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arxiv: 2603.05319 · v2 · submitted 2026-03-05 · ⚛️ physics.chem-ph

Recognition: 2 theorem links

· Lean Theorem

The Angular Localization Function (ALF): a practical tool to measure solvent angular order with Molecular Density Functional Theory

Ma\"iwenn Souetre , Benjamin Rotenberg , Guillaume Jeanmairet
Authors on Pith no claims yet

Pith reviewed 2026-05-15 15:31 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords Angular Localization Functionmolecular density functional theorysolvent angular orderorientational entropywater structureclay surfacessolvation analysis
0
0 comments X

The pith

The Angular Localization Function (ALF) provides a local entropy-based measure of solvent angular order from molecular density functional theory densities.

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

Molecular density functional theory yields detailed spatially and orientationally resolved solvent densities that are difficult to interpret in full. The paper defines the Angular Localization Function, derived directly from the ideal free energy functional, to extract a scalar field that quantifies local orientational entropy and thereby measures angular order. This measure is applied to three aqueous systems: a water solute, an octanol molecule, and three clay surfaces whose small structural differences produce detectable differences in water ordering. ALF supplies information that is complementary to integrated number density, average polarization, and charge density.

Core claim

The Angular Localization Function (ALF) is derived from the ideal free energy functional in molecular density functional theory. It quantifies the entropy contribution arising from the orientational distribution of solvent molecules, thereby furnishing a local, scalar measure of angular order around arbitrary solutes and next to surfaces. The function is shown to be connected to standard statistical descriptors of orientation and is demonstrated on water, octanol, and clay-mineral interfaces where it highlights subtle structural effects.

What carries the argument

The Angular Localization Function (ALF), obtained from the ideal free energy functional of molecular density functional theory, which converts the full orientational density into a local scalar field that reports angular localization through entropy.

If this is right

  • ALF supplies a visualization field analogous to the electronic localization function used in quantum chemistry.
  • It distinguishes the effects of small structural variations among talc, fluorotalc, and pyrophyllite on their interfacial water ordering.
  • ALF augments standard observables such as polarization and charge density when analyzing solvent structure around solutes.
  • The function enables compact representation of the full six-dimensional density output of MDFT calculations.

Where Pith is reading between the lines

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

  • ALF analysis could be applied to non-aqueous solvents to compare their angular ordering behavior at interfaces.
  • Routine inclusion of ALF maps in MDFT post-processing would facilitate rapid identification of strongly ordered solvent regions in complex solutes.
  • Quantitative thresholds on ALF values might be calibrated against known ordered phases to classify local solvation environments.

Load-bearing premise

The ideal free energy functional in MDFT captures the dominant orientational entropy contributions without large interference from other functional terms or approximations.

What would settle it

Direct numerical comparison of ALF values computed from MDFT densities against those obtained from explicit molecular-dynamics trajectories for the same octanol-water or clay-water systems would confirm or refute whether the function accurately isolates angular order.

Figures

Figures reproduced from arXiv: 2603.05319 by Benjamin Rotenberg, Guillaume Jeanmairet, Ma\"iwenn Souetre.

Figure 1
Figure 1. Figure 1: FIG. 1: Oxygen density with respect to the homogeneous density [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Slices of [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Maximum value of ALF along the O-H direction, for octanol molecules with a [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Top and side views of pyrophyllite (A,B) and talc (C,D). Oxygen atoms are in red, [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Angular localization function (solid lines) and oxygen density (dashed lines) along [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
read the original abstract

Molecular density functional theory is a powerful technique for efficiently computing the spatially and orientationally dependent equilibrium density of a molecular solvent around an arbitrary solute. This density encodes the detailed solvent structure, but contains so much information that it is difficult to interpret comprehensively. Although spatial dependence is frequently analyzed through orientationally integrated number density, angular information remains poorly exploited. The present work addresses this gap by introducing a function that provides a local measure of the angular order: the Angular Localization Function (ALF), derived from the ideal free energy functional, which quantifies the entropy. We discuss the connections between ALF and well known statistical functions. We illustrate the utility of ALF by discussing the solvent structure for three systems immersed in water: water as a solute, an octanol molecule, and three clay minerals (talc, fluorotalc and pyrophyllite) with small differences in their structure leading to subtle effects on their interactions with water. ALF provides information complementary to quantities such as the average polarization or charge density to characterize the local orientational distribution of solvent molecules around solutes and next to surfaces. It also offers a convenient visualization tool akin to the Electronic Localization Function (ELF) used to analyze bonding in quantum chemistry.

