Improvement of the convergence of the linear variation method due to a variation of the basis Original Research Article

A method is given which improves the convergence of the linear variation method. The matrix of the Hamiltonian is set up in an appropriate orthonormal basis set, the functions of which contain some parameters. They are chosen in such a way that the trace of the matrix becomes minimal, yielding a minimal sum of eigenvalues of the matrix. This subsequent variation of the basis increases the number of converged eigenvalues, i.e. eigenvalues of the matrix, which do not deviate from the eigenvalues of the Hamiltonian.