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An exponential interaction is constructed so that one-dimensional atoms andchains of atoms mimic the general behavior of their three-dimensionalcounterparts. Relative to the more commonly used soft-Coulomb interaction, theexponential greatly diminishes the computational time needed for calculatinghighly accurate quantities with the density matrix renormalization group. Thisis due to the use of a small matrix product operator and to exponentiallyvanishing tails. Furthermore, its more rapid decay closely mimics the screenedCoulomb interaction in three dimensions. Choosing parameters to best matchearlier calculations, we report results for the one dimensional hydrogen atom,uniform gas, and small atoms and molecules both exactly and in the localdensity approximation.

One Dimensional Mimicking of Electronic Structure: The Case for Exponentials