Variational quantum Monte Carlo ground state of GaAs

A highly accurate many-partice calculation for the GaAs bulk is applied to provide several properties of the semiconductor like the lattice constant, bulk modulus, charge transfer of the bonding, or correlation energy. These results demonstrate the progress which has been made with many-partice solutions of the Schrödinger equation in solid state physics.

The variational quantum Monte Carlo method is an attractive technique for many-particle calculations, because the quality of the result is controlled by a simple rule: the lower the energy the better the wave function. Additionally, the statistical error of an expectation value can be safely estimated. Thus this method is really ab initio, not relying on any uncontrolled quantity, such as an unknown correlation function in case of the local density approximation. Of course, the main advantage of these quantum Monte Carlo calculations lies in the inclusion of many-particle interactions. In sharp contrast to the one-particle approximation of the usual density functional approaches, in the presented study 256 valence electrons have been considered.

Fig. 1: Total energy vs. lattice constant of GaAs from a VQMC calculation including 256 valence electrons; the curve is a quadratic fit. For that fit the dashed curve gives the confidence interval taking one standard deviation. A larger image is available here.

In the first many-particle calculation of GaAs several ground state properties have been determined. Fig. 1 shows the total energy as a function of the lattice constant. The resulting lattice constant is in very good agreement with the experimental value and better than the results from density functional calculations. Besides other properties, the ionicity of the ions and the covalent bond charge were estimated. In contrast to expectations from rough qualitative arguments, a surprisingly slight charge accumulations of 0.13 electron per bond appears on the occupied Ga-As bond .

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Acknowledgment: We are indebted to Dr. E. Pehlke for various disdussions on the topic of DFT. The work was supported by the Deutsche Forschungsgemeinschaft under grants No. Scha. 360/8-1, 360/8-2.

1996
CAU Kiel
Physics
Theory
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20.12.2000