Finding the difference in Helmholtz free energy using thermodynamic integration

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In summary, the conversation discusses the process of thermodynamic integration and the desire to compare results between a real gas and an ideal gas, specifically for a Lennard-Jones fluid. The individual is seeking examples of how the integration of the average derivative of coupled potential energy is performed for this system.
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VVS2000
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Finding out difference in helmholtz free energy using thermodynamic integration by using a ideal gas system as reference and lennard jones system as our system of interest
If there any solved papers or even python simulations to find this please share
I understood the process of thermodynamic integration but computationally I want to see how this integration of average of derivative of coupled potential energy is done
 
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You want to compare the result for a real gas with that for an ideal gas, right? Any particular scenario you want to look at?
 
  • #3
Chestermiller said:
You want to compare the result for a real gas with that for an ideal gas, right? Any particular scenario you want to look at?
Yeah for a lennard jones fluid, and basically I want to perform a computation of this integration process
But I am not able to understand how this integration is performed
 
  • #4
VVS2000 said:
Yeah for a lennard jones fluid, and basically I want to perform a computation of this integration process
But I am not able to understand how this integration is performed
Please provide a specific example of a physical system passing from an initial state to final state.
 

FAQ: Finding the difference in Helmholtz free energy using thermodynamic integration

What is Helmholtz free energy?

Helmholtz free energy, often denoted as \( A \) or \( F \), is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at constant temperature and volume. It is defined as \( A = U - TS \), where \( U \) is the internal energy, \( T \) is the temperature, and \( S \) is the entropy of the system.

What is thermodynamic integration?

Thermodynamic integration is a method used to calculate free energy differences between two states of a system. It involves integrating the derivative of the free energy with respect to a coupling parameter \( \lambda \) that interpolates between the initial and final states. This parameter \( \lambda \) typically ranges from 0 to 1.

How is thermodynamic integration implemented in practice?

In practice, thermodynamic integration involves performing a series of simulations at different values of the coupling parameter \( \lambda \). For each value of \( \lambda \), the average of the derivative of the potential energy with respect to \( \lambda \) is computed. The free energy difference is then obtained by numerically integrating these averages over the range of \( \lambda \).

What are the advantages of using thermodynamic integration?

Thermodynamic integration is advantageous because it can provide accurate free energy differences for systems where other methods might fail. It is particularly useful for systems with complex energy landscapes or when dealing with phase transitions. Additionally, it is a general method that can be applied to a wide variety of systems and conditions.

What are the common challenges in thermodynamic integration?

Common challenges in thermodynamic integration include ensuring adequate sampling at each value of \( \lambda \), dealing with statistical errors, and choosing an appropriate path for the integration. Poor sampling can lead to inaccurate estimates of the free energy difference, and the integration path must be chosen to avoid regions where the system might undergo abrupt changes.

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