Sustainable Nanotechnology: Opportunities and Challenges for

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Review Article pubs.acs.org/JPCB

Sustainable Nanotechnology: Opportunities and Challenges for Theoretical/Computational Studies Qiang Cui,*,† Rigoberto Hernandez,*,‡ Sara E. Mason,*,§ Thomas Frauenheim,∥ Joel A. Pedersen,⊥ and Franz Geiger# †

Department of Chemistry and Theoretical Chemistry Institute, University of WisconsinMadison, 1101 University Avenue, Madison, Wisconsin 53706, United States ‡ Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States § Department of Chemistry, University of Iowa, E331 Chemistry Building, Iowa City, Iowa 52242-1294, United States ∥ Bremen Center for Computational Materials Science, Univ of Bremen, D-28359 Bremen, Germany ⊥ Departments of Soil Science, Civil & Environmental Engineering, and Chemistry, University of WisconsinMadison, 1525 Observatory Drive, Madison, Wisconsin 53706, United States # Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60201, United States ABSTRACT: For assistance in the design of the next generation of nanomaterials that are functional and have minimal health and safety concerns, it is imperative to establish causality, rather than correlations, in how properties of nanomaterials determine biological and environmental outcomes. Due to the vast design space available and the complexity of nano/bio interfaces, theoretical and computational studies are expected to play a major role in this context. In this minireview, we highlight opportunities and pressing challenges for theoretical and computational chemistry approaches to explore the relevant physicochemical processes that span broad length and time scales. We focus discussions on a bottom-up framework that relies on the determination of correct intermolecular forces, accurate molecular dynamics, and coarse-graining procedures to systematically bridge the scales, although top-down approaches are also effective at providing insights for many problems such as the effects of nanoparticles on biological membranes.

1. INTRODUCTION: ROLES OF THEORY AND COMPUTATION IN THE DEVELOPMENT OF SUSTAINABLE NANOTECHNOLOGY

encouraged programs that systematically analyze EHS issues of nanotechnology. The interactions between nanomaterials and biological systems are complex and involve physical, chemical, and biological processes that span broad length and spatial scales.9,10 For instance, the following interactions have been observed: nanomaterials often acquire biomolecular “coronas” by binding to proteins, lipids, and other biological components;11 nanomaterials may also be involved in electron transfer chains in cells and generation of reactive oxygen species (ROS) that damage cellular components;12,13 nanomaterials often undergo chemical transformations (e.g., dissolution, aggregation) due to interactions with biomolecules, leading to the generation of potentially toxic species and disruption of cellular membranes.14−16 Therefore, to properly address the EHS issues of nanotechnology, it is essential to understand the mechanistic details of nanomaterials/biological system interactions; i.e., it is essential to establish causality, rather than correlations, in how

Development of sustainable technologies to address fundamental societal needs such as clean air, clean water, and clean energy supplies is one of the grand challenges that we face today. Nanotechnology holds great promise in this regard because controlling the composition and structure at the nanoscale leads to greater controls of the physical and chemical properties, and thus the functions, of materials. Indeed, nanotechnology has already led to numerous applications in the areas of, for example, batteries,1 electronics,2 water desalination,3 drug/gene delivery,4−6 and diagnostics.4,7 There is little doubt that the impact of nanotechnology will only increase in the future. At the same time, it is also important to consider the sustainability of nanotechnologies, particularly their potential to elicit detrimental biological outcomes. The small size and often reactive nature of nanomaterials raise concern about their potential environmental, health, and safety (EHS) impacts. This has been realized, for example, from the very beginning of the National Nano Initiative,8 which © 2016 American Chemical Society

