Active-learning for global optimization of Ni-Ceria nanoparticles: The case of Ce4-xNixO8- x (x = 1, 2, 3).

Ni-CeO2 nanoparticles (NPs) are promising nanocatalysts for water splitting and water gas shift reactions due to the ability of ceria to temporarily donate oxygen to the catalytic reaction and accept oxygen after the reaction is completed. Therefore, elucidating how different properties of the Ni-Ceria NPs relate to the activity and selectivity of the catalytic reaction, is of crucial importance for the development of novel catalysts. In this work the active learning (AL) method based on machine learning regression and its uncertainty is used for the global optimization of Ce(4-x)NixO(8-x) (x = 1, 2, 3) nanoparticles, employing density functional theory calculations. Additionally, further investigation of the NPs by mass-scaled parallel-tempering Born-Oppenheimer molecular dynamics resulted in the same putative global minimum structures found by AL, demonstrating the robustness of our AL search to learn from small datasets and assist in the global optimization of complex electronic structure systems.

Reinforcement learning for in silico determination of adsorbate-substrate structures.

Reinforcement learning (RL) methods have helped to define the state of the art in the field of modern artificial intelligence, mostly after the breakthrough involving AlphaGo and the discovery of novel algorithms. In this work, we present a RL method, based on Q-learning, for the structural determination of adsorbate@substrate models in silico, where the minimization of the energy landscape resulting from adsorbate interactions with a substrate is made by actions on states (translations and rotations) chosen from an agent's policy. The proposed RL method is implemented in an early version of the reinforcement learning software for materials design and discovery (RLMaterial), developed in Python3.x. RLMaterial interfaces with deMon2k, DFTB+, ORCA, and Quantum Espresso codes to compute the adsorbate@substrate energies. The RL method was applied for the structural determination of (i) the amino acid glycine and (ii) 2-amino-acetaldehyde, both interacting with a boron nitride (BN) monolayer, (iii) host-guest interactions between phenylboronic acid and ß-cyclodextrin and (iv) ammonia on naphthalene. Density functional tight binding calculations were used to build the complex search surfaces with a reasonably low computational cost for systems (i)-(iii) and DFT for system (iv). Artificial neural network and gradient boosting regression techniques were employed to approximate the Q-matrix or Q-table for better decision making (policy) on next actions. Finally, we have developed a transfer-learning protocol within the RL framework that allows learning from one chemical system and transferring the experience to another, as well as from different DFT or DFTB levels.

How important is the amount of exact exchange for spin-state energy ordering in DFT? Case study of molybdenum carbide cluster, Mo4C2.

Since the form of the exact functional in density functional theory is unknown, we must rely on density functional approximations (DFAs). In the past, very promising results have been reported by combining semi-local DFAs with exact, i.e. Hartree-Fock, exchange. However, the spin-state energy ordering and the predictions of global minima structures are particularly sensitive to the choice of the hybrid functional and to the amount of exact exchange. This has been already qualitatively described for single conformations, reactions, and a limited number of conformations. Here, we have analyzed the mixing of exact exchange in exchange functionals for a set of several hundred isomers of the transition metal carbide, Mo4C2. The analysis of the calculated energies and charges using PBE0-type functional with varying amounts of exact exchange yields the following insights: (1) The sensitivity of spin-energy splitting is strongly correlated with the amount of exact exchange mixing. (2) Spin contamination is exacerbated when correlation is omitted from the exchange-correlation functional. (3) There is not one ideal value for the exact exchange mixing which can be used to parametrize or choose among the functionals. Calculated energies and electronic structures are influenced by exact exchange at a different magnitude within a given distribution; therefore, to extend the application range of hybrid functionals to the full periodic table the spin-energy splitting energies should be investigated.

QMLMaterial─A Quantum Machine Learning Software for Material Design and Discovery.

