### Abstract

New methods for integrating the Car-Parrinello equations with ultrasoft pseudopotentials are introduced. In particular, the difficulties associated with the generalized orthonormality constraint condition 〈φ _{i}|Ŝ({R_{I}})|φ_{j}〉 = δ_{ij} are addressed. It is shown that the equations of motion can be integrated using the velocity Verlet/RATTLE scheme, and a new method, the constrained nonorthogonal orbital method, that eliminates the need to enforce this constraint explicitly is introduced. In this new scheme, the generalized orthonormality constraint is satisfied implicitly, thus allowing the freedom to choose simpler constraint conditions. We show that usual N^{3} scaling associated with the calculation of the Lagrange multipliers in the constraint force can be reduced to an N^{2} calculation by the use of a simple set of norm or length constraints on the electronic orbitals without sacrificing accuracy. The constrained nonorthogonal orbital method is shown to be considerably simpler to implement and more efficient than the standard approach to the ultrasoft pseudopotential problem.

Original language | English (US) |
---|---|

Pages (from-to) | 859-871 |

Number of pages | 13 |

Journal | The Journal of chemical physics |

Volume | 102 |

Issue number | 2 |

State | Published - 1995 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of chemical physics*,

*102*(2), 859-871.

**Integrating the Car-Parrinello equations. III. Techniques for ultrasoft pseudopotentials.** / Hutter, Jürg; Tuckerman, Mark; Parrinello, Michele.

Research output: Contribution to journal › Article

*The Journal of chemical physics*, vol. 102, no. 2, pp. 859-871.

}

TY - JOUR

T1 - Integrating the Car-Parrinello equations. III. Techniques for ultrasoft pseudopotentials

AU - Hutter, Jürg

AU - Tuckerman, Mark

AU - Parrinello, Michele

PY - 1995

Y1 - 1995

N2 - New methods for integrating the Car-Parrinello equations with ultrasoft pseudopotentials are introduced. In particular, the difficulties associated with the generalized orthonormality constraint condition 〈φ i|Ŝ({RI})|φj〉 = δij are addressed. It is shown that the equations of motion can be integrated using the velocity Verlet/RATTLE scheme, and a new method, the constrained nonorthogonal orbital method, that eliminates the need to enforce this constraint explicitly is introduced. In this new scheme, the generalized orthonormality constraint is satisfied implicitly, thus allowing the freedom to choose simpler constraint conditions. We show that usual N3 scaling associated with the calculation of the Lagrange multipliers in the constraint force can be reduced to an N2 calculation by the use of a simple set of norm or length constraints on the electronic orbitals without sacrificing accuracy. The constrained nonorthogonal orbital method is shown to be considerably simpler to implement and more efficient than the standard approach to the ultrasoft pseudopotential problem.

AB - New methods for integrating the Car-Parrinello equations with ultrasoft pseudopotentials are introduced. In particular, the difficulties associated with the generalized orthonormality constraint condition 〈φ i|Ŝ({RI})|φj〉 = δij are addressed. It is shown that the equations of motion can be integrated using the velocity Verlet/RATTLE scheme, and a new method, the constrained nonorthogonal orbital method, that eliminates the need to enforce this constraint explicitly is introduced. In this new scheme, the generalized orthonormality constraint is satisfied implicitly, thus allowing the freedom to choose simpler constraint conditions. We show that usual N3 scaling associated with the calculation of the Lagrange multipliers in the constraint force can be reduced to an N2 calculation by the use of a simple set of norm or length constraints on the electronic orbitals without sacrificing accuracy. The constrained nonorthogonal orbital method is shown to be considerably simpler to implement and more efficient than the standard approach to the ultrasoft pseudopotential problem.

UR - http://www.scopus.com/inward/record.url?scp=0000948202&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000948202&partnerID=8YFLogxK

M3 - Article

VL - 102

SP - 859

EP - 871

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 2

ER -