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Within the framework of the exact muffin-tin orbitals (EMTO) theory we have developed a new method to calculate the total energy for random substitutional alloys. The problem of disorder is treated within the coherent potential approximation (CPA), and the total energy is obtained using the full charge density (FCD) technique. The FCD-EMTO-CPA method is suitable for determination of energy changes due to anisotropic lattice distortions in random alloys. In particular, we calculate the elastic constants of the Cu-rich face centered cubic Cu-Zn alloys ( alpha-brass) and optimize the c/a ratio for the hexagonal Zn-rich alloys for both the epsilon and eta phases.

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The Airy gas model of the edge electron gas is used to construct an exchange-energy functional which is an alternative to those obtained in the local density and generalized gradient approximations. Test calculations for rare gas atoms, molecules, solids and surfaces show that the Airy gas functional performs better than the local density approximation in all cases and better than the generalized gradient approximation for solids and surfaces.