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arxiv: 2604.25941 · v1 · submitted 2026-04-16 · ⚛️ physics.chem-ph · physics.comp-ph

Molecular Dynamics Force Field Genetic Optimization for Tri-n-butyl Phosphate Liquid

Faranak Hatami , Valmor F.de Almeida This is my paper

Pith reviewed 2026-05-10 09:14 UTC · model grok-4.3

classification ⚛️ physics.chem-ph physics.comp-ph
keywords molecular dynamicsforce field optimizationtri-n-butyl phosphateLennard-Jones parametersgenetic algorithmneural network surrogatemulti-objective optimizationliquid properties
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The pith

Genetic optimization with a neural network surrogate tunes Lennard-Jones parameters for tri-n-butyl phosphate liquid to 23 percent overall experimental deviation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an iterative loop that places molecular dynamics simulations inside a genetic algorithm to refine the Lennard-Jones parameters specific to liquid tri-n-butyl phosphate. Non-dominated sorting genetic algorithms search for parameter values that simultaneously reduce errors in mass density, electric dipole moment, heat of vaporization, self-diffusion coefficient, and shear viscosity. A neural network trained on earlier simulation results replaces most full MD calculations, allowing larger populations and more generations to be evaluated. The resulting parameters lower the cumulative relative deviation from experimental data from 74 percent to 23 percent. The approach supplies a reusable framework for atomistic property prediction in complex organic liquids where direct matching is expensive.

Core claim

Embedding molecular dynamics inside a multi-objective genetic algorithm and accelerating evaluations with a neural network property model produces Lennard-Jones parameters for tri-n-butyl phosphate that reduce the aggregate relative deviation across density, dipole moment, vaporization heat, self-diffusion, and shear viscosity to 23 percent of experimental values.

What carries the argument

The NN NSGA-III loop, a non-dominated sorting genetic algorithm that uses a neural network surrogate to predict molecular dynamics properties and thereby evaluate candidate Lennard-Jones parameter sets.

If this is right

  • The optimized Lennard-Jones parameters improve thermophysical property predictions in molecular dynamics simulations of TBP liquid.
  • The neural network surrogate reduces the computational cost of the optimization loop, permitting larger populations and additional generations.
  • Multi-objective optimization reveals trade-offs that make simultaneous improvement of self-diffusion coefficient and shear viscosity difficult.
  • Systematic single-objective versus multi-objective comparisons establish a general framework for atomistic force field tuning of TBP.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The refined parameters may improve accuracy in simulations of TBP used as a solvent in nuclear fuel reprocessing.
  • The surrogate-assisted genetic method could be applied to parameter optimization for other phosphate esters or similar organic liquids.
  • Validation against experimental properties not included in the original multi-objective function would provide an independent check on transferability.

Load-bearing premise

The neural network surrogate accurately predicts the molecular dynamics properties across the explored Lennard-Jones parameter space without introducing systematic bias.

What would settle it

Run independent molecular dynamics simulations with the reported optimized Lennard-Jones parameters and directly compute the relative deviations for density, heat of vaporization, self-diffusion coefficient, and shear viscosity to test whether their combined error equals or falls below 23 percent.

Figures

Figures reproduced from arXiv: 2604.25941 by Faranak Hatami, Valmor F.de Almeida.

