A measure of basis efficiency at solving the Schrödinger torsion equation. Reaching the variational limit

Abstract

The procedure of the numerical solution of the Schrödinger torsion equation in matrix form in the planar wave basis set was considered. The concept of the largest level number that has reached the variation limit for a given number of basis functions was introduced as a quantitative measure of the basis efficiency. The rate of convergence to reliable values of levels and transitions has been studied. The problem of the maximum possible energy level number computed with the required accuracy for a given basis size has been solved. It was demonstrated that the number of levels that have reached the variational limit has linear relationship with the number of basis functions, and the angular slope coefficients of such dependencies are quite close to each other and equal to roughly 0.96. This allows prediction of the accuracy of the calculation method and conscious choice of the basis power.