RESUMO
A computational scheme to perform accurate numerical calculations of electrostatic potentials and interaction energies for molecular systems has been developed and implemented. Molecular electron and energy densities are divided into overlapping atom-centered atomic contributions and a three-dimensional molecular remainder. The steep nuclear cusps are included in the atom-centered functions making the three-dimensional remainder smooth enough to be accurately represented with a tractable amount of grid points. The one-dimensional radial functions of the atom-centered contributions as well as the three-dimensional remainder are expanded using finite element functions. The electrostatic potential is calculated by integrating the Coulomb potential for each separate density contribution, using our tensorial finite element method for the three-dimensional remainder. We also provide algorithms to compute accurate electron-electron and electron-nuclear interactions numerically using the proposed partitioning. The methods have been tested on all-electron densities of 18 reasonable large molecules containing elements up to Zn. The accuracy of the calculated Coulomb interaction energies is in the range of 10(-3) to 10(-6) E(h) when using an equidistant grid with a step length of 0.05 a(0).
RESUMO
The direct approach to gravitation and electrostatics (DAGE) algorithm is an accurate, efficient, and flexible method for calculating electrostatic potentials. In this paper, we show that the algorithm can be easily extended to consider systems with many different kinds of periodicities, such as crystal lattices, surfaces, or wires. The accuracy and performance are nearly the same for periodic and aperiodic systems. The electrostatic potential for semiperiodic systems, namely defects in crystal lattices, can be obtained by combining periodic and aperiodic calculations. The method has been applied to an ionic model system mimicking NaCl, and to a corresponding covalent model system.