The Microscopic Physical Cause for the Density Maximum of Liquid Water

Predicting and Understanding Non-Covalent Interactions Using Novel Forms of Symmetry-Adapted Perturbation Theory

Although sometimes derided as "weak" interactions, non-covalent forces play a critical role in ligand binding and crystal packing and in determining the conformational landscape of flexible molecules. Symmetry-adapted perturbation theory (SAPT) provides a framework for accurate ab initio calculation of intermolecular interactions and furnishes a natural decomposition of the interaction energy into physically meaningful components: semiclassical electrostatics (rigorously obtained from monomer charge densities), Pauli or steric repulsion, induction (including both polarization and charge transfer), and dispersion. This decomposition helps to foster deeper understanding of non-covalent interactions and can be used to construct transferable, physics-based force fields. Separability of the SAPT interaction energy also provides the flexibility to construct composite methods, a feature that we exploit to improve the description of dispersion interactions. These are challenging to describe accurately because they arise from nonlocal electron correlation effects that appear for the first time at second order in perturbation theory but are not quantitatively described at that level.As with all quantum-chemical methods, a major limitation of SAPT is nonlinear scaling of the computational cost with respect to system size. This cost can be significantly mitigated using "SAPT0(KS)", which incorporates monomer electron correlation by means of Kohn-Sham (KS) molecular orbitals from density functional theory (DFT), as well as by an "extended" theory called XSAPT, developed by the authors. XSAPT generalizes traditional dimer SAPT to many-body systems, so that a ligand-protein interaction (for example) can be separated into contributions from individual amino acids, reducing the cost of the calculation below that of even supramolecular DFT while retaining the accuracy of high-level ab initio quantum chemistry.This Account provides an overview of the SAPT0(KS) approach and the XSAPT family of methods. Several low-cost variants are described that provide accuracy approaching that of the best ab initio benchmarks yet are affordable enough to tackle ligand-protein binding and sizable host-guest complexes. These variants include SAPT+aiD, which uses ab initio atom-atom dispersion potentials ("+aiD") in place of second-order SAPT dispersion, and also SAPT+MBD, which incorporates many-body dispersion (MBD) effects that are important in the description of nanoscale materials. Applications to drug binding highlight the size-extensive nature of dispersion, which is not a weak interaction in large systems. Other applications highlight how a physics-based analysis can sometimes upend conventional wisdom regarding intermolecular forces. In particular, careful reconsideration of π-π interactions makes clear that the quadrupolar electrostatics (or "Hunter-Sanders") model of π-π stacking should be replaced by a "van der Waals model" in which conformational preferences arise from a competition between dispersion and Pauli repulsion. Our analysis also suggests that molecular shape, rather than aromaticity per se, is the key factor driving strong stacking interactions. Looking forward, we anticipate that XSAPT-based methods can play a role in screening of drug candidates and in materials design.

A polarizable QM/MM approach to the molecular dynamics of amide groups solvated in water

The infrared (IR) spectra of polypeptides are dominated by the so-called amide bands. Because they originate from the strongly polar and polarizable amide groups (AGs) making up the backbone, their spectral positions sensitively depend on the local electric fields. Aiming at accurate computations of these IR spectra by molecular dynamics (MD) simulations, which derive atomic forces from a hybrid quantum and molecular mechanics (QM/MM) Hamiltonian, here we consider the effects of solvation in bulk liquid water on the amide bands of the AG model compound N-methyl-acetamide (NMA). As QM approach to NMA we choose grid-based density functional theory (DFT). For the surrounding MM water, we develop, largely based on computations, a polarizable molecular mechanics (PMM) model potential called GP6P, which features six Gaussian electrostatic sources (one induced dipole, five static partial charge distributions) and, therefore, avoids spurious distortions of the DFT electron density in hybrid DFT/PMM simulations. Bulk liquid GP6P is shown to have favorable properties at the thermodynamic conditions of the parameterization and beyond. Lennard-Jones (LJ) parameters of the DFT fragment NMA are optimized by comparing radial distribution functions in the surrounding GP6P liquid with reference data obtained from a "first-principles" DFT-MD simulation. Finally, IR spectra of NMA in GP6P water are calculated from extended DFT/PMM-MD trajectories, in which the NMA is treated by three different DFT functionals (BP, BLYP, B3LYP). Method-specific frequency scaling factors are derived from DFT-MD simulations of isolated NMA. The DFT/PMM-MD simulations with GP6P and with the optimized LJ parameters then excellently predict the effects of aqueous solvation and deuteration observed in the IR spectra of NMA. As a result, the methods required to accurately compute such spectra by DFT/PMM-MD also for larger peptides in aqueous solution are now at hand.

Characterisation of the thermodynamics, structure and dynamics of a water-like model in 2- and 3-dimensions

The physical properties of colloidal particles suspended in an aqueous environment are well-understood when the latter is considered to be a continuum and a structureless medium. However, this approach fails to explain complex phenomena, for example, the critical Casimir forces among colloids and the colloidal self-assembly near critical solvents, and the inertial contribution of the solvent molecules on the diffusion of non-spherical Brownian particles. Therefore, the role played by the solvent on the physical properties of colloidal dispersions is of paramount relevance. Recently, there has been an interest in the (non-trivial) diffusion mechanisms of a nano-colloidal particle in a solvent that undergoes a vapour-liquid transition. Nonetheless, the models typically used to incorporate the solvent details do not capture quantitatively the thermodynamic properties of real substances. It is then important to study the Brownian motion of colloids in more realistic models. To reach such goal, one first has to characterise the thermodynamic states and the microscopic features of the solvent. Hence, in this contribution, we have investigated the coexistence densities of a core-softened potential in two- and three-dimensions, whose potential parameters are able to capture some anomalies of water. We show that in the two-dimensional case, the potential model exhibits, besides the normal vapour-liquid coexistence region, additional liquid-liquid coexistence densities. We particularly focus our attention to the structural properties and the dynamical behaviour of the solvent around the liquid-liquid critical point and assess the differences with the three-dimensional case.

