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In this paper, we analyze the numerical aspects of the inherently multi-reference density matrix renormalization group (DMRG) calculations on top of the periodic Kohn-Sham density functional theory (DFT) using the complete active space (CAS) approach. Following the technical outline related to the computation of the Hamiltonian matrix elements and to the construction of the active space, we illustrate the potential of the framework by studying the vertical many-body energy spectrum of hexagonal boron nitride (hBN) nano-flakes embedding a single boron vacancy point defect with prominent multi-reference character. We investigate the consistency of the DMRG energy spectrum from the perspective of sample size, basis size, and active space selection protocol. Results obtained from standard quantum chemical atom-centered basis calculations and plane-wave based counterparts show excellent agreement. Furthermore, we also discuss the spectrum of the periodic sheet which is in good agreement with extrapolated data of finite clusters. These results pave the way toward applying DMRG method in extended correlated solid state systems, such as point qubit in wide band gap semiconductors.