Automatic Determination of Tight-Binding Parameters in Bulk Systems
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Automatic Determination of Tight-Binding Parameters in Bulk Systems Yasuaki Ohtani1, Takeo Fujiwara2, Shinya Nishino2, Takashi Suzuki1, Susumu Yamamoto3, Yasunari Zempo4 1
Hulinks Inc. 5-14 Nihonbashi Hakozaki-cho, Chuo-ku, Tokyo 103-0015 Japan The Univ. of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 Japan 3 Tokyo Univ. of Technology, 1404-1 Katakura-cho, Hachiohji, Tokyo 192-0982 Japan 4 Hosei University, 3-7-2 Kajino-cho, Koganei, Tokyo 184-8584 Japan 2
ABSTRACT We have studied a procedure to determine Tight-Binding (TB) parameters automatically, by which the band structure of the crystalline solid can be reproduced so as to be good agreement with that of first-principles molecular dynamics calculation. According to this procedure, we determine TB parameter sets for silicon and diamond accurately, and a fairly good set for their compound SiC. INTRODUCTION There is no doubt that computational simulations are now important to develop new materials and nano-scale processing technologies such as semiconductor devices, Lithium-ion batteries and organic EL materials. In the research and the development of these areas, both structural and electronic studies must be considered. To realize this purpose, TB simulations based first-principles molecular-dynamics are frequently used from the point of the total computational cost instead of a more accurate conventional technique such as LDA calculations, because, in the above area, large-scale and long-time dynamics calculations are required for the investigation of the systems. Our group developed a program named “ELSES” (Extra Large Scale Electronic Structure Calculation Program), based on Extended Hückel Molecular Orbital-Atom Super-Position and Electron Delocalization (EHMO-ASPED) Tight-Binding (TB) theory [1]. The charge self-consistency corresponding to various atom configurations in molecules and materials is also taken into account. As ELSES is a really order N operating program [2], it realizes the quantum dynamics calculations of 106 atoms system (~a few 10nm scale) and nanoseconds dynamics (long-time) of 103 atoms system using by personal computer or cluster computer. Although the TB technique has a various potentiality, the parameters should be transferable in various circumstances. The procedure to determine a parameter set for the macromolecules was developed by Nishino and Fujiwara [3]. Now we extend the procedure for the bulk systems.
THEORY The total Hamiltonian is written as follows [1].
where is the extended Hückel Hamiltonian, is the repulsive Hamiltonian and is the charge self-consistent Hamiltonian, respectively. Now we determine TB parameters by using only . The effect of repulsive force can be treated independently. The diagonal elements of the Extended Hückel Hamiltonian are empirically determined from ionic energies, and the off-diagonal elements of are given by using the overlapping integrals as follows;
where is the modified Wolfsberg-Helmholtz constant which represents the distortion of wavefunctions and is a function of an interatomic dista
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