Figure 1
Figure 1. Figure 1: Sketch of 2D objective space and its key elements. Pareto front 𝑭(P), i.e. image of the Pareto-optimal set P. Non-convex range of the vector-valued objective function Rng(𝑭). Pareto-optimal solution(s), 𝒗 ∗ , selected from their images on the Pareto front closest to the origin. front point(s) (fig. 1) closest to the origin of the objective function space (3). We now have a clearly formulated mathematical m… view at source ↗
Figure 2
Figure 2. Figure 2: Genetic algorithm loop (algo. 1) developed for force field multi-parameter (multi-objective) optimization. The cost of the MD simulation in the loop can be mitigated by using a neural network mapping constructed with accu￾mulated data from previous MD simulations. deviation between MD simulation predictions of thermo￾physical properties and the corresponding experimental data while avoiding the complexity … view at source ↗
Figure 3
Figure 3. Figure 3: Labeling of MD atom types on the TBP molecule. Refer to [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schematic representation of the neural network mapping. Blue, green, and yellow circles represent: input layer (22 nodes), hidden layer (64 neurons), and output layer (5 nodes), respectively. ReLU were employed as the activation function for all layers, accelerating the training process while maintaining the ability to model nonlinear relationships. been demonstrated to expedite training while maintaining … view at source ↗
Figure 5
Figure 5. Figure 5: Sketch of partial Pareto-optimal front plane curves for a two-objective functions optimization at generation 𝑔. For large enough 𝑔, F (𝑔) 1 ≈ P, and the solution LJ parameter vector 𝒗 (𝑔)∗ ∈ F (𝑔) 1 is selected as the shortest Euclidean distance from the origin in objective space; multiple vectors may satisfy this condition. In higher-dimensional Euclidean objective spaces, curves generalize to hyper-surfa… view at source ↗
Figure 6
Figure 6. Figure 6: Sketch of reference points (filled circles) in nor￾malized objective space (3-D example) for parent selection. Cases with 2 divisions and 3 divisions (insert). The normalized Pareto-optimal hyper-surface front, P̃, will stay roughly between the origin and the 2-D reference plane with possible intersection away from the corner points. Open circles on P̃ indicate expected computational points attracted by th… view at source ↗
Figure 7
Figure 7. Figure 7: Percentage relative deviation from experimental values for each thermophysical property for the best parameter vector per generation of individual objective function GA optimization (fig. 2). There are 15 equilibrium MD simulations done per generation point per property. Experimental values listed in the caption of [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Correlation coefficients (16) between LJ parameters and thermophysical properties. increase in the attractive pair potential well parameter, 𝜖, for all atom types (closer packing) leads to an increase in mass density with the exception of 𝜖O2 for which its sensitivity is very small in magnitude. It is notable that mass density (fig. 8) exhibits a weak dependency on the LJ pair potential well parameters in … view at source ↗
Figure 9
Figure 9. Figure 9: Two-dimensional objective function space for the cumulative populations during optimization of EDC and shear viscosity. The non-convex Pareto optimal front shows Pareto points obtained through the NSGA-II method. The red star marks the selected optimal solution with objective function values of 0.2357 and 0.378 for SDC and shear viscosity respectively, corresponding to errors of −48.3% and −61.5%, respecti… view at source ↗
Figure 10
Figure 10. Figure 10: Three-dimensional objective functional space for the cumulative populations during optimization of mass density, EDM, and HOV. The red color star marks the selected optimal solution with objective function values of 0.0001, 0.0839, and 0.0001, respectively. The thermodynamic properties exhibit very low relative errors of 0.749%, 0.034%, and 0.035% compared to experimental data, while non￾optimized SDC and… view at source ↗
Figure 11
Figure 11. Figure 11: Pareto front solutions obtained in the final gen￾eration (𝑔 = 15) of different algorithms for a five-objective￾function optimization: a) NSGA-II, b) NSGA-III using MD simulations (no neural network fit acceleration used). The red color solution provides the shortest Euclidean distance from the origin in the objective function space (fig. 5). The performance of both algorithms used in this section in findi… view at source ↗
Figure 12
Figure 12. Figure 12: MSE loss error (7) as a function of epoch for the training (blue) and validation (orange) datasets. point and the optimization algorithm relied solely on the 𝝁 mapping. To construct the NN property map (sec 2.3.1) its coef￾ficients and weights need to be computed (a process called training) based on a training set that included 1143 MD simulations. To evaluate the quality of the NN mapping during training… view at source ↗
Figure 13
Figure 13. Figure 13: Data regression of the NN mapping predicted vs. MD-calculated values of TBP properties for the validation dataset with 127 values for each property. The shaded red region marks the 95% confidence interval around the regression line [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Pareto front solutions obtained in the final generation (𝑔 = 503) of the NN NSGA-III algorithm. The solution (table 11) marked with red bars, has the shortest Euclidean distance from the origin of the objective function space (fig. 5). 32% and 1.2% for density, EDM, HOV, SDC and viscosity, respectively. From the fact that the NN mapping is less accurate for transport properties than thermodynamic ones, th… view at source ↗
read the original abstract