Received: April 19, 2016 Revised: June 16, 2016 Published: July 7, 2016 7297

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The Journal of Physical Chemistry B nanomaterials impact biological outcomes.9,17−20 Only with this level of understanding can we design21 the next generation of nanomaterials that are functional yet have minimal deleterious EHS concerns. As summarized by some of us and our co-workers in a recent Perspective, 19 now is an exciting time to study how nanomaterials interact with and impact biological systems. With novel experimental techniques in nanomaterials synthesis, imaging, spectroscopies, and various high-throughput genomics, proteomics, and metabolomics approaches, it is now possible to prepare well-characterized nanomaterials and to analyze their interactions with biological systems at unprecedented levels of physical and chemical detail. To help better understand sophisticated experimental measurements and ultimately guide the design of new experimental investigations, it is essential to conduct theoretical and computational studies on the nano/bio interface. Although this urgent need has clearly been recognized, as evidenced by the increasing number of relevant publications,22−25 we feel it is timely to highlight a number of opportunities and pressing challenges. Through this mini-review, we hope to stimulate more theoretical and computational chemists to bring their expertise to help design a new generation of sustainable nanotechnology that is optimized for both high-performance and environmentally benign properties.

Figure 1. Study of chemical processes at the nano/bio interface, including several possible chemical reactions at the surface of nanomaterials, including acid−base chemistry, oxidation−reduction reactions, and release of metal ions stimulated by the adsorption of molecules from the environment. These can be studied using (a) QM calculations or (b) QM/MM calculations.

in molecular descriptions at the cost of accuracy in predicting the physical properties of solids.37 For further improved accuracy, embedding methods38−40 in which a local region is described with a high-level ab initio QM method (e.g., multireference configuration interaction or coupled cluster) are attractive; this is particularly important when the chemical reaction involves open-shell species or electronically excited states, for which DFT methods have well-established limitations that need to be alleviated with further developments.41 Several embedding schemes have been proposed in the literature;38−40 the approach of Miller and Manby39 using a projector operator appears most straightforward to implement and also has the attractive feature of being exact in the limit of DFT-in-DFT embedding. The accuracy of the embedding approach has been analyzed for molecular systems, for which the error seems to be dominated by the nonadditive exchange-correlation contribution;42 a similar analysis for materials systems has not yet been conducted. Another modeling challenge lies in the task of deciphering the electronic structure of nanomaterials. Most DFT implementations incorporate Bloch’s theorem and k-space sampling to calculate the total energy. The resulting conventional electronic structure descriptions, such as band structure, thus inherently rely on perfect (or nearly so) periodic structures. In the modeling of defect structures and nanoparticles, it is the local electronic structure in real space (analyzed in terms of, for example, local density of states, molecular orbitals, partial charges, or induced charge densities) that is more useful in developing a chemical understanding of structure−reactivity relationships.43−45 When considering chemical reactivity at the nano/bio interface, it is important to recognize that the condensed phase environment plays a major role. To describe some effects such as bulk solvation and pH, a good starting point is a dielectric continuum model, which has a long history in molecular quantum chemistry46 but only became widely available to QM packages for materials applications more recently.47,48 For example, a DFT plus continuum solvent approach has been applied to describe the adsorption of contaminant ions to aqueous aluminum hydroxide nano-

2. DISCUSSION: RESEARCH OPPORTUNITIES AND CHALLENGES AT MULTIPLE SCALES As emphasized in the Introduction, the impact of nanomaterials on biological systems often involves complex physical interactions and chemical reactions. Therefore, this research area is rich in opportunities and challenges that span multiple disciplines and scales. In the following, we organize our discussion in terms of three subsections that focus on specific length scales, although a proper coupling (e.g., information transfer) among these scales is clearly essential and, in fact, represents an important challenge. 2.1. Chemistry at the Nano/Bio Interface: Classical and Quantum Potential Functions. When exposed to biological systems, nanomaterials are potentially involved in a broad range of chemical reactions (Figure 1a). For example, the pKa values of water molecules bound to the surface of many metal oxide nanoparticles are significantly shifted and are involved in acid−base chemistry at the interface.26,27 Nanomaterials that contain transition metal ions can participate in oxidation−reduction reactions and generate ROS in the cell.12,13 Coupled with various chemical reactions at the interface, nanomaterials may undergo dissolution and release ions into the environment.14,15 Finally, nanomaterials are also rich in photochemistry.28 To describe the pathway, energetics, and kinetics of these chemical reactions, quantum mechanics (QM) methods are required. In most cases, plane-wave-based density functional theory (DFT) is an adequate choice.29,30 Many nanomaterials contain transition metal ions, which involve localized and thus strongly correlated d electrons, for which DFT+U is needed for a qualitatively correct description;31 for carbon-based nanomaterials, a careful treatment of many-body dispersion is also essential.32,33 Alternatively, hybrid functionals can be used.34,35 Complications in the use of hybrid functionals include the high computational cost incurred, especially in periodic calculations,36 the lack of any a priori knowledge of the amount of exact exchange to include for optimal results, and improvement 7298

