Pith. sign in

REVIEW 3 major objections 6 minor 40 references

Autodifferentiable Geometric Restraints for Enhanced Sampling Simulations with Classical and Machine Learned Force Fields

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A gradient correction removes restraint bias from free-energy simulations.

desk verdict Useful PySAGES implementation and solid benchmarks, but the paper overclaims Eq. 5's validity for arbitrary restraints; the derivation only supports CV-dependent restraints, and the funnel applications rely on separate volume corrections. read the letter →

arxiv 2504.13575 v1 pith:S6GXUHIR submitted 2025-04-18 physics.comp-ph

Gustavo R. Pérez-Lemus , Cintia A. Menendez , Yinan Xu , Pablo F. Zubieta Rico , Yezhi Jin , Juan J. de Pablo This is my paper · ORCID
classification physics.comp-ph
keywords autodifferentiablerestraintsadaptivebiasingforcefreeenergycorrectioncollectivevariablesmachinelearnedfieldsbindingenhancedsamplinggeometric
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that any smooth geometric restraint can be added to an adaptive-biasing-force free-energy calculation and its effect removed exactly with a correction built from the restraint's gradient. If correct, this would let simulations use complex, physically motivated restraints — funnel shapes, RMSD anchors, confinement walls — to speed up sampling without distorting the final free-energy landscape, in both classical and machine-learned force fields. The authors demonstrate the correction on alanine dipeptide, a host–guest binding complex, a protein–ligand benchmark, and methane activation on a nickel surface, reporting binding free energies close to experiment and faster convergence than unrestrained methods.

What carries the argument

The load-bearing object is the gradient-correction identity $\nabla_\xi A = \nabla_\xi A' + \langle \nabla U_R \cdot w \rangle_\xi$, derived from the Darve et al. ABF force expression. It states that the biased thermodynamic force differs from the unbiased force only by the biased-ensemble average of the restraint gradient contracted with the mass-scaled Jacobian $w$ of the coordinate transformation. Because this term is accumulated in the same way as the ABF force, no reweighting or additional sampling is needed: the restraint merely reshapes the biased distribution while the true free-energy gradient is recovered from the accumulated correction, provided the restraint is differentiable so that its gradient can be computed by automatic differentiation.

What would settle it

Take a model where a restraint depends on a coordinate orthogonal to the sampled collective variable, run a biased simulation, apply only Eq. 5, and compare the corrected free-energy profile to a long unbiased reference simulation; if the profiles differ beyond statistical error, the claim that any differentiable restraint can be removed by Eq. 5 is falsified.

Watch

Extended reading notes

Core claim

The central claim is that the identity $\nabla_\xi A = \nabla_\xi A' + \langle \nabla U_R \cdot w \rangle_\xi$ removes the contribution of an external restraint $U_R$ from a biased ABF simulation, yielding the unbiased free-energy gradient $\nabla_\xi A$. Here $w$ is the mass-scaled Jacobian of the collective-variable transformation and the average is taken in the biased ensemble; in practice, the correction term is accumulated on the fly just like the biasing force itself. The authors assert that because the restraint only needs to be a differentiable function of the coordinates, automatic differentiation makes the method applicable to arbitrary geometric restraints and to machine-learned force fields. They show the recovery of the correct free-energy surface for alanine dipeptide in both classical and implicit MLFF forms, and they use funnel-shaped restraints to accelerate binding free-energy calculations for a host–guest complex and a trypsin–benzamidine benchmark, plus a catalytic methane-on-nickel system where restraint geometry reveals an entropic contribution.

Load-bearing premise

The correction is derived under the assumption that the restraint's effect is captured by its gradient along the sampled collective variables; when the restraint also pushes on directions that are not sampled, the unbiased and biased ensembles differ in ways Eq. 5 alone does not fix, so the paper must rely on separate volume corrections.

