@inproceedings{Bacalis_Xiong_Karaoulanis_2009, title={Remarks on the Hylleraas-Undheim and MacDonald Higher Roots, And Functionals Having Local Minimum at The Excited States}, volume={1148}, ISBN={ISBN: 978-0-7354-0685-8}, ISSN={0094-243X}, archiveLocation={Ινστιτούτο Θεωρητικής και Φυσικής Χημείας (ΙΘΦΧ) - Επιστημονικό έργο}, url={https://hdl.handle.net/10442/12643}, abstractNote={The excited states, being energy saddle points in the Hamiltonian eigenfunction Hilbert space, cannot be computed variationally by minimization of the energy. Thus, functionals are presented, that have local minimum at the bound excited states of a non-degenerate Hamiltonian, allowing the computation at any desired accuracy, by using crude approximations of the lower lying states. They are useful for larger systems, because the higher roots of the standard secular equation have, by the Hylleraas-Undheim and MacDonald theorem, several restrictions, which render them of lower quality relative to the lowest root, if the latter is good enough. Preliminary test-results are presented for He (1)S 1 s2s.}, booktitle={Computational Methods in Science and Engineering, Vol 2: Advances in Computational Science}, publisher={Springer New York LLC}, author={Bacalis, Naoum C. and Xiong, Z. and Karaoulanis, D.}, editor={Simos, TE and Maroulis, GEditors}, year={2009}, pages={372–375} }