Effect of the exchange-correlation energy and temperature on the generalized phase diagram of the 4d transition metals

Very recently, we have used first-principles methods to calculate the zero-temperature phase diagram of all the 4d transition metals up to P 500GPa. Even though we used a very accurate implementation of density functional theory and the accurate exchange-correlation functional of Wu and Cohen, we found that solid-solid transition pressures were underestimated by 10GPa with respect to room-temperature measurements. Here, we report the dependence of the transition pressures on the choice of the exchange-correlation functional. We also perform first-principles calculations of the harmonic phonon frequencies of molybdenum and zirconium in different crystalline structures in order to extend the phase diagram to non-zero temperatures. We use the results to discuss the reasons for the earlier disagreements between calculated and experimental transition pressures.