Evaluation Of Electron Repulsion Integrals Research Articles

Integral evaluation in the case of a helium atom positioned off-center in a spherical box

A variational approach to the problem of multielectron atoms placed off-center in a spherical box leads to the difficult evaluation of electron repulsion integrals in an environment where spherical symmetry is no longer present. A technique for the evaluation of the electron repulsion integrals generated by this situation is developed and tested for the case of a helium atom placed off-center in a spherical box. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 459–467, 1999

Methods for rapid evaluation of electron repulsion integrals in large-scale LCGO calculations

A method is proposed for efficient use of molecular symmetry in the evaluation of two-electron integrals. This provides a means of avoiding the recalculation of symmetry-redundant integrals, and of symmetry-blocking matrices and supermatrices without the usual time-consuming transformation procedures. Various methods for speeding up the calculation of integrals are also discussed. Integral calculation times are given for some representative molecules.

Tango-95. An electronic structure program for modeling chemisorption

tango-95, an ab initio electronic structure program based in part on the disco program of Almlöf, is described, with emphasis on the two electron integral evaluation. The program was developed largely for calculations on systems containing many metal atoms for heterogeneous catalysis studies. The evaluation of electron repulsion integrals was optimized for systems containing clusters of atoms which model metal surfaces. We show that the McMurchie and Davidson method (J. Comput. Phys., 26 (1978) 218) is appropriate in this context and we describe our implementation of the method for scalar processors. This implementation minimizes memory operations, and also floating point operations for important cases. We also comment on other features of the program such as gradient calculation, convergence algorithms, calculation of correlation energy and parallelization.

Three-center expansion of electron repulsion integrals with linear combination of atomic electron distributions

A new systematic way of constructing auxiliary basis functions for approximating the evaluation of electron repulsion integrals is proposed and applied to SCF and MCSCF wavefunction calculations. In the approximation, the one-electron density is expanded in terms of a linear combination of atomic electron distributions (LCAD), and the four-center two-electron repulsion integrals are reduced to the three- and two-center quantities. This results in a high-accuracy approximation as well as a large reduction in disk storage and input/output requirement, proportional to N 3 rather than N 4, N being the number of basis functions. Numerical results indicate that the error from the present approximation decreases as the size of molecular basis functions increases and that the LCAD version of MCSCF calculations requires only a fractional amount of the CPU time required in the conventional procedure without loss of accuracy.

Recurrence relations for the evaluation of electron repulsion integrals over spherical Gaussian functions

AbstractRecurrence relations are derived for the evaluation of two‐electron repulsion integrals (ERIs) over Hermite and spherical Gaussian functions. Through such relations, a generic ERI or ERI derivative may be reduced to “basic” integrals, i.e., true and auxiliary integrals involving only zero angular momentum functions. Extensive use is made of differential operators, in particular, of the spherical tensor gradient 𝒴(∇). Spherical Gaussians, being nonseparable in the x, y, and z coordinates, were not included in previous formulations. The advantages of using spherical Gaussians instead of Cartesian or Hermite Gaussians are briefly discussed. © 1993 John Wiley & Sons, Inc.

Development of a restricted Hartree—Fock program INDMOL on PARAM: A highly parallel computer

AbstractParallelization of the SCF method for closed‐shell molecules on the highly parallel transputer‐based system PARAM is described. The parallelization has been implemented on three different hardware and software environments: (1) a network of bare 64 transputers; (2) configuration 1 plus a back‐end file system (BFS); and (3) configuration 2 with one INTEL i860 processor. The evaluation of electron repulsion integrals (ERIs) and setting up of the Fock matrix is carried out in parallel on 64 nodes using minimal communication strategies. A good load balance is achieved for ERI evaluation with the help of bounds, local symmetry features, and the shell concept, as well as a data randomization technique, resulting into almost linear speedup (for ERI evaluation). In configurations 2 and 3, BFS is used for parallel storage and retrieval of ERIs. Further, in 3 matrix operations are implemented as remote procedure calls on the i860 processor. Routine techniques of level shifting and extrapolation are used for accelerating SCF convergence. The resulting package, INDMOL, has been tested for some randomly selected molecules having up to 255 contractions. Using configuration 3, a factor of 2 to 5 in computation time is obtained over 1, for the systems for which the ERIs cannot be stored in the distributed core memory. In summary, a heterogeneous system, as in configuration 3, can indeed be optimally exploited for programming peculiar diverse requirements of the SCF procedure. © 1993 John Wiley & Sons, Inc.

An efficient method of implementing the horizontal recurrence relation in the evaluation of electron repulsion integrals using Cartesian Gaussian functios

The tree search problem is considered for optimizing the horizontal recurrence relation step, which is a three-dimensional recurrence relation used in generating two-electron integrals. By eliminating redundant work, it is possible to achieve 13%, 25%, 38% and 44% savings in floating point operations and 21%, 34% and 53% reductions in memory requirements for the (ff|ff), (gg|gg), (hh|hh) and (ii|ii) cases, respectively. These savings and reductions will lead to quite efficient two-electron integral and derivative programs when high angular momentum functions are included.