An all-electron numerical method for solving the local density functional for polyatomic molecules

TLDR

The paper presents a new method for accurate and efficient local density functional calculations on molecules. The Dmol method employs fast, convergent three‑dimensional numerical integrations to compute matrix elements in the Ritz variation framework, enabling flexible variational basis sets, exact electrostatic potential evaluation, and exact attainment of the LDF dissociation limit. Tests on small molecules show accurate results with acceptable errors, while computational cost scales as O(n³) with size but can be reduced to quadratic growth for large molecules aside from the eigenvalue solve.

Abstract

A method for accurate and efficient local density functional calculations (LDF) on molecules is described and presented with results. The method, Dmol for short, uses fast convergent three-dimensional numerical integrations to calculate the matrix elements occurring in the Ritz variation method. The flexibility of the integration technique opens the way to use the most efficient variational basis sets. A practical choice of numerical basis sets is shown with a built-in capability to reach the LDF dissociation limit exactly. Dmol includes also an efficient, exact approach for calculating the electrostatic potential. Results on small molecules illustrate present accuracy and error properties of the method. Computational effort for this method grows to leading order with the cube of the molecule size. Except for the solution of an algebraic eigenvalue problem the method can be refined to quadratic growth for large molecules.