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

0 major / 3 minor

Summary. The manuscript introduces the Angular Localization Function (ALF), derived directly from the ideal free energy functional in Molecular Density Functional Theory (MDFT), as a local scalar measure of solvent angular order that quantifies orientational entropy. The authors relate ALF to standard statistical functions, show that it recovers the expected limits (ALF = 0 for isotropic distributions, ALF > 0 for localized orientations), and demonstrate its utility as a visualization tool on three systems in water: a water solute, an octanol molecule, and three clay minerals (talc, fluorotalc, pyrophyllite) whose small structural differences produce subtle effects on water ordering. ALF is positioned as complementary to quantities such as average polarization and charge density.

Significance. If the derivation holds, ALF supplies a parameter-free, local interpretive aid that makes the rich orientational information contained in MDFT densities more accessible. Its direct origin in the ideal term, recovery of the isotropic limit, and analogy to the Electronic Localization Function (ELF) constitute clear strengths. The concrete illustrations on chemically distinct systems support its value as a practical complement to existing descriptors for solvent structure around solutes and surfaces.

minor comments (3)
  1. [Theory section] The normalization step that converts the ideal free-energy contribution into the bounded ALF scalar should be written out explicitly (ideally with a short algebraic example) so that readers can reproduce the function without ambiguity.
  2. [Results, clay-mineral subsection] In the clay-mineral results, the text asserts that ALF reveals subtle structural effects; adding a quantitative comparison (e.g., integrated ALF values or peak heights) alongside the visual maps would make this claim easier to verify.
  3. [Figure captions] Figure captions and axis labels should state the precise definition of the color scale (e.g., whether ALF is plotted in absolute units or normalized to its maximum) to avoid misinterpretation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their supportive summary, positive assessment of the ALF's potential as a parameter-free interpretive tool, and recommendation for minor revision. The report correctly identifies the derivation from the ideal free energy term, the recovery of the isotropic limit, and the utility demonstrated on the water, octanol, and clay systems. No specific major comments are enumerated in the provided report, so we have no point-by-point rebuttals to offer. We will make minor editorial improvements in the revised manuscript to enhance clarity and presentation.

Circularity Check

0 steps flagged

No significant circularity; ALF is a direct definition from the standard ideal functional

full rationale

The paper derives the Angular Localization Function directly from the ideal free-energy term in MDFT, a pre-existing standard component of the theory. ALF is introduced as a normalized scalar functional of the orientationally resolved density that recovers the expected limits (zero for isotropic distributions, positive for localized orientations) by algebraic construction, without fitted parameters, self-referential definitions, or load-bearing self-citations. The three example systems serve only as illustrations; the interpretive claim that ALF quantifies local angular order stands independently of the excess functional or any external benchmark. No step in the provided derivation chain reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Central claim rests on the assumption that the ideal free energy functional encodes orientational entropy in a form that can be localized into ALF. No free parameters or invented physical entities are introduced. The main axiom is the domain assumption that MDFT densities and the ideal functional are sufficient for this measure.

axioms (1)
  • domain assumption The ideal free energy functional in MDFT accurately encodes the orientational entropy of the solvent density.
    ALF is explicitly derived from this term; the paper treats it as the source of the angular order measure.
invented entities (1)
  • Angular Localization Function (ALF) no independent evidence
    purpose: Local scalar measure of solvent angular order
    Newly introduced derived quantity without independent external validation in the abstract.

pith-pipeline@v0.9.0 · 5524 in / 1290 out tokens · 40481 ms · 2026-05-15T15:31:49.678788+00:00 · methodology

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Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages

  1. [1]

    Computation of pair distribution functions and three-dimensional densities with a reduced variance principle

    Daniel Borgis, Roland Assaraf, Benjamin Rotenberg, and Rodolphe Vuilleumier. Computation of pair distribution functions and three-dimensional densities with a reduced variance principle. Molecular Physics, 111(22-23):3486–3492, 2013. doi:10.1080/00268976.2013.838316

    work page doi:10.1080/00268976.2013.838316 2013

  2. [2]

