# How does one compute the boiling point of a liquid made of a particular molecule?

This question is in relation to Anomalous boiling point of "iso-" alkanes on Chemistry SE.

I want to compute the boiling point of the different isomers of an n-carbon alkane to check what factors are affecting the boiling point since the empirically determined density trend and boiling point trend are not the same.

• Molecules don't really boil; liquids do. What you need to do is thermodynamical modeling of the liquid. Commented Aug 26, 2020 at 11:42
• +1. There's people here with more experience than me in MD, but what I can say is that if you start with a forcefield(FF) and an initial configuration of the liquid, and run a molecular dynamics simulation at various temperatures, you will find that at some temperature the molecules evaporate (you may assume constant pressure for all of this). It then becomes a question of accuracy. Are you going to use QMD, AIMD, AI-QMD, etc. and how accurate is your FF. I'd reproduce a boiling point 1st. Commented Aug 26, 2020 at 15:39

I would like to start off by saying this is first and foremost a thermodynamic problem.

Secondly, and as a result of thermodynamics, refer to Gibbs Phase Rule which says

$$$$F = C - P + 2$$$$ Where F = degrees of freedom, C = number of components, and P = number of phases. You seem to be after a pure liquid so $$C=1$$, and, you are after boiling, so there is a liquid and vapor, so, $$P=2$$

Hence, $$F = 1-2 +2 = 1$$. You have 1 degree of freedom you must set before you can do anything. You need to set temperature, or pressure, or some other intensive variable because it turns out a pure liquid of anything can boil at many different conditions - infinitely many. Water only boils at 100 Celsius if the pressure is fixed at 1 bar. If you change the pressure, the water will boil at a different temperature.

## Solving for the boiling point

The thermodynamics is the main thing. At the boiling point the chemical potential, pressure and temperature of the molecule will be the same in both phases. So, you need to calculate the chemical potential and either pressure or temperature depending on what you decided to set as your degree of freedom. You can use anything for this. You can use

1. macroscopic thermodynamic equations of state to calculate P,V or T and chemical potential.
2. Gibbs Ensemble Monte Carlo which simultaneously simulates a vapor and liquid simulations and does many fast and inaccurate chemical potential trial calculations via particle swaps between boxes, and also measures P to ensure all equilibrium criteria are met.
3. You can use Molecular dynamics with Free energy calculations to manually calculate the free energy of the particles and from this directly calculate the chemical potentials in the vapor and liquid for the molecule of interest, it is trivial to calculate the P, T , V or whatever else you need in MD. While Gibbs ensemble does thousands of quick, somewhat sloppy chemical potential calculations, this will do very expensive and accurate, single calculations.

There are vapor-liquid coexistence methods for essentially tracing the boiling point as a function of a variable and these typically use free energy methods such as thermodynamic integration and free energy perturbation (because these all directly lead to chemical potentials which is the overarching requirement).

David Kofke is a great researcher whose work you should look into if you are wanting to use molecular based force-field models, for instance A comparison of molecular-based models to determine vapor-liquid phase coexistence in hydrogen fluoride. There are many others who do molecular based modelling, but you can use any scale of modelling so long as the thermodynamic requirements are met - and again, this comes down to chemical potentials being equal in each phase, as well as typically T and pressure. You need to specify 1 and only 1 intensive variable (T, P, density etc).

## Final Note:

Some people like to use fugacity rather than chemical potential. I do not know why. Fugacity is theoretically fine to use, but such a mess to think about.