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indium ground state or the complex aGa structure. Nevertheless, the method correctly predicts the ground state properties of all of these materials. The method also generates

an electronic density of states for aGa which is very close to the results of first-principles calculations. [14] Can this method be extended even further to the right of the periodic table, specificallv to carbon and silicon? In this paper we develop a slightly modified version of the parametrization scheme developed in Ref. [11], applied to carbon and silicon. In the sections below we introduce the method, and discuss the properties predicted by our parameters. METHOD The tight-binding parametrization of Refs. [10, 11] consists of a prescription for specifying the behavior of the on-site parameters as a function of the local environment, and 221 Mat. Res. Soc. Symp. Proc. Vol. 491 © 1998 Materials Research Society

Table I: The Slater-Koster tight-binding parameters for carbon, generated from the database described in the text. On-Site Parameters (Eqs. (1) and (2)) A 1.59901905594 Orbital ce (Ry) 3 (Ry) y (Ry) s -0.102789972814 -1.62604640052 -178.884826119 p 0.542619178314 2.73454062799 -67.139709883 Hopping Parameters (Eqs. (3)) Orbital a (Ry) b (Ry/Bohr) c (Ry/Bohr 2 ) HSSO 74.0837449667 -18.3225697598 -12.5253007169 H

~pa

Hppo H~p•

Orbital SSSO S'pa Sppo Spp•

-7.9172955767

3.6163510241

x (Ry) 4516.11342028 438.52883145 d (Bohr 1 / 2 ) 1.41100521808

1.0416715714

1.16878908431

-5.7016933899 1.0450894823 1.5062731505 24.9104111573 -5.0603652530 -3.6844386855 Overlap Parameters (Eqs. (4)) p (Bohr-1) q (Bohr- 2 ) r (Bohr- 3 ) 1.56010486948 -0.308751658739 0.18525064246 1.85250642463 -2.50183774417 0.178540723033 -1.29666913067 0.28270660019 -0.022234235553 0.74092406925 -0.07310263856 0.016694077196

1.13627440135 1.36548919302 s (Bohr- 1/ 2 ) 1.13700564649 1.12900344616 0.76177690688 1.02148246334

a parametrization of the hopping and overlap matrix elements. We begin by discussing the behavior of the on-site terms, which are allowed to vary depending upon the local environment of each atom. This environment is determined by defining a pseudo-atomic density for each atom, (1) A ,2,RjRJif(IR 3 - Rij) where Rk is the position of the kth atom, the sum is over all neighbors of atom i, and where f(R) is a cutoff function as defined in Ref. [11]. In this paper we choose the cutoff

so that f(R) vanishes when R > 10.5 atomic units for carbon, and when R > 12.5 atomic units for silicon. The on-site terms on each atom are given by a Birch-like equation

S+

4 hit = oYe+/ Otpi2/3 + 'Yipi4/3

X•i•

(2)

In both carbon and silicon we naturally consider only e = s, p, so, including the A in equation (1), there are a total of nine parameters which determine the on-site terms on each atom. The two-center Slater-Koster hopping terms for the Hamiltonian are simply polynomials times an exponential cutoff, Htp(R) = (au',. + bitgR + cfewgR 2 ) exp(-de,IR)f (R)

(3)

where f(R) is the same cutoff as above. The overlap parameters have been modified fro