Electronic, structural, vibrational and elastic properties of PaN have been studied both at ambient and high pressures, using first principles methods with several commonly used parameterizations of the exchange-correlation energy. The generalized gradient approximation (GGA) reproduces the ground state properties satisfactorily. Under pressure PaN is found to undergo a structural transition from NaCl to the R-3m structure near 58 GPa. The high pressure behavior of the acoustic phonon branch along the (1,0,0) and (1,1,0) directions, and the C44 elastic constant are anomalous, which signals the structural transition. With GGA exchange-correlation, a topological transition in the charge density occurs near the structural transition which may be regarded as a quantum phase transition, where the order parameter obeys a mean field scaling law. However, the topological transition is absent when other exchange-correlation functionals are invoked (local density approximation (LDA) and hybrid functional). Therefore, this constitutes an example of GGA and LDA leading to qualitatively different predictions, and it is of great interest to examine experimentally whether this topological transition occurs.
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