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Potential-functional embedding theory for molecules and materials

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10.1063/1.3659293

### Abstract

We introduce a potential-functional embedding theory by reformulating a recently proposed density-based embedding theory in terms of functionals of the embedding potential. This potential-functional based theory completes the dual problem in the context of embedding theory for which density-functional embedding theory has existed for two decades. With this potential-functional formalism, it is straightforward to solve for the unique embedding potential shared by all subsystems. We consider charge transfer between subsystems and discuss how to treat fractional numbers of electrons in subsystems. We show that one is able to employ different energy functionals for different subsystems in order to treat different regions with theories of different levels of accuracy, if desired. The embedding potential is solved for by directly minimizing the total energy functional, and we discuss how to efficiently calculate the gradient of the total energy functional with respect to the embedding potential. Forces are also derived, thereby making it possible to optimize structures and account for nuclear dynamics. We also extend the theory to spin-polarized cases. Numerical examples of the theory are given for some homo- and hetero-nuclear diatomic molecules and a more complicated test of a six-hydrogen-atom chain. We also test our theory in a periodic bulk environment with calculations of basic properties of bulk NaCl, by treating each atom as a subsystem. Finally, we demonstrate the theory for water adsorption on the MgO(001)surface.

© 2011 American Institute of Physics

Received 21 July 2011
Accepted 19 October 2011
Published online 17 November 2011

Acknowledgments: We thank Dr. Florian Libisch for a critical reading of the manuscript. We appreciate Dr. Youqi Ke, Dr. Michele Pavone, and Peilin Liao for many insightful discussions and Dr. Maytal Toroker for help with setting up the water/MgO calculations. This work was supported by the Office of Naval Research and the National Science Foundation.

Article outline:

I. INTRODUCTION

II. THEORY

A. Potential-functional formalism for embedding theory

B. Definition of the subsystem energy

C. Definition of the interaction energy

D. Direct minimization of the total energy

E. Uniqueness of the embedding potential

F. Minimization of the total energy with respect to the embedding potential

G. Optimizing subsystem electron numbers

H. Working with nonlocal pseudopotentials and entropy

I. First-order correction used in the Wu-Yang OEP

J. Forces

K. Spin-polarized systems

III. NUMERICAL DETAILS

IV. RESULTS AND DISCUSSION

A. Diatomic molecules

B. H_{6} chain

C. NaCl bulk crystal

D. H_{2}O on MgO(001)

V. CONCLUSIONS

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2011-11-17

2014-04-18

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