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Density functional theory with fractional orbital occupations

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10.1063/1.3703894

### Abstract

In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory(DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H_{2} and N_{2}, and twisted ethylene, while performing similar to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are “challenging problems” for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level *ab initio* data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.

© 2012 American Institute of Physics

Received 23 January 2012
Accepted 29 March 2012
Published online 17 April 2012

Acknowledgments: This work was supported by National Science Council of Taiwan (Grant No. NSC98-2112-M-002-023-MY3), National Taiwan University (Grant Nos. 99R70304 and 10R80914-1), and NCTS of Taiwan. We are grateful to the Computer and Information Networking Center at NTU for the support of high-performance computing facilities.

Article outline:

I. INTRODUCTION

II. RATIONALE FOR FRACTIONAL ORBITAL OCCUPATIONS

III. TAO-DFT

A. Self-consistent equations

B. Spin-polarized formalism

C. Analytical nuclear gradients

D. Local density approximation

E. Strong static correlation from TAO-LDA

IV. NUMERICAL INVESTIGATIONS OF AN OPTIMAL θ VALUE

A. Single-reference systems

1. Reaction energies

2. Equilibrium geometries

B. Multi-reference systems

1. Dissociation of H_{2} and N_{2}

2. Twisted ethylene

3. Singlet-triplet energy gaps of linear acenes

V. DEFINITION OF AN OPTIMAL θ VALUE

VI. CONCLUSIONS

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2012-04-17

2014-04-16

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