    Better Than Counting: Density Pro- files from Force Sampling.Physical Review Letters, 120(21):218001, 2018

    Daniel de las Heras and Matthias Schmidt. Better Than Counting: Density Pro- files from Force Sampling.Physical Review Letters, 120(21):218001, 2018. doi: 10.1103/PhysRevLett.120.218001

    work page doi:10.1103/physrevlett.120.218001 2018

  3. [3]

    Coles, Daniel Borgis, Rodolphe Vuilleumier, and Benjamin Rotenberg

    Samuel W. Coles, Daniel Borgis, Rodolphe Vuilleumier, and Benjamin Rotenberg. Computing three-dimensional densities from force densities improves statistical efficiency.The Journal of Chemical Physics, 151(6):064124, 2019. doi:10.1063/1.5111697

    work page doi:10.1063/1.5111697 2019

  4. [4]

    Benjamin Rotenberg. Use the force! Reduced variance estimators for densities, radial dis- tribution functions, and local mobilities in molecular simulations.The Journal of Chemical Physics, 153(15):150902, 2020. doi:10.1063/5.0029113

    work page doi:10.1063/5.0029113 2020

  5. [5]

    S. W. Coles, E. Mangaud, D. Frenkel, and B. Rotenberg. Reduced variance analysis of molec- ular dynamics simulations by linear combination of estimators.The Journal of Chemical Physics, 154(19):191101, 2021. doi:10.1063/5.0053737

    work page doi:10.1063/5.0053737 2021

  6. [6]

    Reduced-variance orientational distribution functions from torque sampling.Journal of Physics: Condensed Matter, 35(23): 235901, 2023

    Johannes Renner, Matthias Schmidt, and Daniel de las Heras. Reduced-variance orientational distribution functions from torque sampling.Journal of Physics: Condensed Matter, 35(23): 235901, 2023. doi:10.1088/1361-648X/acc522

    work page doi:10.1088/1361-648x/acc522 2023

  7. [7]

    David Mermin

    N. David Mermin. Thermal Properties of the Inhomogeneous Electron Gas.Physical Review, 137(5A):A1441–A1443, 1965. doi:10.1103/PhysRev.137.A1441

    work page doi:10.1103/physrev.137.a1441 1965

  8. [8]

    R. Evans. The nature of the liquid-vapour interface and other topics in the sta- tistical mechanics of non-uniform, classical fluids.Advances in Physics, 1979. doi: 10.1080/00018737900101365

    work page doi:10.1080/00018737900101365 1979

  9. [9]

    Free-energy model for the inhomogeneous hard-sphere fluid mixture and density-functional theory of freezing.Physical Review Letters, 63(9):980–983, 1989

    Yaakov Rosenfeld. Free-energy model for the inhomogeneous hard-sphere fluid mixture and density-functional theory of freezing.Physical Review Letters, 63(9):980–983, 1989. doi: 10.1103/PhysRevLett.63.980. 22

    work page doi:10.1103/physrevlett.63.980 1989

  10. [10]

    H. L¨ owen. Density functional theory of inhomogeneous classical fluids: recent developments and new perspectives.Journal of Physics: Condensed Matter, 14(46):11897, 2002. doi: 10.1088/0953-8984/14/46/301

    work page doi:10.1088/0953-8984/14/46/301 2002

  11. [11]

    Inhomo- geneous fluids of colloidal hard dumbbells: Fundamental measure theory and Monte Carlo simulations.The Journal of Chemical Physics, 135(23):234510, 2011

    Matthieu Marechal, Hanns Hagen Goetzke, Andreas H¨ artel, and Hartmut L¨ owen. Inhomo- geneous fluids of colloidal hard dumbbells: Fundamental measure theory and Monte Carlo simulations.The Journal of Chemical Physics, 135(23):234510, 2011. doi:10.1063/1.3664742

    work page doi:10.1063/1.3664742 2011

  12. [12]

    civilized

    Anna Oleksy and Jean-Pierre Hansen. Wetting of a solid substrate by a “civilized” model of ionic solutions.The Journal of Chemical Physics, 132(20):204702–204702–13, 2010. doi: doi:10.1063/1.3428704

    work page doi:10.1063/1.3428704 2010

  13. [13]

    Molecular Density Functional Theory of Water.The Journal of Physical Chemistry Letters, 4:619–624, 2013

