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Exact constraint of density functional approximations at the semiclassical limit
1Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
The Journal of Chemical Physics
|May 2, 2025
Summary
We introduce the semiclassical limit (ℏ → 0) for electronic systems, revealing its connection to challenging strong correlations. Our analysis shows density functional approximations (DFAs) fail in this limit, suggesting new avenues for improved DFA development.
Area of Science:
- Quantum chemistry
- Computational physics
- Electronic structure theory
Background:
- The semiclassical limit (ℏ → 0) offers a unique perspective on electronic systems.
- Strong correlation presents significant challenges for conventional quantum mechanical methods.
- Density functional approximations (DFAs) are widely used but have known limitations.
Purpose of the Study:
- To introduce and analyze the semiclassical limit for electronic systems.
- To investigate the behavior of density functional approximations (DFAs) in this limit.
- To explore the potential of semiclassical analysis for developing improved DFAs.
Main Methods:
- Solving Schrödinger equations in the limit ℏ → 0.
- Analyzing the performance of mainstream density functional approximations (DFAs) as ℏ → 0.
- Connecting DFA energy underestimation in strongly correlated systems to effective Planck's constant (ℏeff).
Main Results:
- The semiclassical limit reveals a type of strong correlation difficult for multi-configurational methods.
- Mainstream DFAs exhibit erroneous divergent energy behavior as ℏ → 0, violating exact constraints.
- DFA energies for strongly correlated transition-metal diatomics are significantly underestimated, linked to small estimated ℏeff.
Conclusions:
- Semiclassical analysis provides a valuable tool for understanding electronic systems and strong correlation.
- Current mainstream DFAs fail to satisfy fundamental constraints in the semiclassical limit.
- This work demonstrates the utility of semiclassical analysis and its potential to inspire the development of more accurate DFAs.
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