Probing the partition function for temperature-dependent potentials with nested sampling

Area of Science:

• Computational physics
• Statistical mechanics
• Physical chemistry

Background:

• Thermodynamic properties are typically derived from the partition function.
• Evaluating the partition function for many-atom systems is computationally challenging due to the summation over microscopic states.
• Nested sampling, a Bayesian method, can compute the partition function and density of states efficiently, but struggles with temperature-dependent potentials.

Purpose of the Study:

• To develop a novel method for efficiently computing partition functions with temperature-dependent potentials.
• To overcome the computational limitations of standard nested sampling for temperature-dependent systems.
• To restore the efficiency of nested sampling for calculating thermodynamic properties across various temperatures.

Main Methods:

• Introduction and implementation of an extended partition function approach.
• Treating temperature as an additional parameter to be sampled within nested sampling.
• Applying the extended partition function method to compute quantum partition functions for harmonic potentials and Lennard-Jones clusters.

Main Results:

• The extended partition function allows for nested sampling in a single run, irrespective of temperature dependence.
• The new method significantly reduces computational time compared to performing nested sampling at each temperature.
• Demonstrated superior performance for computing quantum partition functions for specific systems at low temperatures.

Conclusions:

• The extended partition function method offers a computationally efficient solution for calculating thermodynamic properties.
• This approach is particularly advantageous for systems with temperature-dependent effective potentials.
• The method shows promise for broader applications in statistical mechanics and computational chemistry.