Structural elucidation of chemical compounds is challenging experimentally, and theoretical chemistry methods have added important insight into molecules, nanoparticles, alloys, and materials geometries and properties. However, finding the optimum structures is a bottleneck due to the huge search space, and global search algorithms have been used successfully for this purpose. In this work, we present the quantum machine learning software/agent for materials design and discovery (QMLMaterial), intended for automatic structural determination in silico for several chemical systems: atomic clusters, atomic clusters and the spin multiplicity together, doping in clusters or solids, vacancies in clusters or solids, adsorption of molecules or adsorbents on surfaces, and finally atomic clusters on solid surfaces/materials or encapsulated in porous materials. QMLMaterial is an artificial intelligence (AI) software based on the active learning method, which uses machine learning regression algorithms and their uncertainties for decision making on the next unexplored structures to be computed, increasing the probability of finding the global minimum with few calculations as more data is obtained. The software has different acquisition functions for decision making (e.g., expected improvement and lower confidence bound). Also, the Gaussian process is available in the AI framework for regression, where the uncertainty is obtained analytically from Bayesian statistics. For the artificial neural network and support vector regressor algorithms, the uncertainty can be obtained by K-fold cross-validation or nonparametric bootstrap resampling methods. The software is interfaced with several quantum chemistry codes and atomic descriptors, such as the many-body tensor representation. QMLMaterial's capabilities are highlighted in the current work by its applications in the following systems: Na20, Mo6C3 (where the spin multiplicity was considered), H2O@CeNi3O5, Mg8@graphene, Na3Mg3@CNT (carbon nanotube).

GAMaterial-A genetic-algorithm software for material design and discovery.

Genetic algorithms (GAs) are stochastic global search methods inspired by biological evolution. They have been used extensively in chemistry and materials science coupled with theoretical methods, ranging from force-fields to high-throughput first-principles methods. The methodology allows an accurate and automated structural determination for molecules, atomic clusters, nanoparticles, and solid surfaces, fundamental to understanding chemical processes in catalysis and environmental sciences, for instance. In this work, we propose a new genetic algorithm software, GAMaterial, implemented in Python3.x, that performs global searches to elucidate the structures of atomic clusters, doped clusters or materials and atomic clusters on surfaces. For all these applications, it is possible to accelerate the GA search by using machine learning (ML), the ML@GA method, to build subsequent populations. Results for ML@GA applied for the dopant distributions in atomic clusters are presented. The GAMaterial software was applied for the automatic structural search for the Ti6 O12 cluster, doping Al in Si11 (4Al@Si11 ) and Na10 supported on graphene (Na10 @graphene), where DFTB calculations were used to sample the complex search surfaces with reasonably low computational cost. Finally, the global search by GA of the Mo8 C4 cluster was considered, where DFT calculations were made with the deMon2k code, which is interfaced with GAMaterial.

Automatic structural elucidation of vacancies in materials by active learning.

Finding the optimum structures of non-stoichiometric or berthollide materials, such as (1D, 2D, 3D) materials or nanoparticles (0D), is challenging due to the huge chemical/structural search space. Computational methods coupled with global optimization algorithms have been used successfully for this purpose. In this work, we have developed an artificial intelligence method based on active learning (AL) or Bayesian optimization for the automatic structural elucidation of vacancies in solids and nanoparticles. AL uses machine learning regression algorithms and their uncertainties to take decisions (from a policy) on the next unexplored structures to be computed, increasing the probability of finding the global minimum with few calculations. The methodology allows an accurate and automated structural elucidation for vacancies, which are common in non-stoichiometric (berthollide) materials, helping to understand chemical processes in catalysis and environmental sciences, for instance. The AL vacancies method was implemented in the quantum machine learning software/agent for material design and discovery (QMLMaterial). Also, two additional acquisition functions for decision making were implemented, besides the expected improvement (EI): the lower confidence bound (LCB) and the probability of improvement (PI). The new software was applied for the automatic structural search for graphite (C36) with 3 (C36-3) and 4 (C36-4) carbon vacancies and C60 (C60-4) fullerene with 4 carbon vacancies. DFTB calculations were used to build the complex search surfaces with reasonably low computational cost. Furthermore, with the AL method for vacancies, it was possible to elucidate the optimum oxygen vacancy distribution in CaTiO3 perovskite by DFT, where a semiconductor behavior results from oxygen vacancies. Throughout the work, a Gaussian process with its uncertainty was employed in the AL framework using different acquisition functions (EI, LCB and PI), and taking into account different descriptors: Ewald sum matrix and sine matrix. Finally, the performance of the proposed AL method was compared to random search and genetic algorithm.

