Introducción al estudio de la superficie de energía potencial en moléculas desde el contexto de la matemática discreta: una guía conceptual para estudiantes de ciencias e ingeniería

• DOI: https://doi.org/10.22533/at.ed.153222529046

• Palavras-chave: Superficie de energía potencial, función del espacio conformacional, modelado matemático, homología persistente, teoría de Morse discreta.

• Keywords: Potential energy surface, conformational space function, mathematical modeling, persistent homology, discrete Morse theory.

• Abstract: The theoretical and experimental study of molecules frequently converges on two fundamental concepts: the conformational space function and the potential energy surface (PES). These mathematical functions are key to understanding the structural and energetic behavior of molecular systems. This article offers a pedagogical guide to these concepts, highlighting their conceptual relevance and the role of their mathematical formulation in chemical analysis. It explores how tools of modern discrete mathematics, such as discrete Morse theory and persistent homology, allow for the topological modeling and analysis of these energy landscapes. Emphasis is placed on intuitive explanations, illustrative examples, and the challenges associated with applying these methods to real molecular systems. Finally, open questions are raised and future perspectives for the study of these models from an interdisciplinary perspective are presented.