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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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In electrical engineering, the analysis of networks composed of passive linear components — resistors (R), capacitors (C), and inductors (L) — is fundamental. These components are organized into circuits where the relationship between input and output can be analyzed using transfer functions. The transfer function of an RLC circuit, which relates the voltage across a capacitor to the input voltage, can be derived using Kirchhoff's laws.
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Electrical analogy between a capacitor and the condensed linear response function.

Rémi Grincourt1, Olivier Aroule1, Christophe Morell1

  • 1Université de Lyon, Institut des Sciences Analytiques, UMR 5280, CNRS, Université Lyon 1, 5 rue de la Doua, F-69100, Villeurbanne, France.

Journal of Molecular Modeling
|November 19, 2025
PubMed
Summary
This summary is machine-generated.

We introduce a novel analogy comparing classical capacitors to the linear response function in conceptual density functional theory (CDFT). This capacitor analogy offers new physical interpretations of chemical reactivity and enhances theoretical chemistry concepts.

Keywords:
CDFTLinear responseReactivity

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Area of Science:

  • Theoretical Chemistry
  • Computational Chemistry
  • Quantum Chemistry

Background:

  • Explores a novel analogy between classical capacitors and conceptual density functional theory (CDFT).
  • Draws parallels between electrostatic behavior and chemical reactivity described by the linear response function in CDFT.

Purpose of the Study:

  • To illustrate the capacitor analogy on molecular systems.
  • To generalize the analogy to larger systems.
  • To extend the relationship to other chemical descriptors and offer new physical interpretations.

Main Methods:

  • Utilized the ADF package for all calculations.
  • Optimized molecules at the PBE0/TZP level, including scalar relativistic effects.
  • Developed an in-house Python program for data extraction, visualization, and analysis of condensed linear response functions.

Main Results:

  • Demonstrated the capacitor analogy on molecular systems from diatomics to larger molecules.
  • Showed the extension of this relationship to other chemical descriptors.
  • Provided new physical interpretations for chemical reactivity.

Conclusions:

  • The capacitor analogy offers fresh insights into chemical reactivity.
  • Enriches the conceptual framework of theoretical chemistry.
  • Highlights the utility of electrostatic analogies in understanding chemical phenomena.