Editorial extensions

If this is right

  • Geometric restraints can be used freely with ABF-family methods, since the unbiased free-energy surface is recovered by adding the accumulated restraint-gradient term.
  • The same correction works for machine-learned force fields, where automatic differentiation of the restraint is straightforward, making it practical to combine MLFFs with complex spatial restraints in binding and catalysis simulations.
  • Funnel-shaped restraints can accelerate convergence of absolute binding free energies, matching experimental values with shorter simulation times and, in some cases, a single exploratory collective variable.
  • The restraint-radius dependence observed in methane activation suggests that geometric restraints can be used to probe entropic contributions by selectively freezing or permitting motion of particular atoms.
  • Because the correction is accumulated on the fly, it adds negligible overhead to existing ABF implementations and extends naturally to neural-network and spectral-decomposition variants.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same gradient-correction idea may transfer to other bias-based enhanced sampling methods, such as metadynamics or umbrella sampling, whenever the restraint is differentiable in the sampled coordinates, though each method would need its own reweighting or on-the-fly correction scheme.
  • One testable extension is to define restraints through a neural network itself — for example, a learned funnel shape or a learned confining boundary — since automatic differentiation already supplies the needed gradients.
  • The paper's broad statement that any differentiable restraint can be corrected by Eq. 5 goes beyond the derivation when the restraint acts on coordinates orthogonal to the sampled collective variable; in such cases the unbiased and biased ensembles differ in ways that likely require the separate volume corrections the authors apply for funnel restraints.
  • A direct numerical test could quantify how large the orthogonal-restraint error becomes: run a biased simulation with a restraint on an unsampled coordinate, apply only Eq. 5, and compare against a long unbiased reference.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper introduces the use of general, autodifferentiable geometric restraints within the ABF family of enhanced sampling methods implemented in the PySAGES library, with support for classical and machine-learned force fields. The central theoretical claim is Eq. (5): if a restraint potential U_R is added to the physical potential, the unbiased free energy gradient can be recovered from the biased simulation by adding the average force contribution ⟨∇U_R·w⟩_ξ. The authors demonstrate the approach on four systems: alanine dipeptide in explicit water and in a coarse-grained MLFF (where the restraint is a function of the sampled dihedrals), CB8–G6 host–guest binding with a funnel restraint, trypsin–benzamidine binding with an RMSD plus funnel restraint, and methane activation on Ni(111) with positional restraints on atoms. Free-energy profiles and binding free energies are compared with experimental values and previous OneOPES/metadynamics results, and convergence improvements are reported, particularly for Spectral ABF.

Significance. If the central claim is valid, the paper offers a practically useful contribution: it extends the set of restraint potentials that can be combined with advanced sampling in a differentiable and GPU-friendly way, and it provides benchmarks showing competitive or improved convergence for binding free-energy calculations. The explicit integration with machine-learned force fields is timely, and the use of automatic differentiation simplifies the implementation of complex restraint geometries. The paper also makes good use of external references for experimental and prior computational values in the CB8 and trypsin benchmarks. However, the theoretical generality claimed in Section 2 is broader than what the derivation actually supports: Eq. (5) is exact only when the restraint depends solely on the sampled collective variables, not for arbitrary differentiable functions of all coordinates. The practical demonstrations that use restraints on orthogonal degrees of freedom (funnel and positional restraints) rely on separate volume corrections or do not attempt to remove the restraint bias at all.

