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Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method

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From Wave Function Sign Structure to Static Correlation.

Matúš Dubecký¹

¹Department of Physics, Faculty of Science, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic.

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|July 15, 2026

Summary

We developed a new way to partition electronic correlation energy, separating static and dynamic correlation effects. This clarifies the successes and failures of quantum chemistry methods like diffusion Monte Carlo.

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Area of Science:

Quantum Chemistry
Computational Physics
Theoretical Chemistry

Background:

Electronic correlation energy (E_cor) is crucial for accurate molecular simulations.
Existing methods struggle to consistently partition different correlation types (dynamic, static, nondynamic).
The single-determinant (SD) node is a common approximation in quantum chemistry.

Purpose of the Study:

To introduce a variational nodal partition of correlation energy.
To clearly distinguish between static and dynamic correlation components.
To provide transparency into the performance of quantum chemical methods.

Main Methods:

Defined a variational nodal partition: E_cor = E_sym + E_stat.
Introduced E_stat as the correlation component from replacing the exact node with the SD node.
Isolated Fermionic sign-structure correlation within E_stat.

Main Results:

Naturally emerged three state-based correlation components.
Clarified the definitions of dynamic, strong, nondynamic, and static correlation.
Provided a transparent understanding of diffusion Monte Carlo (DMC) successes and failures.

Conclusions:

The proposed nodal partition offers a clearer framework for understanding electronic correlation.
This work enhances the interpretability of quantum chemical calculations.
The method provides insights into the limitations and strengths of various computational approaches.