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This work represents the first chapter of a project on the foundations offirst-principle calculations of the electron transport in crystals at finitetemperatures. We are interested in the range of temperatures, where mostelectronic components operate, that is, room temperature and above. The aim isa predictive first-principle formalism that combines ab-initio moleculardynamics and a finite-temperature Kubo-formula for homogeneous thermodynamicphases. The input for this formula is the ergodic dynamical system$(\Omega,\mathbb G,{\rm d}\mathbb P)$ defining the crystalline phase, where$\Omega$ is the configuration space for the atomic degrees of freedom, $\mathbbG$ is the space group acting on $\Omega$ and ${\rm d}\mathbb P$ is the ergodicGibbs measure relative to the $\mathbb G$-action. The present work develops analgorithmic method for quantifying $(\Omega,\mathbb G,{\rm d}\mathbb P)$ fromfirst principles. Using the silicon crystal as a working example, we find theGibbs measure to be extremely well characterized by a multivariate normaldistribution, which can be quantified using a small number of parameters. Thelatter are computed at various temperatures and communicated in the form of atable. Using this table, one can generate large and accuratethermally-disordered atomic configurations to serve, for example, as input forsubsequent simulations of the electronic degrees of freedom.

Disordered Crystals from First Principles I: Quantifying the Configuration Space