Development of a Cartesian sinc DVR basis for single and double ionization

In this investigation, we explore properties of a grid-based representation designed to calculate phenomena involving single and double (auto)ionization. The method employs a powerful representation of the two-electron operator within a basis of sinc functions. It consists of a tensor decomposition of the operator such that two-electron matrix elements may be computed in O(N$^2$) operations, as opposed to the O(N$^4$) calculations required for the usual Gaussian basis sets used in quantum chemistry. The basis and methods are tested with the hydrogen atom and H$_2^+$. Results indicate that, in addition to being more scalable, the technique is more accurate than variational method.