  In this article, we combine the periodic sinc basis set with a curvilinear
coordinate system for electronic structure calculations. This extension allows
for variable resolution across the computational domain, with higher resolution
close to the nuclei and lower resolution in the inter-atomic regions. We
address two key challenges that arise while using basis sets obtained by such a
coordinate transformation. First, we use pseudospectral methods to evaluate the
integrals needed to construct the Hamiltonian in this basis. Second, we
demonstrate how to construct an appropriate coordinate transformation by
solving the Monge-Amp\`ere equation using a new approach that we call the
cyclic Knothe-Rosenblatt flow. The solution of both of these challenges enables
mean-field calculations at a cost that is log-linear in the number of basis
functions. We demonstrate that our method approaches the complete basis set
limit faster than basis sets with uniform resolution. We also emphasize how
these basis sets satisfy the diagonal approximation, which is shown to be a
consequence of the pseudospectral method. The diagonal approximation is highly
desirable for the solution of the electronic structure problem in many
frameworks, including mean field theories, tensor network methods, quantum
computing, and quantum Monte Carlo.
