Abstract: Provided are methods and systems for determining the structure of a composite or solid solution material for an electrode in lithium-ion batteries. In one embodiment, a method is presented where a building-block database of hypothetical structures containing only one transition metal atom is constructed by use of quantum simulation. Then, a composite model set of structures containing two or more transition metal atoms is constructed by calculating a linear average of parent components from the building-block database of hypothetical structures to determine lattice constants and atomic coordinates of candidates. The composite model set is screened with a local order matrix to subclassify composite models into a subset, such that the composite models share the same property in local transition metal ordering. Still yet, a representative from each subset is selected and a quantum simulation on the representative models is performed to determine the structure of the material.