Solution of atomic orbitals in an interpolating wavelet basis
Tommi Höynälänmaa, Tapio T. Rantala, K. Ruotsalainen · Physical Review E · 2004
The Schrödinger equation of hydrogenic atoms and the Hartree-Fock equations of some many-electron atoms are solved using interpolating wavelets as basis functions. The nonstandard operator form is used to compute operators in basis sets including multiple resolution levels. We introduce an algorithm for converting matrices from nonstandard operator form to standard operator form. We also consider the different components of the Hamiltonian and Fock operators separately and derive analytic formulas for their evaluation. Extension to many-electron atoms is done within the Hartree-Fock formalism. Convergence of atomic parameters such as orbital eigenvalues with respect to the number of resolution levels is inspected numerically for hydrogenlike atoms (ions) and some light many-electron atoms (helium, lithium, beryllium, neon, sodium, magnesium, and argon).