Thermodynamic integration with harmonic reference: Difference between revisions
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A_{1} = A_{0} + \Delta A_{0\rightarrow 1} | A_{1} = A_{0} + \Delta A_{0\rightarrow 1} | ||
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where <math>\Delta A_{0\rightarrow 1}</math> is anharmonic free energy. The latter term | where <math>\Delta A_{0\rightarrow 1}</math> is anharmonic free energy. The latter term can be determined by means of thermodynamic integration | ||
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\Delta A_{0\rightarrow 1} = \int_0^1 d\lambda \langle V_1 -V_0 \rangle_\lambda | |||
</math> | |||
with <math>V_i</math> being the potential energy of system <math>i</math>, <math>\lambda</math> is a coupling constant and | |||
Revision as of 07:35, 1 November 2023
The Helmholtz free energy ([math]\displaystyle{ A }[/math]) of a fully interacting system (1) can be expressed in terms of that of harmonic system (0) as follows
- [math]\displaystyle{ A_{1} = A_{0} + \Delta A_{0\rightarrow 1} }[/math]
where [math]\displaystyle{ \Delta A_{0\rightarrow 1} }[/math] is anharmonic free energy. The latter term can be determined by means of thermodynamic integration
- [math]\displaystyle{ \Delta A_{0\rightarrow 1} = \int_0^1 d\lambda \langle V_1 -V_0 \rangle_\lambda }[/math]
with [math]\displaystyle{ V_i }[/math] being the potential energy of system [math]\displaystyle{ i }[/math], [math]\displaystyle{ \lambda }[/math] is a coupling constant and