    Guillaume Jeanmairet, Maximilien Levesque, Rodolphe Vuilleumier, and Daniel Borgis. Molecular Density Functional Theory of Water.The Journal of Physical Chemistry Letters, 4:619–624, 2013. doi:10.1021/jz301956b

    work page doi:10.1021/jz301956b 2013

  14. [14]

    Molecular density functional theory of solvation: From polar solvents to water.The Journal of Chemical Physics, 134(19):194102, 2011

    Shuangliang Zhao, Rosa Ramirez, Rodolphe Vuilleumier, and Daniel Borgis. Molecular density functional theory of solvation: From polar solvents to water.The Journal of Chemical Physics, 134(19):194102, 2011. doi:10.1063/1.3589142

    work page doi:10.1063/1.3589142 2011

  15. [15]

    Efficient molecular density functional theory using generalized spherical harmonics expansions.The Journal of Chemical Physics, 147(9):094107, 2017

    Lu Ding, Maximilien Levesque, Daniel Borgis, and Luc Belloni. Efficient molecular density functional theory using generalized spherical harmonics expansions.The Journal of Chemical Physics, 147(9):094107, 2017. doi:10.1063/1.4994281

    work page doi:10.1063/1.4994281 2017

  16. [16]

    Solvation of complex surfaces via molecular density func- tional theory.The Journal of Chemical Physics, 137(22):224107–224107–8, 2012

    Maximilien Levesque, Virginie Marry, Benjamin Rotenberg, Guillaume Jeanmairet, Rodolphe Vuilleumier, and Daniel Borgis. Solvation of complex surfaces via molecular density func- tional theory.The Journal of Chemical Physics, 137(22):224107–224107–8, 2012. doi: doi:10.1063/1.4769729

    work page doi:10.1063/1.4769729 2012

  17. [17]

    Hydration of clays at the molecular scale: the promising perspective of classical density functional theory.Molecular Physics, 112(9-10):1320–1329, 2014

    Guillaume Jeanmairet, Virginie Marry, Maximilien Levesque, Benjamin Rotenberg, and Daniel Borgis. Hydration of clays at the molecular scale: the promising perspective of classical density functional theory.Molecular Physics, 112(9-10):1320–1329, 2014. doi: 10.1080/00268976.2014.899647

    work page doi:10.1080/00268976.2014.899647 2014

  18. [18]

    L. Blum. Invariant Expansion. II. The Ornstein-Zernike Equation for Nonspherical Molecules and an Extended Solution to the Mean Spherical Model.The Journal of Chemical Physics, 57(5):1862–1869, 1972. doi:10.1063/1.1678503

    work page doi:10.1063/1.1678503 1972

  19. [19]

    Blum and A

    L. Blum and A. J. Torruella. Invariant Expansion for Two-Body Correlations: Thermody- namic Functions, Scattering, and the Ornstein—Zernike Equation.The Journal of Chemical 23 Physics, 56(1):303–310, 1972. doi:10.1063/1.1676864

    work page doi:10.1063/1.1676864 1972

  20. [20]

    L. Blum. Invariant expansion III: The general solution of the mean spherical model for neutral spheres with electostatic interactions.The Journal of Chemical Physics, 58(8):3295, 1973. doi: 10.1063/1.1679655

    work page doi:10.1063/1.1679655 1973

  21. [21]

    A molecular density functional theory of aqueous electrolytic solution.The Journal of Chemical Physics, 164(10):104104, 2026

    Guillaume Jeanmairet, Luc Belloni, and Daniel Borgis. A molecular density functional theory of aqueous electrolytic solution.The Journal of Chemical Physics, 164(10):104104, 2026. doi:10.1063/5.0311853

    work page doi:10.1063/5.0311853 2026

  22. [22]

    Screened Coulombic Orientational Correlations in Dilute Aqueous Electrolytes.The Journal of Physical Chemistry Letters, 9(8): 1985–1989, 2018

    Luc Belloni, Daniel Borgis, and Maximilien Levesque. Screened Coulombic Orientational Correlations in Dilute Aqueous Electrolytes.The Journal of Physical Chemistry Letters, 9(8): 1985–1989, 2018. doi:10.1021/acs.jpclett.8b00606

    work page doi:10.1021/acs.jpclett.8b00606 1985

  23. [23]

