A bottom-up field-theoretic framework via hierarchical coarse-graining: Generalized mode theory

Area of Science:

• Computational Chemistry and Physics
• Materials Science
• Statistical Mechanics

Background:

• Particle-based simulations face limitations in exploring large spatiotemporal scales due to computational expense.
• Existing field-theoretic simulations often rely on top-down approximations and lack direct connection to atomistic interactions.

Purpose of the Study:

• To develop a hierarchical bottom-up framework for constructing field-theoretic models of molecular liquids from microscopic details.
• To generalize field-theoretic methods to arbitrary pair potentials, extending their applicability.
• To provide a theoretical foundation for scalable, bottom-up field-theoretic simulations.

Main Methods:

• Developed a hierarchical coarse-graining framework mapping atomistic interactions to coarse-grained potentials.
• Utilized a perturbative expansion in reciprocal space to regularize short-range divergences.
• Generalized the Hubbard-Stratonovich transformation using two auxiliary fields for arbitrary pair potentials.

Main Results:

• Introduced a generalized mode theory extending bottom-up field-theoretic modeling beyond positive-definite kernels.
• Demonstrated compatibility with existing field-theoretic sampling strategies.
• Established a theoretical foundation combining formal derivations with numerical regularization and mode-truncation.

Conclusions:

• The presented framework enables the construction of field-theoretic models directly from atomistic simulations.
• This approach overcomes limitations of existing methods, paving the way for efficient, large-scale simulations of molecular systems.
• The generalized mode theory offers a powerful tool for multiscale modeling in chemistry and physics.