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Local Spectral Formulation of the One-Determines-All (ODA) Principle for Multistate Density Functionals

This article is a preprint and has not been certified by peer review.

Authors

    Jiali Gao,  
    Jiali Gao
    • Beijing University Shenzhen Graduate School
    • Shenzhen Bay Laboratory image/svg+xml
    Yangyi Lu
    Yangyi Lu
Categories
Computational Biology & Bioinformatics
Keywords
Computational Chemistry; Quantum Chemistry; Density Functional Theory

Abstract

Multistate density functional theory (MSDFT) generalizes Kohn–Sham density functional theory to a finite subspace of interacting states through a Hamiltonian matrix functional of the matrix density D(r). A central challenge is to construct matrix functionals that preserve subspace unitary invariance while encoding nontrivial state coupling. Here we show that any local, unitary-equivariant matrix functional of D(r) must be co-diagonalizable with D(r), and is therefore completely specified by a scalar generator acting on its eigenvalues. This establishes a one-to-all mapping from a scalar generator to the full matrix functional. As a consequence, the construction of N2 matrix elements is reduced to a single scalar mapping evaluated on the eigenvalue spectrum at each spatial grid point. The formalism is illustrated using a four-state Hubbard model, where exact reconstruction is achieved with a known scalar function, and deviations from this mapping can be systematically corrected within the spectral framework. The results provide a rigorous foundation for constructing local matrix exchange–correlation functionals with computational complexity comparable to Kohn–Sham DFT, and offer a practical route toward scalable MSDFT approximations.

References

1. Lu, Y.; Gao, J. Multistate Density Functional Theory of Excited States. J. Phys. Chem. Lett. 2022, 13, 7762–7769, DOI: 10.1021/acs.jpclett.2c02088.

2. Lu, Y.; Gao, J. Multistate Density Functional Theory: Theory, Methods, and Applications. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2025, 15, 1–35, DOI:10.1002/wcms.70043.

3. Lu, Y.; Gao, J. Fundamental Variable and Density Representation in Multistate DFT for Excited States. J. Chem. Theory Comput. 2022, 18, 7403–7411, DOI: 10.1021/acs.jctc.2c00859.

4. Lu, Y.; Gao, J. Structure of Multi-State Correlation in Electronic Systems. J. Chem. Theory Comput. 2024, 20, 8474–8481, DOI: 10.1021/acs.jctc.4c00545.

5. Cohen, A. J.; Mori-Sanchez, P.; Yang, W. T. Challenges for Density Functional Theory. Chemical Reviews 2012, 112, 289320.

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DOI:

https://doi.org/10.65215/LTSpreprints.2026.04.09.000181

Submission ID:

181

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Posted

2026-04-09

How to Cite

Gao, J., & Lu, Y. (2026). Local Spectral Formulation of the One-Determines-All (ODA) Principle for Multistate Density Functionals. LangTaoSha Preprint Server. https://doi.org/10.65215/LTSpreprints.2026.04.09.000181

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Declaration of Competing Interests

The authors declare no competing interests to disclose.

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