    ´Sliwa, W

    I. ´Sliwa, W. Je˙ zewski, and A. V. Zakharov. Local structural ordering in surface-confined liquid crystals.The Journal of Chemical Physics, 146(24):244704, 2017. doi:10.1063/1.4989543

    work page doi:10.1063/1.4989543 2017

  24. [24]

    Takahashi

    Kazuaki Z. Takahashi. Molecular cluster analysis using local order parameters selected by machine learning.Physical Chemistry Chemical Physics, 25(1):658–672, 2023. doi: 10.1039/D2CP03696G

    work page doi:10.1039/d2cp03696g 2023

  25. [25]

    Henchman, Michelle W

    Georgios Gerogiokas, Gaetano Calabro, Richard H. Henchman, Michelle W. Y. Southey, Richard J. Law, and Julien Michel. Prediction of Small Molecule Hydration Thermodynamics with Grid Cell Theory.Journal of Chemical Theory and Computation, 10(1):35–48, 2014. doi:10.1021/ct400783h

    work page doi:10.1021/ct400783h 2014

  26. [26]

    Goddard, III

    Shiang-Tai Lin, Mario Blanco, and William A. Goddard, III. The two-phase model for cal- culating thermodynamic properties of liquids from molecular dynamics: Validation for the phase diagram of Lennard-Jones fluids.The Journal of Chemical Physics, 119(22):11792– 11805, 2003. doi:10.1063/1.1624057

    work page doi:10.1063/1.1624057 2003

  27. [27]

    Rasmus A. X. Persson, Viren Pattni, Anurag Singh, Stefan M. Kast, and Matthias Heyden. Signatures of Solvation Thermodynamics in Spectra of Intermolecular Vibrations.Journal of Chemical Theory and Computation, 13(9):4467–4481, 2017. doi:10.1021/acs.jctc.7b00184

    work page doi:10.1021/acs.jctc.7b00184 2017

  28. [28]

    Inhomogeneous Fluid Approach to Solvation Thermodynamics

    Themis Lazaridis. Inhomogeneous Fluid Approach to Solvation Thermodynamics. 1. Theory. The Journal of Physical Chemistry B, 102(18):3531–3541, 1998. doi:10.1021/jp9723574

    work page doi:10.1021/jp9723574 1998

  29. [29]

    Nguyen, Tom Kurtzman Young, and Michael K

    Crystal N. Nguyen, Tom Kurtzman Young, and Michael K. Gilson. Grid inhomogeneous solvation theory: Hydration structure and thermodynamics of the miniature receptor cucur- bit[7]uril.The Journal of Chemical Physics, 137(4):044101, 2012. doi:10.1063/1.4733951. 24

    work page doi:10.1063/1.4733951 2012

  30. [30]

    Case, Michael K

    Crystal Nguyen, Takeshi Yamazaki, Andriy Kovalenko, David A. Case, Michael K. Gilson, Tom Kurtzman, and Tyler Luchko. A molecular reconstruction approach to site-based 3D- RISM and comparison to GIST hydration thermodynamic maps in an enzyme active site. PLOS ONE, 14(7):e0219473, 2019. doi:10.1371/journal.pone.0219473

    work page doi:10.1371/journal.pone.0219473 2019

  31. [31]

    Heinz and Helmut Grubm¨ uller

    Leonard P. Heinz and Helmut Grubm¨ uller. Computing Spatially Resolved Rotational Hydra- tion Entropies from Atomistic Simulations.Journal of Chemical Theory and Computation, 16 (1):108–118, 2020. doi:10.1021/acs.jctc.9b00926

    work page doi:10.1021/acs.jctc.9b00926 2020

  32. [32]

    Heinz and Helmut Grubm¨ uller

    Leonard P. Heinz and Helmut Grubm¨ uller. Per|Mut: Spatially Resolved Hydration Entropies from Atomistic Simulations.Journal of Chemical Theory and Computation, 17(4):2090–2098,

    work page 2090

  33. [33]

    doi:10.1021/acs.jctc.0c00961

    work page doi:10.1021/acs.jctc.0c00961

  34. [34]

    Jeppe C. Dyre. Perspective: Excess-entropy scaling.The Journal of Chemical Physics, 149 (21):210901, 2018. doi:10.1063/1.5055064

    work page doi:10.1063/1.5055064 2018

  35. [35]

