We present three theoretical models of various degree of completeness to explore the chemical phase space available to the Glu4His2Zn2 cofactor found in the four-helix bundle of de novo designed metalloprotein Duo Ferro 1. We have found that the planewave DFT geometry optimization of 94-atom Model I, which contains both the protein scaffold constraints as well as the second shell hydrogen bonding network, reproduces the crystal structure bonding with remarkable accuracy (0.34 A). Surprisingly, the geometry optimization of 66-atom Model II (lacking the second shell hydrogen bonding) and 48-atom Model III (being also free of the protein scaffold constraints) still result in the fidelity with the crystallographic structure (RMSDs 0.29 and 0.34 A, respectively). To examine whether these structures are close to the global minimum as well as to investigate various conformational transitions to which the di-Zn cofactor may be susceptible to, we have carried out a 10 ps Car-Parrinello Molecular Dynamics (CPMD) simulation of Model III. We suggest that weak hydrogen bonds between imidazole hydrogens and carboxylate oxygens modulate the dynamical behavior of the system. One part of the molecule was found to be rigid due to the particular H(imidazole)-O(carboxylate) interaction restricting both the motion of the imidazole ring as well as the terminal carboxylate conformational mobility. The second half of the system was very flexible demonstrating a coupling of a transient formation of H(imidazole)-O(carboxylate) bonds with the spinning of the imidazole ring and syn-anti isomerization of the terminal carboxylate group. In addition, two low-energy snapshots from the 10 ps CPMD run were quenched, and their geometries were optimized, leading to two new isomers 48 kJ/mol lower in energy than the one associated with the crystal structure. We suggest that periodic quenching of the CPMD simulation snapshots of a minimalist model may be used as an efficient method to generate a large number of competitive local minima, which may be consequently pruned by imposing the protein scaffold constraints as well as further tuned by the second shell hydrogen bonding network.