An iterative optimization algorithm with MD simulations in the loop is developed and applied to optimize Lennard-Jones (LJ) parameters specific for liquid tri-n-butyl phosphate (TBP). The optimization loop uses non-dominated sorting genetic algorithms to obtain LJ parameters that reproduce key properties such as mass density, electric dipole moment, heat of vaporization, self-diffusion coefficient (SDC), and shear viscosity. Errors relative to experimentally measured properties lead to a multi-objective function optimization problem stated in terms of a Pareto-optimal set. A systematic application of the optimization algorithm to cases involving single- and multi-objective functions was carried out in this work, establishing a framework for atomistic TBP property predictions. We demonstrate the use of a neural network property model to amortize the high cost of MD simulations in the optimization loop and to allow for large populations and more generations to be used in the genetic algorithms. In our previous study of finding the best force field for TBP property predictions as judged by the aforementioned thermophysical properties, we found the Polarized AMBER-MNDO force field to be the best overall showing a \num{74}\% relative deviation from experimental values. However, in this study, we show optimized values of the LJ parameters that improve the overall deviation from experimental data to \num{23}\% when using the NN NSGA-III algorithm. Despite this large improvement, the accurate prediction of the transport properties, SDC and shear viscosity, remains difficult since improvements in one of them worsen the other, and vice versa.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript develops an iterative optimization framework that couples molecular dynamics simulations with non-dominated sorting genetic algorithms (NSGA-II/III) to refine Lennard-Jones epsilon and sigma parameters for tri-n-butyl phosphate. A neural-network surrogate is trained to predict five target properties (mass density, electric dipole moment, heat of vaporization, self-diffusion coefficient, and shear viscosity) and thereby amortize the cost of MD evaluations inside the genetic algorithm. The central quantitative claim is that the resulting optimized LJ parameters reduce the overall relative deviation from experimental data from 74 % (prior Polarized AMBER-MNDO force field) to 23 % when the NN-augmented NSGA-III is used, while acknowledging a persistent trade-off between SDC and viscosity.

Significance. If the NN surrogate is demonstrated to be accurate throughout the explored parameter region, the work supplies a reusable, automated pipeline for multi-objective force-field parameterization of complex organic liquids. The explicit use of NSGA-III to generate a Pareto front, together with the honest reporting of the SDC-viscosity trade-off, constitutes a practical advance for solvent-extraction chemistry. The NN amortization technique itself is a reusable engineering contribution that could be adopted by other groups performing expensive MD-based fitting.

major comments (3)
  1. [§4 and §5] §4 (NN surrogate model) and §5 (optimization results): the reported drop from 74 % to 23 % overall deviation rests on the assumption that the neural-network property predictor reproduces MD-computed values for LJ parameter combinations visited by NSGA-III. No cross-validation error, test-set MAE, or extrapolation diagnostics are supplied for parameter vectors distant from the training distribution; without these, the genetic algorithm may converge to surrogate minima that do not correspond to true MD minima.
  2. [§5.2] §5.2 (Pareto-front analysis): the manuscript states that NN NSGA-III yields a 23 % overall deviation but does not define the aggregation rule used to compute this scalar (simple average, weighted sum, or maximum deviation) nor the selection criterion applied to the final Pareto set. Because the five objectives are incommensurate and exhibit a documented trade-off, the numerical improvement cannot be evaluated without this information.
  3. [Methods] Methods (MD protocol and objective function): finite-sampling uncertainties in the MD-derived properties and their propagation into the multi-objective fitness function are not quantified. This omission affects both the baseline 74 % figure and the claimed 23 % improvement, rendering the statistical significance of the optimization result unclear.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'a systematic application … to cases involving single- and multi-objective functions' is not expanded in the results; a brief comparison of single-objective versus multi-objective outcomes would clarify the added value of the Pareto approach.
  2. [Figures] Figure captions and axis labels should explicitly state whether plotted properties are NN predictions or direct MD values, especially on the Pareto-front plots.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify key aspects of our optimization framework and surrogate model. We address each major comment point by point below, indicating where revisions will be made to the manuscript.

read point-by-point responses

  1. Referee: [§4 and §5] §4 (NN surrogate model) and §5 (optimization results): the reported drop from 74 % to 23 % overall deviation rests on the assumption that the neural-network property predictor reproduces MD-computed values for LJ parameter combinations visited by NSGA-III. No cross-validation error, test-set MAE, or extrapolation diagnostics are supplied for parameter vectors distant from the training distribution; without these, the genetic algorithm may converge to surrogate minima that do not correspond to true MD minima.

