## Density functionals for surface science: Exchange-correlation model development with Bayesian error estimation

Publication: Research - peer-review › Journal article – Annual report year: 2012

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**Density functionals for surface science: Exchange-correlation model development with Bayesian error estimation.** / Wellendorff, Jess; Lundgård, Keld Troen; Møgelhøj, Andreas; Petzold, Vivien Gabriele; Landis, David; Nørskov, Jens K.; Bligaard, Thomas; Jacobsen, Karsten Wedel.

Publication: Research - peer-review › Journal article – Annual report year: 2012

### Harvard

*Physical Review B (Condensed Matter and Materials Physics)*, vol 85, no. 23, pp. 235149. DOI: 10.1103/PhysRevB.85.235149

### APA

*Physical Review B (Condensed Matter and Materials Physics)*,

*85*(23), 235149. DOI: 10.1103/PhysRevB.85.235149

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### MLA

*Physical Review B (Condensed Matter and Materials Physics)*. 2012, 85(23). 235149. Available: 10.1103/PhysRevB.85.235149

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### Bibtex

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### RIS

TY - JOUR

T1 - Density functionals for surface science: Exchange-correlation model development with Bayesian error estimation

AU - Wellendorff,Jess

AU - Lundgård,Keld Troen

AU - Møgelhøj,Andreas

AU - Petzold,Vivien Gabriele

AU - Landis,David

AU - Nørskov,Jens K.

AU - Bligaard,Thomas

AU - Jacobsen,Karsten Wedel

PY - 2012

Y1 - 2012

N2 - A methodology for semiempirical density functional optimization, using regularization and cross-validation methods from machine learning, is developed. We demonstrate that such methods enable well-behaved exchange-correlation approximations in very flexible model spaces, thus avoiding the overfitting found when standard least-squares methods are applied to high-order polynomial expansions. A general-purpose density functional for surface science and catalysis studies should accurately describe bond breaking and formation in chemistry, solid state physics, and surface chemistry, and should preferably also include van der Waals dispersion interactions. Such a functional necessarily compromises between describing fundamentally different types of interactions, making transferability of the density functional approximation a key issue. We investigate this trade-off between describing the energetics of intramolecular and intermolecular, bulk solid, and surface chemical bonding, and the developed optimization method explicitly handles making the compromise based on the directions in model space favored by different materials properties. The approach is applied to designing the Bayesian error estimation functional with van der Waals correlation (BEEF-vdW), a semilocal approximation with an additional nonlocal correlation term. Furthermore, an ensemble of functionals around BEEF-vdW comes out naturally, offering an estimate of the computational error. An extensive assessment on a range of data sets validates the applicability of BEEF-vdW to studies in chemistry and condensed matter physics. Applications of the approximation and its Bayesian ensemble error estimate to two intricate surface science problems support this.

AB - A methodology for semiempirical density functional optimization, using regularization and cross-validation methods from machine learning, is developed. We demonstrate that such methods enable well-behaved exchange-correlation approximations in very flexible model spaces, thus avoiding the overfitting found when standard least-squares methods are applied to high-order polynomial expansions. A general-purpose density functional for surface science and catalysis studies should accurately describe bond breaking and formation in chemistry, solid state physics, and surface chemistry, and should preferably also include van der Waals dispersion interactions. Such a functional necessarily compromises between describing fundamentally different types of interactions, making transferability of the density functional approximation a key issue. We investigate this trade-off between describing the energetics of intramolecular and intermolecular, bulk solid, and surface chemical bonding, and the developed optimization method explicitly handles making the compromise based on the directions in model space favored by different materials properties. The approach is applied to designing the Bayesian error estimation functional with van der Waals correlation (BEEF-vdW), a semilocal approximation with an additional nonlocal correlation term. Furthermore, an ensemble of functionals around BEEF-vdW comes out naturally, offering an estimate of the computational error. An extensive assessment on a range of data sets validates the applicability of BEEF-vdW to studies in chemistry and condensed matter physics. Applications of the approximation and its Bayesian ensemble error estimate to two intricate surface science problems support this.

U2 - 10.1103/PhysRevB.85.235149

DO - 10.1103/PhysRevB.85.235149

M3 - Journal article

VL - 85

SP - 235149

JO - Physical Review B

T2 - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 23

ER -