Modeling metal-based nanoparticles: environment and dynamical effects
- Florent Calvo (CECAM-FR-RA et CBP, France)
- Magali Benoit (CEMES-CNRS, Toulouse, France)
- Nathalie TARRAT (CEMES-CNRS, France)
Since the 1980s and the early works on metal clusters, research on metal-based nanoparticles has shown impressive advances both experimentally and theoretically. From the computational perspective, the potential applications in various fields and the unprecedented level of details reached by modern microscopy and spectroscopy techniques have motivated progress along various directions aiming to improve predictability of the calculations and expanding their transferability toward realistic environments.
Methodology improvements are still essential in order to model increasingly large systems that include the nanoparticle and its environment, either explicitly or using more approximate descriptions ranging from coarse-grained approaches to implicit media or hybrid schemes. Advances in electronic structure descriptions relevant to the present community are especially concerned with the treatment of non-covalent forces, the description of metal/oxides and metal/organic contacts (including possible charge transfer), and the upscaling of existing codes toward extended sizes [1-3]. Electronic structure theory methods, also possibly beyond (time-dependent) DFT methods, are essential to calculate optical spectra and connecting with plasmonic applications [4-6]. Simplified methods such as DFTB [7,8] or reactive force fields [9,10] are attractive approaches to bridge the time and length scale gaps, but their accuracy and transferability are not guaranteed and they rely on higher-level methods which have their own issues. For magnetism, tight-binding models are also attractive because they can account for the environment at reasonable cost . Coarse-graining has also become an important strategy in the community, especially when dealing with assemblies of particles in complex 2D or 3D media.
In addition to the fundamental issue of describing correctly the interactions for increasingly large systems, the field faces the need for accounting for dynamical processes and long-time kinetics. This new challenge is being tackled differently throughout the community. Methodology developments designed to improve the sampling of reaction paths, such as metadynamics  or accelerated molecular dynamics  are of high potential interest for nanosystems, as shown by promising recent applications . Beyond equilibrium pathways, calculating reaction rates for rearrangements is another ambitious objective in itself, for which computational strategies along various lines are nowadays available [15,16] but not so much widespread in the nanoscale field.
In catalysis, chemical reactivity was traditionally addressed using accurate characterization of the reaction pathways using quantum chemistry approaches and focusing on the energetics of reactants, products and barriers and evaluating rates through transition state theory. The presence of multiple coexisting pathways and the need to account for the support has lead various groups to consider more realistic approaches based on kinetic Monte Carlo (still using typically DFT ingredients) with the substrate explicitly included . KMC approaches have also been used to explore the formation of carbides on iron NPs .
Beyond catalysis, the influence of stabilizing molecules on metal NPs has received increasing attention in the very recent years too. Coating agents have been shown to influence the morphology of metal NPs, and the use of different such agents may dynamically favor asymmetric growth and possibly Janus-type particles . The coating process itself has been studied using atomistic  and coarse-grained approaches, notably for the important case of corona formation relevant in life sciences [21,22]. Metal NPs used as sensors are a specific case in which the adsorption of a (bio)molecule is detected by changes in the optical response. In order to reach the sensitivity required by such devices, the optical spectrum must not only be determined accurately, but sources of noise must be evaluated as well. The role of molecular motion on the NP could be recently addressed for nanorods of varying shape ratios using stochastic models of diffusion . One challenge for nanomedicine is the multivalent nature of the NPs coated with drugs, or their ability to form multiple bonds with target cells but also undesired surrounding bodies. Targeted delivery requires a much better understanding of the various interactions and especially the adhesion kinetics on the scale of tens or hundreds of nanometers, and coarse-grained approaches have only recently appeared . Similar approaches have been applied to get insight into the kinetics of targeted diagnosis and therapy, shedding light onto the role of size and shape [25,26]. At the atomistic level of details, molecular dynamics simulations were found necessary to explain the selective reactions of functionalized gold NPs with enzymes .
Nanoalloys have also been extensively studied in the last few years. Their relaxation involves different mechanisms in which chemical ordering can be varied from some prepared initial conditions toward the (free energy) minimum state. Experimental evidence has been provided that the shape and chemical ordering within such nanoparticles cannot be explained by pure energetic or structural arguments, the kinetics (and possibly the measurement apparatus itself) playing a role too . Such relaxation processes have been studied using lattice models  and off-lattice through discrete path sampling .
