in the literature. The relationships obtained are valid for the arbitrary quantum numbers, screening constants, and location of orbitals. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Auxiliary functions for molecular integrals with Slater-type orbitals.INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2008Abstract The Gauss transform of Slater-type orbitals is used to express several types of molecular integrals involving these functions in terms of simple auxiliary functions. After reviewing this transform and the way it can be combined with the shift operator technique, a master formula for overlap integrals is derived and used to obtain multipolar moments associated to fragments of two-center distributions and overlaps of derivatives of Slater functions. Moreover, it is proved that integrals involving two-center distributions and irregular harmonics placed at arbitrary points (which determine the electrostatic potential, field and field gradient, as well as higher order derivatives of the potential) can be expressed in terms of auxiliary functions of the same type as those appearing in the overlap. The recurrence relations and series expansions of these functions are thoroughly studied, and algorithms for their calculation are presented. The usefulness and efficiency of this procedure are tested by developing two independent codes: one for the derivatives of the overlap integrals with respect to the centers of the functions, and another for derivatives of the potential (electrostatic field, field gradient, and so forth) at arbitrary points. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Erratum: On the calculation of arbitrary multielectron molecular integrals over slater-type orbitals using recurrence relations for overlap integrals.INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2008No abstract is available for this article. [source] Extrapolation methods for improving convergence of spherical Bessel integrals for the two-center Coulomb integralsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 11 2006Hassan Safouhi Abstract Multi-center two-electron Coulomb integrals over Slater-type functions are required for any accurate molecular electronic structure calculations. These integrals, which are numerous, are to be evaluated rapidly and accurately. Slater-type functions are expressed in terms of the so-called B functions, which are best suited to apply the Fourier transform method. The Fourier transform method allowed analytic expressions for these integrals to be developed. Unfortunately, the analytic expressions obtained turned out to be extremely difficult to evaluate accurately due to the presence of highly oscillatory spherical Bessel integrals. In this work, we used techniques based on nonlinear transformation and extrapolation methods for improving convergence of these oscillatory spherical Bessel integrals. These techniques, which led to highly efficient and rapid algorithms for the numerical evaluation of three- and four-center two-electron Coulomb and exchange integrals, are now shown to be applicable to the two-center two-electron Coulomb integrals. The numerical results obtained for the molecular integrals under consideration illustrate the efficiency of the algorithm described in the present work compared with algorithms using the epsilon (,) algorithm of Wynn and Levin's u transform. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Auxiliary functions for molecular integrals with Slater-type orbitals.INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 9 2006Abstract Many types of molecular integrals involving Slater functions can be expressed, with the ,-function method in terms of sets of one-dimensional auxiliary integrals whose integrands contain two-range functions. After reviewing the properties of these functions (including recurrence relations, derivatives, integral representations, and series expansions), we carry out a detailed study of the auxiliary integrals aimed to facilitate both the formal and computational applications of the ,-function method. The usefulness of this study in formal applications is illustrated with an example. The high performance in numerical applications is proved by the development of a very efficient program for the calculation of two-center integrals with Slater functions corresponding to electrostatic potential, electric field, and electric field gradient. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Evaluation of Two-center One- and Two-electron Integrals over Slater Type OrbitalsCHINESE JOURNAL OF CHEMISTRY, Issue 5 2006Yusuf Yakar Abstract A formulation previously presented by the authors for coulomb integrals was generalized to other two-center integrals, except exchange integral. Within this frame, molecular integrals were expressed in terms of some new functions closely related to the well-known incomplete gamma functions and these functions recursively evaluated. Special issues arising in the case of hybrid integrals were addressed, and the results were compared with the ones found in the literature. [source] | ||||||||||