Illustration of the linear-muffin-tin-orbital tight-binding representation: Compact orbitals and charge density in Si

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Abstract
Plots of the tight-binding (TB) orbitals recently derived by exact transformation of the conventional set of linear muffin-tin orbitals (LMTO’s) are presented for crystalline silicon. The TB-LMTO’s are found to be extremely compact. As a simple application we show how non-spherically-averaged charge densities may be obtained from standard LMTO calculations. For silicon this charge density is found to be in excellent agreement with the one obtained from a linear augmented plane-wave full-potential calculation. This is true even when the LMTO calculation employs the atomic-sphere approximation for the one-electron potential. A self-contained account of the TB-MTO formalism is presented and a simple way of including the quadratic energy dependence of the MTO’s is derived.