Thermodynamic integration with harmonic reference: Difference between revisions

Revision as of 07:35, 1 November 2023

The Helmholtz free energy ( $A$ ) of a fully interacting system (1) can be expressed in terms of that of harmonic system (0) as follows

{\displaystyle A_{1} = A_{0} + \Delta A_{0\rightarrow 1} }

where $\Delta A_{0\rightarrow 1}$ is anharmonic free energy. The latter term can be determined by means of thermodynamic integration

{\displaystyle \Delta A_{0\rightarrow 1} = \int_0^1 d\lambda \langle V_1 -V_0 \rangle_\lambda }

with $V_i$ being the potential energy of system $i$ , $\lambda$ is a coupling constant and

@@ Line 2: / Line 2: @@
 :<math>
 A_{1} = A_{0} + \Delta A_{0\rightarrow 1}
- </math>
+</math>
-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
+:<math>
+\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