Hexatetra-Carbon: A Novel Two-Dimensional Semiconductor Allotrope of Carbon.

Employing first-principles calculations based on density functional theory (DFT), we designed a novel two-dimensional (2D) elemental monolayer allotrope of carbon called hexatetra-carbon. In the hexatetra-carbon structure, each carbon atom bonds with its four neighboring atoms in a 2D double layer crystal structure, which is formed by a network of carbon hexagonal prisms. Based on our calculations, it is found that hexatetra-carbon exhibits a good structural stability as confirmed by its rather high calculated cohesive energy -6.86 eV/atom, and the absence of imaginary phonon modes in its phonon dispersion spectra. Moreover, compared with its hexagonal counterpart, i.e., graphene, which is a gapless material, our designed hexatetra-carbon is a semiconductor with an indirect band gap of 2.20 eV. Furthermore, with a deeper look at the hexatetra-carbon, one finds that this novel monolayer may be obtained from bilayer graphene under external mechanical strain conditions. As a semiconductor with a moderate band gap in the visible light range, once synthesized, hexatetra-carbon would show promising applications in new opto-electronics technologies.

A new active learning approach for adsorbate-substrate structural elucidation in silico.

Adsorbate interactions with substrates (e.g. surfaces and nanoparticles) are fundamental for several technologies, such as functional materials, supramolecular chemistry, and solvent interactions. However, modeling these kinds of systems in silico, such as finding the optimum adsorption geometry and energy, is challenging, due to the huge number of possibilities of assembling the adsorbate on the surface. In the current work, we have developed an artificial intelligence (AI) approach based on an active learning (AL) method for adsorption optimization on the surface of materials. AL uses machine learning (ML) regression algorithms and their uncertainties to make a decision (based on a policy) for the next unexplored structures to be computed, increasing, though, the probability of finding the global minimum with a small number of calculations. The methodology allows an accurate and automated structural elucidation of the adsorbate on the surface, based on the minimization of the total electronic energy. The new AL method for adsorption optimization was developed and implemented in the quantum machine learning software/agent for material design and discovery (QMLMaterial) program and was applied for C60@TiO2 anatase (101). It marks another software extension with a new feature in addition to the automatic structural elucidation of defects in materials and of nanoparticles as well. SCC-DFTB calculations were used to build the complex search surfaces with a reasonably low computational cost. An artificial neural network (NN) was employed in the AL framework evaluated together with two uncertainty quantification methods: K-fold cross-validation and non-parametric bootstrap (BS) resampling. Also, two different acquisition functions for decision-making were used: expected improvement (EI) and the lower confidence bound (LCB).

Multiscale molecular modelling: from electronic structure to dynamics of nanosystems and beyond.

