2020/05/22 by Nicholas H. Stair, Francesco A. Evangelista, Stair, Nicholas H. +1 · 1 citation
Physics and Astronomy · Chemistry · #Physics of Superconductivity and Magnetism #Advanced Chemical Physics Studies #Advanced NMR Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2005.11349
This work explores the ability of classical electronic structure methods to\nefficiently represent (compress) the information content of full configuration\ninteraction (FCI) wave functions. We introduce a benchmark set of four hydrogen\nmodel systems of different dimensionality and distinctive electronic\nstructures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D\nclose-packed pyramid. To assess the ability of a computational method to\nproduce accurate and compact wave functions, we introduce the accuracy volume,\na metric that measures the number of variational parameters necessary to\nachieve a target energy error. Using this metric and the hydrogen models, we\nexamine the performance of three classical deterministic methods: i) selected\nconfiguration interaction (sCI) realized both via an a posteriori and\nvariational selection of the most important determinants, ii) rank-reduced FCI,\nobtained by an a posteriori singular value decomposition of the FCI tensor\n(SVD-FCI), and iii) the matrix product state representation obtained via the\ndensity matrix renormalization group (DMRG). We find that DMRG generally gives\nthe most efficient wave function representation for all systems, particularly\nin the 1D chain with a localized basis. For the 2D and 3D systems, all methods\nperform best with a delocalized basis, and the efficiency of sCI is closer to\nthat of DMRG, with the former having and accuracy volume approximately twice as\nlarge in the strong correlation regime. Compared to sCI, the SVD-FCI scheme is\ngenerally found to require a slightly larger number of parameters to achieve\nthe same energy accuracy.\n