Electronic Structure Calculations Using A Modified Thomas-Fermi Approximation
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Electronic Structure Calculations Using A Modified Thomas-Fermi Approximation
Gregory C. Dente GCD Associates, 2100 Alvarado NE, Albuquerque, NM 87110 Michael Tilton Boeing, P.O. Box 5670, Kirtland AFB, NM 87185
ABSTRACT We have recently developed an accurate and easily implemented approach to many-electron calculations, based on a modified Thomas-Fermi approximation. Specifically, we derived an electron density approximation, the first term of which is the Thomas-Fermi result, while the remaining terms substantially corrected the density near the nucleus. In a first application, we used the new density to accurately calculate the details of the self-consistent ion cores, as well as the ionization potentials for the outer s-orbital bound to the closed-shell ion core of the Group III, IV and V elements. Next, we demonstrated that the new density expression allows us to separate closed-shell core electron densities from valence electron densities. When we calculated the valence kinetic energy density, we showed that it separated into two terms: the first exactly cancelled the potential energy due to the ion core in the core region; the second was the residual kinetic energy density resulting from the envelopes of the valence electron orbitals. These features allowed us to write a functional for the total valence energy dependant only on the valence density. This equation provided the starting point for a large number of electronic structure calculations. Here, we used it to calculate the band structures of several Group IV and Group III-V semiconductors. We emphasize that this report only provides a summary; detailed derivations of all results are in Reference 5. INTRODUCTION Calculating the properties of atoms, molecules and solids has been one of the primary objectives of physics for the last century. However, as researchers began to tackle many-electron problems, the calculations quickly became complicated and unwieldy. As an alternative to solving for an N-electron wave function, they soon developed methods that dealt directly with the electron density, which are now called density functional theories, DFTs. The earliest example of a DFT was developed in the late
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1920s; this is the Thomas-Fermi model, one of the earliest schemes for calculating the N-electron problem while enforcing the Pauli exclusion principle and wave-particle duality.1,2 This paper will summarize our results for a new density expression, one that bears a resemblance to Thomas-Fermi. Additionally, the new method leads to two remarkably helpful developments. First, we can readily separate valence electron densities from core electron densities. Second, we can show that the valence kinetic energy density can be separated into a term that exactly cancels the potential, due to the nucleus and closed-shell core electrons in the core region, while the remaining term can be interpreted as a residual kinetic energy density generated by the envelopes of the valence orbitals. This type of kinetic energy cancellation is a critical element for mak
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