Important contemporary biological and materials problems often depend on interactions that span orders of magnitude differences in spatial and temporal dimensions. This Tutorial Review attempts to provide an introduction to such fascinating problems through a series of case studies, aimed at beginning researchers, graduate students, postdocs and more senior colleagues who are changing direction to focus on multiscale aspects of their research. The choice of specific examples is highly personal, with examples either chosen from our own work or outstanding multiscale efforts from the literature. I start with various embedding schemes, as exemplified by polarizable continuum models, 3-D RISM, molecular DFT and frozen-density embedding. Next, QM/MM (quantum mechanical/molecular mechanical) techniques are the workhorse of pm-to-nm/ps-to-ns simulations; examples are drawn from enzymes and from nanocatalysis for oil-sands upgrading. Using polarizable force-fields in the QM/MM framework represents a burgeoning subfield; with examples from ion channels and electron dynamics in molecules subject to strong external fields, probing the atto-second dynamics of the electrons with RT-TDDFT (real-time - time-dependent density functional theory) eventually coupled with nuclear motion through the Ehrenfest approximation. This is followed by a section on coarse graining, bridging dimensions from atoms to cells. The penultimate chapter gives a quick overview of multiscale approaches that extend into the meso- and macro-scales, building on atomistic and coarse-grained techniques to enter the world of materials engineering, on the one hand, and cell biology, on the other. A final chapter gives just a glimpse of the burgeoning impact of machine learning on the structure-dynamics front. I aim to capture the excitement of contemporary leading-edge breakthroughs in the description of physico-chemical systems and processes in complex environments, with only enough historical content to provide context and aid the next generation of methodological development. While I aim also for a clear description of the essence of methodological breakthroughs, equations are kept to a minimum and detailed formalism and implementation details are left to the references. My approach is very selective (case studies) rather than exhaustive. I think that these case studies should provide fodder to build as complete a reference tree on multiscale modelling as the reader may wish, through forward and backward citation analysis. I hope that my choices of cases will excite interest in newcomers and help to fuel the growth of multiscale modelling in general.

Self-Consistent Auxiliary Density Perturbation Theory.

The working equations for the extension of auxiliary density perturbation theory (ADPT) to hybrid functionals, employing the variational fitting of the Fock potential, are derived. The response equations in the resulting self-consistent ADPT (SC-ADPT) are solved iteratively with an adapted Eirola-Nevanlinna algorithm. As a result, a memory and CPU time efficient implementation of perturbation theory free of four-center electron repulsion integrals (ERIs) is obtained. Our validation calculations of SC-ADPT static and dynamic polarizabilities show quantitative agreement with corresponding coupled perturbed Hartree-Fock and Kohn-Sham results employing four-center ERIs. The comparison of SC-ADPT hybrid functional polarizabilities with coupled cluster reference calculations yield semiquantitative agreement. The presented systematic study of the dynamic polarizabilities of oligothiophenes shows that hybrid functionals can overcome the pathological misplacement of excitation poles by the local density and generalized gradient approximations. Good agreement with experimental dynamic polarizabilities for all studied oligothiophenes is achieved with range-separated hybrid functionals in the framework of SC-ADPT.

Reliability of semiempirical and DFTB methods for the global optimization of the structures of nanoclusters.

In this work, we explore the possibility of using computationally inexpensive electronic structure methods, such as semiempirical and DFTB calculations, for the search of the global minimum (GM) structure of chemical systems. The basic prerequisite that these inexpensive methods will need to fulfill is that their lowest energy structures can be used as starting point for a subsequent local optimization at a benchmark level that will yield its GM. If this is possible, one could bypass the global optimization at the expensive method, which is currently impossible except for very small molecules. Specifically, we test our methods with clusters of second row elements including systems of several bonding types, such as alkali, metal, and covalent clusters. The results reveal that the DFTB3 method yields reasonable results and is a potential candidate for this type of applications. Even though the DFTB2 approach using standard parameters is proven to yield poor results, we show that a re-parametrization of only its repulsive part is enough to achieve excellent results, even when applied to larger systems outside the training set.

Benchmarking polarizable and non-polarizable force fields for Ca2+-peptides against a comprehensive QM dataset.

