The landing zone - Ground for model transfer in chemistry

Area of Science:

• Interdisciplinary scientific modeling
• Mathematical physics
• Theoretical chemistry

Background:

• Mathematical models, termed 'templates,' are often transferred across scientific disciplines.
• Successful transfer requires specific formal and conceptual prerequisites.
• Identifying these prerequisites is crucial for advancing interdisciplinary research.

Purpose of the Study:

• To introduce the concept of a "landing zone" as an ontological framework for successful template transfer.
• To explore the conceptual features enabling the generalization of mathematical tools across domains.
• To provide a case study demonstrating the application of the landing zone concept.

Main Methods:

• Conceptual analysis of model transferability.
• Introduction of the "landing zone" as an ontological prerequisite.
• Case study using the Quantum Theory of Atoms in Molecules (QTAIM) in chemistry.
• Examination of transferred templates: the virial theorem and the wave function from physics.

Main Results:

• The "landing zone" is defined as an ontology that facilitates the transfer of mathematical templates.
• In the QTAIM case study, the "topological atom" serves as the landing zone.
• This landing zone justifies the application of the virial theorem and wave function in chemistry.
• It establishes the in-principle stability and representational transformation needed for these templates.

Conclusions:

• The landing zone concept provides a framework for understanding and enabling cross-disciplinary model transfer.
• Ontological innovations, like the topological atom, are key to grounding transferred templates in new scientific contexts.
• This approach enhances the scientific utility of mathematical tools in diverse fields.