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Figure 2. Issues of particular importance to the sampling of nano/bio interfaces. (a) A simple example of a short peptide (RGD) adsorbed to the TiO2 (rutile) surface. (b) Enhanced sampling algorithms83 are required to obtain a reliable free energy surface (in terms of the peptide backbone ϕ, ψ angles), even for the simple tripeptide shown in part a; comparison is made between 10 ns of enhanced sampling (left panel) and 100 ns of normal sampling (right panel). In each panel, the scatter plots show the sampled ϕ−ψ values, and the contour plots are the corresponding free energy surfaces. (c) Multidimensional reaction coordinates, including the description of local solvation(s),84 are required to describe interfacial binding processes; DB (doubly bound), SB (singly bound), and UB (unbound) indicate different configurations of a formate ion at/near the TiO2 surface. (d) For functionalized nanoparticles, properly determining the titration states for surface residues is important for modeling their interaction with other molecules. Panels b and c are adapted with permission from refs 83 and 84. Copyright 2014 and 2013, respectively, American Chemical Society.

particles.49,50 These studies make direct connections to experiment by rationalizing crystal structures and by providing mechanistic insights. In many cases, the nano/bio interface is complex and highly heterogeneous; for example, nanomaterials can be exposed to multicomponent solution, lipid membranes, and other biological molecules. Under these conditions, the molecular nature of the environment needs to be represented explicitly. To balance computational accuracy and efficiency, hybrid methods51−53 such as QM/MM (Figure 1b) and a multilayer QM/ QM′/MM approach are most attractive. Although the basic framework for these methods has been well-established by now,54−56 a few remarks are warranted. First, it remains computationally expensive to conduct extensive sampling (see further discussions in section 2.2) with DFT or ab initio QM-based hybrid methods; thus, the most promising approach is to integrate automated reaction path search algorithms with the minimum-free-energy-path approach of Yang et al.,57 in which finite-temperature sampling is conducted for the MM region with frozen QM atoms while the QM geometry is relaxed according to the potential of mean force gradient. Alternatively, combining extensive sampling using a low-level QM-based method and limited sampling using a high-level QM/MM potential to obtain free energies is another possibility,58,59 although adequate convergence relies on a good level of consistency between the low- and high-level

QM potentials.58,60,61 In this regard, the density-functionaltight-binding (DFTB) approach62,63 can be a promising lowlevel QM method; its applicability to a broad range of nanomaterials has been dramatically enhanced in recent years with a general parametrization for the majority of the periodic table64 and automated optimization algorithms for refinement for specific systems.65 Continuing developments of DFTB such as the improvement of noncovalent interactions,66 description of transition metal ions,67 and electronically excited state dynamics68 are particularly valuable to the study of nano/bio interfaces. Another issue warranting discussion concerns the MM force field for the nano/bio interface in QM/MM (and classical) simulations. Due to historical reasons, MM force fields for inorganic materials and biomolecules have been developed in separate communities; thus, compatibility of these force fields is limited, and several authors emphasized the importance of carefully benchmarking,69 for example, the cross-terms in the force field between the inorganic and biomolecular components.70 In recent years, efforts have been invested to develop MM force fields for inorganic materials (e.g., gold) in the same framework of popular biomolecular MM models to ensure applicability to nano/bio interfaces.71−73 Along this line, we note that, due to the heterogeneous nature of the interface, it is likely that an explicit treatment of electronic polarization (or nonadditivity74) is more important compared to bulk 7299

