Mean-Field Theory of Water-Water Correlations in Electrolyte Solutions

Long-range ion induced water-water correlations were recently observed in femtosecond elastic second harmonic scattering experiments of electrolyte solutions. To further the qualitative understanding of these correlations, we derive an analytical expression that quantifies ion induced dipole-dipole correlations in a non-interacting gas of dipoles. This model is a logical extension of Debye-H\"uckel theory that can be used to qualitatively understand how the combined electric field of the ions induces correlations in the orientational distributions of the water molecules in an aqueous solution. The model agrees with results from molecular dynamics simulations and provides an important starting point for further theoretical work

Second-Harmonic Scattering as a Probe of Structural Correlations in Liquids

Second-harmonic scattering experiments of water and other bulk molecular liquids have long been assumed to be insensitive to interactions between the molecules. The measured intensity is generally thought to arise from incoherent scattering due to individual molecules. We introduce a method to compute the second-harmonic scattering pattern of molecular liquids directly from atomistic computer simulations, which takes into account the coherent terms. We apply this approach to large-scale molecular dynamics simulations of liquid water, where we show that nanosecond second-harmonic scattering experiments contain a coherent contribution arising from radial and angular correlations on a length scale of < 1 nm, much shorter than had been recently hypothesized (Shelton, D. P. J. Chem. Phys. 2014, 141). By combining structural correlations from simulations with experimental data (Shelton, D. P. J. Chem. Phys. 2014, 141), we can also extract an effective molecular hyperpolarizability in the liquid phase. This work demonstrates that second-harmonic scattering experiments and atomistic simulations can be used in synergy to investigate the structure of complex liquids, solutions, and biomembranes, including the intrinsic intermolecular correlations

Solvent Fluctuations and Nuclear Quantum Effects Modulate the Molecular Hyperpolarizability of Water

Second-Harmonic Scatteringh (SHS) experiments provide a unique approach to probe non-centrosymmetric environments in aqueous media, from bulk solutions to interfaces, living cells and tissue. A central assumption made in analyzing SHS experiments is that the each molecule scatters light according to a constant molecular hyperpolarizability tensor $\boldsymbol{\beta}^{(2)}$. Here, we investigate the dependence of the molecular hyperpolarizability of water on its environment and internal geometric distortions, in order to test the hypothesis of constant $\boldsymbol{\beta}^{(2)}$. We use quantum chemistry calculations of the hyperpolarizability of a molecule embedded in point-charge environments obtained from simulations of bulk water. We demonstrate that both the heterogeneity of the solvent configurations and the quantum mechanical fluctuations of the molecular geometry introduce large variations in the non-linear optical response of water. This finding has the potential to change the way SHS experiments are interpreted: in particular, isotopic differences between H$_2$O and D$_2$O could explain recent second-harmonic scattering observations. Finally, we show that a simple machine-learning framework can predict accurately the fluctuations of the molecular hyperpolarizability. This model accounts for the microscopic inhomogeneity of the solvent and represents a first step towards quantitative modelling of SHS experiments

A Transferable Machine-Learning Model of the Electron Density

The electronic charge density plays a central role in determining the behavior of matter at the atomic scale, but its computational evaluation requires demanding electronic-structure calculations. We introduce an atom-centered, symmetry-adapted framework to machine-learn the valence charge density based on a small number of reference calculations. The model is highly transferable, meaning it can be trained on electronic-structure data of small molecules and used to predict the charge density of larger compounds with low, linear-scaling cost. Applications are shown for various hydrocarbon molecules of increasing complexity and flexibility, and demonstrate the accuracy of the model when predicting the density on octane and octatetraene after training exclusively on butane and butadiene. This transferable, data-driven model can be used to interpret experiments, initialize electronic structure calculations, and compute electrostatic interactions in molecules and condensed-phase systems

Fast-Forward Langevin Dynamics with Momentum Flips

Stochastic thermostats based on the Langevin equation, in which a system is coupled to an external heat bath, are popular methods for temperature control in molecular dynamics simulations due to their ergodicity and their ease of implementation. Traditionally, these thermostats suffer from sluggish behaviour in the limit of high friction, unlike thermostats of the Nos\'e-Hoover family whose performance degrades more gently in the strong coupling regime. We propose a simple and easy-to-implement modification to the integration scheme of the Langevin algorithm that addresses the fundamental source of the overdamped behaviour of high-friction Langevin dynamics: if the action of the thermostat causes the momentum of a particle to change direction, it is flipped back. This fast-forward Langevin equation preserves the momentum distribution, and so guarantees the correct equilibrium sampling. It mimics the quadratic behavior of Nos\'e-Hoover thermostats, and displays similarly good performance in the strong coupling limit. We test the efficiency of this scheme by applying it to a 1-dimensional harmonic oscillator, as well as to water and Lennard-Jones polymers. The sampling efficiency of the fast-forward Langevin equation thermostat, measured by the correlation time of relevant system variables, is at least as good as the traditional Langevin thermostat, and in the overdamped regime the fast-forward thermostat performs much better, improving the efficiency by an order of magnitude at the highest frictions we considered.Comment: Accepted for publication by J. Chem. Phys.; 7 pages, 6 figure

