The ratio of the mean square amplitude root of thermal vibrations and the interatomic distance is a universal constant delta(ls) at the melting temperature T-m. The classical Gibbs free energy change completed by a volume energy saving epsilon(ls) (or Delta epsilon(lg)) x Delta H-m that governs the liquid to solid and liquid to ultra-stable glass transformations leads to a universal constant equal to delta(ls) (or (delta(lg)), Delta H-m being the crystal melting enthalpy. The minimum values 0.217 of epsilon(ls) and 0.103 of delta(ls) are used to predict ultra-stable glass formation in pure metallic liquid elements at a universal reduced temperature theta(g) = (T-g - T-m)/T-m = 0.6223. (C) 2016 Elsevier B.V. All rights reserved.