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We propose and implement a particularly effective method for calculating theBerry curvature arising from adiabatic evolution of Bloch states in wave vectork space. The method exploits a unique feature of the Korringa-Kohn-Rostoker(KKR) approach to solve the Schr\"odinger or Dirac equations. Namely, it isbased on the observation that in the KKR method k enters the calculation viathe structure constants which depend only on the geometry of the lattice butnot the crystal potential. For both the Abelian and non-Abelian Berry curvaturewe derive an analytic formula whose evaluation does not require any numericaldifferentiation with respect to k. We present explicit calculations for Al, Cu,Au, and Pt bulk crystals.

On calculating the Berry curvature of Bloch electrons using the KKR method