Daniel Borgis

Molecular Density Functional Theory of Water.

Three-dimensional implementations of liquid-state theories offer an efficient alternative to computer simulations for the atomic-level description of aqueous solutions in complex environments. In this context, we present a (classical) molecular density functional theory (MDFT) of water that is derived from first principles and is based on two classical density fields, a scalar one, the particle density, and a vectorial one, the multipolar polarization density. Its implementation requires as input the partial charge distribution of a water molecule and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric constants. It has to be complemented by a solute-solvent three-body term that reinforces tetrahedral order at short-range. The approach is shown to provide the correct 3-D microscopic solvation profile around various molecular solutes, possibly possessing H-bonding sites, at a computer cost two to three orders of magnitude lower than with explicit simulations.

Scalar fundamental measure theory for hard spheres in three dimensions: application to hydrophobic solvation.

Hard-sphere mixtures provide one a solvable reference system that can be used to improve the density functional theory of realistic molecular fluids. We show how the Kierlik-Rosinbergs scalar version of the fundamental measure density functional theory of hard spheres [E. Kierlik and M. L. Rosinberg, Phys. Rev. A 42, 3382 (1990)], which presents computational advantages with respect to the original Rosenfelds vectorial formulation or its extensions, can be implemented and minimized in three dimensions to describe fluid mixtures in complex environments. This implementation is used as a basis for defining a molecular density functional theory of water around molecular hydrophobic solutes of arbitrary shape.

Combining a polarizable force‐field and a coarse‐grained polarizable solvent model. II. Accounting for hydrophobic effects

A revised and improved version of our efficient polarizable force‐field/coarse grained solvent combined approach (Masella, Borgis, and Cuniasse, J. Comput. Chem. 2008, 29, 1707) is described. The polarizable pseudo‐particle solvent model represents the macroscopic solvent polarization by induced dipoles placed on mobile pseudo‐particles. In this study, we propose a new formulation of the energy term handling the nonelectrostatic interactions among the pseudo‐particles. This term is now able to reproduce the energetic and structural response of liquid water due to the presence of a hydrophobic spherical cavity. Accordingly, the parameters of the energy term handling the nonpolar solute/solvent interactions have been refined to reproduce the free‐solvation energy of small solutes, based on a standard thermodynamic integration scheme. The reliability of this new approach has been checked for the properties of solvated methane and of the solvated methane dimer, as well as by performing 10 × 20 ns molecular dynamics (MD) trajectories for three solvated proteins. A long‐time stability of the protein structures along the trajectories is observed. Moreover, our method still provides a measure of the protein solvation thermodynamic at the same accuracy as standard Poisson–Boltzman continuum methods. These results show the relevance of our approach and its applicability to massively coupled MD schemes to accurately and intensively explore solvated macromolecule potential energy surfaces.

Nuclear quantum effects in electronically adiabatic quantum time correlation functions: Application to the absorption spectrum of a hydrated electron

A general formalism for introducing nuclear quantum effects in the expression of the quantum time correlation function of an operator in a multilevel electronic system is presented in the adiabatic limit. The final formula includes the nuclear quantum time correlation functions of the operator matrix elements, of the energy gap, and their cross terms. These quantities can be inferred and evaluated from their classical analogs obtained by mixed quantum-classical molecular dynamics simulations. The formalism is applied to the absorption spectrum of a hydrated electron, expressed in terms of the time correlation function of the dipole operator in the ground electronic state. We find that both static and dynamic nuclear quantum effects distinctly influence the shape of the absorption spectrum, especially its high energy tail related to transitions to delocalized electron states. Their inclusion does improve significantly the agreement between theory and experiment for both the low and high frequency edges of the spectrum. It does not appear sufficient, however, to resolve persistent deviations in the slow Lorentzian-like decay part of the spectrum in the intermediate 2-3 eV region.

