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Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual...
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Merging Ion Concentration Polarization between Juxtaposed Ion Exchange Membranes to Block the Propagation of the Polarization Zone
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A Flexible and Generalized Constant-Potential Framework in i-PI.

Chenyu Zhang1, Ruoting Zhao2, Zhengda He3

  • 1Hefei National Research Center for Physical Sciences at Microscale, Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, P. R. China.

Journal of Chemical Theory and Computation
|May 28, 2026
PubMed
Summary
This summary is machine-generated.

We developed a flexible constant-potential molecular dynamics framework for electrochemical interfaces. This method enables accurate simulations by interpolating between integer electron descriptions, improving portability and extensibility for various electronic-structure codes.

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Area of Science:

  • Computational chemistry
  • Materials science
  • Electrochemistry

Background:

  • Realistic simulations of electrochemical interfaces under operating conditions require constant-potential molecular dynamics.
  • Existing frameworks often lack portability and extensibility due to tight coupling with specific electronic-structure codes.
  • Simulations are further complicated by integer-electron constraints in some codes.

Purpose of the Study:

  • To present a flexible, portable, and extensible constant-potential molecular dynamics framework.
  • To enable simulations interfacing with multiple density functional theory (DFT) engines and machine-learning potentials.
  • To overcome integer-electron limitations in DFT codes.

Main Methods:

  • Implemented a constant-potential framework within the i-PI driver, introducing an explicit electronic degree of freedom and a potentiostat module.
  • Employed a mixed-Hamiltonian interpolation scheme, running two adjacent integer-charge clients in parallel and linearly interpolating their properties.
  • Validated the method on a 1D double-well model and an Al(111) surface.

Main Results:

  • Demonstrated stable potential control and well-behaved charge fluctuations on model systems.
  • Successfully coupled constant-potential ab initio molecular dynamics (AIMD) with enhanced sampling.
  • Enabled efficient characterization of potential-dependent reactivity and free-energy landscapes for CO2 reduction on NiN4-doped graphene.

Conclusions:

  • The developed framework offers a portable and scalable platform for constant-potential simulations.
  • It supports diverse electronic-structure clients and has potential for machine-learning potentials.
  • This work facilitates rigorous simulations of electrochemical interfaces under operating conditions.