Efficient Treatment of Local Meta-generalized Gradient Density Functionals via Auxiliary Density Expansion

The Density Fitting J + X Approximation

Alyssa V. Bienvenu, Gerald Knizia

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We report an efficient technique to treat density functionals of the meta-generalized gradient approximation (mGGA) class in conjunction with density fitting of Coulomb terms (DF-J) and exchange-correlation terms (DF-X). While the kinetic energy density τ cannot be computed in the context of a DF-JX calculation, we show that the Laplacian of the density υ can be computed with almost no extra cost. With this technique, υ-form mGGAs become only slightly more expensive (10%-20%) than GGAs in DF-JX treatment - and several times faster than regular τ-based mGGA calculations with DF-J and regular treatment of the density functional. We investigate the translation of υ-form mGGAs into τ-form mGGAs by employing a kinetic energy functional but find this insufficiently reliable at this moment. However, υ and τ are believed to carry essentially equivalent information beyond ρ and ||∇ρ|| (Phys. Rev. B 2007, 75, 155109, DOI: 10.1103/PhysRevB.75.155109), so a reparametrization of accurate mGGAs from the τ-form into the υ-form should be possible. Once such functionals become available, we expect the presented technique to become a powerful tool in the computation of reaction paths, intermediates, and transition states of medium sized molecules.

Original languageEnglish (US)
Pages (from-to)1297-1303
Number of pages7
JournalJournal of Chemical Theory and Computation
Volume14
Issue number3
DOIs
StatePublished - Mar 13 2018

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deuterium fluorides
functionals
Kinetic energy
gradients
expansion
approximation
kinetic energy
Molecules
flux density
Costs
costs
moments
molecules

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Physical and Theoretical Chemistry

Cite this

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title = "Efficient Treatment of Local Meta-generalized Gradient Density Functionals via Auxiliary Density Expansion: The Density Fitting J + X Approximation",
abstract = "We report an efficient technique to treat density functionals of the meta-generalized gradient approximation (mGGA) class in conjunction with density fitting of Coulomb terms (DF-J) and exchange-correlation terms (DF-X). While the kinetic energy density τ cannot be computed in the context of a DF-JX calculation, we show that the Laplacian of the density υ can be computed with almost no extra cost. With this technique, υ-form mGGAs become only slightly more expensive (10{\%}-20{\%}) than GGAs in DF-JX treatment - and several times faster than regular τ-based mGGA calculations with DF-J and regular treatment of the density functional. We investigate the translation of υ-form mGGAs into τ-form mGGAs by employing a kinetic energy functional but find this insufficiently reliable at this moment. However, υ and τ are believed to carry essentially equivalent information beyond ρ and ||∇ρ|| (Phys. Rev. B 2007, 75, 155109, DOI: 10.1103/PhysRevB.75.155109), so a reparametrization of accurate mGGAs from the τ-form into the υ-form should be possible. Once such functionals become available, we expect the presented technique to become a powerful tool in the computation of reaction paths, intermediates, and transition states of medium sized molecules.",
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AB - We report an efficient technique to treat density functionals of the meta-generalized gradient approximation (mGGA) class in conjunction with density fitting of Coulomb terms (DF-J) and exchange-correlation terms (DF-X). While the kinetic energy density τ cannot be computed in the context of a DF-JX calculation, we show that the Laplacian of the density υ can be computed with almost no extra cost. With this technique, υ-form mGGAs become only slightly more expensive (10%-20%) than GGAs in DF-JX treatment - and several times faster than regular τ-based mGGA calculations with DF-J and regular treatment of the density functional. We investigate the translation of υ-form mGGAs into τ-form mGGAs by employing a kinetic energy functional but find this insufficiently reliable at this moment. However, υ and τ are believed to carry essentially equivalent information beyond ρ and ||∇ρ|| (Phys. Rev. B 2007, 75, 155109, DOI: 10.1103/PhysRevB.75.155109), so a reparametrization of accurate mGGAs from the τ-form into the υ-form should be possible. Once such functionals become available, we expect the presented technique to become a powerful tool in the computation of reaction paths, intermediates, and transition states of medium sized molecules.

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