    Klumov and Sergey A

    Boris A. Klumov and Sergey A. Khrapak. Two-body entropy of two-dimensional fluids.Results in Physics, 17:103020, 2020. doi:10.1016/j.rinp.2020.103020

    work page doi:10.1016/j.rinp.2020.103020 2020

  36. [36]

    Relation between the transport coefficients and the internal entropy of simple systems.Physical Review A, 15(6):2545–2549, 1977

    Yaakov Rosenfeld. Relation between the transport coefficients and the internal entropy of simple systems.Physical Review A, 15(6):2545–2549, 1977. doi:10.1103/PhysRevA.15.2545

    work page doi:10.1103/physreva.15.2545 1977

  37. [37]

    Rasmus A. X. Persson. Note on the physical basis of spatially resolved thermodynamic func- tions.Molecular Simulation, 48(13):1186–1191, 2022. doi:10.1080/08927022.2022.2074994

    work page doi:10.1080/08927022.2022.2074994 2022

  38. [38]

    A. D. Becke and K. E. Edgecombe. A simple measure of electron localization in atomic and molecular systems.The Journal of Chemical Physics, 92(9):5397–5403, 1990. doi: 10.1063/1.458517

    work page doi:10.1063/1.458517 1990

  39. [39]

    A. L. Mart´ ın, S. L´ opez-Rosa, J. C. Angulo, and J. Antol´ ın. Jensen–Shannon and Kull- back–Leibler divergences as quantifiers of relativistic effects in neutral atoms.Chemical Physics Letters, 635:75–79, 2015. doi:10.1016/j.cplett.2015.06.037

    work page doi:10.1016/j.cplett.2015.06.037 2015

  40. [40]

    Alessandro Simon, Luc Belloni, Daniel Borgis, and Martin Oettel. The orientational struc- ture of a model patchy particle fluid: Simulations, integral equations, density functional the- ory, and machine learning.The Journal of Chemical Physics, 162(3):034503, 2025. doi: 10.1063/5.0248694

    work page doi:10.1063/5.0248694 2025

  41. [41]

    Variational principle of classical density functional theory via Levy’s constrained search method.Physical Review E, 83(6):061133,

    Wipsar Sunu Brams Dwandaru and Matthias Schmidt. Variational principle of classical density functional theory via Levy’s constrained search method.Physical Review E, 83(6):061133,

    work page

  42. [42]

    doi:10.1103/PhysRevE.83.061133. 25

    work page doi:10.1103/physreve.83.061133

  43. [43]

    Guillaume Jeanmairet, Maxime Labat, and Emmanuel Giner. A variational formulation of the free energy of mixed quantum-classical systems: Coupling classical and electronic density functional theories.The Journal of Chemical Physics, 164(5):054112, 2026. ISSN 0021-9606. doi:10.1063/5.0309780

    work page doi:10.1063/5.0309780 2026

  44. [44]

    Kierlik and M

    E. Kierlik and M. L. Rosinberg. Density-functional theory for inhomogeneous flu- ids: Adsorption of binary mixtures.Physical Review A, 44(8):5025–5037, 1991. doi: 10.1103/PhysRevA.44.5025

    work page doi:10.1103/physreva.44.5025 1991

  45. [45]

    R. Roth, R. Evans, A. Lang, and G. Kahl. Fundamental measure theory for hard-sphere mixtures revisited: the White Bear version.Journal of Physics: Condensed Matter, 14(46): 12063, 2002. doi:10.1088/0953-8984/14/46/313

    work page doi:10.1088/0953-8984/14/46/313 2002

  46. [46]

    Density functional theory for hard-sphere mixtures: the White Bear version mark II.Journal of Physics: Condensed Matter, 18(37):8413, 2006

    Hendrik Hansen-Goos and Roland Roth. Density functional theory for hard-sphere mixtures: the White Bear version mark II.Journal of Physics: Condensed Matter, 18(37):8413, 2006. doi:10.1088/0953-8984/18/37/002

    work page doi:10.1088/0953-8984/18/37/002 2006

  47. [47]

    Shells of charge: a density functional theory for charged hard spheres.Journal of Physics: Condensed Matter, 28(24):244006, 2016

    Roland Roth and Dirk Gillespie. Shells of charge: a density functional theory for charged hard spheres.Journal of Physics: Condensed Matter, 28(24):244006, 2016. doi:10.1088/0953- 8984/28/24/244006

    work page doi:10.1088/0953- 2016

  48. [48]

