Project B1: Inverse problems in coarse-grained particle simulations

Coarse-graining (CG) methods are an indispensable tool in computational materials science, but the associated upscaling and downscaling processes have to be designed with great care to allow for a proper interpretation of the computed results. Each of these interscale transfers comes along with important inverse problems to be resolved, most of which are ill-posed, or ill-conditioned at the very least. The purpose of this project is to apply rigorous techniques from the mathematical field of inverse and ill-posed problems to attack these fundamental problems in the multiscale simulation of soft matter, and to provide a mathematically rigorous foundation of existing and/or new upscaling processes.

n the first two funding phases we have developed the mathematical foundation for a rigorous analysis of iterative methods that are currently being used for the computation of effective pair potentials of sophisticated CG models. We have used this insight to come up with new algorithms for this purpose, which are well suited to match certain structural as well as thermodynamical quantities of interest. These methods have been implemented and explored on real physical test cases.

In the third funding phase we want to extend these algorithms to systems with different types of CG beads in bonded and nonbonded chemical environments. We further plan to reformulate the mathematical foundation and study the inverse problem as a variational problem from a relative entropy point of view. This should allow for alternative mathematical techniques to treat convergence and stability issues of established iterative schemes. With the newly available algorithms we want to derive a transferable CG model for aqueous solutions of a thermo-responsive polymer. We plan to study structural transitions at the level of single and multiple chains in relation to the macroscopic solution phase behavior in the presence of cosolvents. To bridge the gap between local structure and macroscopic phase behavior, we plan to couple the CG particle model to a fieldtheoretical description (collaboration with project C1). The workplan involves critical testing of transferability properties of the CG particle model required to predictively model macroscopic phase behavior and polymer coil-globule transitions occurring upon crossing of phase boundaries. As a second demonstration of the ad-
vances made with the methods developed in this project we plan to improve nonpolarizable force fields for strongly hydrated ions based on ab-initio MD reference ensembles obtained with multi-resolution algorithms (collaboration with project B5).

Publications

Pressure-induced pKa variations influence conformations of pH-sensitive polymers
Ved Mahajan, Varun Mandalaparthy, Nico F.A. van der Vegt
The Journal of Chemical Physics 164, 084907 (2026)
Link: https://doi.org/10.1063/5.0303682

Thermoresponsivity and cononsolvency of a minimal polymer model in mixed solvents
Ved Mahajan, Nico F.A. van der Vegt
The Journal of Chemical Physics 164, 124901 (2026)
Link: https://doi.org/10.1063/5.0325441

Beyond Electrostatic Screening: Effect of Ion Pairing on Acid-Base Equilibria in Complex Electrolyte Solutions
Varun Mandalaparthy, Johannes Hunger, Mischa Bonn, Nico F.A. van der Vegt
Journal of Physical Chemistry Letters 17, 511-518 (2026)
Link: https://doi.org/10.1021/acs.jpclett.5c03363

A generic model for pH-sensitive collapse of hydrophobic polymers
Varun Mandalaparthy, Nico F.A. van der Vegt
Phys. Chem. Chem. Phys. 27, 6984-6993 (2025)
Link: https://doi.org/10.1039/d4cp04756g

Determination of aqueous solubility of NaCl in molecular dynamics simulation using the Kirkwood-Buff method
Abishek Chattopadhyay, Varun Mandalaparthy, Nico F. A. van der Vegt
The Journal of Chemical Physics 162, 174116 (2025)
Link: https://doi.org/10.1063/5.0264104

Stability, Speed, and Constraints for Structural Coarse-Graining in VOTCA
Marvin P. Bernhardt, Martin Hanke, Nico F.A. van der Vegt
J. Chem. Theory Comput. 19, 580-595 (2023)
Link: https://doi.org/10.1021/acs.jctc.2c00665

Anions and Cations Affect Amino Acid Dissociation Equilibria via Distinct Mechanisms
Varun Mandalaparthy, Madhusmita Tripathy, Nico F.A. van der Vegt
Journal of Physical Chemistry Letters 14, 9250-9256 (2023)
Link: https://doi.org/10.1021/acs.jpclett.3c02062