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elevate the effective temperature of selected degrees of freedom87,88 and leave the solvent, for example, at room temperature. Another issue to highlight is that specific environmental degrees of freedom need to be sampled explicitly when studying physical processes at the nano/bio interface. If particle-based methods are required, then this could be performed with molecular dynamics techniques in or out of equilibrium.89 We use a simple example of ion binding to the rutile surface to illustrate the point. Since water molecules bind strongly to the rutile surface, desolvation of the potential binding site is expected to be an important part of the ion binding process. This is supported by two-dimensional free energy simulations84 in which the level of hydration (s) of the potential binding site is explicitly included as an order parameter, in addition to the more intuitive variable (z) that measures the distance between the ion and the rutile surface. The computed two-dimensional free energy surface (Figure 2c) indicates that the change in s, rather than that in z, dictates the motion that overcomes the rate-limiting barrier for binding. Interestingly, committor analysis84 using configurations sampled from the putative transition state ensemble based on the two-dimensional free energy surface suggested that s and z are, in fact, not sufficient for describing the (un)binding kinetics; additional variable(s) that describe the local hydrogen bonding network bridging the ion and the binding site are likely needed. This simple example helps to highlight the challenges associated with understanding the microscopic mechanism of physicochemical processes at complex interfaces. Systematic analyses using techniques such as transition path/interface sampling90,91 are valuable for extracting the identity of true reaction coordinates to formulate quantitative theories that predict the kinetics of interfacial processes.92 The other aspect of sampling concerns the chemical space of nano/bio interfaces, and the most prominent example is the protonation state of titratable residues at the interface.93 Nanomaterials are often functionalized with ligands or polymers that contain titratable groups. For construction of a microscopic model for studying physicochemical processes at nano/bio interfaces, it is important to determine the protonation pattern of these titratable groups. Although this is an “old” problem for the biophysical community,94 it is rarely addressed systematically for nanomaterials95,96 or nano/bio interfaces. The number of titratable groups can be large; for example, for a 4 nm diameter nanoparticle functionalized with amines, ∼400 titratable groups are present at a modest functionalization density of 90 molecules per nm2 (Figure 2d). With such a large number of titratable groups strongly coupled to each other, standard methods like constant pH simulations97 are not easy to converge; in the presence of a large number of charged ligands, the counterion concentration can be extraordinarily high within a typical simulation cell (∼10 nm per dimension) and may lead to artifacts in simulation results. Furthermore, protonation states of titratable groups may undergo substantial changes when the nanomaterial interacts with other charged biomolecules;98 novel sampling schemes are needed to take this into consideration in an efficient manner. Finally, it is also important to establish ways to quantitatively compare predicted charge state with experimental measurements. The typical experimental observable is the ζ potential, whose microscopic computation is not straightforward. A promising approach might be to compute mobility from microscopic simulations and compare it to

