A comparative review of 50 analytical representation of potential energy interaction for diatomic systems: 100 years of history

Araújo, Judith P.; Ballester, Maikel Y.

doi:10.1002/qua.26808

Cited by 54 publications

(35 citation statements)

References 200 publications

(739 reference statements)

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“…For a comprehensive overview of empirical potentials we recommend the work of Araújo and Ballester [2]. Below we give a casual overview of the most important empirical potentials mentioned in this contribution.…”

Section: Empirical Potentialsmentioning

confidence: 99%

Symbolic Regression in Materials Science: Discovering Interatomic Potentials from Data

Burlacu¹,

Kommenda²,

Kronberger³

et al. 2022

Preprint

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Particle-based modeling of materials at atomic scale plays an important role in the development of new materials and understanding of their properties. The accuracy of particle simulations is determined by interatomic potentials, which allow to calculate the potential energy of an atomic system as a function of atomic coordinates and potentially other properties. First-principles-based ab initio potentials can reach arbitrary levels of accuracy, however their aplicability is limited by their high computational cost.Machine learning (ML) has recently emerged as an effective way to offset the high computational costs of ab initio atomic potentials by replacing expensive models with highly efficient surrogates trained on electronic structure data. Among a plethora of current methods, symbolic regression (SR) is gaining traction as a powerful "white-box" approach for discovering functional forms of interatomic potentials.This contribution discusses the role of symbolic regression in Materials Science (MS) and offers a comprehensive overview of current methodological challenges and state-of-the-art results. A genetic programming-based approach for modeling atomic potentials from raw data (consisting of snapshots of atomic positions and associated potential energy) is presented and empirically validated on ab initio electronic structure data.

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Section: Empirical Potentialsmentioning

confidence: 99%

Symbolic Regression in Materials Science: Discovering Interatomic Potentials from Data

Burlacu¹,

Kommenda²,

Kronberger³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Unfortunately, the choice of suitable approximants may be a complicated task because the shapes of the genuine functions are not known a priori and because the elementary mathematical functions available may not be flexible enough (see, e.g., refs − and references therein). Therefore, despite the broad variety of their literature variants (especially in the case of the potential energy function), they easily become rather too awkward to allow “smooth” fitting. For instance, to describe quantitatively an ab initio potential energy function of He 2 supporting only one bound state, Janzen and Aziz had to use 45 fitting parameters, and even the best approximants directly fitted to experimental data (see, e.g., ref ) may still not provide reliable predictions.…”

Section: Introductionmentioning

confidence: 99%

Reduced Radial Curves of Diatomic Molecules

Špirko

2023

J. Chem. Theory Comput.

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The prospect of using the concept of a universal reduced potential energy curve (RPC) for a broader class of radial molecular functions is explored by performing appropriate model calculations for the electric dipole moment functions of the hydrogen halides HF, HCl, and HBr. The reduced radial functions of the model systems, constructed from their best available theoretical approximants, coincide so closely that they can be used as few-parameter universal representations of functions available in the literature. Given the mathematical nature of the problem addressed here, the results are not limited to the functions studied but can be applied equally well to all radial molecular functions that have similar shapes, such as electric quadrupole moment and dipole polarizability functions.

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“…Up to now, many exponential-type potentials, including the Morse [30,31], Hulthén [32][33][34][35][36][37][38], Woods-Saxon [27,[39][40][41][42][43], Rosen-Morse [44][45][46][47][48], Eckart-type [49][50][51], Manning-Rosen [52][53][54], Deng-Fan [55,56], Pöschl-Teller like [57], Mathieu [58], sine-type hyperbolic [59] and Schiöberg [60][61][62][63] potentials have been investigated, and some analytical bound state solutions were obtained using an approximation for these models in l ≠ 0 state. Some known exponential potentials can also be transformed into a hyperbolic potential model, which can help understand quantum systems' natural dynamics [64][65][66][67][68][69][70][71][72][73][74][75]<...…”

Section: Introductionmentioning

confidence: 99%

Generalised tanh-shaped hyperbolic potential: Klein–Gordon equation's bound state solution

Badalov

2023

Commun. Theor. Phys.

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The development of potential theory heightens the understanding of fundamental interactions in quantum systems. In this paper, the bound state solution of the modified radial Klein-Gordon equation is presented for generalised tanh-shaped hyperbolic potential from the Nikiforov-Uvarov method. The resulting energy eigenvalues and corresponding radial wave functions are expressed in terms of the Jacobi polynomials for arbitrary $l$ states. It is also demonstrated that energy eigenvalues strongly correlate with potential parameters for quantum states. Considering particular cases, the generalised tanh-shaped hyperbolic potential and its derived energy eigenvalues exhibit good agreement with the reported findings. Furthermore, the rovibrational energies are calculated for three representative diatomic molecules, namely $\rm{H_{2}}$, $\rm{HCl}$ and $\rm{O_{2}}$. The lowest excitation energies are in perfect agreement with experimental results. Overall, the potential model is displayed to be a viable candidate for concurrently prescribing numerous quantum systems.

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A comparative review of 50 analytical representation of potential energy interaction for diatomic systems: 100 years of history

Cited by 54 publications

References 200 publications

Symbolic Regression in Materials Science: Discovering Interatomic Potentials from Data

Symbolic Regression in Materials Science: Discovering Interatomic Potentials from Data

Reduced Radial Curves of Diatomic Molecules

Generalised tanh-shaped hyperbolic potential: Klein–Gordon equation's bound state solution

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