Solvation Behavior of Elastin-like Polypeptides in Divalent Metal Salt Solutions
Yani Zhao, Swaminath Bharadwaj, Ryan L. Myers, Halil Okur, Pho T. Bui, Mengrui Cao, Lauren K. Welch, Tinglu Wang, Paul S. Cremer, Nico F.A. van der Vegt
Journal of Physical Chemistry Letters 14, 10113-10118 (2023)
Link: https://doi.org/10.1021/acs.jpclett.3c02476

Small-to-large length scale transition of TMAO interaction with hydrophobic solutes
Angelina Folberth, Swaminath Bharadwaj, Nico F.A. van der Vegt
Phys. Chem. Chem. Phys. 24, 2080-2087 (2022)
Link: https://doi.org/10.1039/d1cp05167a

Cononsolvency of thermoresponsive polymers: where we are now and where we are going
S. Bharadwaj, B.-J. Niebuur, K. Nothdurft, W. Richtering, N.F.A. van der Vegt, C.M. Papadakis
Soft Matter 18, 2884-2909 (2022)
Link: https://doi.org/10.1039/d2sm00146b

Solvation shell thermodynamics of extended hydrophobic solutes in mixed solvents
Madhusmita Tripathy, Swaminath Bharadwaj, Nico F.A. van der Vegt
The Journal of Chemical Physics 156, 164901 (2022)
Link: https://doi.org/10.1063/5.0090646

Nonadditive ion effects on the coil-globule equilibrium of PNIPAM: a computer simulation study
Yani Zhao, Saminath Bharadwaj, Nico F.A. van der Vegt
Phys. Chem. Chem. Phys. 24, 10346-10355 (2022)
Link: https://doi.org/10.1039/d2cp00057a

A variational framework for the inverse Henderson problem of statistical mechanics
Fabio Frommer and Martin Hanke
Letters in Mathematical Physics 112, 71, (2022)
Link: https://doi.org/10.1007/s11005-022-01563-w

Where Lennard-Jones Potentials Fail: Iterative Optimization of Ion–Water Pair Potentials Based on Ab Initio Molecular Dynamics Data
Marvin P. Bernhardt, Yuki Nagata, Nico F.A. van der Vegt
Journal of Physical Chemistry Letters 13, 16, 3712–3717 (2022)
Link: https://doi.org/10.1021/acs.jpclett.2c00121

Direct Calculation of Entropic Components in Cohesive Interaction Free Energies
Saminath Bharadwaj, Shadrack B. Jabes, Nico F. A. van der Vegt
The Journal of Physical Chemistry B 125, 11026-11035 (2021)
Link: https://doi.org/10.1021/acs.jpcb.1c05748

Coarse-grained model of a nanoscale-segregated ionic liquid for simulations of low-temperature structure and dynamics
Sebastian Kloth, Marvin P Bernhardt, Nico F A van der Vegt, Michael Vogel
Journal of Physics: Condensed Matter 33 (20), 204002 (2021)
Link: https://doi.org/10.1088/1361-648X/abe606

An interplay of excluded-volume and polymer–(co)solvent attractive interactions regulates polymer collapse in mixed solvents
Swaminath Bharadwaj, Divya Nayar, Cahit Dalgicdir, Nico F. A. van der Vegt
The Journal of Chemical Physics154 (13), 134903 (2021)
Link: https://doi.org/10.1063/5.0046746

Iterative integral equation methods for structural coarse-graining
Marvin P. Bernhardt, Martin Hanke, Nico F. A. van der Vegt
The Journal of Chemical Physics 154 (8), 084118 (2021)
Link: https://doi.org/10.1063/5.0038633

Application of the 2PT model to understanding entropy change in molecular coarse-graining
Marvin P. Bernhardt, Marco Dallavalle, Nico F. A. Van der Vegt
Soft Materials 18 (2-3), 274-289 (2020)
Link: https://doi.org/10.1080/1539445X.2020.1737118

A generalized Newton iteration for computing the solution of the inverse Henderson problem
Fabrice Delbary, Martin Hanke, Dmitry Ivanizki
Inverse Problems in Science and Engineering, 1-25 (2020)
Link: https://doi.org/10.1080/17415977.2019.1710504

Does Preferential Adsorption Drive Cononsolvency?
Swaminath Bharadwaj, Nico F. A. van der Vegt
Macromolecules 52 (11), 4131-4138 (2019)
Link: https://doi.org/10.1021/acs.macromol.9b00575