simulations; the fact that many nanomaterials contain ionic or metallic components further supports the importance of electronic polarization.75 Therefore, a worthwhile research direction is to develop polarizable force fields for nanomaterials that are compatible with their biomolecular counterparts. In this context, the Drude oscillator model appears most promising since well-tested models already exist for water, ions, and, more recently, proteins and lipids.76 Compared to data in the biophysics literature, the amount of quantitative experimental data for the nano/bio interface is quite limited. This limitation underscores the importance of pursuing polarizable force field developments based on reliable QM calculations rather than empirical adjustments to experimental data. A promising strategy that has (re)emerged in recent years is to carefully dissect the physical components of fundamental intermolecular interactions using a QM-based energy decomposition scheme and then use the results to guide the development of the corresponding terms in the MM force field.77,78 Before concluding this subsection, we emphasize that QMbased calculations also enable the prediction of various spectroscopic observables, which provide opportunities for calibrating computational models and aiding the interpretation of experimental measurements. When explicit time-dependence is not essential, static QM or QM/MM calculations based on snapshots collected from classical or low-level QM(/MM) simulations are adequate.79 For sophisticated time-resolved measurements, computational strategies need to be established to balance efficiency and accuracy, in the same vein as recent developments for the interpretation of nonlinear spectroscopies for water, air/water interface, and proteins at the membrane/ water interface.80,81 For spectroscopies that probe the electronic structure and dynamics of nanomaterials, efficient time-dependent QM approaches need to be further developed.68,82 2.2. Complex Interactions at the Nano/Bio Interface: Enhanced Sampling of Configurational and Chemical Space. Conducting adequate sampling of the configuration space is a universal challenge to condensed phase simulations. Nano/bio interfaces are no exception. In this subsection, we briefly highlight three aspects of sampling that are particularly important to the study of these interfaces (Figure 2). First of all, many nanomaterials involve highly charged components (e.g., oxide), which interact strongly with solution components, including biomolecules. As a result of such strong interactions, sampling of the configurational space is easily trapped in local minima. Figure 2a shows the example of a short peptide (Arg-Gly-Asp) interacting with the rutile (TiO2) surface. Both charged groups are strongly bound to the surface, thus limiting the sampling of the peptide conformation in regular MD simulations as evidenced by the poor coverage of the ϕ−ψ map over even 100 ns of sampling (Figure 2b). This simple example highlights the need for enhanced sampling methods for studying nano/bio interfaces. Since one major cause for the inefficient sampling is the surface/biomolecule interactions, a sensible approach is to use Hamiltonian replica exchange and related methods83,85 in which the surface/ biomolecule interaction is reduced in replicas other than the physical system. For further enhancement of the sampling of the biomolecule’s internal structure, it is productive to further couple the Hamiltonian replica exchange with other technique, such as temperature replica exchange or simulated tempering.86 For reduction of the number of replicas needed, it is ideal to 7300

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The Journal of Physical Chemistry B experimental (electrophoresis) data. To observe significant drifts of the nanoparticle, the magnitude of the electric field applied in microscopic simulations likely needs to be substantially higher than that applied in macroscopic measurements; thus, novel nonequilibrium simulation protocols99 need to be developed to avoid potential artifacts associated with the application of large electric fields. In the context of simulating highly charged nanomaterials, it is worth emphasizing again the importance of properly modeling the ionic strength of the environment, which varies widely.100,101 Conditions of ionic strengths in the 0.1−1 M range are readily simulated in typical molecular dynamics calculations as the ratio of a Na+:Cl− ion pair to the number of water molecules in the simulation box is around 1:50. Yet, incorporating ionic strength in the sub-1 mM to 10 mM concentration regime into molecular dynamics simulations is much more difficult. The ratio of Na+:Cl− ion pairs to water molecules is orders of magnitude smaller than in the cases discussed above, and even if a simulation box were to be built that allows for millimolar salt concentrations, the ions would not sample all available space in a reasonable amount of simulation time. As such, a major frontier to be explored is to develop new methods for effectively studying nanomaterials interactions in aqueous environments that feature 0.1−10 mM ionic strength. Indeed, formation of contact ion pairs or shared ion clouds,102 which is common at high salt concentrations in solution, can also occur at markedly lower ionic strength in interfacial environments,103 where the speciation of ions may differ substantially from the one in bulk aqueous phase. We expect processes at the nano/bio interface to be subject to these phenomena as well. To this end, there is an urgent need to go beyond mean field theory using molecular level models. 2.3. Toward Large Length Scales: Coarse-Grained Models for Structure and Dynamics. In addition to dissolution, nanomaterials may undergo other kinds of transformations, such as aggregation and acquisition of various “coronas” that consist of lipids, proteins, and other biomolecules.11 The interaction of nanomaterials with biomolecules may also lead to substantial impacts on the morphology of cell membranes, and organization of proteins in the membrane, which in turn may trigger cellular signaling events.10 Imaging analysis of gold nanoparticles wrapped with PAH (poly(allylamine hydrochloride)) on lipid membranes leads to striking structures that reach the micron length scale (F. M. Geiger, private communication). Therefore, in addition to atomistic models discussed in the last two subsections, it is essential to develop coarse-grained (CG) models that access the large length (≥100 nm) and time (≥μs−ms) scales that are relevant to the behaviors and impact of nanomaterials in biological settings (Figure 3a,b). Development of effective CG models is an active area of research in many disciplines such as biophysics and soft matter materials science.106−109 Both “bottom-up” and “top-down” approaches have been developed and applied to various problems. For example, several CG models for lipids have been developed,110−112 among which MARTINI110 is perhaps the most well-known and has been successfully applied to study, for example, phase behaviors of lipid mixtures and membrane remodelling processes. The MARTINI model has been extended recently to more diverse molecules, including not only biomolecules (proteins, nucleic acids, carbohydrates) but also various nanoparticles.109 This enables the investigation of how functionalized gold nanoparticles impact lipid

