Nested Basin-Sampling.

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Thermodynamics

Background:

• Evaluating thermodynamic properties in systems with broken ergodicity is computationally challenging.
• Traditional methods like standard nested sampling (NS) may fail to capture subtle phase transitions.
• Efficient sampling schemes are crucial for accurate thermodynamic calculations.

Purpose of the Study:

• To develop an embarrassingly parallel method for thermodynamic property evaluation.
• To introduce a novel sampling scheme, the No Galilean U-Turn Sampler (NoGUTS).
• To assess the performance of the new method against existing techniques for complex systems.

Main Methods:

• Development of nested basin-sampling (NBS), an embarrassingly parallel approach.
• Introduction of the NoGUTS sampler, integrating No U-Turn Sampler (NUTS) and Galilean Monte Carlo.
• Application to a 31-atom Lennard-Jones cluster exhibiting a low-temperature phase transition.

Main Results:

• NBS successfully reproduced the full heat capacity curve, including a solid-solid phase transition.
• The NoGUTS sampler demonstrated efficient generation of new live points.
• Standard nested sampling (NS) failed to resolve the low-temperature phase transition at similar computational cost.

Conclusions:

• NBS provides an accurate and efficient method for evaluating thermodynamic properties in systems with broken ergodicity.
• The NoGUTS sampler enhances sampling efficiency for complex energy landscapes.
• NBS offers a significant improvement over standard NS for resolving phase transitions.