Why is modelling water so difficult? There are several models of water that have come into existence so far. Nevertheless, there is no one particular model which effectively gives all the properties of water correctly. A model like TIP3P gives me thermodynamically favourable values but diffusivity is overestimated. The case is just vice-versa with SPC/E model. 
Why is it so difficult to model water molecule precisely ? What are the problems involved in it ? Why can't proper ab initio quantum mechanical calculations for the molecule give me proper results ?
 A: Because the Turbulence is not known. 
Turbulence is a surface in (inside) the fluid. This means in a molecular level the very same; 
1. if the water molecule has an influence on it's neighbour molecule 
or 
2. it doesn't have an influence to all of it's neighbour molecule. 


*

*If this surface is there (opt 2), the creation of the surface tension consumes energy.

*If the surfaces have high velocity difference, they behave through friction and collision, instead of elastic and/or viscous forces.


This is the so called "navier stokes Existency and smoothness problem", which is considered as an Mathematical problem, though it is a physical Problem, as the premises of the problem are physically false defined. 
I have had a paper about this in my desk since 2012. But it seems to take some time till this is recognized. Here's some stuff which might be interesting; -or not. 
And if you wan't to have some fancy QED level explanation to it; the surface has an electromagnetic force which propels against all the other surfaces, and though this force is small, it's enough to keep the parts apart when they have enough velocity difference.  
And hey, if you don't agree with my explanation about the turbulence, My answer is still correct. That is the reason why "your" mathematics doesn't work; You just don't have the physics right. Feel completely free to find your own "right".