Figure 3. Example of processes at the nano/bio interface that require coarse-grained models. (a) Aggregation of nanoparticles, binding to, and translocation across the lipid membrane. (b) Interaction between nanoparticle with complex cell membrane (the outer membrane of Gram-negative bacteria104,105), which includes not only lipids but also other components such as lipopolysaccharide. (c) Formation of a lipid corona around a functionalized nanoparticle.

membrane morphologies to different degrees (e.g., pore formation or wrapping) depending on the surface charges.113 We have recently developed a CG model for PAH in the MARTINI framework and used it to study the process of lipid corona formation of PAH wrapped gold nanoparticles (Figure 3c). For models of realistic cellular membranes, it is important to develop CG models for other membrane components such as lipopolysaccharides (Figure 3b), integral and peripheral membrane proteins, and glycolipids. Finally, continuum mechanics models are effective at modeling large-scale membrane deformations around nanoparticles114 and proteins,115 although development of such models for highly heterogeneous systems remains more limited compared to particle-based models. The accuracy and transferability of a CG model depend on the physical components included in the model, the functional forms used to describe these physical interactions, and how parameters in the model are developed. For example, we emphasized the importance of explicitly including multipole moments for CG models of water116 for the description of interfacial properties such as surface tension and the dipole potential at a lipid membrane/water interface;117 we also showed that relatively subtle changes (∼1 kJ/mol!) in specific pairwise interactions in the CG model can lead to significant changes in the phase behavior of lipid/peptide mixtures.118 Most CG models developed in the literature were developed on the basis of structural (e.g., pair distribution functions) and/or thermodynamic (e.g., transfer free energy,110 relative entropy,119 or force on CG sites107) properties; even so, it is not always straightforward to capture the proper components (e.g., enthalpy vs entropy) of thermodynamic driving forces.120 An important challenge lies in the development of theoretical frameworks for CG models that satisfy dynamical consistency in the sense that they properly maintain the correct time scales for key dynamical properties despite the reduction in the model’s resolution. This is important for predicting the long-time 7301

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following the force-matching approach (also referred to as the multiscale coarse-graining approach),124,125 Voth and coworkers126 can obtain approximate dynamical consistency with respect to the self-diffusion coefficients through the introduction of fictitious particles subject to Langevin forces. This clever approach unfortunately introduces additional, though modest, numerical cost, and may not be accurate when there are correlations between the coarse-grained particles or hydrodynamic effects that the fictitious particles are unable to capture. Despite the fact that most coarse-grained models do not necessarily provide exact time scales or even dynamically consistent ones, this has not stopped the community from doing the simulations. Such simulations are compelling because they provide visualizations of the pathways for insertions or transport in crowded environments such as those encountered by the sustainable engineered nanomaterials that are the focus of this minireview. They can, perhaps, be regarded as semiempirical in the sense that the coarse-grained models are validated by their agreement to experiment with respect to structure and transport. Figure 3a illustrates scenarios in which the interaction between nanoparticles, and that between nanoparticles and membranes, are not fully understood. To fully address not just the equilibrium structure but also the nonequilibrium behavior requires simultaneous descriptions of the atomic scales and the much larger length and longer times scales of the membrane. In addition, as emphasized in Figure 3b,c, in vivo, neither the membrane nor the corona are homogeneous, and this adds to the complexity and difficulty in naive rescalings of the structure and effective equations of motion.

