A theory of electronic structure for coarse-grained resolutions

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Materials Science

Background:

• Accurate electronic structure modeling is crucial for understanding molecular behavior.
• Current methods often require significant computational resources, limiting system size and complexity.
• Coarse-graining (CG) offers a way to reduce computational cost by simplifying molecular representations.

Purpose of the Study:

• To develop a novel stochastic diabatic projection method for constructing coarse-grained electronic structure models.
• To enable the systematic reproduction of electronic structure renormalized over eliminated degrees of freedom.
• To bridge the gap between fine-grained (FG) and coarse-grained (CG) molecular resolutions.

Main Methods:

• A stochastic diabatic projection method was employed.
• Minimization of relative entropy between FG and CG joint electronic-nuclear distributions was used.
• Derivation of a stochastic effective Hamiltonian was performed.

Main Results:

• The method constructs electronic structure models at CG molecular resolutions.
• A stochastic effective Hamiltonian was derived, decomposing CG configuration-dependent electronic structure.
• The Hamiltonian separates electronic structure into deterministic means and residual fluctuations.

Conclusions:

• The developed framework systematically reproduces renormalized electronic structure.
• This approach effectively bridges downfolding and molecular coarse-graining theories.
• The method provides a pathway for more efficient yet accurate modeling of complex molecular systems.