major comments (3)
  1. [Sec. 2, Eqs. (4)-(5)] The step from Eq. (4) to Eq. (5) equates the conditional average over the biased configurational distribution with the conditional average over the unbiased distribution. This equality is exact only when U_R is constant on the ξ-fixed submanifold, i.e., when U_R = U_R(ξ). For a general differentiable restraint U_R(x) that depends on orthogonal degrees of freedom, the biased and unbiased conditional ensembles differ, and the averages differ by a factor involving the conditional mean of exp(-βU_R). Consequently, the sentence in Section 2 that "the external potential U_R can be any differentiable function of the coordinates" is not supported by the derivation. The ADP test (U_R(φ,ψ)) lies inside the validity domain, but the funnel restraint in Eq. (6) and the catalysis restraints in Eq. (13) depend on variables orthogonal to the sampled CVs. Please narrow the claim to CV-dependent restraints, or provide the corrected general expression (e.g., involving a conditional free-energy or Jacobian term) and state its domain of applicability.
  2. [Sec. 2.2, Eqs. (6)-(10)] For the CB8–G6 system, the funnel restraint U_R depends on ξ⊥, which is orthogonal to the sampled CV ξ∥. The paper correctly uses the volume correction formulas in Eqs. (8)-(10), but this is a different mechanism from Eq. (5). The text should clearly state that Eq. (5) does not apply to restraints on ξ⊥, and that the binding free energy is obtained by the standard cylindrical-restraint volume correction. Without this clarification, the reader may incorrectly infer that the numerical agreement in Table 1 validates Eq. (5) for arbitrary restraints.
  3. [Sec. 2.4, Eqs. (12)-(13)] The catalysis restraint acts on individual atomic coordinates z_i and r_i, not on the sampled collective variables (z and CN). The results in Fig. 4 show that when hydrogen atoms are restrained, the free-energy profile depends on the restraint radius, indicating that the restraint bias is not removed. If the intention is to claim that the general framework of Eq. (5) can recover an unbiased profile in the presence of such restraints, a demonstration is needed; if instead the restraint is used only to control sampling and probe entropic effects, the connection to Eq. (5) should be clarified or removed. As written, the section leaves open the question of which correction, if any, is being applied.
minor comments (6)
  1. [Abstract] Line: "given simulations" should be "given simulation".
  2. [Sec. 2, Eqs. (1)-(2)] The notation in Eq. (1) is unclear: the subscript on the ensemble average is not defined before use, and the quantity "w·p" is not clearly introduced as a scalar or tensor contraction. Please also check the sign convention against Darve et al. and define all symbols consistently.
  3. [Sec. 2.1, Fig. 1] The caption states that the classical and MLFF systems obtain the correct FES using Eq. (5), but the figure caption does not specify the grid resolution or the restraint parameters used; those details appear only later in Section 4.1. For reproducibility, it would be helpful to state them in the caption or refer explicitly to the Methods section.
  4. [Sec. 2.2, Fig. 2a] The caption uses "cylinder restrain"; likely "cylinder restraint" is intended.
  5. [Sec. 4.4, Eq. (18)] In the coordination number definition, r_ij is not defined. It should be explicitly stated that r_ij is the distance between the i-th hydrogen and the carbon atom, or otherwise clarified.
  6. [Sec. 4.4] The statement that "the mass of hydrogens was increased to 2 a.u." is a common trick for increasing the time step, but it changes the kinetic energy and possibly entropy. A brief comment on how this affects the reported free energies would be appropriate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the restraint correction (Eq. 5) is derived as a thermodynamic identity, and the benchmarks are grounded externally or by standard literature formulas; same-group MLFF citations are not load-bearing for the core derivation.

full rationale

The central free-energy correction is self-contained. Equations (1)-(5) are an algebraic manipulation of the Darve et al. ABF mean-force identity applied to the modified potential U' = U + U_R; the correction term <∇U_R·w>_xi is accumulated from the biased trajectory and is not fitted to the target free energy. The ADP 'recovery' benchmark therefore checks implementation and convergence rather than supplying the value of A, so it is not a fitted input presented as a prediction. The ADP MLFF is trained on forces from the same classical model, citing prior work by the same group [27]; that makes the MLFF demonstration an internal-consistency check, but it is not load-bearing for Eq. (5), which is an identity independent of the force-field functional form. The CB8-G6 and trypsin-benzamidine results are anchored to experimental binding free energies and to OneOPES/OPES literature values [30,34,35], and they use the standard funnel/volume corrections rather than Eq. (5) to obtain absolute binding free energies. The methane section uses the same group's earlier MLFF and entropy conclusion [36] as a qualitative comparison, not as the proof of the method. One scope caveat should be flagged: the sentence after Eq. (5) claiming U_R 'can be any differentiable function of the coordinates' is broader than the derivation supports, because Eq. (5) is exact as written when the average involves a well-defined conditional ensemble and is applied to restraints on the sampled collective variables; for orthogonal-degree-of-freedom restraints, such as the funnel restraint, the paper correctly uses the separate volume corrections in Eqs. (7)-(10). That is a correctness/validity caveat, not a circularity, so it does not raise the circularity score. No circular step exhibiting a reduction of the predicted quantity to the input was found.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central calculation relies on the standard ABF mean-force identity and on the assumption that the chosen CV captures the relevant physics. No new physical entities are introduced. The hand-chosen restraint parameters (amplitudes, funnel radii, force constants) affect the demonstrations but are not fit to the target free energies; R_cyl in the CB8 case is tuned using an unrestrained run of the same system. The MLFF models are imported from prior work by the authors and assume the trained potentials are accurate in the sampled regions.

