Communications on quantum similarity, part 3: a geometric-quantum similarity molecular superposition algorithm

Area of Science:

• Computational chemistry
• Quantum chemistry

Background:

• Molecular superposition is crucial for comparing molecular structures.
• Existing methods may not fully optimize structural alignment based on quantum properties.

Purpose of the Study:

• To present a novel algorithm, geometric-quantum similarity molecular superposition (GQSMS), for optimal molecular superposition.
• To develop a method that utilizes quantum similarity principles for enhanced molecular alignment.

Main Methods:

• The geometric-quantum similarity molecular superposition (GQSMS) algorithm is introduced.
• Quantum similarity matrices (QSMs) are constructed using quantum similarity integrals (QSIs) dependent on squared intermolecular atomic distances.
• Kruskal minimum spanning trees are employed for ordering molecular sets.

Main Results:

• The GQSMS algorithm yields optimal molecular superposition based on quantum similarity.
• The resulting QSMs exhibit optimal QSI elements and a positive definite global matrix structure.
• Jacobi rotations and inward functions are explored for QSM refinement and scaling.

Conclusions:

• The GQSMS algorithm provides an effective approach for optimal molecular superposition.
• The method enhances the analysis of molecular sets through structured QSMs.
• Further refinements using Jacobi rotations and inward functions improve QSM utility.