2D-Raman-THz spectroscopy: a sensitive test of polarizable water models

In a recent paper, the experimental 2D-Raman-THz response of liquid water at ambient conditions has been presented [J. Savolainen, S. Ahmed, and P. Hamm, Proc. Natl. Acad. Sci. U. S. A. 110, 20402 (2013)]. Here, all-atom molecular dynamics simulations are performed with the goal to reproduce the experimental results. To that end, the molecular response functions are calculated in a first step, and are then convoluted with the laser pulses in order to enable a direct comparison with the experimental results. The molecular dynamics simulation are performed with several different water models: TIP4P/2005, SWM4-NDP, and TL4P. As polarizability is essential to describe the 2D-Raman-THz response, the TIP4P/2005 water molecules are amended with either an isotropic or a anisotropic polarizability a posteriori after the molecular dynamics simulation. In contrast, SWM4-NDP and TL4P are intrinsically polarizable, and hence the 2D-Raman-THz response can be calculated in a self-consistent way, using the same force field as during the molecular dynamics simulation. It is found that the 2D-Raman-THz response depends extremely sensitively on details of the water model, and in particular on details of the description of polarizability. Despite the limited time resolution of the experiment, it could easily distinguish between various water models. Albeit not perfect, the overall best agreement with the experimental data is obtained for the TL4P water model.

Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations

Recently, a novel approach to hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations has been suggested [Schwörer et al., J. Chem. Phys. 138, 244103 (2013)]. Here, the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10(3)-10(5) molecules as negative gradients of a DFT/PMM hybrid Hamiltonian. The electrostatic interactions are efficiently described by a hierarchical fast multipole method (FMM). Adopting recent progress of this FMM technique [Lorenzen et al., J. Chem. Theory Comput. 10, 3244 (2014)], which particularly entails a strictly linear scaling of the computational effort with the system size, and adapting this revised FMM approach to the computation of the interactions between the DFT and PMM fragments of a simulation system, here, we show how one can further enhance the efficiency and accuracy of such DFT/PMM-MD simulations. The resulting gain of total performance, as measured for alanine dipeptide (DFT) embedded in water (PMM) by the product of the gains in efficiency and accuracy, amounts to about one order of magnitude. We also demonstrate that the jointly parallelized implementation of the DFT and PMM-MD parts of the computation enables the efficient use of high-performance computing systems. The associated software is available online.

Structural Evolution of Supercritical CO2 across the Frenkel Line

Here, we study structural properties of the supercritical carbon dioxide and discover the existence of persistent medium-range order correlations, which make supercritical carbon dioxide nonuniform and heterogeneous on an intermediate length scale. We report on the CO2 heterogeneity shell structure where, in the first shell, both carbon and oxygen atoms experience gas-like-type interactions with short-range order correlations while within the second shell, oxygen atoms essentially exhibit a liquid-like type of interactions due to localization of transverse-like phonon packets. Importantly, we highlight a catalytic role of atoms inside of the nearest-neighbor heterogeneity shell in providing a mechanism for diffusion and proving the existence of an additional thermodynamic boundary in the supercritical carbon dioxide on an intermediate length scale. Finally, we discuss important implications for answering the intriguing question whether Venus may have had CO2 oceans and urge for an experimental detection of this persistent local-order heterogeneity.

Polarizable six-point water models from computational and empirical optimization

Tröster et al. (J. Phys. Chem B 2013, 117, 9486-9500) recently suggested a mixed computational and empirical approach to the optimization of polarizable molecular mechanics (PMM) water models. In the empirical part the parameters of Buckingham potentials are optimized by PMM molecular dynamics (MD) simulations. The computational part applies hybrid calculations, which combine the quantum mechanical description of a H2O molecule by density functional theory (DFT) with a PMM model of its liquid phase environment generated by MD. While the static dipole moments and polarizabilities of the PMM water models are fixed at the experimental gas phase values, the DFT/PMM calculations are employed to optimize the remaining electrostatic properties. These properties cover the width of a Gaussian inducible dipole positioned at the oxygen and the locations of massless negative charge points within the molecule (the positive charges are attached to the hydrogens). The authors considered the cases of one and two negative charges rendering the PMM four- and five-point models TL4P and TL5P. Here we extend their approach to three negative charges, thus suggesting the PMM six-point model TL6P. As compared to the predecessors and to other PMM models, which also exhibit partial charges at fixed positions, TL6P turned out to predict all studied properties of liquid water at p0 = 1 bar and T0 = 300 K with a remarkable accuracy. These properties cover, for instance, the diffusion constant, viscosity, isobaric heat capacity, isothermal compressibility, dielectric constant, density, and the isobaric thermal expansion coefficient. This success concurrently provides a microscopic physical explanation of corresponding shortcomings of previous models. It uniquely assigns the failures of previous models to substantial inaccuracies in the description of the higher electrostatic multipole moments of liquid phase water molecules. Resulting favorable properties concerning the transferability to other temperatures and conditions like the melting of ice are also discussed.