# Information-Theoretic and Conceptual Density Functional Theory Insights on Frustration in Molecular Clusters

## TL;DR

This paper explores how molecular clusters become frustrated when their structures must change to stabilize, using energy and information theory to better understand and quantify this phenomenon.

## Contribution

The study introduces a systematic analysis of frustration in molecular clusters using energy decomposition, conceptual DFT, and information-theoretic measures.

## Key findings

- Total frustration energy correlates strongly with energy components and CDFT indices.
- Only certain information-theoretic measures consistently correlate with frustration across systems.
- (HF)n clusters show excellent correlations due to their simple hydrogen-bonding structure.

## Abstract

Frustration is an intrinsic feature of molecular complexes, arising when individual constituents must distort from their optimal isolated geometries to achieve collective stabilization. Although energetic frustration can be defined as the average distortion energy associated with complex formation, its quantitative origin and its connection to other molecular descriptors remain insufficiently understood. In this work, we systematically investigate frustration in four representative molecular complexes—two homogeneous clusters, (H2O)n and (HF)n, and two charged clusters, H3O+(H2O)n and F−(H2O)n (n = 1–20)—using three complementary density-based frameworks: (i) total-energy decomposition, (ii) global conceptual DFT (CDFT) descriptors, and (iii) information-theoretic approach (ITA) quantities. Strong linear correlations between the total frustration energy and most energy components, as well as CDFT indices, are revealed, enabling a quantitative interpretation of frustration from energetic and electronic-structure perspectives. Among ITA measures, only a subset, including Shannon entropy, Ghosh–Berkowitz–Parr entropy, Rényi entropy, and the relative Fisher information, exhibits robust and consistent correlations with frustration across all systems, indicating their suitability as ITA-based frustration descriptors. Particularly, the (HF)n clusters show uniformly excellent correlations for all descriptors due to their structurally simple and homogeneous hydrogen-bonding environment. Overall, this work provides a comprehensive density-based understanding of frustration and clarifies which descriptors reliably track its behavior. These insights establish a foundation for applying ITA and CDFT analyses to frustrated phenomena in broader chemical contexts, which could be applied to other systems, including molecular recognition, conformational dynamics, and catalysis.