The Broyden (Broyden—Fletcher—Goldfarb—Shanno or BFGS) algorithm can be known in the matter modeling to optimize a crystal lattice geometry — to clarify positions of nodes of a crystal lattice in calculation process of eigenvalues and eigenfunctions with a Hartree-Fock (or DFT) method. How much will the Broyden algorithm be clarifying right (energetically beneficial) positions of atomic nuclei if a crystal lattice of a substance will intentionally be significantly distorted? But what things can be done if a hypothetical alloy (some mix of metals and non-metals in some proportion, which is raised to the monocrystalline solid level) is never explored before, including analyzing in an X-ray diffractometer to define positions of nuclei of lattice of a monocrystalline solid? Whether can the Broyden algorithm correctly upbuild a crystalline structure of some alloy? If it cannot, so is there a way to roughly calculate this thing maybe before a Hartree-Fock (or DFT) calculation and free software implementing such a calculation?
Or to put it more simply
is it possible to calculate an "a priori" alloy?