free parameters (7)
  • ADP classical restraint amplitude = 20 kJ/mol
    Hand-chosen amplitude for U_R(φ, ψ) = 20(cos(2φ) + sin(2ψ)); affects the demonstrated correction but is not fit to a target.
  • ADP MLFF restraint amplitude = 0.3125 eV
    Hand-chosen amplitude for the implicit MLFF test; arbitrary scale.
  • CB8-G6 cylinder radius R_cyl = 0.2 nm
    Selected from unrestrained Spectral ABF runs to avoid perturbing the bound state; a data-driven protocol choice.
  • Trypsin RMSD restraint target ξ0 = 0.09
    Taken from the OneOPES repository, not fitted in this work.
  • Trypsin funnel force constants and shape parameters = k1 = 800,000 kJ/mol/nm^2, k2 = 10,000 kJ/mol/nm^2, Z0 = 0.4 nm, Rcyl = 0.2 nm
    Hand-chosen protocol parameters imported from the OneOPES setup.
  • Methane restraint force constant = 3 eV/Å^2
    Hand-chosen for C, H, and Ni restraints; affects the studied FEP dependence on restraint radius.
  • Methane z_max = 19 Å
    Chosen to prevent hydrogen atoms from crossing the Ni slab; simulation box height is 22.1 Å.
assumptions (5)
  • standard math ABF mean force identity from Darve et al.
    Eq. 2 is cited to Ref. [26] and not re-derived; the entire correction scheme builds on this identity.
  • domain assumption The sampled collective variable fully captures the free energy landscape of interest
    The binding free energy equations (8)-(10) assume the PMF along the funnel axis is sufficient; one-dimensional sampling in trypsin and CB8 relies on this.
  • domain assumption The machine-learned force fields are accurate in the sampled regions
    The ADP implicit MLFF and the Ni methane MLFF are taken from prior work [27, 36]; no error quantification is provided here.
  • domain assumption Eq. 5 with the correct sign is exact for restraints that depend only on the sampled CVs
    The ADP demonstration uses U_R(φ, ψ), so the correction is exact; the paper does not state this restriction in Sec. 2.
  • domain assumption The funnel volume correction V_bulk = ∫π f^2(ξ)dξ accurately accounts for the standard-state volume
    Eqs. 8-10 use this to convert restrained PMFs to absolute binding free energies, following the established funnel metadynamics approach.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Autodifferentiable Geometric Restraints for Enhanced Sampling Simulations with Classical and Machine Learned Force Fields." pith.science (2026). https://pith.science/paper/S6GXUHIR

@misc{pith2026250413575,
  author       = {Pith},
  title        = {Pith review of: Autodifferentiable Geometric Restraints for Enhanced Sampling Simulations with Classical and Machine Learned Force Fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S6GXUHIR}},
  note         = {Machine review of arXiv:2504.13575}
}
read the original abstract

The use of external restraints is ubiquitous in advanced molecular simulation techniques. In general, restraints serve to reduce the configurational space that is available for sampling, thereby reducing the computational demands associated with a given simulations. Examples include the use of positional restraints in docking simulations or positional restraints in studies of catalysis. Past work has sought to couple complex restraining potentials with enhanced sampling methods, including Metadynamics or Extended Adaptive Biasing Force approaches. Here, we introduce the use of more general geometric potentials coupled with enhanced sampling methods that incorporate neural networks or spectral decomposition to achieve more efficient sampling in the context of advanced materials design.

Figures

Figures reproduced from arXiv: 2504.13575 by the authors.

Figure 1
Figure 1. Geometric restraint application example. a) Alanine dipeptide in water is mod [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Geometric restraint simulations for the CB8–G6 system. a) Scheme of the geometric restraint and the cylindrical restrain used in the simulation with snapshot of the system capturing different rebinding events with the geometric restraint in PySAGES. b) Free energy profiles along the CV used at 300 ns of simulation, the bound and unbound interface regions are highlighted by orange lines. c) Unrestrained simulation wi… view at source ↗
Figure 3
Figure 3. Convergence in the free energy landscape of a Ligand-Protein complex. A) [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: External restraints in catalysis simulations for accelerate convergence and en [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

40 extracted references · 38 canonical work pages

  1. [1]

    Calculation of protein-ligand binding affini- ties

    Michael K Gilson and Huan-Xiang Zhou. Calculation of protein-ligand binding affini- ties. Annu. Rev. Biophys. Biomol. Struct., 36:21–42, 2007

    work page 2007

  2. [2]

    Ab initio molecular dynamics with enhanced sampling in heterogeneous catalysis

    GiovanniMaria Piccini, Mal-Soon Lee, Simuck F Yuk, Difan Zhang, Greg Collinge, Loukas Kollias, Manh-Thuong Nguyen, Vassiliki-Alexandra Glezakou, and Roger Rousseau. Ab initio molecular dynamics with enhanced sampling in heterogeneous catalysis. Catalysis Science & Technology, 12(1):12–37, 2022

    work page 2022

  3. [3]

    Understanding atomic-scale behavior of liquid crystals at aqueous interfaces

    Hadi Ramezani-Dakhel, Monirosadat Sadati, Mohammad Rahimi, Abelardo Ramirez-Hernandez, Benoît Roux, and Juan J de Pablo. Understanding atomic-scale behavior of liquid crystals at aqueous interfaces. Journal of chemical theory and com- putation, 13(1):237–244, 2017

    work page 2017

  4. [4]

    Dft in a nutshell

    Kieron Burke and Lucas O Wagner. Dft in a nutshell. International Journal of Quan- tum Chemistry, 113(2):96–101, 2013. 15

    work page 2013

  5. [5]

    Classical molecular dynamics

    Charles L Brooks, David A Case, Steve Plimpton, Benoît Roux, David Van der Spoel, and Emad Tajkhorshid. Classical molecular dynamics. The Journal of chemical physics, 154(10), 2021

    work page 2021

  6. [6]

    Machine learning force fields

    Oliver T Unke, Stefan Chmiela, Huziel E Sauceda, Michael Gastegger, Igor Poltavsky, Kristof T Schütt, Alexandre Tkatchenko, and Klaus-Robert Müller. Machine learning force fields. Chemical Reviews, 121(16):10142–10186, 2021

    work page 2021

  7. [7]

    Enhanced sampling methods for molecular dynamics simulations

    Jérôme Hénin, Tony Lelièvre, Michael R Shirts, Omar Valsson, and Lucie Delemotte. Enhanced sampling methods for molecular dynamics simulations. arXiv preprint arXiv:2202.04164, 2022

    arXiv 2022

  8. [8]

    Well-tempered meta- dynamics: A smoothly converging and tunable free-energy method

    Alessandro Barducci, Giovanni Bussi, and Michele Parrinello. Well-tempered meta- dynamics: A smoothly converging and tunable free-energy method. Phys. Rev. Lett., 100:020603, Jan 2008

    work page 2008

Show all 40 references
  1. [9]

    Unified approach to enhanced sampling

    Michele Invernizzi, Pablo M Piaggi, and Michele Parrinello. Unified approach to enhanced sampling. Physical Review X, 10(4):041034, 2020

    2020

  2. [10]

    Nonphysical sampling distributions in monte carlo free-energy estimation: Umbrella sampling

    Glenn M Torrie and John P Valleau. Nonphysical sampling distributions in monte carlo free-energy estimation: Umbrella sampling. Journal of computational physics, 23(2):187–199, 1977

    1977

  3. [11]

    The adaptive biasing force method: Everything you al- ways wanted to know but were afraid to ask

    Jeffrey Comer, James C Gumbart, Jérôme Hénin, Tony Lelièvre, Andrew Pohorille, and Christophe Chipot. The adaptive biasing force method: Everything you al- ways wanted to know but were afraid to ask. The Journal of Physical Chemistry B , 119(3):1129–1151, 2015

    2015

  4. [12]

    Extended adap- tive biasing force algorithm

    Haohao Fu, Xueguang Shao, Christophe Chipot, and Wensheng Cai. Extended adap- tive biasing force algorithm. an on-the-fly implementation for accurate free-energy calculations. Journal of chemical theory and computation , 12(8):3506–3513, 2016

    2016

  5. [13]

    Thermodynamics and kinetics of drug-target binding by molecular simulation

    Sergio Decherchi and Andrea Cavalli. Thermodynamics and kinetics of drug-target binding by molecular simulation. Chemical Reviews, 120(23):12788–12833, 2020

    2020

  6. [14]

    Accurate determination of protein: ligand stan- dard binding free energies from molecular dynamics simulations

    Haohao Fu, Haochuan Chen, Marharyta Blazhynska, Emma Goulard Coderc de Lacam, Florence Szczepaniak, Anna Pavlova, Xueguang Shao, James C Gumbart, 16 François Dehez, Benoît Roux, et al. Accurate determination of protein: ligand stan- dard binding free energies from molecular dy...

