Calculation of Simple Thermodynamic Properties

A wide variety of thermodynamic properties can be calculated from computer simulations a comparison of experimental and calculated values for such properties is an important way in which the accuracy of the simulation and the underlying energy model can be quantified. Simulation methods also enable predictions to be made of the thermodynamic properties of systems for which there is no experimental data, or for which experimental data is difficult or impossible to obtain. Simulations can also provide struchrral information about the 

The internal energy is easily obtained from a simulation as the ensemble average of the energies of the states that are examined during the course of the simulation  

At a phase transition the heat capacity will often show a characteristic dependence upon the temperature (a first-order phase transition is characterised by an infinite heat capacity at the transition but in a second-order phase transition the heat capacity changes discontinuously) Monitoring the heat capacity as a function of temperature may therefore enable phase transitions to be detected. Calculations of the heat capacity can also be compared with experimental results and so be used to check the energy model or the simulation protocol. 

The heat capacity is formally defined as the partial derivative of the internal energy with respect to temperature  

An alternative way to write this expression uses the relationship  

---