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The effective concentration of a species in a solution can be expressed precisely in terms of its activity. Activity considers the effect of electrolytes present in the vicinity of the species of interest and depends on the ionic strength of the solution. The activity of a species is expressed as the product of molar concentration and the activity coefficient of the species.
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New Permutationally Invariant Polynomial Potential Energy Surfaces for H5O2+ with Fast Analytical Gradients

Saikiran Kotaru1, Chen Qu2, Paul L Houston3

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|January 7, 2026
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Summary
This summary is machine-generated.

New potential energy surfaces (PESs) for the protonated water dimer offer precise fits and fast gradients, improving hydrated proton studies. These advancements utilize permutationally invariant polynomials and reverse differentiation for enhanced computational efficiency.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Molecular dynamics

Background:

  • The protonated water dimer is crucial for understanding the hydrated proton.
  • Previous computational models had limitations in precision and gradient calculation speed.

Purpose of the Study:

  • To develop improved potential energy surfaces (PESs) for the protonated water dimer.
  • To enable faster and more accurate gradient calculations for simulations.

Main Methods:

  • Linear regression with permutationally invariant polynomials (PIPs).
  • Reverse differentiation for efficient gradient computation.
  • Fitting to high-level CCSD(T) data up to 110,000 cm⁻¹.

Main Results:

  • New PESs provide more precise fits to CCSD(T) data compared to previous models.
  • Fast gradients are achieved via reverse differentiation, significantly outperforming numerical gradients.
  • The new surfaces show good agreement with CCSD(T) benchmarks and Diffusion Monte Carlo zero-point energies.

Conclusions:

  • The developed PESs offer a significant advancement for studying the hydrated proton.
  • Enhanced computational efficiency through fast gradients will facilitate more extensive molecular simulations.
  • These improved models contribute to a deeper understanding of proton transfer in aqueous systems.