Thermodynamic integration

<p>Thermodynamic integration is a method used to compare the difference in <a href="/facts/Thermodynamic_free_energy/GtjtQqnq">free energy</a> between two given states (e.g., A and B) whose potential energies 
  
    
      
        
          U
          
            A
          
        
      
    
    {\displaystyle U_{A}}
  
 and 
  
    
      
        
          U
          
            B
          
        
      
    
    {\displaystyle U_{B}}
  
 have different dependences on the spatial coordinates. Because the free energy of a system is not simply a function of the phase space coordinates of the system, but is instead a function of the <a href="/facts/Boltzmann_distribution/XBU530uu">Boltzmann-weighted</a> integral over phase space (i.e. <a href="/facts/Partition_function_(statistical_mechanics)/q65sJrrn">partition function</a>), the free energy difference between two states cannot be calculated directly from the potential energy of just two coordinate sets (for state A and B respectively). In thermodynamic integration, the free energy difference is calculated by defining a thermodynamic path between the states and integrating over ensemble-averaged enthalpy changes along the path. Such paths can either be real chemical processes or alchemical processes. An example alchemical process is the Kirkwood's coupling parameter method.
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Thermodynamic integration open-in-new

Thermodynamic integration