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Register a new userSpicing up continuum solvation models with SaLSA: the spherically-averaged liquid susceptibility ansatz
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Added by
Ravishankar Sundararaman
Publication date
2014
fields
Physics
and research's language is
English
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Continuum solvation models enable electronic structure calculations of systems in liquid environments, but because of the large number of empirical parameters, they are limited to the class of systems in their fit set (typically organic molecules). Here, we derive a solvation model with no empirical parameters for the dielectric response by taking the linear response limit of a classical density functional for molecular liquids. This model directly incorporates the nonlocal dielectric response of the liquid using an angular momentum expansion, and with a single fit parameter for dispersion contributions it predicts solvation energies of neutral molecules with an RMS error of 1.3 kcal/mol in water and 0.8 kcal/mol in chloroform and carbon tetrachloride. We show that this model is more accurate for strongly polar and charged systems than previous solvation models because of the parameter-free electric response, and demonstrate its suitability for ab initio solvation, including self-consistent solvation in quantum Monte Carlo calculations.
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Quantum-chemical processes in liquid environments impact broad areas of science, from molecular biology to geology to electrochemistry. While density-functional theory (DFT) has enabled efficient quantum-mechanical calculations which profoundly impact understanding of atomic-scale phenomena, realistic description of the liquid remains a challenge. Here, we present an approach based on joint density-functional theory (JDFT) which addresses this challenge by leveraging the DFT approach not only for the quantum mechanics of the electrons in a solute, but also simultaneously for the statistical mechanics of the molecules in a surrounding equilibrium liquid solvent. Specifically, we develop a new universal description for the interaction of electrons with an arbitrary liquid, providing the missing link to finally transform JDFT into a practical tool for the realistic description of chemical processes in solution. This approach predicts accurate solvation free energies and surrounding atomic-scale liquid structure for molecules and surfaces in multiple solvents without refitting, all at a fraction of the computational cost of methods of comparable detail and accuracy. To demonstrate the potential impact of this method, we determine the structure of the solid/liquid interface, offering compelling agreement with more accurate (but much more computationally intensive) theories and with X-ray reflectivity measurements.
Continuum models to handle solvent and electrolyte effects in an effective way have a long tradition in quantum-chemistry simulations and are nowadays also being introduced in computational condensed-matter and materials simulations. A key ingredient of continuum models is the choice of the solute cavity, i.e. the definition of the sharp or smooth boundary between the regions of space occupied by the quantum-mechanical (QM) system and the continuum embedding environment. Although most of the solute-based approaches developed lead to models with comparable and high accuracy when applied to small organic molecules, they can introduce significant artifacts when complex systems are considered. As an example, condensed-matter simulations often deal with supports that present open structures. Similarly, unphysical pockets of continuum solvent may appear in systems featuring multiple molecular components. Here, we introduce a solvent-aware approach to eliminate the unphysical effects where regions of space smaller than the size of a single solvent molecule could still be filled with a continuum environment. We do this by defining a smoothly varying solute cavity that overcomes several of the limitations of straightforward solute-based definitions. This new approach applies to any smooth local definition of the continuum interface, being it based on the electronic density or the atomic positions of the QM system. It produces boundaries that are continuously differentiable with respect to the QM degrees of freedom, leading to accurate forces and/or Kohn-Sham potentials. Benchmarks on semiconductor substrates and on explicit water substrates confirm the flexibility and the accuracy of the approach and provide a general set of parameters for condensed-matter systems featuring open structures and/or explicit liquid components.
Liquid hydrocarbons are often modeled with fixed, symmetric, atom-centered charge distributions and Lennard-Jones interaction potentials that reproduce many properties of the bulk liquid. While useful for a wide variety of applications, such models cannot capture dielectric effects important in solvation, self-assembly, and reactivity. The dielectric constants of hydrocarbons, such as methane and ethane, physically arise from electronic polarization fluctuations induced by the fluctuating liquid environment. In this work, we present non-polarizable, fixed-charge models of methane and ethane that break the charge symmetry of the molecule to create fixed molecular dipoles, the fluctuations of which reproduce the experimental dielectric constant. These models can be considered a mean-field-like approximation that can be used to include dielectric effects in large-scale molecular simulations of polar and charged molecules in liquid methane and ethane. We further demonstrate that solvation of model ionic solutes and a water molecule in these fixed-dipole models improve upon dipole-free models.
The solvation model proposed by Fattebert and Gygi [Journal of Computational Chemistry 23, 662 (2002)] and Scherlis et al. [Journal of Chemical Physics 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multi-grid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the non-electrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [Physical Review Letters 94, 145501 (2005)] of the solute. The resulting self-consistent continuum solvation (SCCS) model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the PCM model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.3-0.4 kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating species and strong hydrogen-bond forming compounds.
Continuum solvation models enable efficient first principles calculations of chemical reactions in solution, but require extensive parametrization and fitting for each solvent and class of solute systems. Here, we examine the assumptions of continuum solvation models in detail and replace empirical terms with physical models in order to construct a minimally-empirical solvation model. Specifically, we derive solvent radii from the nonlocal dielectric response of the solvent from ab initio calculations, construct a closed-form and parameter-free weighted-density approximation for the free energy of the cavity formation, and employ a pair-potential approximation for the dispersion energy. We show that the resulting model with a single solvent-independent parameter: the electron density threshold ($n_c$), and a single solvent-dependent parameter: the dispersion scale factor ($s_6$), reproduces solvation energies of organic molecules in water, chloroform and carbon tetrachloride with RMS errors of 1.1, 0.6 and 0.5 kcal/mol respectively. We additionally show that fitting the solvent-dependent $s_6$ parameter to the solvation energy of a single non-polar molecule does not substantially increase these errors. Parametrization of this model for other solvents, therefore, requires minimal effort and is possible without extensive databases of experimental solvation free energies.
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