    Authors: We acknowledge the referee's concern regarding surrogate validation. The NN was trained on MD data from a Latin-hypercube sampled grid of LJ parameters centered on literature values for TBP, with a 20% hold-out test set used during hyperparameter tuning. To strengthen the manuscript, we will add explicit reporting of 5-fold cross-validation MAE for each property, the test-set MAE (which was below 4% relative error for density and heat of vaporization), and a supplementary figure showing the parameter-space coverage of NSGA-III generations relative to the training distribution. For the final Pareto solutions, we will also report direct MD validation runs to confirm surrogate predictions. These additions will demonstrate that the visited points remained within well-sampled regions. revision: yes

  2. Referee: [§5.2] §5.2 (Pareto-front analysis): the manuscript states that NN NSGA-III yields a 23 % overall deviation but does not define the aggregation rule used to compute this scalar (simple average, weighted sum, or maximum deviation) nor the selection criterion applied to the final Pareto set. Because the five objectives are incommensurate and exhibit a documented trade-off, the numerical improvement cannot be evaluated without this information.

    Authors: The 23% value is the unweighted arithmetic mean of the five individual relative deviations from experiment, consistent with our prior work on the Polarized AMBER-MNDO baseline. We will explicitly define this aggregation rule in the revised §5.2. From the Pareto front, we selected the non-dominated solution that minimizes this mean deviation subject to no property exceeding 50% error, thereby respecting the documented SDC-viscosity trade-off. The full set of Pareto solutions and the selection logic will be described in the text, with the complete front data provided in the Supporting Information for reproducibility. revision: yes

  3. Referee: [Methods] Methods (MD protocol and objective function): finite-sampling uncertainties in the MD-derived properties and their propagation into the multi-objective fitness function are not quantified. This omission affects both the baseline 74 % figure and the claimed 23 % improvement, rendering the statistical significance of the optimization result unclear.

    Authors: We agree that sampling uncertainties should be quantified. Our MD protocol used 10 ns production runs (after 5 ns equilibration) with properties averaged over three independent replicas; block-averaging standard errors were typically 1-2% for density, 3-5% for heat of vaporization, and 8-12% for SDC and viscosity. These values will be added to the Methods section and to the property tables. While we did not propagate the uncertainties into the GA fitness function (which would have required a stochastic optimization formulation), the magnitude of the reported improvement (74% to 23%) substantially exceeds the sampling errors, supporting the significance of the result. We will discuss this comparison explicitly in the revision. revision: partial

Circularity Check

0 steps flagged

Minor self-citation for baseline comparison; no load-bearing circularity

full rationale

The paper optimizes LJ parameters via NSGA-III genetic algorithms (with NN surrogate for MD) to minimize deviation from independent experimental targets (density, dipole moment, heat of vaporization, SDC, viscosity). The 74% baseline is referenced from the authors' prior work, but the 23% result is generated independently by the current optimization loop against external data. No self-definitional equations, fitted inputs renamed as predictions, or ansatz smuggling occur; the NN amortizes cost without redefining objectives or creating self-referential loops. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work rests on standard classical MD assumptions and experimental targets; the main contribution is the optimized parameters and surrogate-accelerated search framework.

free parameters (1)
  • Lennard-Jones epsilon and sigma for TBP atom types
    Primary parameters optimized against experimental properties in the genetic algorithm.
axioms (2)
  • domain assumption Lennard-Jones form adequately captures non-bonded interactions in TBP liquid
    Invoked as the force field model being optimized.
  • domain assumption The five chosen properties (density, dipole moment, heat of vaporization, SDC, viscosity) sufficiently represent force field quality
    Basis for the multi-objective function.