    2022

  7. [15]

    Calculation of absolute protein–ligand binding free energy from computer simulations

    Hyung-June Woo and Benoît Roux. Calculation of absolute protein–ligand binding free energy from computer simulations. Proceedings of the National Academy of Sci- ences, 102(19):6825–6830, 2005

    2005

  8. [16]

    Funnel metady- namics as accurate binding free-energy method

    Vittorio Limongelli, Massimiliano Bonomi, and Michele Parrinello. Funnel metady- namics as accurate binding free-energy method. Proceedings of the National Academy of Sciences, 110(16):6358–6363, 2013

    2013

  9. [17]

    Accurate global ma- chine learning force fields for molecules with hundreds of atoms

    Stefan Chmiela, Valentin Vassilev-Galindo, Oliver T Unke, Adil Kabylda, Huziel E Sauceda, Alexandre Tkatchenko, and Klaus-Robert Müller. Accurate global ma- chine learning force fields for molecules with hundreds of atoms. Science Advances, 9(2):eadf0873, 2023

    2023

  10. [18]

    DeePMD-kit v2: A software pack- age for deep potential models

    Jinzhe Zeng, Duo Zhang, Denghui Lu, Pinghui Mo, Zeyu Li, Yixiao Chen, Marián Rynik, Li’ang Huang, Ziyao Li, Shaochen Shi, et al. DeePMD-kit v2: A software pack- age for deep potential models. The Journal of Chemical Physics, 159(5), 2023

    2023

  11. [19]

    Learning local equivariant representa- tions for large-scale atomistic dynamics

    Albert Musaelian, Simon Batzner, Anders Johansson, Lixin Sun, Cameron J Owen, Mordechai Kornbluth, and Boris Kozinsky. Learning local equivariant representa- tions for large-scale atomistic dynamics. Nature Communications, 14(1):579, 2023

    2023

  12. [20]

    Modeling chemical reactions in classical molecular dynamics simulations

    Jacob R Gissinger, Benjamin D Jensen, and Kristopher E Wise. Modeling chemical reactions in classical molecular dynamics simulations. Polymer, 128:211–217, 2017

    2017

  13. [21]

    The role of dynamics in heterogeneous catalysis: Surface diffusivity and n2 decomposition on fe (111)

    Luigi Bonati, Daniela Polino, Cristina Pizzolitto, Pierdomenico Biasi, Rene Eckert, Stephan Reitmeier, Robert Schlögl, and Michele Parrinello. The role of dynamics in heterogeneous catalysis: Surface diffusivity and n2 decomposition on fe (111). Pro- ceedings of the National A...

    2023

  14. [22]

    PySAGES: Flexible, advanced sampling methods accelerated with GPUs

    Pablo F Zubieta Rico, Ludwig Schneider, Gustavo R Pérez-Lemus, Riccardo Alessan- dri, Siva Dasetty, Trung D Nguyen, Cintia A Menéndez, Yiheng Wu, Yezhi Jin, Yinan Xu, et al. PySAGES: Flexible, advanced sampling methods accelerated with GPUs. npj Computational Materials, 10(1):...

    2024

  15. [23]

    Adaptive enhanced sampling by force-biasing using neural networks

    Ashley Z Guo, Emre Sevgen, Hythem Sidky, Jonathan K Whitmer, Jeffrey A Hubbell, and Juan J De Pablo. Adaptive enhanced sampling by force-biasing using neural networks. The Journal of chemical physics, 148(13), 2018

    2018

  16. [24]

    Combined force-frequency sampling for simulation of systems hav- ing rugged free energy landscapes

    Emre Sevgen, Ashley Z Guo, Hythem Sidky, Jonathan K Whitmer, and Juan J De Pablo. Combined force-frequency sampling for simulation of systems hav- ing rugged free energy landscapes. Journal of chemical theory and computation , 16(3):1448–1455, 2020

    2020

  17. [25]

    Zubieta Rico, Gustavo R

    Pablo F. Zubieta Rico, Gustavo R. Pérez-Lemus, and Juan J. de Pablo. Efficient sam- pling of free energy landscapes with functions in Sobolev spaces. The Journal of Chemical Physics, 162(8):084109, 02 2025

    2025

  18. [26]

    Adaptive biasing force method for scalar and vector free energy calculations

    Eric Darve, David Rodríguez-Gómez, and Andrew Pohorille. Adaptive biasing force method for scalar and vector free energy calculations. The Journal of chemical physics, 128(14), 2008

    2008

  19. [27]

    Gustavo Perez-Lemus, Yinan Xu, Yezhi Jin, Pablo Zubieta Rico, and Juan de Pablo. The importance of sampling the dynamical modes: Reevaluating benchmarks for invariant and equivariant features of machine learning potentials for simulation of free energy landscapes. The Journal ...

