# Has the exact formula for computing the density of water in terms of temperature ever been determined?

According to a simplified quantum mechanics theory where electrons and nuclei are point charges and there's no nuclear chemistry, and the gravitational constant and cosmological constant are zero, with all physical constants derivable only from the following constants: speed of light; Planch's constant; proton charge; Coulomb's constant; electron mass; and proton mass; has anyone ever determined the exact formula for the density of water in its liquid phase at 1 atm in terms of temperature and those 6 physical constants? The atmosphere unit and the exact celsius scale itself are defined in terms of the triple point of water which in turn can be computed in terms of those 6 physical constants. Is it also true that the density of supercooled water and superheated water can't be determined exactly because they're not infinitely stable and will eventually undergo homogenous nucleation of the stable phase? Is it true that the less supercooled water is, the lower the space-time probability density of homogenous nucleation so the more accurately its density can be determined but its density can only be determined exactly from its freezing point to its boiling point? However, the reciprocal of the space-time probability density of homogenous nucleation probably varies superexponentially as the reciprocal of the amount supercooled the water is. Is it even true that the function that determines the density of water in terms of temperature is analytic at all temperatures above the freezing point and below the boiling point but not analytic at the freezing point or boiling point?

Beyond that, for even something as simple as $\ce{H_2}$, as considered using the non-relativistic Schrodinger equation, there is no exact solution for even the wavefunction of one molecule.