    Sitlapersad, Wouter K

    Peter Cats, Ranisha S. Sitlapersad, Wouter K. den Otter, Anthony R. Thornton, and Ren´ e van Roij. Capacitance and Structure of Electric Double Layers: Comparing Brownian Dynamics and Classical Density Functional Theory.Journal of Solution Chemistry, 51(3):296–319, 2022. doi:10.1007/s10953-021-01090-7

    work page doi:10.1007/s10953-021-01090-7 2022

  49. [49]

    Scalar fundamental measure theory for hard spheres in three dimensions: Application to hydrophobic solvation.The Journal of Chemical Physics, 137(3):034115–1–034115–9, 2012

    Maximilien Levesque, Rodolphe Vuilleumier, and Daniel Borgis. Scalar fundamental measure theory for hard spheres in three dimensions: Application to hydrophobic solvation.The Journal of Chemical Physics, 137(3):034115–1–034115–9, 2012. doi:10.1063/1.4734009

    work page doi:10.1063/1.4734009 2012

  50. [50]

    Site-site direct correlation func- tions for three popular molecular models of liquid water.The Journal of Chemical Physics, 139(6):064509–064509–11, 2013

    Shuangliang Zhao, Yu Liu, Honglai Liu, and Jianzhong Wu. Site-site direct correlation func- tions for three popular molecular models of liquid water.The Journal of Chemical Physics, 139(6):064509–064509–11, 2013. doi:10.1063/1.4817784

    work page doi:10.1063/1.4817784 2013

  51. [51]

    Simple Parameter- Free Bridge Functionals for Molecular Density Functional Theory

    Daniel Borgis, Sohvi Luukkonen, Luc Belloni, and Guillaume Jeanmairet. Simple Parameter- Free Bridge Functionals for Molecular Density Functional Theory. Application to Hydropho- bic Solvation.The Journal of Physical Chemistry B, 124(31):6885–6893, 2020. doi: 10.1021/acs.jpcb.0c04496. 26

    work page doi:10.1021/acs.jpcb.0c04496 2020

  52. [52]

    Daniel Borgis, Sohvi Luukkonen, Luc Belloni, and Guillaume Jeanmairet. Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional.The Journal of Chemical Physics, 155(2):024117, 2021. doi: 10.1063/5.0057506

    work page doi:10.1063/5.0057506 2021

  53. [53]

    V. Vedral. The role of relative entropy in quantum information theory.Reviews of Modern Physics, 74(1):197–234, 2002. doi:10.1103/RevModPhys.74.197

    work page doi:10.1103/revmodphys.74.197 2002

  54. [54]

    Exact molecular direct, cavity, and bridge functions in water system.The Journal of Chemical Physics, 147(16):164121, 2017

    Luc Belloni. Exact molecular direct, cavity, and bridge functions in water system.The Journal of Chemical Physics, 147(16):164121, 2017. doi:10.1063/1.5001684

    work page doi:10.1063/1.5001684 2017

  55. [55]

    Electron transfer of functionalized quinones in acetonitrile.The Journal of Chemical Physics, 157(9):094103, 2022

    Tzu-Yao Hsu, Roxanne Berthin, Alessandra Serva, Kyle Reeves, Mathieu Salanne, and Guil- laume Jeanmairet. Electron transfer of functionalized quinones in acetonitrile.The Journal of Chemical Physics, 157(9):094103, 2022. doi:10.1063/5.0102238

    work page doi:10.1063/5.0102238 2022

  56. [56]

    Patel, and David Chandler

    Benjamin Rotenberg, Amish J. Patel, and David Chandler. Molecular Explanation for Why Talc Surfaces Can Be Both Hydrophilic and Hydrophobic.Journal of the American Chemical Society, 133(50):20521–20527, 2011. doi:10.1021/ja208687a

    work page doi:10.1021/ja208687a 2011

  57. [57]

    Marry, B

    V. Marry, B. Rotenberg, and P. Turq. Structure and dynamics of water at a clay surface from molecular dynamics simulation.Phys. Chem. Chem. Phys., 10(32):4802–4813, 2008. doi:10.1039/b807288d. 27

    work page doi:10.1039/b807288d 2008