    2024

  20. [28]

    Integrated modeling program, applied chemical theory (impact)

    Jay L Banks, Hege S Beard, Yixiang Cao, Art E Cho, Wolfgang Damm, Ramy Farid, Anthony K Felts, Thomas A Halgren, Daniel T Mainz, Jon R Maple, et al. Integrated modeling program, applied chemical theory (impact). Journal of computational chem- istry, 26(16):1752–1780, 2005

    2005

  21. [29]

    Overview of the sampl6 host–guest binding affinity prediction challenge

    Andrea Rizzi, Steven Murkli, John N McNeill, Wei Yao, Matthew Sullivan, Michael K Gilson, Michael W Chiu, Lyle Isaacs, Bruce C Gibb, David L Mobley, et al. Overview of the sampl6 host–guest binding affinity prediction challenge. Journal of computer- aided molecular design, 32(...

    2018

  22. [30]

    Machine learning and enhanced sampling simulations for computing the potential of mean force and standard binding free energy

    Martina Bertazzo, Dorothea Gobbo, Sergio Decherchi, and Andrea Cavalli. Machine learning and enhanced sampling simulations for computing the potential of mean force and standard binding free energy. Journal of chemical theory and computation , 17(8):5287–5300, 2021. 18

    2021

  23. [31]

    free energy simula- tions of single and double ion occupancy in gramicidin a

    Benoît Roux, Olaf S Andersen, and Toby W Allen. Comment on “free energy simula- tions of single and double ion occupancy in gramicidin a”[ j. chem. phys. 126, 105103 (2007)]. The Journal of chemical physics, 128(22), 2008

    2007

  24. [32]

    Standard free energy of binding from a one-dimensional potential of mean force

    Slimane Doudou, Neil A Burton, and Richard H Henchman. Standard free energy of binding from a one-dimensional potential of mean force. Journal of chemical theory and computation, 5(4):909–918, 2009

    2009

  25. [33]

    VMD – Visual Molecular Dynamics

    William Humphrey, Andrew Dalke, and Klaus Schulten. VMD – Visual Molecular Dynamics. Journal of Molecular Graphics, 14:33–38, 1996

    1996

  26. [34]

    Water regulates the residence time of benzamidine in trypsin

    Narjes Ansari, Valerio Rizzi, and Michele Parrinello. Water regulates the residence time of benzamidine in trypsin. Nature Communications, 13(1):5438, 2022

    2022

  27. [35]

    OneOPES, a combined enhanced sampling method to rule them all

    Valerio Rizzi, Simone Aureli, Narjes Ansari, and Francesco Luigi Gervasio. OneOPES, a combined enhanced sampling method to rule them all. Journal of Chem- ical Theory and Computation , 19(17):5731–5742, 2023

    2023

  28. [36]

    A molecular view of methane activation on Ni (111) through enhanced sampling and machine learning

    Yinan Xu, Yezhi Jin, Jireh S García Sánchez, Gustavo R Pérez-Lemus, Pablo F Zubi- eta Rico, Massimiliano Delferro, and Juan J de Pablo. A molecular view of methane activation on Ni (111) through enhanced sampling and machine learning. The Jour- nal of Physical Chemistry Letter...

    2024

  29. [37]

    https://github.com/depablogroup/ConstraintFreeMLIP

  30. [38]

    Development and testing of a general amber force field

    Junmei Wang, Romain M Wolf, James W Caldwell, Peter A Kollman, and David A Case. Development and testing of a general amber force field. Journal of computa- tional chemistry, 25(9):1157–1174, 2004

    2004

  31. [39]

    Automatic atom type and bond type perception in molecular mechanical calculations

    Junmei Wang, Wei Wang, Peter A Kollman, and David A Case. Automatic atom type and bond type perception in molecular mechanical calculations. Journal of molecu- lar graphics and modelling, 25(2):247–260, 2006

    2006

  32. [40]

    A purely algebraic justifica- tion of the kabsch-umeyama algorithm

    Jim Lawrence, Javier Bernal, and Christoph Witzgall. A purely algebraic justifica- tion of the kabsch-umeyama algorithm. Journal of research of the National Institute of Standards and Technology, 124:1, 2019. 19

    2019

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.