dynamics of a system or the behavior of a system under nonequilibrium conditions, such as in shear flow. Naive coarsegraining can lead to differing time scales in the dynamics of the coarse-grained variables even when very few fine-grained variables are removed. For example, some of us found that the structure of a suspension of Janus particles, illustrated in Figure 4, was retained by a corresponding suspension of

Figure 4. Janus particles at a high packing fraction (0.4) and a mean pairwise well depth of 3kBT are shown with respect to the fine-grained (at left) and coarse-grained representation (at right) in which the nature of the face charges are either retained (as shown in red or blue) or spherically averaged (as shown in green). The renderings at the top show the corresponding structures at the initial time (t = 0) in which the centers of mass are in identical positions. After evolution of the two systems, the final structures at the later time continue to have the same center of masses only if the equations of motion are dynamically consistent.

3. CONCLUDING REMARKS An ultimate goal in sustainable nanotechnology is the development of nanomaterials that fit in the intersection of the design space leading to functionality and that producing environmentally benign materials. Doing so without requiring laborious experimental searches requires reliable and validated computational models that can correctly characterize the structure and dynamics of nanomaterials at many scales in many different environments. Through this minireview, we have provided a view on the promise of and challenges for theoretical chemistry tools relying on the determination of correct intermolecular forces, accurate molecular dynamics, and coarse-graining procedures. Although we have discussed these three topics separately, systematic information transfer among them is clearly key to the success of such bottom-up approaches. Top-down approaches relying on semiempirical models also provide insight into the effects of nanomaterials on biological structures such as lipid membranes. They also provide target frameworks for coarse-graining the finer-grained representations if only we can do so accurately with respect to structure and dynamics. All of these models benefit from direct comparison and validation by experimental probes that themselves are limited to particular length and times scales though collectively can access scales from angstroms to meters, all of which are relevant to the analysis of nanomaterials in realistic biological and environmental settings. Finally, although we have focused our discussions on mechanistic analysis, considering the vast design space available to chemistry and materials,127 there is little doubt that multiscale computations will play an explicit role in aiding the design128,129 of nanomaterials with desired functional and EHS properties.

spherically symmetric particles interacting through renormalized pairwise potentials;121 the time scales, however, were not retained as the naive coarse-grained model exhibited much faster diffusion.122 Such speedups have generally been seen in coarse-grained simulations as a useful feature in that they allow for the possibility of accessing longer time scales and not just longer length scales.107,109 However, they are challenged by the possibility of dynamical inconsistency between different coarsegrained variables as they may perhaps not be synchronized in the same way in different representations. In the limit of linearized dynamics, dynamical consistency can be retained by uniform rescaling in time using an ad hoc factor. Moreover, in the Janus system, we found that dynamical consistency could be recovered through the use of a friction term obtained directly from the known fluctuations in the fine-grained representation.122 The question remains, however, whether such a procedure is dynamically consistent across all of the dynamical observables. One approach toward this in the context of polymers is that of Guenza and cowokers.123 They develop integral equation theories connecting correlation functions between different variables at different length scales so as to correct for the time scale inconsistencies that arise through the coarse-graining. These analytic models are powerful but difficult to apply as the complexity and heterogeneity in the system grow. On the other hand, if one coarse-grains the system 7302

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AUTHOR INFORMATION

and civil and environmental engineering at the University of WisconsinMadison, where he leads interdisciplinary research projects focused on environmental interfacial chemistry. Specific interests include molecular-scale interactions of biomolecules with engineered nanoparticles, processes governing the environmental transmission of prion diseases, and the interaction of polar and ionizable organic molecules with natural organic matter and mineral surfaces.

