Overview

Clusters are aggregates consisting of a few to thousands of atoms or molecules. They have attracted considerable interest because they form a new class of materials with properties that can differ significantly from those of individual molecules or bulk matter. Another key factor driving research is the size-dependent evolution of cluster properties. The study of clusters has become an interdisciplinary field, combining atomic physics, quantum chemistry, and several other areas. Atomic and molecular clusters have been investigated extensively due to their potential applications in catalysis, medicine, and nanoelectronics. Clusters exhibit unique physical and chemical properties, and understanding how their geometric and electronic structures evolve with size is central to modern nanoscience. Theoretical research is particularly important because experimental methods often cannot directly determine cluster structures, and interpreting spectroscopic or mass spectrometric data typically requires robust theoretical models. Quantum chemical approaches, such as Density Functional Theory (DFT) and the Hartree-Fock method, become computationally expensive and less practical for larger clusters (more than 30 atoms) due to the high cost and the presence of numerous local minima. Therefore, developing efficient global optimization algorithms and empirical potential functions is essential for predicting and understanding cluster structures and properties. Structure determination at the nanoscale is one of the most challenging problems in contemporary nanoscience. Even simple binary systems, well characterized in bulk, can exhibit surprising diversity in small clusters. To study this behavior, a combination of global optimization techniques and quantum chemical methods is often applied, providing a detailed view of the energy landscapes. This approach highlights important aspects of searching the configurational space of isolated clusters to identify the lowest-energy or most stable atomic and molecular arrangements. The complexity of this problem depends on the number of atoms in the cluster, the methods used to generate trial configurations, and the computational cost of modeling interactions. Typically, low-lying local minima are identified using global optimization algorithms with interatomic potentials, which offer a cost-effective alternative to DFT and can be refined later for more accurate results.

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