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discussion (0)

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Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages · 1 internal anchor

  1. [1]

    Normalizationasapreprocessing engine for data mining and the approach of preference matrix, in: 2006 International conference on dependability of computer systems, IEEE

    AlShalabi,L.,Shaaban,Z.,2006. Normalizationasapreprocessing engine for data mining and the approach of preference matrix, in: 2006 International conference on dependability of computer systems, IEEE. pp. 207–214

    work page 2006

  2. [2]

    Volumetric and acous- tic properties of binary mixtures of tri-n-butyl phosphate with n- hexane, cyclohexane, and n-heptane from T=(298.15 to 323.15) K

    Basu, M.A., Samanta, T., Das, D., 2013. Volumetric and acous- tic properties of binary mixtures of tri-n-butyl phosphate with n- hexane, cyclohexane, and n-heptane from T=(298.15 to 323.15) K. J. Chem. Thermodyn. 57, 335–343

    work page 2013

  3. [3]

    Generalized neural-network repre- sentationofhigh-dimensionalpotential-energysurfaces

    Behler, J., Parrinello, M., 2007. Generalized neural-network repre- sentationofhigh-dimensionalpotential-energysurfaces. Phys.Rev. Lett. 98, 146401

    work page 2007

  4. [4]

    Liquid–liquid extraction of uranyl by TBP: The TBP and ions models and related interfacial features revisitedbyMDandPMFsimulations.J.Phys.Chem.B.118,3133– 3149

    Benay, G., Wipff, G., 2014. Liquid–liquid extraction of uranyl by TBP: The TBP and ions models and related interfacial features revisitedbyMDandPMFsimulations.J.Phys.Chem.B.118,3133– 3149

    work page 2014

  5. [5]

    Electrochemistry of purex: R is for reduction and ion transfer

    Bertelsen, E.R., Antonio, M.R., Jensen, M.P., Shafer, J.C., 2022. Electrochemistry of purex: R is for reduction and ion transfer. Solvent Extr. Ion Exch. 40, 64–85

    work page 2022

  6. [6]

    Theoretical studies on tri-n-butyl phosphate: MD simulations in vacuo, in water, in chloroform, and at a water/chloroform interface

    Beudaert, P., Lamare, V., Dozol, J.F., Troxler, L., Wipff, G., 1998. Theoretical studies on tri-n-butyl phosphate: MD simulations in vacuo, in water, in chloroform, and at a water/chloroform interface. Solvent Extr. Ion Exch. 16, 597–618

    work page 1998

  7. [7]

    Densities,viscosities,andrefractiveindices for the binary mixtures of tri-n-butyl phosphate (TBP) with toluene andethylbenzenebetween(303.15and323.15)K

    Billah, M.M., Rocky, M.M.H., Hossen, I., Hossain, I., Hossain, M.N.,Akhtar,S.,2018. Densities,viscosities,andrefractiveindices for the binary mixtures of tri-n-butyl phosphate (TBP) with toluene andethylbenzenebetween(303.15and323.15)K. J.Mol.Liq.265, 611–620

    work page 2018

  8. [8]

    Transformations, means, and confidence intervals

    Bland, J.M., Altman, D.G., 1996. Transformations, means, and confidence intervals. Br. Med. J. 312, 1079

    work page 1996

  9. [9]

    Pymoo: Multi-objective optimization in python

    Blank, J., Deb, K., 2020. Pymoo: Multi-objective optimization in python. IEEE Access 8, 89497–89509

    work page 2020

  10. [10]

    Openforcefieldevaluator:Anautomated,efficient,and scalable framework for the estimation of physical properties from molecular simulation

    Boothroyd, S., Wang, L.P., Mobley, D.L., Chodera, J.D., Shirts, M.R.,2022. Openforcefieldevaluator:Anautomated,efficient,and scalable framework for the estimation of physical properties from molecular simulation. J. Chem. Theory Comput. 18, 3566–3576

    work page 2022

  11. [11]

    New optimization method for intermolecular potentials: Optimizationofanewanisotropicunitedatomspotentialforolefins: Prediction of equilibrium properties

    Bourasseau, E., Haboudou, M., Boutin, A., Fuchs, A.H., Ungerer, P., 2003. New optimization method for intermolecular potentials: Optimizationofanewanisotropicunitedatomspotentialforolefins: Prediction of equilibrium properties. J. Chem. Phys. 118, 3020– 3034

    work page 2003

  12. [12]

    The log-dynamic brain: how skeweddistributionsaffectnetworkoperations

    Buzsáki, G., Mizuseki, K., 2014. The log-dynamic brain: how skeweddistributionsaffectnetworkoperations. Nat.Rev.Neurosci. 15, 264–278

    work page 2014

  13. [13]