Explicit description of atomic polarizability is critical for the accurate treatment of inter-molecular interactions by force fields (FFs) in molecular dynamics (MD) simulations aiming to investigate complex electrostatic environments such as metal-binding sites of metalloproteins. Several models exist to describe key monovalent and divalent cations interacting with proteins. Many of these models have been developed from ion-amino-acid interactions and/or aqueous-phase data on cation solvation. The transferability of these models to cation-protein interactions remains uncertain. Herein, we assess the accuracy of existing FFs by their abilities to reproduce hierarchies of thousands of Ca2+-dipeptide interaction energies based on density-functional theory calculations. We find that the Drude polarizable FF, prior to any parameterization, better approximates the QM interaction energies than any of the non-polarizable FFs. Nevertheless, it required improvement in order to address polarization catastrophes where, at short Ca2+-carboxylate distances, the Drude particle of oxygen overlaps with the divalent cation. To ameliorate this, we identified those conformational properties that produced the poorest prediction of interaction energies to reduce the parameter space for optimization. We then optimized the selected cation-peptide parameters using Boltzmann-weighted fitting and evaluated the resulting parameters in MD simulations of the N-lobe of calmodulin. We also parameterized and evaluated the CTPOL FF, which incorporates charge-transfer and polarization effects in additive FFs. This work shows how QM-driven parameter development, followed by testing in condensed-phase simulations, may yield FFs that can accurately capture the structure and dynamics of ion-protein interactions.

Theoretical Investigation of 6-Mercaptopurine Isomers' Adsorption on the Au(001) Surface: Revealing the Fate of Different Isomers.

Density functional theory (DFT) calculations were performed for the adsorption of different isomers of 6-mercaptopurine on the Au(001) surface. All of the configurations of four thione and two thiol isomers were considered. The results show that the thione isomers adsorbed more strongly on the Au(001) surface compared with the thiol ones. In all of the configurations, the calculated binding energy of ma-8 is the largest, in which the S atom of 6-mercaptopurine binds strongly with one Au atom on the monodentate sites and 6-mercaptopurine retains a flat geometry, predominantly with an approximately 30° orientation between the C-S bond and the Au-Au bond of the catalyst. Additionally, the 6-mercaptopurines in ma-2, mb-5, and mc-3 also bind more strongly onto the surface, which show relatively higher stability on the surfaces, indicating a high preference for adsorption. Charge density differences and TDOS analyses for the four configurations also show that the electronic charges are accumulated between Au and S atoms in the Au-S bonds, indicating occurrence of adsorption and chemical-bond formation.

Molecular Simulations with in-deMon2k QM/MM, a Tutorial-Review.

deMon2k is a readily available program specialized in Density Functional Theory (DFT) simulations within the framework of Auxiliary DFT. This article is intended as a tutorial-review of the capabilities of the program for molecular simulations involving ground and excited electronic states. The program implements an additive QM/MM (quantum mechanics/molecular mechanics) module relying either on non-polarizable or polarizable force fields. QM/MM methodologies available in deMon2k include ground-state geometry optimizations, ground-state Born-Oppenheimer molecular dynamics simulations, Ehrenfest non-adiabatic molecular dynamics simulations, and attosecond electron dynamics. In addition several electric and magnetic properties can be computed with QM/MM. We review the framework implemented in the program, including the most recently implemented options (link atoms, implicit continuum for remote environments, metadynamics, etc.), together with six applicative examples. The applications involve (i) a reactivity study of a cyclic organic molecule in water; (ii) the establishment of free-energy profiles for nucleophilic-substitution reactions by the umbrella sampling method; (iii) the construction of two-dimensional free energy maps by metadynamics simulations; (iv) the simulation of UV-visible absorption spectra of a solvated chromophore molecule; (v) the simulation of a free energy profile for an electron transfer reaction within Marcus theory; and (vi) the simulation of fragmentation of a peptide after collision with a high-energy proton.

Heterogeneous reactions of SO2 on the hematite(0001) surface.

