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Title: mBEEF-vdW: Robust fitting of error estimation density functionals

Abstract

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator over the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene onmore » the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.« less

Authors:
 [1];  [1];  [1];  [2];  [3]
  1. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. Technical Univ. of Denmark, Lyngby (Denmark)
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1349403
Alternate Identifier(s):
OSTI ID: 1259991
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 93; Journal Issue: 23; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Lundgaard, Keld T., Wellendorff, Jess, Voss, Johannes, Jacobsen, Karsten W., and Bligaard, Thomas. mBEEF-vdW: Robust fitting of error estimation density functionals. United States: N. p., 2016. Web. https://doi.org/10.1103/PhysRevB.93.235162.
Lundgaard, Keld T., Wellendorff, Jess, Voss, Johannes, Jacobsen, Karsten W., & Bligaard, Thomas. mBEEF-vdW: Robust fitting of error estimation density functionals. United States. https://doi.org/10.1103/PhysRevB.93.235162
Lundgaard, Keld T., Wellendorff, Jess, Voss, Johannes, Jacobsen, Karsten W., and Bligaard, Thomas. Wed . "mBEEF-vdW: Robust fitting of error estimation density functionals". United States. https://doi.org/10.1103/PhysRevB.93.235162. https://www.osti.gov/servlets/purl/1349403.
@article{osti_1349403,
title = {mBEEF-vdW: Robust fitting of error estimation density functionals},
author = {Lundgaard, Keld T. and Wellendorff, Jess and Voss, Johannes and Jacobsen, Karsten W. and Bligaard, Thomas},
abstractNote = {Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator over the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.},
doi = {10.1103/PhysRevB.93.235162},
journal = {Physical Review B},
number = 23,
volume = 93,
place = {United States},
year = {2016},
month = {6}
}

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Cited by: 5 works
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