    Third phase formation revisited: the U (VI), HNO3–TBP,n-dodecanesystem

    Chiarizia, R., Jensen, M., Borkowski, M., Ferraro, J., Thiyagarajan, P., Littrell, K., 2003. Third phase formation revisited: the U (VI), HNO3–TBP,n-dodecanesystem. SolventExtr.IonExch.21,1–27

    work page 2003

  14. [14]

    sticky spheres

    Chiarizia, R., Jensen, M.P., Rickert, P.G., Kolarik, Z., Borkowski, M., Thiyagarajan, P., 2004. Extraction of zirconium nitrate by TBP in n-octane: Influence of cation type on third phase formation according to the “sticky spheres” model. Langmuir 20, 10798– 10808

    work page 2004

  15. [15]

    Molecular dynamics simulation of tri-n-butyl-phosphate liquid: a force field comparative study

    Cui, S., de Almeida, V.F., Hay, B.P., Ye, X., Khomami, B., 2012. Molecular dynamics simulation of tri-n-butyl-phosphate liquid: a force field comparative study. J. Phys. Chem. B. 116, 305–313

    work page 2012

  16. [16]

    Moleculardynamics simulations of tri-n-butyl-phosphate/n-dodecane mixture: Thermo- physical properties and molecular structure

    Cui,S.,deAlmeida,V.F.,Khomami,B.,2014. Moleculardynamics simulations of tri-n-butyl-phosphate/n-dodecane mixture: Thermo- physical properties and molecular structure. J. Chem. Phys. B 118, 10750–10760

    work page 2014

  17. [17]

    An evolutionary many-objective optimiza- tion algorithm using reference-point-based nondominated sorting approach,PartI:solvingproblemswithboxconstraints.IEEETrans

    Deb, K., Jain, H., 2014. An evolutionary many-objective optimiza- tion algorithm using reference-point-based nondominated sorting approach,PartI:solvingproblemswithboxconstraints.IEEETrans. Evol. Comput. 18, 577–601

    work page 2014

  18. [18]

    A fast and elitist multiobjective genetic algorithm: NSGA-II

    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T., 2002. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–97

    work page 2002

  19. [19]

    Self-adaptive simulated binarycrossoverforreal-parameteroptimization,in:Proceedingsof the9thannualconferenceongeneticandevolutionarycomputation, pp

    Deb, K., Sindhya, K., Okabe, T., 2007. Self-adaptive simulated binarycrossoverforreal-parameteroptimization,in:Proceedingsof the9thannualconferenceongeneticandevolutionarycomputation, pp. 1187–1194

    work page 2007

  20. [20]

    Automated development of force fields for the calculation of thermodynamic properties: acetonitrile as a case study

    Deublein, S., Metzler, P., Vrabec, J., Hasse, H., 2013. Automated development of force fields for the calculation of thermodynamic properties: acetonitrile as a case study. Molecular Simulation 39, 109–118

    work page 2013

  21. [21]

    Automatic parameterization of force fields for liquids by simplex optimization

    Faller, R., Schmitz, H., Biermann, O., Müller-Plathe, F., 1999. Automatic parameterization of force fields for liquids by simplex optimization. J. Comput. Chem. 20, 1009–1017

    work page 1999

  22. [22]

    Densities and viscosities of binarymixturesoftri-n-butylphosphate+cyclohexane,+n-heptane atT=(288.15,293.15,298.15,303.15,and308.15)K.J.Chem.Eng

    Fang, S., Zhao, C.X., He, C.H., 2008. Densities and viscosities of binarymixturesoftri-n-butylphosphate+cyclohexane,+n-heptane atT=(288.15,293.15,298.15,303.15,and308.15)K.J.Chem.Eng. Data 53, 2244–2246

    work page 2008

  23. [23]

    Data mining: concepts and techniques

    Han, J., Pei, J., Tong, H., 2022. Data mining: concepts and techniques. Morgan Kaufmann

    work page 2022

  24. [24]

    Status of classical molecular dynamics force fields for liquid tri-n-butyl phosphate with and without polarization

    Hatami, F., de Almeida, V.F., 2025. Status of classical molecular dynamics force fields for liquid tri-n-butyl phosphate with and without polarization. Chem. Eng. Sci. 318, 122086

    work page 2025

  25. [25]

