Excited States of Generalized Moments Expansion

A newly developed generalized moments expansion, \textrm{GMX}$(m,n)$, based on the \textquotedblleft\emph{t}-expansion\textquotedblright\ of Horn and Weinstein has proved useful in the calculation of the ground--state energy of a number of Hamiltonian systems in both quantum chemistry and physics. As has been shown elsewhere (Phys.~Lett.~\textbf{A}349, 320 [2006]) the well-known Connected Moments Expansion (\textrm{CMX}) of Cioslowski (PRL 58, 83 [1987]) is just a special case of $\mathrm{GMX}=\mathrm{GMX}(1,1)$. A number of years ago Marko\v{s} and Olejn\'{\i}k were able to generalize the \textrm{CMX} to include excited states (PRD 42, 2943 [1990]). Here we have extended this work to the \textrm{GMX} with applications to a number of systems.