Quantifying the spin-orbit effect in molecular clusters using Steradians and Spin-Orbit geometries

The manuscript discusses the concepts of spin-orbit coupling in atomic physics and Molecular Quantum Similarity (MQS) in molecular clusters. Spin-orbit coupling arises from the interaction between an electron's spin and its motion around the nucleus and plays a crucial role in determining energy levels and spectral lines in atoms with heavy nuclei. On the other hand, MQS is a computational approach to compare the electronic density distributions in different molecular systems. In this order of ideas, the study aims to answer questions about electronic and structural differences caused by the spin-orbit effect from the standard geometry (Steradians geometry) using the MQS framework. The MQS is based on the Molecular Quantum Similarity Measure (MQSM) using different positive operators such as Dirac delta and Coulomb operators to quantify the similarity between molecular systems. The paper presents tables with MQSM indices and Euclidean distances for different molecular clusters using both spin-orbit (SO) and standard geometry (SR). The results show significant effects of spin-orbit coupling on the similarity measures between different molecules. The manuscript suggests that understanding the relationship between spin-orbit effects and quantum similarity could lead to deeper insights into electronic interactions in complex molecular systems and has potential applications in quantum mechanics and molecular physics.