Quantum discord is a function of density-matrix elements (and through them, e.~g., of temperature, applied fields, time, and so forth). The domain of such a function in the case of two-qubit system with X or centrosymmetric (CS) density matrix can consist at most of three subdomains: two ones, where the quantum discord is expressed in closed analytical forms (Q_0 and Q_{pi/2}), and an intermediate subdomain in which for determining the quantum discord Q_theta it is required to solve numerically a one-dimensional minimization problem to find the optimal measurement angle thetain(0,pi/2). Exact equations for determining the boundaries between these subdomains are obtained and solved for a number of models. The Q_theta subdomains are discovered in the anisotropic spin dimers in external field. On the other hand, coinciding boundaries and therefore sudden transitions between optimal measurement angles theta=pi/2 and theta=0 are observed in dynamics of spin currying particles in closed nanopore and also in phase flip channels. In latter cases the solutions are entirely analytical.
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