Accurate molecular polarizabilities with coupled-cluster theory and machine learning

The molecular polarizability describes the tendency of a molecule to deform or polarize in response to an applied electric field. As such, this quantity governs key intra- and inter-molecular interactions such as induction and dispersion, plays a key role in determining the spectroscopic signatures of molecules, and is an essential ingredient in polarizable force fields and other empirical models for collective interactions. Compared to other ground-state properties, an accurate and reliable prediction of the molecular polarizability is considerably more difficult as this response quantity is quite sensitive to the description of the underlying molecular electronic structure. In this work, we present state-of-the-art quantum mechanical calculations of the static dipole polarizability tensors of 7,211 small organic molecules computed using linear-response coupled-cluster singles and doubles theory (LR-CCSD). Using a symmetry-adapted machine-learning based approach, we demonstrate that it is possible to predict the molecular polarizability with LR-CCSD accuracy at a negligible computational cost. The employed model is quite robust and transferable, yielding molecular polarizabilities for a diverse set of 52 larger molecules (which includes challenging conjugated systems, carbohydrates, small drugs, amino acids, nucleobases, and hydrocarbon isomers) at an accuracy that exceeds that of hybrid density functional theory (DFT). The atom-centered decomposition implicit in our machine-learning approach offers some insight into the shortcomings of DFT in the prediction of this fundamental quantity of interest

Hiring Teams, Firms and Lawyer: Evidence of the Evolving Relationships in the Corporate Legal Market

How are relationships between corporate clients and law firms evolving? Drawing on interview and survey data from 166 chief legal officers of S&P 500 companies from 2006–2007, we find that—contrary to standard depictions of corporate client-provider relationships—(1) large companies have relationships with ten to twenty preferred providers; (2) these relationships continue to be enduring; and (3) clients focus not only on law firm platforms and lead partners, but also on teams and departments within preferred providers, allocating work to these subunits at rival firms over time and following “star” lawyers, especially if they move as part of a team. The combination of long-term relationships and subunit rivalry provides law firms with steady work flows and allows companies to keep cost pressure on firms while preserving relationship-specific capital, quality assurance, and soft forms of legal capacity insurance. Our findings have implications for law firms, corporate departments, and law schools

Hiring Teams, Firms, and Lawyers: Evidence of the evolving Relationship in the Corporate Legal Market

How are relationships between corporate clients and law firms evolving? Drawing on interview and survey data from 166 chief legal officers of S&P 500 companies from 2006-2007, we find that-contrary to standard depictions of corporate client-provider relationships-(1) large companies have relationships with ten to twenty preferred providers; (2) these relationships continue to be enduring, and (3) clients focus not only on law firm platforms and lead partners, but also on teams and departments within preferred providers, allocating work to these subunits at rival firms over time and following star lawyers, especially if they move as part of a team. The combination of long-term relationships and subunit rivalry provides law firms with steady work flows and allows companies to keep cost pressure on firms while preserving relationship-specific capital, quality assurance, and soft forms of legal capacity insurance. Our findings have implications for law firms, corporate departments, and law schools

Transferable Machine-Learning Model of the Electron Density

The electronic charge density plays a central role in determining the behavior of matter at the atomic scale, but its computational evaluation requires demanding electronic-structure calculations. We introduce an atom-centered, symmetry-adapted framework to machine-learn the valence charge density based on a small number of reference calculations. The model is highly transferable, meaning it can be trained on electronic-structure data of small molecules and used to predict the charge density of larger compounds with low, linear-scaling cost. Applications are shown for various hydrocarbon molecules of increasing complexity and flexibility, and demonstrate the accuracy of the model when predicting the density on octane and octatetraene after training exclusively on butane and butadiene. This transferable, data-driven model can be used to interpret experiments, accelerate electronic structure calculations, and compute electrostatic interactions in molecules and condensed-phase systems

Habituation based synaptic plasticity and organismic learning in a quantum perovskite

A central characteristic of living beings is the ability to learn from and respond to their environment leading to habit formation and decision making. This behavior, known as habituation, is universal among all forms of life with a central nervous system, and is also observed in single-cell organisms that do not possess a brain. Here, we report the discovery of habituation-based plasticity utilizing a perovskite quantum system by dynamical modulation of electron localization. Microscopic mechanisms and pathways that enable this organismic collective charge-lattice interaction are elucidated by first-principles theory, synchrotron investigations, ab initio molecular dynamics simulations, and in situ environmental breathing studies. We implement a learning algorithm inspired by the conductance relaxation behavior of perovskites that naturally incorporates habituation, and demonstrate learning to forget: A key feature of animal and human brains. Incorporating this elementary skill in learning boosts the capability of neural computing in a sequential, dynamic environment.United States. Army Research Office (Grant W911NF-16-1-0289)United States. Air Force Office of Scientific Research (Grant FA9550-16-1-0159)United States. Army Research Office (Grant W911NF-16-1-0042