Dealing with the exponential wall in electronic structure calculations

The Journal of Chemical Physics
Peter Fulde, Hermann Stoll

Abstract

An alternative to the density functional theory is the use of wavefunction based electronic structure calculations for solids. In order to perform them, the Exponential Wall (EW) problem has to be resolved. It is caused by an exponential increase of the number of configurations with increasing electron number N. There are different routes one may follow. One is to characterize a many-electron wavefunction by a vector in Liouville space with a cumulant metric rather than in Hilbert space. This removes the EW problem. Another is to model the solid by an impurity or fragment embedded in a bath which is treated at a much lower level than the former. This is the case in the Density Matrix Embedding Theory (DMET) or the Density Embedding Theory (DET). The latter two are closely related to a Schmidt decomposition of a system and to the determination of the associated entanglement. We show here the connection between the two approaches. It turns out that the DMET (or DET) has an identical active space as a previously used Local Ansatz, based on a projection and partitioning approach. Yet, the EW problem is resolved differently in the two cases. By studying a H10 ring, these differences are analyzed with the help of the method of increm...Continue Reading

References

Aug 15, 1991·Physical Review. B, Condensed Matter·M V Ganduglia-Pirovano, G Stollhoff
Sep 15, 1992·Physical Review. B, Condensed Matter·H Stoll
Sep 3, 1990·Physical Review Letters·G König, G Stollhoff
Dec 12, 2012·Physical Review Letters·Gerald Knizia, Garnet Kin-Lic Chan
Aug 12, 2014·The Journal of Chemical Physics·Ireneusz W BulikGustavo E Scuseria
Sep 17, 2015·The Journal of Chemical Physics·Sandeep Sharma, Ali Alavi
Mar 12, 2013·Journal of Chemical Theory and Computation·Gerald Knizia, Garnet Kin-Lic Chan
May 10, 2016·Journal of Chemical Theory and Computation·Sebastian WoutersGarnet K-L Chan

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Citations

Jan 21, 2019·The Journal of Chemical Physics·P Fulde
Jul 1, 2019·The Journal of Chemical Physics·Paul M Zimmerman, Alan E Rask
Feb 10, 2021·The Journal of Physical Chemistry. a·Isolde SandlerJunming Ho
Dec 10, 2019·Journal of Chemical Theory and Computation·Zhi-Hao CuiGarnet Kin-Lic Chan
Dec 29, 2020·The Journal of Physical Chemistry Letters·Janus J Eriksen

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