### Abstract

We derive a formula for the atomic force within the LSDA+U formalism by differentiating analytically the LSDA+U total-energy functional with respect to atomic positions. The rotationally invariant form of the LSDA+U functional and the fully localized limit for the double-counting term are considered. The electronic wave functions are expanded with either plane waves or pseudoatomic orbitals (PAOs). In the PAO-basis case, the Pulay correction is also considered and included. Our formula for the atomic force is numerically tested with antiferromagnetic bulk NiO and reproduces successfully the forces obtained from numerical derivative of the total-energy values with respect to atomic displacements. As an application, we study atomic vibrations in NiO and MnO, and obtain transverse-optic phonon frequencies which are consistent with previous theoretical results. Our force formula will make it very efficient to perform large-scale calculations of atomic and phononic structures of strongly correlated materials using the LSDA+U method.

Original language | English |
---|---|

Article number | 155122 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 80 |

Issue number | 15 |

DOIs | |

Publication status | Published - 2009 Oct 15 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

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*Physical Review B - Condensed Matter and Materials Physics*, vol. 80, no. 15, 155122. https://doi.org/10.1103/PhysRevB.80.155122

**First-principles calculation of atomic force in the LSDA+U formalism.** / Park, Se Young; Choi, Hyoung Joon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - First-principles calculation of atomic force in the LSDA+U formalism

AU - Park, Se Young

AU - Choi, Hyoung Joon

PY - 2009/10/15

Y1 - 2009/10/15

N2 - We derive a formula for the atomic force within the LSDA+U formalism by differentiating analytically the LSDA+U total-energy functional with respect to atomic positions. The rotationally invariant form of the LSDA+U functional and the fully localized limit for the double-counting term are considered. The electronic wave functions are expanded with either plane waves or pseudoatomic orbitals (PAOs). In the PAO-basis case, the Pulay correction is also considered and included. Our formula for the atomic force is numerically tested with antiferromagnetic bulk NiO and reproduces successfully the forces obtained from numerical derivative of the total-energy values with respect to atomic displacements. As an application, we study atomic vibrations in NiO and MnO, and obtain transverse-optic phonon frequencies which are consistent with previous theoretical results. Our force formula will make it very efficient to perform large-scale calculations of atomic and phononic structures of strongly correlated materials using the LSDA+U method.

AB - We derive a formula for the atomic force within the LSDA+U formalism by differentiating analytically the LSDA+U total-energy functional with respect to atomic positions. The rotationally invariant form of the LSDA+U functional and the fully localized limit for the double-counting term are considered. The electronic wave functions are expanded with either plane waves or pseudoatomic orbitals (PAOs). In the PAO-basis case, the Pulay correction is also considered and included. Our formula for the atomic force is numerically tested with antiferromagnetic bulk NiO and reproduces successfully the forces obtained from numerical derivative of the total-energy values with respect to atomic displacements. As an application, we study atomic vibrations in NiO and MnO, and obtain transverse-optic phonon frequencies which are consistent with previous theoretical results. Our force formula will make it very efficient to perform large-scale calculations of atomic and phononic structures of strongly correlated materials using the LSDA+U method.

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U2 - 10.1103/PhysRevB.80.155122

DO - 10.1103/PhysRevB.80.155122

M3 - Article

AN - SCOPUS:71449107957

VL - 80

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 15

M1 - 155122

ER -