**the main equation**
I am doing molecular dynamics simulation. Internal energy in my system means total energy because it is thermodynamics system. I need integration constant because I want to report the thermodynamic properties, not their change. I want to explain it more in detail, so you can help me.
Ein=∫Pin/rho^2 d rho +F(T)= RT{ (e*rho^2)+(f*rho)+(g*rho^4)}+F(T)
Cp=R{ (a*rho^2)+(b*rho)+(c*rho^4)}+F'(T)
in these formulas: rho= density. e,f,g,a,b,c = temperature dependant coefficients. Pin= internal pressure. Ein= internal energy=total energy. F(T)= integration constant. F'(T)= temperature derivation of integration constant.
I calculate enthalpy from Ein and then calculate Cp. My main problem is that according to the article that I used, these integration constants, which are y-intercept,( F(T) and F'(T)) should be an ideal contribution of corresponding thermodynamical properties, but in MD and its numerical solutions, these parameters are just y-intercepts. So if I have enough data in MD (from high rho to zero rho) these y-intercepts would be an ideal contribution( because they are in rho=0) and it would be easy for me to have them. In my case, there is no way to calculate all the rho until zero( I work between 4.8-4.9 mol/lit), so I just extrapolate the thermodynamical properties against rho and then find y-intercept which is not ideal contribution ( and not temperature dependent and fluctuational to temperature) because this charts cannot properly extrapolate and find the exact ideal contribution( the thermodynamical properties at zero rho) because every extrapolation in different temperature would find the easiest way to reach y-intercept. So I cannot say that this is an ideal contribution at all, I need these y-intercepts( in my case not ideal contribution) to calculate the properties correctly, but the only way could be some mathematical methods to calculate F(T) and F'(T). Do you know any methods? or is there anything which you can advice me to do?
Thanks in advance
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Last edited by Geraili; Sep 11th 2017 at 09:21 AM.
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