Heterogeneous reactions at the surfaces of mineral dusts represent a key process in the formation of atmospheric aerosols. To quantify the rate of aerosol formation in climate modeling as well as combat hazardous aerosols, a deep understanding of the mechanisms of these reactions is essential. In the present work, density functional theory calculations, including a Hubbard-like +U correction, were employed to elucidate the reaction between SO2 and the hematite(0001) surface. Three reaction conditions are considered: dry, wet, and aerobic. In the absence of water and oxygen, adsorption energies of SO2 on the clean Fe-O3-Fe-termination were found to be about -0.8 to -1.0 eV and resulted in the formation of an adsorbed SO3-like species. The addition of water leads to surface hydroxylation and has little effect on promoting the SO2 adsorption. Under such circumstances, an HSO3-like species was formed with a smaller adsorption energy of about -0.5 eV. By contrast, the presence of molecular oxygen enhances the SO2 adsorption significantly as the two species combine to form sulfate SO4 2-, with adsorption energies of -1.31 to -1.64 eV. The calculated vibrational frequencies of the adsorbate species provide insight into the surface bonding and a useful spectral fingerprinting for experimental measurements. These results elucidate the atomistic mechanism of the reaction between SO2 and hematite and highlight the important role of atmospheric O2 in the formation of sulfates.

Simulating Electron Dynamics in Polarizable Environments.

We propose a methodology for simulating attosecond electron dynamics in large molecular systems. Our approach is based on the combination of real time time-dependent-density-functional theory (RT-TDDFT) and polarizable Molecular Mechanics (MMpol) with the point-charge-dipole model of electrostatic induction. We implemented this methodology in the software deMon2k that relies heavily on auxiliary fitted densities. In the context of RT-TDDFT/MMpol simulations, fitted densities allow the cost of the calculations to be reduced drastically on three fronts: (i) the Kohn-Sham potential, (ii) the electric field created by the (fluctuating) electron cloud which is needed in the QM/MM interaction, and (iii) the analysis of the fluctuating electron density on-the-fly. We determine conditions under which fitted densities can be used without jeopardizing the reliability of the simulations. Very encouraging results are found both for stationary and time-dependent calculations. We report absorption spectra of a dye molecule in the gas phase, in nonpolarizable water, and in polarizable water. Finally, we use the method to analyze the distance-dependent response of the environment of a peptide perturbed by an electric field. Different response mechanisms are identified. It is shown that the induction on MM sites allows excess energy to dissipate from the QM region to the environment. In this regard, the first hydration shell plays an essential role in absorbing energy. The methodology presented herein opens the possibility of simulating radiation-induced electronic phenomena in complex and extended molecular systems.

Electronic properties of carbon nanotubes complexed with a DNA nucleotide.

Electronic properties of carbon nanotubes (CNTs) play an important role in their interactions with nano-structured materials. In this work, interactions of adenosine monophosphate (AMP), a DNA nucleotide, with metallic and semi-conducting CNTs are studied using the density functional tight binding (DFTB) method. The electronic structure of semi-conducting CNTs was found to be changed as they turned to metallic CNTs in a vacuum upon interaction with the nucleotide while metallic CNTs remain metallic. Specifically, the band gap of semi-conducting CNTs was decreased by 0.79 eV on average while nearly no change was found in the metallic tubes. However, our investigations showed that the presence of explicit water molecules prevents the metallicity change and only small changes in the CNT band gap occur. According to our charge analysis, the average negative charge accumulated on CNTs upon interaction with the AMP was determined to be 0.77 e in a vacuum while it was 0.03 e in solution. Therefore, it is essential to include explicit water molecules in simulating complexes formed by DNA nucleotides and CNTs which were ignored in several past studies performed using quantum mechanical approaches.

LiCl solvation in N-methyl-acetamide (NMA) as a model for understanding Li(+) binding to an amide plane.