A note on the uniqueness result for the inverse Henderson problem
F. Frommer, M. Hanke, S. Jansen
Journal of Mathematical Physics 60 (9), 093303 (2019)
Link: https://doi.org/10.1063/1.5112137

Relative entropy indicates an ideal concentration for structure-based coarse graining of binary mixtures
David Rosenberger and Nico F. A. van der Vegt
Physical Review E99, 053308 (2019)
Link: https://doi.org/10.1103/PhysRevE.99.053308

Transferability of Local Density-Assisted Implicit Solvation Models for Homogeneous Fluid Mixtures
David Rosenberger, Tanmoy Sanyal, M. Scott Shell, and Nico F. A. van der Vegt
Journal of Chemical Theory and Computation 15, 2881-2895 (2019)
Link: https://doi.org/10.1021/acs.jctc.8b01170

A generalization of the Carnahan-Starling approach with applications to four- and five-dimensional hard sphere
Dmitry Ivanizki
Phys. Lett. A 382, 1745-1751 (2018)
Link: https://doi.org/10.1016/j.physleta.2018.04.036

Cosolvent effects on polymer hydration drive hydrophobic collapse
Divya Nayar and Nico F. A. van der Vegt
The Journal of Physical Chemistry B 122, 3587-3595 (2018)
Link: https://doi.org/10.1021/acs.jpcb.7b10780

Addressing the temperature transferability of structure based coarse graining models
David Rosenberger and Nico F. A. van der Vegt
The Journal of Physical Chemistry 20, 6617-6628 (2018)
Link: https://doi.org/10.1039/c7cp08246k

Fréchet differentiability of molecular distribution functions II. The Ursell function
Martin Hanke
Letters in Mathematical Physics 108 (2), 307-329 (2018)
Link: https://doi.org/10.1007/s11005-017-1010-7

Well-Posedness of the Iterative Boltzmann Inversion
Martin Hanke
Journal of Statistical Physics 170 (3), 536-553 (2018)
Link: https://doi.org/10.1007/s10955-017-1944-2

Evaluation of mapping schemes for systematic coarse graining of higher alkanes
Marco Dallavalle, Nico F. A. van der Vegt
Physical Chemistry Chemical Physics 19 (34), 23034-23042 (2017)
Link: https://doi.org/10.1039/c7cp03926c

The Hydrophobic Effect and the Role of Cosolvents
Nico F. A. van der Vegt, Divya Nayar
The Journal of Physical Chemistry B121 (43), 9986-9998 (2017)
Link: https://doi.org/10.1021/acs.jpcb.7b06453

Molecular origin of urea driven hydrophobic polymer collapse and unfolding depending on side chain chemistry
Divya Nayar, Angelina Folberth, Nico F. A. van der Vegt
Physical Chemistry Chemical Physics 19 (28), 18156-18161 (2017)
Link: https://doi.org/10.1039/c7cp01743j

Fréchet differentiability of molecular distribution functions I. L^∞ analysis
Martin Hanke
Letters in Mathematical Physics 108 (2), 285-306 (2017)
Link: https://doi.org/10.1007/s11005-017-1009-0

An inverse problem in statistical mechanics
Martin Hanke
in Oberwolfach Reports, Editor: Gerhard Huisken, ChapterReport No. 08/2017, EMS, Zürich, Series:Oberwolfach Reports, Vol.14, 424-426 (2017)
Link: https://doi.org/10.4171/OWR/2017/8

Comparison of Different TMAO Force Fields and Their Impact on the Folding Equilibrium of a Hydrophobic Polymer
Francisco Rodríguez-Ropero, Philipp Rötzscher, Nico F. A. van der Vegt
The Journal of Physical Chemistry B120 (34), 8757-8767 (2016)
Link: https://doi.org/10.1021/acs.jpcb.6b04100

Comparison of iterative inverse coarse-graining methods
David Rosenberger, Martin Hanke, Nico F.A. van der Vegt
The European Physical Journal Special Topics 225 (8-9), 1323-1345 (2016)
Link: https://doi.org/10.1140/epjst/e2016-60120-1

Mechanism of Polymer Collapse in Miscible Good Solvents
Francisco Rodríguez-Ropero, Timir Hajari, Nico F. A. van der Vegt
The Journal of Physical Chemistry B119 (51), 15780-15788 (2015)
Link: https://doi.org/10.1021/acs.jpcb.5b10684