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Cluster Sampling Method

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...

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Updated: Jul 13, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Structure search method for atomic clusters based on the dividing rectangles algorithm.

Kansei Kanayama¹, Atsuto Seko¹, Kazuaki Toyoura¹

¹Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan.

Physical Review. E

|October 18, 2023

Summary

This summary is machine-generated.

We developed a new atomic cluster structure search method using the Dividing Rectangles (DIRECT) algorithm. This efficient approach optimizes high-dimensional spaces, outperforming random search for complex materials like phosphorus and sulfur clusters.

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Area of Science:

Computational Chemistry
Materials Science
Optimization Algorithms

Background:

Exploring optimal atomic cluster structures is crucial for understanding material properties.
High-dimensional search spaces pose significant challenges for conventional optimization methods.
The Dividing Rectangles (DIRECT) algorithm offers a deterministic approach to optimization.

Purpose of the Study:

To develop an efficient structure search method for atomic clusters.
To leverage the DIRECT algorithm in high-dimensional search spaces.
To combine DIRECT with gradient-based local optimization for enhanced performance.

Main Methods:

Utilized the Z-matrix representation to define hyperrectangle search spaces.
Integrated the DIRECT algorithm with a gradient-based local optimizer.
Applied the method to Lennard-Jones, phosphorus, and sulfur atomic clusters.

Main Results:

The proposed method demonstrated higher efficiency compared to random search.
Achieved comparable efficiency to basin hopping for structure searching.
Successfully explored complex metastable structures in phosphorus and sulfur clusters.

Conclusions:

The DIRECT-based method provides an efficient strategy for atomic cluster structure optimization.
This approach is particularly effective in high-dimensional and complex energy landscapes.
The findings suggest a promising alternative for computational materials discovery.