  Isosbestic (equal absorption) points in the IR and NIR spectra of liquid
water are a well known feature and they witness the existence of two
populations of oscillators in the probed system. Despite it is a well known
experimental fact, in the mainstream molecular dynamics approach the proposed
theoretical explanations for it are not able to elucidate which is the physical
reason why such a cut off frequency (at the isosbestic point) does exist. We
investigate pure Milli-Q water on increasing the temperature in the vis-NIR
range (400-2500 nm). We specifically payed attention to the first overtone
region (1300-1600 nm) of the OH-bond stretching-mode where an isosbestic point
has been observed. A second derivative analysis clearly shows two modes, which
can be assigned to water molecules involved in different hydrogen bonding
configurations whose relative abundance is controlled by the temperature. We
have also observed that the ratio of these modes follows a van't Hoff behavior
supporting that their energy difference (energy gap) is independent on the
temperature. Furthermore, a log-log plot shows a scale invariance of the
population ratio with respect to the perturbation (temperature), confirming the
existence of a long range correlated dynamics in the liquid. We show that the
two phases differences between energy and entropy estimated from the
experimental data can be compared with the predictions of Quantum Electro
Dynamics (QED) showing a remarkable agreement.
