Thermal stability of water up to super-critical states: Application of the singular value decomposition and grund functions

In the present work a systematic investigation of temperature on the dynamic structure of water and noble gases is given and a simple formula for the temperature dependent distribution functions with two terms is gained. The singular value decomposition tool is applied to temperature dependent radial and spatial distribution functions to decompose them into linear combinations of distant dependent grund radial/spatial distribution functions gi(r) and temperature dependent coefficients ci(T). The method condenses information from a large amount of data into a much smaller and manageable amount without loss of information. For the test systems (TIP3P water and noble gases with different force fields), the main temperature changes are condensed into the second grund function g2 and its coefficient c2. c2 obeys the Boltzmann distribution law and altogether we find thatgrT≈gcr+e−DR⋅T⋅gtrin a temperature range of more than 700 K. We introduce the new property of the thermal stability and the thermal stability energy D. This single energy and the grund functions characterize the structural changes (e.g., hydrogen bonds) in liquids from ambient temperatures up to supercritical states.