What does this research mean for the field?

The leading order term for the finite-size correction in the Coulomb potential at an interior ion in cubic crystals is given by the formula [24r^4-40(x^4+y^4+z^4)]/[9√3 (2p+1)^2]. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To explore the Coulomb potential in finite crystals and develop a method for calculating Madelung constants.

March 7, 2026Journal of Chemical Theory and ComputationOpen Access

The Madelung Problem of Finite Crystals

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To explore the Coulomb potential in finite crystals and develop a method for calculating Madelung constants.
Analyzed the Coulomb potential at interior ions in finite crystals of size p.
Decomposed pairwise contributions into periodic bulk, quadratic boundary, and finite-size correction components.
Utilized a direct-summation scheme for accurate calculations of Madelung constants.
Established a clear additive structure for contributions from neighboring ions.
Identified a leading-order term for finite-size corrections in cubic crystals.
Demonstrated the scheme's accuracy even for small crystal sizes (p=1).

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Implication

Reveals the universal relationships of Madelung constants in finite crystals, suggesting improved calculation methods.

Cite This Study

Zhao et al. (2026) studied this question.

synapsesocial.com/papers/69abc0925af8044f7a4e93d3 https://doi.org/10.1021/acs.jctc.6c00034

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The Madelung Problem of Finite Crystals

Key Points

Discussion

Implication

Cite This Study

The Madelung Problem of Finite Crystals

Key Points

Discussion

Implication

Cite This Study