  The cluster expansion model (CEM) provides a powerful computational framework
for rapid estimation of configurational properties in disordered systems.
However, the traditional CEM construction procedure is still plagued by two
fundamental problems: (i) even when only a handful of site cluster types are
included in the model, these clusters can be correlated and therefore they
cannot independently predict the material property, and (ii) typically few
tens-hundreds of datapoints are required for training the model. To address the
first problem of collinearity, we apply the principal component analysis method
for constructing a CEM. Such an approach is shown to result in a
low-dimensional CEM that can be trained using a small DFT dataset. We use the
ab initio thermodynamic modeling of Cl and Br adsorption on Cu(100) surface as
an example to demonstrate these concepts. A key result is that a CEM containing
10 effective cluster interactions build with only 8 DFT energies (note, number
of training configurations > number of principal components) is found to be
accurate and the thermodynamic behavior obtained is consistent with
experiments. This paves the way for construction of high-fidelity CEMs with
sparse/limited DFT data.
