CE29 - Chimie : analyse, théorie, modélisation

Bridge Functional in Molecular DFT – BRIDGE

BRIDGE functional in Molecular DFT

The solvation properties of molecules/macromolecules are investigated within the classical DFT at the molecular level of description. The HNC approximation used until now ignores the so-called bridge functions, which appear to be non negligible, especially in aqueous solvents. The project proposes different routes to produce efficient bridge functional/functions.

Produce powerful «bridge« functionals for various solute/solvent couples.

The ultimate objective in the present scientific domain is to be able to calculate theoretically, as efficiently as possible, the solvation properties of molecules, macromolecules, interfaces immersed in various solvents. Direct applications can be obviously found in biology, in colloidal physics, in electrochemistry, in energy fields: it is a matter for instance of predicting the solvation free energy of a drug molecule, of a protein and of the drug-protein complex inside the physiological medium, this even before any experimental synthesis of the drug ; of knowing the spatial and orientational distribution of the solvent molecules in the neighbouring of a colloid or a biological macromolecule and their contribution to the X-ray or neutron scattering spectra; of determining the ionic profiles in an aqueous electrolyte in the vicinity of an electrode… The meaning of «as efficiently as possible« is twofold: i) first, one must obviously reproduce the real world and experimental data as close as possible, using pertinent levels of description and valid statistical mechanics black boxes; ii) secondly, one wants to do that numerically demanding job as fast as possible, in order to make it possible systematic and routine analyses. What must be the level of realistic description in this theoretical field? The requirement i) discards the continuous solvent level which considers the solvent as a dielectric medium and misses the specific interactions (hydrogen-bonding…) between the solute sites and the solvent atoms. The requirement ii) discards somewhere the ab-initio level with a full explicit description of all electrons and the need for solving the Schrödinger equation. A good compromise between exactness and speed of resolution, which is the rule in the present domain, is the explicit level of description of the solvent and solute molecules which interact through classical atom-atom or site-site potentials or force fields. The parameters characterizing the Lennard-Jones (LJ) and partial charges coulombic contributions are mainly considered as phenomenological and are usually adjusted in order to reproduce some experimental data of the solvent-solute ensemble.

Different routes are followed in order to produce robust approximations for the missing bridge functionals:
-spherical bridge within WDA
-3 body bridge functional/diagram within the BHP approach
-Solve MDFT/HNC for solute-solvent dimers
-Invert the problem from simulation data for reference solutes

-Bridge functional of spherical symmetry
-Intermediate function t in the BHP approach
-Exact bridge function for ionic solutes of various valence, expressed in terms of angular projections

-Calculate the bridge diagram with the help og the function t for various solutes
-Generalize the inversion of simulation data and rationalize the results for prediction

Published articles:
1. Luukkonen, Levesque, Belloni, Borgis, J. Chem. Phys. 152, 06410 (2020)
2. Borgis, Luukkonen, Belloni, Jeanmairet, J. Phys. Chem. B 124, 6885 (2020)
3. Borgis, Luukkonen, Belloni, Jeanmairet, J. Chem. Phys. 155, 024117 (2021)
4. Jeanmairet, Levesque, Borgis, J. Chem. Theor. Comput. (2020)

The theoretical understanding of solvation properties of molecules / macromolecules / interfaces in the domains of biology, colloidal physics, electrochemistry, etc., requires an explicit molecular solvent level of description with atom-atom classical force-fields. Beside the too much time-consuming numerical simulations, a powerful liquid physics theory has appeared recently, based on the 3D molecular DFT, which enables to calculate very quickly spatial+angular solvent density profiles as well as solvation free energy for any solute. Up to now, this MDFT approach is solved within the HNC approximation which neglects the so-called "bridge" correlation functions. It happens that for highly polar solvents presenting strong hydrogen bonding like water,HNC leads to quantitative disagreements. The BRIDGE project consists then in developing the theory beyond this standard approximation by constructing various bridge functionals or functions. The very wide experience of the team in statistical physics of liquids will make it possible to extend simple spherical liquid approaches to molecular solvents and solutes governed by highly anisotropic interactions and correlations. 4 routes will be explored:
1) We will first ignore the angular dependence and borrow the well-known hard-sphere functionals or construct simple polynomial functionals in a weighted spatial density.
2) We will solve the MDFT/HNC theory around a dimer made of the real solute and an additive solvent molecule at fixed relative position/orientation. That corresponds to use the HNC approximation higher in the hierarchy of the integral equations (for the dimer), so safer for the pair correlation. The solute-solvent bridge function will be extracted from the improved potential of mean force.
3) The exact functional can formally be written as an expansion involving a higher and higher number N of solvent molecules coupled via N-body direct correlation functions, the HNC approximation stopping at N=2. The present fundamental and ambitious route will calculate the next term, the 3-body bridge functional by extending what has been done in the literature for spheres. The bulk function c(3)(1,2,3) will be approximated by t(12)t(13)t(23) with the pair function t derived from a thermodynamical self-consistent relation.
4) This last approach will investigate an inverse route: the exact spatial/angular profiles will be provided by very precise simulation data and the statistical physics problem (Ornstein-Zernike + integral equations) will be inverted in order to produce exact solute-solvent bridge functions. Then, systematic behaviors will be drawn in order to reach the bridge functional.
This ANR project will develop efficient theories, algorithms and numerical codes and will routinely solve MDFT and simulation for a great number of solutes. That requires important computing resources. Once optimized bridge functionals will be validated, MDFT will stand by itself as an efficient and competitive predictive tool, independent from simulations. It will be available to the community in a routinely manner in order to better understand real systems. Such applications will be investigated at the end of the project.
The funding mainly corresponds to 3 years of postdoc and computers/workstations.

Project coordination

Luc Belloni (Nanosciences et innovation pour les matériaux, la biomédecine et l'énergie)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

MdlS Daniel BORGIS
NIMBE Nanosciences et innovation pour les matériaux, la biomédecine et l'énergie
PASTEUR Processus d'Activation Sélectif par Transfert d'Energie Uni-électronique ou Radiatif
PHENIX PHysicochimie des Electrolytes et Nanosystèmes InterfaciauX

Help of the ANR 294,009 euros
Beginning and duration of the scientific project: October 2019 - 42 Months

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