Abstract
We have developed a completely numerical scheme for solution of Poisson’s equation in multicenter systems. We are thus able to numerically calculate the Coulomb potential of arbitrary charge distributions in polyatomic molecules. The method is based on a decomposition of the multicenter Poisson problem into independent single-center problems, each of which is solvable in standard spherical coordinates. In combination with our multicenter numerical integration scheme reported previously, completely numerical evaluation of arbitrary two-electron Coulomb integrals is possible. Test calculations on the classic two-electron Coulomb and exchange integrals of H2 and the Coulomb interaction energies of several model polyatomic systems indicate that the scheme is both practical and accurate.
Keywords
Polyatomic ionCoulombPoisson's equationPoisson distributionPhysicsNumerical integrationCoulomb wave functionScheme (mathematics)Electric potentialElectronQuantum mechanicsClassical mechanicsMoleculeStatistical physicsMathematicsMathematical analysis
Affiliated Institutions
Related Publications
Discrete Variational Method for the Energy-Band Problem with General Crystal Potentials
A general variational method for efficiently calculating energy bands and charge densities in solids is presented; the method can be viewed as a weighted local-energy procedure ...
A multicenter numerical integration scheme for polyatomic molecules
We propose a simple scheme for decomposition of molecular functions into single-center components. The problem of three-dimensional integration in molecular systems thus reduces...
Three‐dimensional numerical integration for electronic structure calculations
Abstract Two three‐dimensional numerical schemes are presented for molecular integrands such as matrix alements of one‐electron operators occuring in the Fock operator and expec...
Precise density-functional method for periodic structures
A density-functional method for calculations on periodic systems (periodicity in one, two, or three dimensions) is presented in which all aspects of numerical precision are effi...
Atomic and molecular calculations with the model potential method. I
A new formulation of the model potential method is introduced for atoms and molecules. The model potential consists of a static local potential which simulates the effect of the...
Publication Info
- Year
- 1988
- Type
- article
- Volume
- 89
- Issue
- 5
- Pages
- 2993-2997
- Citations
- 164
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
164
OpenAlex
Cite This
Axel D. Becke,
Ross M. Dickson
(1988).
Numerical solution of Poisson’s equation in polyatomic molecules.
The Journal of Chemical Physics
, 89
(5)
, 2993-2997.
https://doi.org/10.1063/1.455005
Identifiers
- DOI
- 10.1063/1.455005