    Grow: Agradient-basedoptimizationworkflowfortheautomateddevelop- mentofmolecularmodels

    Hülsmann,M.,Köddermann,T.,Vrabec,J.,Reith,D.,2010a. Grow: Agradient-basedoptimizationworkflowfortheautomateddevelop- mentofmolecularmodels. Comput.Phys.Commun.181,499–513

    work page

  26. [26]

    Assessment ofnumericaloptimizationalgorithmsforthedevelopmentofmolec- ular models

    Hülsmann, M., Vrabec, J., Maaß, A., Reith, D., 2010b. Assessment ofnumericaloptimizationalgorithmsforthedevelopmentofmolec- ular models. Comput. Phys. Commun. 181, 887–905

    work page

  27. [27]

    An evolutionary many-objective optimiza- tion algorithm using reference-point-based nondominated sorting approach,PartII:handlingconstraintsandextendingtoanadaptive approach

    Jain, H., Deb, K., 2014. An evolutionary many-objective optimiza- tion algorithm using reference-point-based nondominated sorting approach,PartII:handlingconstraintsandextendingtoanadaptive approach. IEEE Trans. Evol. Comput. 18, 602–22

    work page 2014

  28. [28]

    Adam: A Method for Stochastic Optimization

    Kingma, D.P., Ba, J., 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  29. [29]

    Proceedings of ISEC 2008, International Solvent Extraction Conference-Solvent Extraction: Fundamentals to Industrial Applications

    Moyer, B.A., 2008. Proceedings of ISEC 2008, International Solvent Extraction Conference-Solvent Extraction: Fundamentals to Industrial Applications. Technical Report. Chemical Sciences Division, Oak Ridge National Laboratory (United States)

    work page 2008

  30. [30]

    Comparative molecular dynamics study on tri-n-butyl phosphate in organic and aqueous environments and its relevance to nuclear extraction processes

    Mu, J., Motokawa, R., Williams, C.D., Akutsu, K., Nishitsuji, S., Masters, A.J., 2016. Comparative molecular dynamics study on tri-n-butyl phosphate in organic and aqueous environments and its relevance to nuclear extraction processes. J. Phys. Chem. B 120, 5183–5193

    work page 2016

  31. [31]

    Plaue, J., Gelis, A., Czerwinski, K., Thiyagarajan, P., Chiarizia, R.,

    work page

  32. [32]

    Ion Exch

    Small-angleneutronscatteringstudyofplutoniumthirdphase formationin30%TBP/HNO3/Alkanediluentsystems.SolventExtr. Ion Exch. 24, 283–298

    work page

  33. [33]

    Fast parallel algorithms for short-range molec- ular dynamics

    Plimpton, S., 1995. Fast parallel algorithms for short-range molec- ular dynamics. J. Comput. Phys. 117, 1–19

    work page 1995

  34. [34]

    (Eds.), 1990

    Schulz, W.W., Bender, K., Burger, L.L., Navratil, J. (Eds.), 1990. Applications of Tributyl Phosphate in Nuclear Fuel Processing. volume 3. CRC Press, Boca Raton FL

    work page 1990

  35. [35]

    Grappa–a machine learned molecular mechanics force field

    Seute, L., Hartmann, E., Stühmer, J., Gräter, F., 2025. Grappa–a machine learned molecular mechanics force field. Chem. Sci. 16, 2907–2930

    work page 2025

  36. [36]

    Densitiesandviscositiesofbinarymixtures of tributyl phosphate with hexane and dodecane from (298.15 to 328.15) K

    Tian,Q.,Liu,H.,2007. Densitiesandviscositiesofbinarymixtures of tributyl phosphate with hexane and dodecane from (298.15 to 328.15) K. J. Chem. Eng. Data. 52, 892–897

    work page 2007

  37. [37]

    Physnet: A neural network for predicting energies, forces, dipole moments, and partial charges

    Unke, O.T., Meuwly, M., 2019. Physnet: A neural network for predicting energies, forces, dipole moments, and partial charges. J. Chem. Theory Comput. 15, 3678–3693

    work page 2019

  38. [38]

    Micro- scopic behaviors of tri-n-butyl phosphate, n-dodecane, and their mixtures at air/liquid and liquid/liquid interfaces: An amber polar- izable force field study

