Molecular integrals with Slater basis. IV. Ellipsoidal coordinate methods for three-center nuclear attraction integrals

Rico, J. Fernández; López, R.; Ramírez, G.
November 1992
Journal of Chemical Physics;11/15/1992, Vol. 97 Issue 10, p7613
Academic Journal
We develop and check an updated version of the ellipsoidal coordinate methods for the calculation of three-center nuclear attraction integrals with Slater-type orbitals (STOs). A first set of recurrence relations allows us to express these integrals in terms of some basic potentials. The basic potentials are classified in short- and long-range types, and then calculated in specific ways from auxiliary functions obtained by using a new set of both stable and fast recurrence relations. Numerical tests show that the procedure enables to reach very high accuracy in the integrals with a low computational cost.


Related Articles

  • Calculation of STOs electron repulsion integrals by ellipsoidal expansion and large-order approximations. Lesiuk, Michał // Journal of Mathematical Chemistry;Feb2016, Vol. 54 Issue 2, p572 

    For general two-electron two-centre integrals over Slater-type orbitals (STOs), the use of the Neumann expansion for the Coulomb interaction potential yields infinite series in terms of few basic functions. In many important cases the number of terms necessary to achieve convergence by a...

  • Directed vertex-connectivity augmentation. Frank, András; Jordán, Tibor // Mathematical Programming;1999, Vol. 84 Issue 3, p537 

    Abstract. The problem of finding a smallest set of new edges to be added to a given directed graph to make it k-vertex-connected was shown to be polynomially solvable recently in [6] for any target connectivity k is greater than or equal to h However, the algorithm given there relied on the...

  • A PRIMAL-DUAL ALGORITHM FOR SUBMODULAR FLOWS. Cunningham, William H.; Frank, Andras // Mathematics of Operations Research;May85, Vol. 10 Issue 2, p251 

    Previously the only polynomial-time solution algorithm to solve the optimal submodular flow problem introduced by Edmonds and Giles was based on the ellipsoid method. Here, modulo an efficient oracle for minimizing certain submodular functions, a polynomial time procedure is presented which uses...

  • Efficient Collision Detection for Moving Ellipsoids Using Separating Planes. Wang, W.; Choi, Y.-K.; Chan, B.; Kim, M.-S.; Wan, J. // Computing;2004, Vol. 72 Issue 1/2, p235 

    We present a simple, accurate and efficient algorithm for collision detection among moving ellipsoids. Its efficiency is attributed to two results: (i) a simple algebraic test for the separation of two ellipsoids, and (ii) an efficient method for constructing a separating plane between two...

  • Khatchian algorithm (1979) Mathematics.  // Dictionary of Theories;2002, p294 

    Information about Khatchian algorithm is presented. It refers to the first polynomial-time method for solving linear programs. It owes its geometric basis in circumscribing the region of interest with ellipsoids.

  • Minimum-Volume Enclosing Ellipsoids and Core Sets. Kumar, P.; Yildirim, E. A.; Zhang, Y. // Journal of Optimization Theory & Applications;Jul2005, Vol. 126 Issue 1, p1 

    We study the problem of computing a (1 + ?)-approximation to the minimum-volume enclosing ellipsoid of a given point set S = {p�, p�, �, pn} ? Rd Based on a simple, initial volume approximation method, we propose a modification of the Khachiyan first-order algorithm. Our analysis...

  • Dynamic fire 3D modeling using a real-time stereovision system. Lucile, Rossi; Moulay, Akhloufi; Yves, Tison // Journal of Communication & Computer;Oct2009, Vol. 6 Issue 10, p54 

    This work presents a new framework for three-dimensional modeling of dynamic fires present in unstructured scenes. The proposed approach addresses the problem of segmenting fire regions using information from YUV and RGB color spaces. Clustering is also used to extract salient points from a pair...

  • The Kinematics and Velocity Ellipsoid Parameters of Open Star Clusters. Elsanhoury, W. H.; Sharaf, M. A.; Nouh, M. I.; Saad, A. S. // Open Astronomy Journal;2013, Vol. 6, p1 

    In terms of the equatorial coordinates, the galactic space velocity components were expressed in closed analytical forms. With the aid of the vectors and matrices analyses expressions for the velocity ellipsoid parameters VEPs in closed analytical forms were also represented. For the...

  • ELLIPSOID ALGORITHM.  // Encyclopedia of Operations Research & Management Science;2001, p243 

    An encyclopedia entry for ellipsoid algorithm is presented. It is the first polynomial-time algorithm for linear programming. It was originally developed as a method for solving convex programming. The history of the topic, description of relevant applications, and overview of present and future...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics