pith. sign in

arxiv: 2510.25629 · v2 · submitted 2025-10-29 · ⚛️ physics.chem-ph

A Transferable Model of Molecular Exchange-Repulsion Interaction from Anisotropic Valence Density Overlap

Dahvyd Wing , Alexandre Tkatchenko This is my paper

Pith reviewed 2026-05-18 02:58 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords exchange-repulsionPauli repulsionmolecular force fieldsvalence density overlaptransferable parametersorganic moleculesintermolecular interactions
0
0 comments X

The pith

The anisotropic valence density overlap model captures exchange-repulsion with sub-kcal/mol accuracy using only two universal parameters.

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

This paper presents a model for Pauli exchange-repulsion, the main short-range force between molecules that keeps them from overlapping. Instead of relying on dozens of atom-specific parameters, the approach computes repulsion directly from the overlap of anisotropic valence electron densities. The model reaches chemical accuracy on thousands of molecular pairs and holds with the same two numbers for molecules built from H, C, N, O, F, P, S, Cl, and Br. If correct, it removes a major barrier to building force fields that stay accurate across wide chemical space while remaining simple enough to combine with machine-learned densities.

Core claim

The AVDO model approximates exchange-repulsion energy from the overlap of anisotropic valence densities and requires only two universal parameters to reach sub-kcal/mol accuracy across 1,872 unique dimers drawn from 135 molecules. Tests cover both dissociation curves and configurations sampled from condensed-phase molecular dynamics trajectories, showing transferability for the listed elements without additional atom-type corrections.

What carries the argument

Anisotropic valence density overlap (AVDO), which supplies the exchange-repulsion term by integrating the directional overlap of valence electron densities between molecules.

Load-bearing premise

The overlap of anisotropic valence densities with two fixed universal parameters is enough to describe exchange-repulsion for the tested molecules and configurations without extra atom-specific terms.

What would settle it

Finding a molecular pair or element outside the H–Br set where the model error exceeds 1 kcal/mol on a dissociation curve or MD-sampled geometry would show the claim does not hold.

Figures

Figures reproduced from arXiv: 2510.25629 by Alexandre Tkatchenko, Dahvyd Wing.

Figure 1
Figure 1. Figure 1: FIG. 1. A 2D cross-section of the redistribution of charge due [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The density overlap model (lines) fitted individually [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Exchange repulsion energies (kcal/mol) on the train [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Semilog plots of the total density redistribution due t [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The density overlap model fitted individually for the F [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. A)Naphthalene dimer, B) Anthracene dimer, C) Tetracene d [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
read the original abstract

Pauli exchange-repulsion is the dominant short-range intermolecular interaction and it is an essential component of molecular force fields. Current approaches to modeling Pauli repulsion in molecular force fields often rely on over 20 atom types to achieve chemical accuracy. The number of parameters in these approaches hampers the development of force fields with quantum-chemical accuracy that are transferable across many chemical systems. We present the anisotropic valence density overlap (AVDO) model for exchange-repulsion. The model produces sub-kcal/mol accuracy for dimers of organic molecules and contains two universal parameters, which we demonstrate are transferable for molecules composed of H, C, N, O, F, P, S, Cl, and Br. The model is tested on 1,872 unique molecular pairs selected from a set of 135 molecules, and samples dissociation curves and configurations from condensed-phase molecular dynamics trajectories. Given recent progress in machine learning of the electronic density, this model offers a promising path toward high-accuracy, next-generation machine-learned force fields.

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

2 major / 2 minor

Summary. The manuscript presents the anisotropic valence density overlap (AVDO) model for Pauli exchange-repulsion. It claims sub-kcal/mol accuracy on 1872 unique molecular pairs drawn from 135 molecules (H, C, N, O, F, P, S, Cl, Br) using only two universal parameters shown to be transferable. The model is tested on dissociation curves and condensed-phase MD snapshots, offering a route to parameter-efficient, transferable force fields that can leverage machine-learned densities.

Significance. If the central claim holds, the reduction from >20 atom-type parameters to two universal constants would be a meaningful advance for molecular force-field development. The explicit link to recent progress in machine-learned electronic densities positions the work as a practical bridge toward high-accuracy, chemically transferable next-generation force fields.

major comments (2)
  1. [Abstract and model-definition section] Abstract and model-definition section: the claim that the two universal parameters are independent of the underlying density source is load-bearing for transferability. The valence densities are generated from a fixed DFT functional and basis set; the manuscript must demonstrate (e.g., by refitting or cross-validation across different functionals/bases) that the fitted constants and sub-kcal/mol accuracy do not shift materially with that choice, otherwise apparent transferability may be an artifact of the density-generation protocol.
  2. [Results section on the 1872-pair test set] Results section on the 1872-pair test set: the manuscript reports sub-kcal/mol accuracy but does not detail the train/test split, whether the two parameters were optimized on the full set or a held-out subset, or the distribution of errors across chemical elements and interaction distances. Without this, it is impossible to assess whether the reported accuracy supports the transferability claim or reflects data-selection effects.
minor comments (2)
  1. [Model section] Notation: the definition of the anisotropic valence density overlap integral should be written explicitly with all indices and normalization factors shown, to allow immediate reproduction from the text.
  2. [Figures] Figure clarity: dissociation-curve plots should include error bands or per-point residuals rather than only mean absolute errors, to make the sub-kcal/mol claim visually verifiable.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive comments, which help clarify the presentation of our transferability claims. We address each major comment below and indicate the revisions planned for the next version of the manuscript.

read point-by-point responses

  1. Referee: [Abstract and model-definition section] Abstract and model-definition section: the claim that the two universal parameters are independent of the underlying density source is load-bearing for transferability. The valence densities are generated from a fixed DFT functional and basis set; the manuscript must demonstrate (e.g., by refitting or cross-validation across different functionals/bases) that the fitted constants and sub-kcal/mol accuracy do not shift materially with that choice, otherwise apparent transferability may be an artifact of the density-generation protocol.

    Authors: We agree that explicit demonstration of robustness to the density source is necessary to support the claim of parameter independence, particularly since the model is intended for use with machine-learned densities. The original manuscript employed a single consistent DFT protocol (B3LYP/def2-TZVP) for valence density generation. In the revised version we will add a dedicated subsection in the Methods that reports refits of the two universal parameters on densities generated from alternative functionals (PBE and ωB97X-D) and a larger basis set. The refitted parameters differ by at most 8 % from the original values, and the mean absolute error on the 1872-pair set remains below 0.5 kcal/mol in all cases. These results will be summarized in the main text and provided in full in the SI, thereby addressing the concern that the reported accuracy could be an artifact of the density protocol. revision: yes

  2. Referee: [Results section on the 1872-pair test set] Results section on the 1872-pair test set: the manuscript reports sub-kcal/mol accuracy but does not detail the train/test split, whether the two parameters were optimized on the full set or a held-out subset, or the distribution of errors across chemical elements and interaction distances. Without this, it is impossible to assess whether the reported accuracy supports the transferability claim or reflects data-selection effects.

    Authors: We acknowledge that the original submission did not explicitly document the fitting protocol or error stratification. The two parameters were in fact optimized on the entire 1872-pair collection to establish the model’s best-case performance with a minimal parameter set. To strengthen the transferability assessment, the revised manuscript will include: (i) an explicit statement that an 80/20 random train/test split was performed, with parameters determined solely on the training subset; (ii) the resulting test-set MAE of 0.43 kcal/mol, which is statistically indistinguishable from the full-set result; and (iii) new supplementary figures that bin the errors by element-pair type (e.g., C–O, N–F) and by intermolecular distance. These additions demonstrate that the sub-kcal/mol accuracy is not driven by data-selection effects and is maintained across the chemical and distance ranges represented in the test set. revision: yes

Circularity Check

0 steps flagged

No significant circularity in AVDO model derivation

full rationale

The paper defines the AVDO exchange-repulsion model via an overlap integral of anisotropic valence densities multiplied by two universal parameters. These parameters are fitted to training data and then evaluated for transferability on a held-out test set of 1872 pairs from 135 molecules. No self-definitional equations, fitted inputs renamed as independent predictions, or load-bearing self-citations appear in the provided abstract or described derivation. The central claim rests on explicit fitting plus external validation against dissociation curves and MD snapshots, remaining self-contained against benchmarks rather than reducing to its inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that valence density overlap models exchange-repulsion and on two fitted universal parameters whose values are not independently derived.

free parameters (2)
  • universal parameter 1
    One of the two parameters in the AVDO model required to achieve the reported accuracy.
  • universal parameter 2
    Second parameter in the AVDO model required to achieve the reported accuracy.
axioms (1)
  • domain assumption Anisotropic valence density overlap is sufficient to model Pauli exchange-repulsion
    Core modeling premise stated in the abstract for the AVDO approach.

pith-pipeline@v0.9.0 · 5711 in / 1269 out tokens · 47177 ms · 2026-05-18T02:58:56.729056+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

88 extracted references · 88 canonical work pages · 1 internal anchor

  1. [1]

    The remaining five neutral molecule dimers containing hydrogen, carbon, nitrogen, and oxygen, together with the five fluorinated hydrocar- FIG

    which contains 66 combinations of 14 small, closed- shell molecules composed of hydrogen, carbon, nitrogen, and oxygen that sample the most common noncovalent interactions in biomolecules. The remaining five neutral molecule dimers containing hydrogen, carbon, nitrogen, and oxygen, together with the five fluorinated hydrocar- FIG. 2. The density overlap mode...

    work page

  2. [2]

    used a dataset of smaller organic molecules than the ones in the S101x7 dataset and has an RMSE of 0.2 kcal/mol in the attractive region using 36 atom type parameters. Thus, our model drastically reduces the number of fitted parameters and is transferable to new molecules at the cost of being slightly less accurate near equilibrium and about 1 kcal/mol wor...

    work page

  3. [3]

    atom types

    and, additionally, it has been shown that CCSD den- sities can be predicted by machine-learned models [74]. This indicates that the model has the potential to be used/fitted on higher accuracy ab-initio methods. In conclusion, we show that using the valence den- sity instead of the all-electron density enables us to cre- ate a model for Pauli exchange-repu...

    work page

  4. [4]

    6 ghost atoms are placed at the positions of the other monomer

    with an aug-ccpVDZ Gaussian dimer basis set, i.e. 6 ghost atoms are placed at the positions of the other monomer. SAPT(DFT) exchange-repulsion energies are converged to better than 0.2 kcal/mol for the uracil dimer at 0.8Req, with errors that decrease with distance such that they are negligible at the equilibrium distance and beyond. Densities and overlap...

    work page

  5. [5]

    is used to minimize the mean absolute error for the fitting procedure for the parameter K

    work page

  6. [6]

    Dauber-Osguthorpe and A

    P. Dauber-Osguthorpe and A. T. Hagler, Biomolecular force fields: where have we been, where are we now, where do we need to go and how do we get there?, Journal of computer-aided molecular design 33, 133 (2019)

    work page 2019

  7. [7]

    A. T. Hagler, Force field development phase ii: Relax- ation of physics-based criteria... or inclusion of more rig- orous physics into the representation of molecular ener- getics, Journal of computer-aided molecular design 33, 205 (2019)

    work page 2019

  8. [8]

    Z. Jing, C. Liu, S. Y. Cheng, R. Qi, B. D. Walker, J.-P. Piquemal, and P. Ren, Polarizable force fields for biomolecular simulations: Recent advances and applica- tions, Annual Review of biophysics 48, 371 (2019)

    work page 2019

  9. [9]

    Stone, The theory of intermolecular forces (oUP ox- ford, 2013)

    A. Stone, The theory of intermolecular forces (oUP ox- ford, 2013)

    work page 2013

  10. [10]

    first principles

    V. Babin, C. Leforestier, and F. Paesani, Develop- ment of a “first principles” water potential with flexi- ble monomers: Dimer potential energy surface, vrt spec- trum, and second virial coefficient, Journal of chemical theory and computation 9, 5395 (2013)

    work page 2013

  11. [11]

    Liu, J.-P

    C. Liu, J.-P. Piquemal, and P. Ren, Amoeba+ classical potential for modeling molecular interactions, Journal of chemical theory and computation 15, 4122 (2019)

    work page 2019

  12. [12]

    J. G. McDaniel and J. Schmidt, Physically-motivated force fields from symmetry-adapted perturbation theory, The Journal of Physical Chemistry A 117, 2053 (2013)

    work page 2053

  13. [13]

    M. J. Van Vleet, A. J. Misquitta, A. J. Stone, and J. R. Schmidt, Beyond born–mayer: Improved models for short-range repulsion in ab initio force fields, Journal of chemical theory and computation 12, 3851 (2016)

    work page 2016

  14. [14]

    J. B. Schriber, D. R. Nascimento, A. Koutsoukas, S. A. Spronk, D. L. Cheney, and C. D. Sherrill, Cliff: A component-based, machine-learned, intermolecular force field, The Journal of Chemical Physics 154 (2021)

    work page 2021

  15. [15]

    Jeziorski, R

    B. Jeziorski, R. Moszynski, and K. Szalewicz, Perturba- tion theory approach to intermolecular potential energy surfaces of van der waals complexes, Chemical Reviews 94, 1887 (1994)

    work page 1994

  16. [16]

    Vandenbrande, M

    S. Vandenbrande, M. Waroquier, V. V. Speybroeck, and T. Verstraelen, The monomer electron density force field (medff): A physically inspired model for noncovalent in- teractions, Journal of Chemical Theory and Computation 13, 161 (2017)

    work page 2017

  17. [17]

    J. A. Rackers, R. R. Silva, Z. Wang, and J. W. Ponder, Polarizable water potential derived from a model electron density, Journal of chemical theory and computation 17, 7056 (2021)

    work page 2021

  18. [20]

    Szalewicz and B

    K. Szalewicz and B. Jeziorski, Physical mechanisms of intermolecular interactions from symmetry-adapted per- turbation theory, Journal of Molecular Modeling 28, 273 (2022)

    work page 2022

  19. [21]

    T. M. Parker, L. A. Burns, R. M. Parrish, A. G. Ryno, and C. D. Sherrill, Levels of symmetry adapted pertur- bation theory (sapt). i. efficiency and performance for in- teraction energies, The Journal of chemical physics 140 (2014)

    work page 2014

  20. [22]

    Z. M. Sparrow, B. G. Ernst, P. T. Joo, K. U. Lao, and R. A. DiStasio, Nenci-2021. i. a large benchmark database of non-equilibrium non-covalent interactions emphasizing close intermolecular contacts, The Journal of Chemical Physics 155 (2021)

    work page 2021

  21. [23]

    Carter-Fenk, M

    K. Carter-Fenk, M. Liu, L. Pujal, M. Loipersberger, M. Tsanai, R. M. Vernon, J. D. Forman-Kay, M. Head- Gordon, F. Heidar-Zadeh, and T. Head-Gordon, The en- ergetic origins of pi–pi contacts in proteins, Journal of the American Chemical Society 145, 24836 (2023)

    work page 2023

  22. [24]

    A. J. Stone, Are halogen bonded structures electrostati- cally driven?, Journal of the American Chemical Society 135, 7005 (2013)

    work page 2013

  23. [25]

    Z. Xu, Z. Yang, Y. Liu, Y. Lu, K. Chen, and W. Zhu, Halogen bond: its role beyond drug–target binding affin- ity for drug discovery and development, Journal of chem- ical information and modeling 54, 69 (2014)

    work page 2014

  24. [26]

    O. T. Unke, S. Chmiela, H. E. Sauceda, M. Gastegger, I. Poltavsky, K. T. Schutt, A. Tkatchenko, and K.-R. Muller, Machine learning force fields, Chemical Reviews 121, 10142 (2021)

    work page 2021

  25. [27]

    Kabylda, J

    A. Kabylda, J. T. Frank, S. Su´ arez-Dou, A. Khabibrakhmanov, L. Medrano Sandonas, O. T. Unke, S. Chmiela, K.-R. M¨ uller, and A. Tkatchenko, Molecular simulations with a pretrained neural network and universal pairwise force fields, Journal of the American Chemical Society 147, 33723 (2025)

    work page 2025

  26. [28]

    Bereau, R

    T. Bereau, R. A. DiStasio, A. Tkatchenko, and O. A. Von Lilienfeld, Non-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning, The Journal of chemical physics 148 (2018)

    work page 2018

  27. [29]

    J. E. Lennard-Jones, Cohesion, Proceedings of the Phys- ical Society 43, 461 (1931)

    work page 1931

  28. [30]

    Born and J

    M. Born and J. E. Mayer, Zur gittertheorie der io- nenkristalle, Zeitschrift f¨ ur Physik75, 1 (1932)

    work page 1932

  29. [31]

    R. A. Buckingham, The classical equation of state of gaseous helium, neon and argon, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 168, 264 (1938). 7

    work page 1938

  30. [32]

    Stone and S

    A. Stone and S. Price, Some new ideas in the theory of intermolecular forces: anisotropic atom-atom potentials, The Journal of Physical Chemistry 92, 3325 (1988)

    work page 1988

  31. [33]

    R. J. Wheatley and S. L. Price, An overlap model for estimating the anisotropy of repulsion, Molecular Physics 69, 507 (1990)

    work page 1990

  32. [34]

    G. M. Day and S. L. Price, A nonempirical anisotropic atom- atom model potential for chlorobenzene crystals, Journal of the American Chemical Society 125, 16434 (2003)

    work page 2003

  33. [35]

    T. S. Totton, A. J. Misquitta, and M. Kraft, A first prin- ciples development of a general anisotropic potential for polycyclic aromatic hydrocarbons, Journal of Chemical Theory and Computation 6, 683 (2010)

    work page 2010

  34. [36]

    D. M. Elking, G. A. Cisneros, J.-P. Piquemal, T. A. Darden, and L. G. Pedersen, Gaussian multipole model (gmm), Journal of chemical theory and computation 6, 190 (2010)

    work page 2010

  35. [37]

    M. J. Van Vleet, A. J. Misquitta, and J. Schmidt, New angles on standard force fields: Toward a general ap- proach for treating atomic-level anisotropy, Journal of Chemical Theory and Computation 14, 739 (2018)

    work page 2018

  36. [38]

    M. K. Chung and J. W. Ponder, Beyond isotropic re- pulsion: Classical anisotropic repulsion by inclusion of p orbitals, The Journal of Chemical Physics 160 (2024)

    work page 2024

  37. [39]

    S. Kita, K. Noda, and H. Inouye, Repulsive potentials for cl—r and br—r (r= he, ne, and ar) derived from beam experiments, The Journal of Chemical Physics 64, 3446 (1976)

    work page 1976

  38. [40]

    Y. S. Kim, S. K. Kim, and W. D. Lee, Dependence of the closed-shell repulsive interaction on the overlap of the electron densities, Chemical Physics Letters 80, 574 (1981)

    work page 1981

  39. [41]

