One- and two-electron integrals over cartesian gaussian functions

McMurchie, L.; Davidson, Ernest R.

doi:10.1016/0021-9991(78)90092-x

Cited by 598 publications

(314 citation statements)

References 7 publications

Supporting

Mentioning

314

Contrasting

Order By: Relevance

“…It is worth mentioning that few authors 6,7 have proposed an alternative approach for an efficient evaluation of the real space terms of the multipolar Ewald sum based on tree-code algorithms 7 or through a McMurchie-Davidson formalism. 6,8 All the self-interaction correction terms for the energy as well as for the potential, electric field, and electric field gradients are properly derived from the work of Aguado and Madden 1 ͓see Eqs. ͑50͒-͑62͒ therein͔.…”

Section: ͑4͒mentioning

confidence: 99%

Notes on “Ewald summation of electrostatic multipole interactions up to quadrupolar level” [J. Chem. Phys. 119, 7471 (2003)]

Laino¹,

Hutter²

2008

The Journal of Chemical Physics

View full text Add to dashboard Cite

Notes on "Ewald summation of electrostatic multipole interactions up to quadrupolar level" [J. Chem. Phys. 119, 7471 (2003) (2003)] published in this journal, Ewald summation expressions were derived for the energy, interatomic forces, pressure tensor, electrostatic field, and electrostatic field gradients in simulation system composed of molecules with charges, induced dipoles, and quadrupoles. In this letter we propose an alternative formulation of the reciprocal space terms generalized to higher multipoles, providing, at the same time, a few important corrections for previously published derivations. The present expressions, more compact than the ones proposed in the original work, provide a straightforward approach to implement an Ewald summation scheme for multipole interactions in codes where a standard Ewald summation is already available. A major result of the present derivation is an increase in the computational efficiency compared to the previous implementation of the several different electrostatic terms.

show abstract

Section: ͑4͒mentioning

confidence: 99%

Notes on “Ewald summation of electrostatic multipole interactions up to quadrupolar level” [J. Chem. Phys. 119, 7471 (2003)]

Laino¹,

Hutter²

2008

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…This problem has received considerable attention in the last fifteen years [27][28][29], and a number of very efficient schemes have been devised. A key feature of these schemes is the use of shells of basis functions, a shell being defined by a set of contracted Gaussian functions of the same L value, located on the same centre, with the same exponents and contraction coefficients but differing in their angular behaviour.…”

Section: Computational Considerationsmentioning

confidence: 99%

Integral processing in beyond‐Hartree‐Fock calculations

Taylor

1987

Int J of Quantum Chemistry

View full text Add to dashboard Cite

The increasing rate at which improvements in processing capacity outstrip improvements in input/output performance of large computers has led to recent attempts to bypass generation of a disk-based integral file. The "direct" SCF method of Almlof and co-workers represents a very successful implementation of this approach. -The present work is concerned with the extension of this general approach to CI and MCSCF calculations. After a discussion of the particular types of MO integrals for which -at least for most current generation machines -disk-based storage seems unavoidable, it is shown how all the necessary integrals can be obtained as matrix elements of Coulomb and exchange operators that can be calculated using a direct approach. Computational implementations of such a scheme are discussed.

show abstract

“…In Cartesian space, Sagui et al 24 utilized Challacombe's efficient McMurchieDavidson recursive scheme 49,50 to enhance calculation efficiency, which scales with multipole order l as O(l 4 ), whereas the spherical harmonic approach developed by Hattig 51,52 scales as O(l 3 ). Given the convenience of Cartesian expressions and the fact that the multipole IPS potentials no longer satisfy Laplace's equation, we present the multipole IPS method in Cartesian space and leave the spherical harmonic expression to future work.…”

Section: Introductionmentioning

confidence: 99%

Isotropic periodic sum for multipole interactions and a vector relation for calculation of the Cartesian multipole tensor

Wu¹,

Pickard²,

Brooks³

2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

Isotropic periodic sum (IPS) is a method to calculate long-range interactions based on the homogeneity of simulation systems. By using the isotropic periodic images of a local region to represent remote structures, long-range interactions become a function of the local conformation. This function is called the IPS potential; it folds long-ranged interactions into a short-ranged potential and can be calculated as efficiently as a cutoff method. It has been demonstrated that the IPS method produces consistent simulation results, including free energies, as the particle mesh Ewald (PME) method. By introducing the multipole homogeneous background approximation, this work derives multipole IPS potentials, abbreviated as IPSMm, with m being the maximum order of multipole interactions. To efficiently calculate the multipole interactions in Cartesian space, we propose a vector relation that calculates a multipole tensor as a dot product of a radial potential vector and a directional vector. Using model systems with charges, dipoles, and/or quadrupoles, with and without polarizability, we demonstrate that multipole interactions of order m can be described accurately with the multipole IPS potential of order 2 or m − 1, whichever is higher. Through simulations with the multipole IPS potentials, we examined energetic, structural, and dynamic properties of the model systems and demonstrated that the multipole IPS potentials produce very similar results as PME with a local region radius (cutoff distance) as small as 6 Å. [http://dx

show abstract

One- and two-electron integrals over cartesian gaussian functions

Abstract: -2-

Cited by 598 publications

References 7 publications

Notes on “Ewald summation of electrostatic multipole interactions up to quadrupolar level” [J. Chem. Phys. 119, 7471 (2003)]

Notes on “Ewald summation of electrostatic multipole interactions up to quadrupolar level” [J. Chem. Phys. 119, 7471 (2003)]

Integral processing in beyond‐Hartree‐Fock calculations

Isotropic periodic sum for multipole interactions and a vector relation for calculation of the Cartesian multipole tensor

Contact Info

Product

Resources

About