Sumrule corrections: A route to error cancellations in correlation matrix renormalisation theory
Abstract
Here, we recently proposed the correlation matrix renormalisation (CMR) theory to efficiently and accurately calculate ground state total energy of molecular systems, based on the Gutzwiller variational wavefunction (GWF) to treat the electronic correlation effects. To help reduce numerical complications and better adapt the CMR to infinite lattice systems, we need to further refine the way to minimise the error originated from the approximations in the theory. This conference proceeding reports our recent progress on this key issue, namely, we obtained a simple analytical functional form for the oneelectron renormalisation factors, and introduced a novel sumrule correction for a more accurate description of the intersite electron correlations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.
 Authors:
 Ames Lab. and Iowa State Univ., Ames, IA (United States)
 Publication Date:
 Research Org.:
 Ames Laboratory (AMES), Ames, IA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1357795
 Report Number(s):
 ISJ9317
Journal ID: ISSN 00268976; TRN: US1702447
 Grant/Contract Number:
 AC0207CH11358
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Molecular Physics
 Additional Journal Information:
 Journal Volume: 115; Journal Issue: 5; Journal ID: ISSN 00268976
 Publisher:
 Taylor & Francis
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 74 ATOMIC AND MOLECULAR PHYSICS; correlation matrix renormalisation; sum rule; Gutzwiller approximation
Citation Formats
Liu, C., Liu, J., Yao, Y. X., Wang, C. Z., and Ho, K. M. Sumrule corrections: A route to error cancellations in correlation matrix renormalisation theory. United States: N. p., 2017.
Web. doi:10.1080/00268976.2017.1278800.
Liu, C., Liu, J., Yao, Y. X., Wang, C. Z., & Ho, K. M. Sumrule corrections: A route to error cancellations in correlation matrix renormalisation theory. United States. doi:10.1080/00268976.2017.1278800.
Liu, C., Liu, J., Yao, Y. X., Wang, C. Z., and Ho, K. M. Mon .
"Sumrule corrections: A route to error cancellations in correlation matrix renormalisation theory". United States.
doi:10.1080/00268976.2017.1278800. https://www.osti.gov/servlets/purl/1357795.
@article{osti_1357795,
title = {Sumrule corrections: A route to error cancellations in correlation matrix renormalisation theory},
author = {Liu, C. and Liu, J. and Yao, Y. X. and Wang, C. Z. and Ho, K. M.},
abstractNote = {Here, we recently proposed the correlation matrix renormalisation (CMR) theory to efficiently and accurately calculate ground state total energy of molecular systems, based on the Gutzwiller variational wavefunction (GWF) to treat the electronic correlation effects. To help reduce numerical complications and better adapt the CMR to infinite lattice systems, we need to further refine the way to minimise the error originated from the approximations in the theory. This conference proceeding reports our recent progress on this key issue, namely, we obtained a simple analytical functional form for the oneelectron renormalisation factors, and introduced a novel sumrule correction for a more accurate description of the intersite electron correlations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.},
doi = {10.1080/00268976.2017.1278800},
journal = {Molecular Physics},
number = 5,
volume = 115,
place = {United States},
year = {Mon Jan 16 00:00:00 EST 2017},
month = {Mon Jan 16 00:00:00 EST 2017}
}

The procedure of the estimates of the higherorder perturbative QCD corrections to the physical quantities is generalized to the case when the quantities under consideration obey the renormalizationgroup equations with the corresponding anomalous dimension functions. This procedure is used to estimate the [alpha][sup 3][sub [ital s]] corrections to the singlet part of the EllisJaffe sum rule for [ital f]=3 number of flavors.

Relativistic corrections to the Bethe sum rule
Relativistic corrections to order ..cap alpha../sup 2/ to the Bethe sum rule have been obtained for a oneelectron system employing the FoldyWouthuysen transformation. The results have wide applications in highZ systems at large momentum transfers.