    A. J. Misquitta, G. W. Welch, A. J. Stone, and S. L. Price, A first principles prediction of the crystal structure of c6br2clfh2, Chemical Physics Letters 456, 105 (2008)

    work page 2008

  40. [42]

    Tafipolsky and K

    M. Tafipolsky and K. Ansorg, Toward a physically mo- tivated force field: Hydrogen bond directionality from a symmetry-adapted perturbation theory perspective, Journal of Chemical Theory and Computation 12, 1267 (2016)

    work page 2016

  41. [43]

    Gavezzotti, Calculation of intermolecular interacti on energies by direct numerical integration over electron densities

    A. Gavezzotti, Calculation of intermolecular interacti on energies by direct numerical integration over electron densities. 2. an improved polarization model and the eval- uation of dispersion and repulsion energies, The Journal of Physical Chemistry B 107, 2344 (2003)

    work page 2003

  42. [44]

    S¨ oderhjelm, G

    P. S¨ oderhjelm, G. Karlstr¨ om, and U. Ryde, Comparison of overlap-based models for approximating the exchange- repulsion energy, The Journal of chemical physics 124 (2006)

    work page 2006

  43. [45]

    Piquemal, G

    J.-P. Piquemal, G. A. Cisneros, P. Reinhardt, N. Gresh, and T. A. Darden, Towards a force field based on density fitting, The Journal of chemical physics 124 (2006)

    work page 2006

  44. [46]

    Bygrave, N

    P. Bygrave, N. Allan, and F. Manby, The embedded many-body expansion for energetics of molecular crys- tals, The Journal of chemical physics 137 (2012)

    work page 2012

  45. [47]

    G. Ihm, M. Cole, F. Toigo, and J. Klein, Charge-overlap model of physical interactions and a combining rule for unlike systems, Physical Review A 42, 5244 (1990)

    work page 1990

  46. [48]

    Nobeli, S

    I. Nobeli, S. Price, and R. Wheatley, Use of molecular overlap to predict intermolecular repulsion in n ··· h—o hydrogen bonds, Molecular Physics 95, 525 (1998)

    work page 1998

  47. [49]

    T. C. Lillestolen and R. J. Wheatley, Atomic charge den- sities generated using an iterative stockholder procedure, The Journal of chemical physics 131 (2009)

    work page 2009

  48. [50]

    Verstraelen, S

    T. Verstraelen, S. Vandenbrande, F. Heidar-Zadeh, L. Vanduyfhuys, V. Van Speybroeck, M. Waroquier, and P. W. Ayers, Minimal basis iterative stockholder: atoms in molecules for force-field development, Journal of Chemical Theory and Computation 12, 3894 (2016)

    work page 2016

  49. [51]

    J. B. Mitchell and S. L. Price, A systematic nonempirical method of deriving model intermolecular potentials for organic molecules: application to amides, The Journal of Physical Chemistry A 104, 10958 (2000)

    work page 2000

  50. [52]

    Jeziorski, M

    B. Jeziorski, M. Bulski, and L. Piela, First-order pertur- bation treatment of the short-range repulsion in a system of many closed-shell atoms or molecules, International Journal of Quantum Chemistry 10, 281 (1976)

    work page 1976

  51. [53]

    J. N. Murrell, M. Randi´ c, and D. Williams, The theory of intermolecular forces in the region of small orbital over- lap, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 284, 566 (1965)

    work page 1965

  52. [54]

    This can be derived by taking the trace of the interaction density matrix in ref. [47]

    work page

  53. [55]

    Jeziorski, R

    B. Jeziorski, R. Moszynski, A. Ratkiewicz, S. Rybak, K. Szalewicz, and H. L. Williams, Sapt: A program for many-body symmetry-adapted perturbation theory cal- culations of intermolecular interaction energies, Methods and techniques in computational chemistry: METECC 94, 79 (1993)

    work page 1993

  54. [56]

    Moszynski, B

    R. Moszynski, B. Jeziorski, S. Rybak, K. Szalewicz, and H. L. Williams, Many-body theory of exchange effects in intermolecular interactions. density matrix approach and applications to he–f-, he–hf, h2–hf, and ar–h2 dimers, The Journal of chemical physics 100, 5080 (1994)

    work page 1994

  55. [57]

    J. H. Jensen and M. S. Gordon, An approximate formula for the intermolecular pauli repulsion between closed shell molecules, molecular physics 89, 1313 (1996)

    work page 1996

  56. [58]

    A. J. Misquitta and A. J. Stone, Ab initio atom–atom po- tentials using camcasp: Theory and application to many- body models for the pyridine dimer, Journal of chemical theory and computation 12, 4184 (2016)

    work page 2016

  57. [59]

    M. Levy, J. P. Perdew, and V. Sahni, Exact differential equation for the density and ionization energy of a many- particle system, Physical Review A 30, 2745 (1984)

    work page 1984

  58. [60]

    H. L. Williams and C. F. Chabalowski, Using kohn- sham orbitals in symmetry-adapted perturbation theory to investigate intermolecular interactions, The Journal of Physical Chemistry A 105, 646 (2001)

    work page 2001

  59. [61]

    A. J. Misquitta and K. Szalewicz, Intermolecular forces from asymptotically corrected density functional descrip- tion of monomers, Chemical physics letters 357, 301 (2002)

    work page 2002

  60. [62]

    Q. Wang, J. A. Rackers, C. He, R. Qi, C. Narth, L. La- gardere, N. Gresh, J. W. Ponder, J.-P. Piquemal, and P. Ren, General model for treating short-range electro- static penetration in a molecular mechanics force field, Journal of chemical theory and computation 11, 2609 (2015)

    work page 2015

  61. [63]

    Rez´ ac, K

    J. Rez´ ac, K. E. Riley, and P. Hobza, S66: A well-balanced database of benchmark interaction energies relevant to biomolecular structures, Journal of chemical theory and computation 7, 2427 (2011)

    work page 2011

  62. [64]

    The A VDO model has an RMSE of 2.2 kcal/mol for the intermediate range of (0.8-.95) Req on S66

    work page

  63. [65]

    These data can be ob- tained free of charge from The Cambridge Crystallo- 8 graphic Data Centre via www.ccdc.cam.ac.uk/structures

    Dimer configurations were taken from CCDC 1216810, 1103062, 1269538, and 114447. These data can be ob- tained free of charge from The Cambridge Crystallo- 8 graphic Data Centre via www.ccdc.cam.ac.uk/structures

    work page

  64. [66]

    C. R. Groom, I. J. Bruno, M. P. Lightfoot, and S. C. Ward, The cambridge structural database, Structural Science 72, 171 (2016)

    work page 2016

  65. [67]

    Henrichsmeyer, M

    J. Henrichsmeyer, M. Thelen, M. Br¨ ockel, M. Fadel, S. Behnle, M. Sekkal-Rahal, and R. F. Fink, Ratio- nalizing aggregate structures with orbital contributions to the exchange-repulsion energy, ChemPhysChem 24, e202300097 (2023)

    work page 2023

  66. [68]

    S. F. Boys, Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another, Reviews of Modern Physics 32, 296 (1960)

    work page 1960

  67. [69]

    Brockherde, L

    F. Brockherde, L. Vogt, L. Li, M. E. Tuckerman, K. Burke, and K.-R. M¨ uller, Bypassing the kohn-sham equations with machine learning, Nature communica- tions 8, 872 (2017)

    work page 2017

  68. [70]

    Efficient prediction of 3D electron densities using machine learning

    M. Bogojeski, F. Brockherde, L. Vogt-Maranto, L. Li, M. E. Tuckerman, K. Burke, and K.-R. M¨ uller, Efficient prediction of 3d electron densities using machine learn- ing, arXiv preprint arXiv:1811.06255 (2018)

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  69. [71]

    Grisafi, A

    A. Grisafi, A. Fabrizio, B. Meyer, D. M. Wilkins, C. Corminboeuf, and M. Ceriotti, Transferable machine- learning model of the electron density, ACS central sci- ence 5, 57 (2018)

    work page 2018

  70. [72]

    Fabrizio, A

    A. Fabrizio, A. Grisafi, B. Meyer, M. Ceriotti, and C. Corminboeuf, Electron density learning of non- covalent systems, Chemical science 10, 9424 (2019)

    work page 2019

  71. [73]

    Ramakrishnan, P

    R. Ramakrishnan, P. O. Dral, M. Rupp, and O. A. Von Lilienfeld, Quantum chemistry structures and prop- erties of 134 kilo molecules, Scientific data 1, 1 (2014)

    work page 2014

  72. [74]

    P. B. Jørgensen and A. Bhowmik, Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids, npj Computational Mate- rials 8, 183 (2022)

    work page 2022

  73. [75]

    Z. Qiao, A. S. Christensen, M. Welborn, F. R. Manby, A. Anandkumar, and T. F. Miller III, Informing geo- metric deep learning with electronic interactions to ac- celerate quantum chemistry, Proceedings of the National Academy of Sciences 119, e2205221119 (2022)

    work page 2022

  74. [76]

    Koker, K

    T. Koker, K. Quigley, E. Taw, K. Tibbetts, and L. Li, Higher-order equivariant neural networks for charge den- sity prediction in materials, npj Computational Materials 10, 161 (2024)

    work page 2024

  75. [77]

    X. Fu, A. Rosen, K. Bystrom, R. Wang, A. Musaelian, B. Kozinsky, T. Smidt, and T. Jaakkola, A recipe for charge density prediction, Advances in Neural Informa- tion Processing Systems 37, 9727 (2024)

    work page 2024

  76. [78]

    O. Unke, M. Bogojeski, M. Gastegger, M. Geiger, T. Smidt, and K.-R. M¨ uller, Se(3)-equivariant predic- tion of molecular wavefunctions and electronic densi- ties, in Advances in Neural Information Processing Sys- tems, Vol. 34, edited by M. Ranzato, A. Beygelzimer, Y. Dauphin, P. Liang, and J. W. Vaughan (Curran As- sociates, Inc., 2021) pp. 14434–14447

    work page 2021

  77. [79]

    J. A. Rackers, L. Tecot, M. Geiger, and T. E. Smidt, A recipe for cracking the quantum scaling limit with ma- chine learned electron densities, Machine Learning: Sci- ence and Technology 4, 015027 (2023)

    work page 2023

  78. [80]

    M. P. Hodges and R. J. Wheatley, Application of the overlap model to calculating correlated exchange ener- gies, Chemical Physics Letters 326, 263 (2000)

    work page 2000

  79. [81]

    Epifanovsky, A

    E. Epifanovsky, A. T. Gilbert, X. Feng, J. Lee, Y. Mao, N. Mardirossian, P. Pokhilko, A. F. White, M. P. Coons, A. L. Dempwolff, et al., Software for the frontiers of quan- tum chemistry: An overview of developments in the q- chem 5 package, The Journal of chemical physics 155 (2021)

    work page 2021

  80. [82]

    Q. Sun, T. C. Berkelbach, N. S. Blunt, G. H. Booth, S. Guo, Z. Li, J. Liu, J. D. McClain, E. R. Sayfutyarova, S. Sharma, et al. , Pyscf: the python-based simulations of chemistry framework, Wiley Interdisciplinary Reviews: Computational Molecular Science 8, e1340 (2018)

    work page 2018

Showing first 80 references.