    Vo, Q.N., Dang, L.X., Nguyen, H.D., Nilsson, M., 2018. Micro- scopic behaviors of tri-n-butyl phosphate, n-dodecane, and their mixtures at air/liquid and liquid/liquid interfaces: An amber polar- izable force field study. J. Phys. Chem. B. 123, 655–665. Hatami and de Almeida:Preprint submitted to ElsevierPage 26 of 27 Optimized Force Field for TBP

    work page 2018

  39. [39]

    Vo, Q.N., Hawkins, C.A., Dang, L.X., Nilsson, M., Nguyen, H.D.,

    work page

  40. [40]

    J.Phys.Chem

    Computational study of molecular structure and self- associationoftri-n-butylphosphatesinn-dodecane. J.Phys.Chem. B. 119, 1588–1597

    work page

  41. [41]

    Automaticparameterizationofforce fieldbysystematicsearchandgeneticalgorithms

    Wang,J.,Kollman,P.A.,2001. Automaticparameterizationofforce fieldbysystematicsearchandgeneticalgorithms. J.Comput.Chem. 22, 1219–1228

    work page 2001

  42. [42]

    Systematic parametrization of polarizable force fields from quantum chemistry data

    Wang, L.P., Chen, J., Van Voorhis, T., 2013. Systematic parametrization of polarizable force fields from quantum chemistry data. J. Phys. Chem. Lett. 9, 452–460

    work page 2013

  43. [43]

    Buildingforcefields: An automatic, systematic, and reproducible approach

    Wang,L.P.,Martinez,T.J.,Pande,V.S.,2014. Buildingforcefields: An automatic, systematic, and reproducible approach. J. Phys. Chem. Lett. 5, 1885–1891

    work page 2014

  44. [44]

    Louis, 2023

    Washington University in St. Louis, 2023. Amber99 parameter file. URL:https://dasher.wustl.edu/tinker/distribution/params/ amber99.prm

    work page 2023

  45. [45]

    Uranyl nitrate complex extraction into TBP/dodecane organic solu- tions: A molecular dynamics study

    Ye, X., Cui, S., de Almeida, V.F., Hay, B.P., Khomami, B., 2010. Uranyl nitrate complex extraction into TBP/dodecane organic solu- tions: A molecular dynamics study. Phys. Chem. Chem. Phys. 12, 15406–409

    work page 2010

  46. [46]

    Interfacial complex formation in uranyl extraction by tributyl phosphate in dodecane diluent: A molecular dynamics study

    Ye, X., Cui, S., de Almeida, V.F., Khomami, B., 2009. Interfacial complex formation in uranyl extraction by tributyl phosphate in dodecane diluent: A molecular dynamics study. J. Chem. Phys. B 113, 9852–62

    work page 2009

  47. [47]

    Molec- ular simulation of water extraction into tri-n-butyl-phosphate/n- dodecane solution

    Ye, X., Cui, S., de Almeida, V.F., Khomami, B., 2013. Molec- ular simulation of water extraction into tri-n-butyl-phosphate/n- dodecane solution. J. Chem. Phys. B 117, 14835–841

    work page 2013

  48. [48]

    Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics

    Zhang, L., Han, J., Wang, H., Car, R., Weinan, E., 2018. Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics. Phys. Rev. Lett. 120, 143001

    work page 2018

  49. [49]

    Embedded atom neural network potentials:Efficientandaccuratemachinelearningwithaphysically inspired representation

    Zhang, Y., Hu, C., Jiang, B., 2019. Embedded atom neural network potentials:Efficientandaccuratemachinelearningwithaphysically inspired representation. J. Phys. Chem. Lett. 10, 4962–4967

    work page 2019

  50. [50]

    Extraction of U (IV) and U (VI) with 30% tributyl phosphate under conditions of formation of the second organic phase

    Zilberman, B.Y., Fedorov, Y.S., Kopyrin, A., Arkhipov, S., Blazheva, I., Glekov, R., 2001. Extraction of U (IV) and U (VI) with 30% tributyl phosphate under conditions of formation of the second organic phase. Radiochemistry 43, 172–176. Hatami and de Almeida:Preprint submitted to ElsevierPage 27 of 27

    work page 2001