Corresponding Authors

*E-mail: [email protected]. Phone: (+1)-608-332-6584. *E-mail: [email protected]. Phone: (+1)-410-516-7429. *E-mail: [email protected]. Phone: (+1)-319-335-2761. Notes

The authors declare no competing financial interest. Biographies

Franz Geiger is a native of Berlin, Germany, where he received his Vordiplom in chemistry at the Technische Universitaet. He earned his Ph.D. at Georgetown University working with Janice Hicks as a NASA Fellow in Earth Systems Science, and was an NOAA Postdoctoral Fellow in Climate and Global Change with Mario Molina and Bernhard Trout at MIT until 2001, after which he joined Northwestern as a professor of chemistry. He leads collaborative research projects involving experimental and computational methods to study the special role that surfaces and interfaces play in the world.

Qiang Cui received a B.S. in Chemical Physics from the University of Science and Technology of China and a Ph.D. in Chemical Physics from Emory University, working with Professor Keiji Morokuma. Following postdoctoral studies at Harvard University with Professor Martin Karplus, in 2001, he joined the University of Wisconsin Madison, where he remained since as a professor of chemistry. He is interested in developing theoretical/computational methods for the analysis of biomolecular systems, especially concerning chemical reactions in enzymes, energy transduction in biomolecular machines, and, more recently, interaction between biomolecules, lipids, and inorganic materials.

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ACKNOWLEDGMENTS The work has been supported by the grant from the National Science Foundation CHE-1503408. We also thank Gene Chong, Caley Allen, Leili Zhang, Xu Huang, and Professor Wonpil Im for assistance in preparation of the figures.

Rigoberto Hernandez completed his B.S.E. degree in Chemical Engineering and Mathematics at Princeton University and a Ph.D. in Chemistry at University of California, Berkeley, working with Professor William H. Miller. He did postdoctoral research with Professors Eli Pollak and Gregory Voth at the Weizmann Institute and the University of Pennsylvania, respectively. Having worked at Georgia Tech for two decades as a professor of chemistry, he moved to Johns Hopkins University in 2016, where he uses theoretical and computational tools to characterize nonequilibrium statistical mechanics and multiscale dynamics of chemical systems. Specific interests include transition state theory of driven chemical reactions, adaptive steered molecular dynamics of proteins, and sustainable nanotechnology.

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Sara E. Mason completed an A.A.S. degree in Chemical Technology from Monroe Community College, followed by a B.S. in Chemistry from St. John Fisher College and a Ph.D. in Chemistry from University of Pennsylvania. She was a NIST Postdoctoral Research Associate through a National Research Council fellowship program, working with Dr. Anne M. Chaka. Since 2010, she has been at the University of Iowa, where her research group uses theory and modeling, largely based off of density functional theory, to study nanomaterials in the environment and in energy applications. The research approach in her group is to use computational chemistry in comparative studies aimed at delineating structure−reactivity relationships, working closely with experimentalists to guide and constrain the modeling efforts. Thomas Frauenheim graduated and completed his doctoral thesis at the Technical University Dresden (Germany) in the theoretical physics department. After postdoctoral research at the Joint Institute for Nuclear Research Dubna (USSR), he accepted an offer from Technical University Chemnitz as an associate professor in Theoretical Physics. He received habilitation at TU Dresden and was a professor at the University of Paderborn (Germany) until 2006. He now holds the position as the founding director of the BCCMS (Bremen Center for Computational Materials Science) and chair professor at University of Bremen. The Frauenheim group is the developer of the DensityFunctional Tight-Binding method and distributes the DFTB+ code worldwide as open source to the computational community. Joel A. Pedersen earned his B.S. degree in Biological Sciences at the University of California, Irvine, his M.S. in Environmental Engineering Science at the California Institute of Technology, and his Dr.Env. in Environmental Science and Engineering at the University of California, Los Angeles. Since 2005, he is a professor of soil science, chemistry, 7303

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DOI: 10.1021/acs.jpcb.6b03976 J. Phys. Chem. B 2016, 120, 7297−7306