In bare metal NPs, shape transformation has been found to play an important role in explaining deviations to thermodynamic influences . Shape transformation by ion implantation, as monitored by the optical response, could be directly simulated by molecular dynamics simulations at the atomistic details . The crystallization of NPs from amorphous state has been studied in details by MD  as well.
Finally, the issue of nanoparticle assembly into ordered aggregates or mesoporous materials has attracted various groups into designing coarse-grained computational protocols for these issues. Such approaches generally rely on the KMC framework and include the various elementary processes at play in the experiment, such as diffusion, ripening/aeging , nucleation and growth as well as precipitation and dissolution . The assembly process itself into crystal structures is a highly nontrivial problem because the interactions between particles depend on their shapes and the coating ligand. One possibility to tune these interactions, which has been explored by coarse-grained simulations too [36,37] is to use molecules that recognize their own family such as DNA, in which Watson-Crick base pairs complement each other naturally. The details of molecular interactions, in particular hydrogen bonds, have also been invoked to explain the formation of chiral self-assemblies of metal NPs , and also to alter the vibrational, viscoelastic or mechanical behavior .
Recently, the need to account explicitly for the environment of metal nanoparticles has arose and a first edition of a CECAM workshop was devoted to this specific issue in 2015. This meeting gathered a variety of researchers originating from physics, chemistry, and life science backgrounds and who are treating their objects of interest through a broad diversity of approaches encompassing electronic structure methods to empirical potentials and coarse-grained models. Here the emphasis was put on modeling the nanoparticles themselves within their environment. Among the critical issues noted during this meeting, the quality of potential energy surfaces, their transferability and the description of interactions at the metal-nonmetal interface were particularly highlighted. Bridging the length scale gap is one main motivation in this field, which requires elaborating hybrid models in which subparts are treated at different degrees of accuracy.
While the need to account for environment remains important, another aspect now demands closer scrutiny, namely the time scale gap. The aforementioned synthesis experiments take place over macroscopically long times. Moreover, experimental advances have made it possible to observe phenomena in situ through electronic microscopes (‘in operando’ conditions), and the real-time manipulation of single nanoparticles has become a reality only fairly recently. Obviously the modeling of potential energy surfaces itself is often driven by the desire to simulate longer time scales, but the processes at play remain difficult to address because they involve rare events. For instance, the rearrangement of a nanoparticle from its chemically synthetized form into a degraded shape is similar to an ageing process and it may further involve a barrier. Individual molecular dynamics simulations, even covering milliseconds, would hardly be able to reproduce any realistic barrier crossing event. In the past years, many algorithms have been devoted to this specific issue, with the purpose of accelerating the dynamics, reconstructing (free) energy pathways not accessible to conventional simulations or even calculating reaction rates. The community of rare events simulations is already well structured, with CECAM workshops being organized on a rather regular basis, but with no specific interest in nanoparticles. The field of nanoparticles modeling is less familiar with these concepts and one goal of the present proposal is to bring the two communities together to exchange ideas and promote methodology advances in a more application-related field where such approaches would be tremendously useful. The questions this workshop aims to address thus belong to two complementary categories:
-How to describe the interaction of a metal-based nanoparticle with its environment, treating electronic structure, and possibly long-range forces as chemically accurate as possible?
-How to transfer the knowledge obtained at the ab initio level to construct lower-level models, hybrid schemes or coarse-grained approaches, and how much transferability can be anticipated?
-How can the properties of the particles be influenced by their environment?
-How to accelerate the dynamics and simulate rare events and access macroscopically long time scales for nanoparticles?
-How to design appropriate reaction coordinates, order parameters, and evaluate transition pathways relevant for nanoparticles?
The workshop will bring together computational researchers working on metal-based nanoparticles, including physicists and chemists, and actively involved in modeling at various scales ranging from pure electronic structure to approximate methods and semi-empirical approaches, as well as experts in the field of rare events and transition pathways, hoping to promote and transfer methods across fields. Following our previous and successful experience, a few experimentalists will also be invited to the workshop to deliver overview talks.
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