The thermodynamics of ion solvation in non-aqueous solvents remains of great significance for understanding cellular transport and ion homeostasis for the design of novel ion-selective materials and applications in molecular pharmacology. Molecular simulations play pivotal roles in connecting experimental measurements to the microscopic structures of liquids. One of the most useful and versatile mimetic systems for understanding biological ion transport is N-methyl-acetamide (NMA). A plethora of theoretical studies for ion solvation in NMA have appeared recently, but further progress is limited by two factors. One is an apparent lack of experimental data on solubility and thermodynamics of solvation for a broad panel of 1 : 1 salts over an appropriate temperature and concentration range. The second concern is more substantial and has to do with the limitations hardwired in the additive (fixed charge) approximations used for most of the existing force-fields. In this submission, we report on the experimental evaluation of LiCl solvation in NMA over a broad range of concentrations and temperatures and compare the results with those of MD simulations with several additive and one polarizable force-field (Drude). By comparing our simulations and experimental results to density functional theory computations, we discuss the limiting factors in existing potential functions. To evaluate the possible implications of explicit and implicit polarizability treatments on ion permeation across biological channels, we performed potential of mean force (PMF) computations for Li(+) transport through a model narrow ion channel with additive and polarizable force-fields.

Quantum effects in cation interactions with first and second coordination shell ligands in metalloproteins.

Despite decades of investigations, the principal mechanisms responsible for the high affinity and specificity of proteins for key physiological cations K(+), Na(+), and Ca(2+) remain a hotly debated topic. At the core of the debate is an apparent need (or lack thereof) for an accurate description of the electrostatic response of the charge distribution in a protein to the binding of an ion. These effects range from partial electronic polarization of the directly ligating atoms to long-range effects related to partial charge transfer and electronic delocalization effects. While accurate modeling of cation recognition by metalloproteins warrants the use of quantum-mechanics (QM) calculations, the most popular approximations used in major biomolecular simulation packages rely on the implicit modeling of electronic polarization effects. That is, high-level QM computations for ion binding to proteins are desirable, but they are often unfeasible, because of the large size of the reactive-site models and the need to sample conformational space exhaustively at finite temperature. Several solutions to this challenge have been proposed in the field, ranging from the recently developed Drude polarizable force-field for simulations of metalloproteins to approximate tight-binding density functional theory (DFTB). To delineate the usefulness of different approximations, we examined the accuracy of three recent and commonly used theoretical models and numerical algorithms, namely, CHARMM C36, the latest developed Drude polarizable force fields, and DFTB3 with the latest 3OB parameters. We performed MD simulations for 30 cation-selective proteins with high-resolution X-ray structures to create ensembles of structures for analysis with different levels of theory, e.g., additive and polarizable force fields, DFTB3, and DFT. The results from DFT computations were used to benchmark CHARMM C36, Drude, and DFTB3 performance. The explicit modeling of quantum effects unveils the key electrostatic properties of the protein sites and the importance of specific ion-protein interactions. One of the most interesting findings is that secondary coordination shells of proteins are noticeably perturbed in a cation-dependent manner, showing significant delocalization and long-range effects of charge transfer and polarization upon binding Ca(2+).

Progress and challenges in simulating and understanding electron transfer in proteins.

This Review presents an overview of the most common numerical simulation approaches for the investigation of electron transfer (ET) in proteins. We try to highlight the merits of the different approaches but also the current limitations and challenges. The article is organized into three sections. Section 2 deals with direct simulation algorithms of charge migration in proteins. Section 3 summarizes the methods for testing the applicability of the Marcus theory for ET in proteins and for evaluating key thermodynamic quantities entering the reaction rates (reorganization energies and driving force). Recent studies interrogating the validity of the theory due to the presence of non-ergodic effects or of non-linear responses are also described. Section 4 focuses on the tunneling aspects of electron transfer. How can the electronic coupling between charge transfer states be evaluated by quantum chemistry approaches and rationalized? What interesting physics regarding the impact of protein dynamics on tunneling can be addressed? We will illustrate the different sections with examples taken from the literature to show what types of system are currently manageable with current methodologies. We also take care to recall what has been learned on the biophysics of ET within proteins thanks to the advent of atomistic simulations.