One Dimensional Mimicking of Electronic Structure: The Case for Exponentials
Abstract
An exponential interaction is constructed so that one-dimensional atoms and chains of atoms mimic the general behavior of their three-dimensional counterparts. Relative to the more commonly used soft-Coulomb interaction, the exponential greatly diminishes the computational time needed for calculating highly accurate quantities with the density matrix renormalization group. This is due to the use of a small matrix product operator and to exponentially vanishing tails. Furthermore, its more rapid decay closely mimics the screened Coulomb interaction in three dimensions. Choosing parameters to best match earlier calculations, we report results for the one dimensional hydrogen atom, uniform gas, and small atoms and molecules both exactly and in the local density approximation.
Cite
@article{arxiv.1504.05620,
title = {One Dimensional Mimicking of Electronic Structure: The Case for Exponentials},
author = {Thomas E. Baker and E. Miles Stoudenmire and Lucas O. Wagner and Kieron Burke and Steven R. White},
journal= {arXiv preprint arXiv:1504.05620},
year = {2016}
}
Comments
10 pages, 9 figures, this version corrects two minus sign typos in Table 1 and the axes/captions of Figs. 2 & 4. The conclusions and benchmark numbers are unchanged