Computing Wigner distributions and time correlation functions using the quantum thermal bath method: application to proton transfer spectroscopy

Langevin dynamics coupled to a quantum thermal bath (QTB) allows for the inclusion of vibrational quantum effects in molecular dynamics simulations at virtually no additional computer cost. We investigate here the ability of the QTB method to reproduce the quantum Wigner distribution of a variety of model potentials, designed to assess the performances and limits of the method. We further compute the infrared spectrum of a multidimensional model of proton transfer in the gas phase and in solution, using classical trajectories sampled initially from the Wigner distribution. It is shown that for this type of system involving large anharmonicities and strong nonlinear coupling to the environment, the quantum thermal bath is able to sample the Wigner distribution satisfactorily and to account for both zero point energy and tunneling effects. It leads to quantum time correlation functions having the correct short-time behavior, and the correct associated spectral frequencies, but that are slightly too overdamped. This is attributed to the classical propagation approximation rather than the generation of the quantized initial conditions themselves.

A Multiscale Coarse-Grained Polarizable Solvent Model for Handling Long Tail Bulk Electrostatics

A multiscale coarse‐grained approach able to handle efficiently the solvation of microscopic solutes in extended chemical environment is described. That approach is able to compute readily and efficiently very long‐range solute/solvent electrostatic microscopic interactions, up to the 1‐μm scale, by considering a reduced amount of computational resources. All the required parameters are assigned to reproduce available data concerning the solvation of single ions. Such a strategy makes it possible to reproduce with good accuracy the solvation properties concerning simple ion pairs in solution (in particular, the asymptotic behavior of the ion pair potentials of mean force). This new method represents an extension of the polarizable pseudoparticle solvent model, which has been recently improved to account for the main features of hydrophobic effects in liquid water (Masella et al., J. Comput. Chem. 2011, 32, 2664). This multiscale approach is well suited to be used for computing the impact of charge changes in free energy computations, in terms of both accuracy and efficiency.

Hydration of clays at the molecular scale: the promising perspective of classical density functional theory

We report here how the hydration of complex surfaces can be efficiently studied, thanks to recent advances in classical molecular density functional theory. This is illustrated on the example of the pyrophyllite clay. After presenting the most recent advances, we show that the strength of this implicit method is that: (1) it is in quantitative or semi-quantitative agreement with reference all-atom simulations (molecular dynamics here) for both the solvation structure and energetics, and (2) the computational cost is two to three orders of magnitude less than in explicit methods. The method remains imperfect in that it locally overestimates the polarisation of water close to hydrophylic sites of the clay. The high numerical efficiency of the method is illustrated and exploited to carry out a systematic study of the electrostatic and van der Waals components of the surface–solvent interactions within the most popular force field for clays, CLAYFF. Hydration structure and energetics are found to weakly depend upon the electrostatics. We conclude on the consequences of such findings on future force-field development.

Molecular density functional theory of water including density-polarization coupling.

We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particles density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.

Electronic Excited State Lifetimes of Anionic Water Clusters: Dependence on Charge Solvation Motif

An ongoing controversy about water cluster anions concerns the electron-binding motif, whether the charge center is localized at the surface or within the cluster interior. Here, mixed quantum-classical dynamics simulations have been carried out for a wide range of cluster sizes (n ≤ 1000) for (H2O)n- and (D2O)n-, based on a nonequilibrium first-order rate constant approach. The computed data are in good general agreement with time-resolved photoelectron imaging results (n ≤ 200). The analysis reveals that, for surface state electrons, the cluster size dependence of the excited state electronic energy gap and the magnitude of the nonadiabatic couplings have compensating influences on the excited state lifetimes: the excited state lifetime for surface states reaches a minimum for n ∼ 150 and then increases for larger clusters. It is concluded that the electron resides in a surface-localized motif in all of these measured clusters, dominating at least up to n = 200.

Efficient molecular density functional theory using generalized spherical harmonics expansions

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.