Modelling realistic TiO2 nanospheres: A benchmark study of SCC-DFTB against hybrid DFT

Characterization of the Coordination and Solvation Dynamics of Solvated Systems─Implications for the Analysis of Molecular Interactions in Solutions and Pure H2O

The characterization of solvation shells of atoms, ions, and molecules in solution is essential to relate solvation properties to chemical phenomena such as complex formation and reactivity. Different definitions of the first-shell coordination sphere from simulation data can lead to potentially conflicting data on the structural properties and associated ligand exchange dynamics. The definition of a solvation shell is typically based on a given threshold distance determined from the respective solute-solvent pair distribution function g(r) (i.e., GC). Alternatively, a nearest neighbor (NN) assignment based on geometric properties of the coordination complex without the need for a predetermined cutoff criterion, such as the relative angular distance (RAD) or the modified Voronoi (MV) tessellation, can be applied. In this study, the effect of different NN algorithms on the coordination number and ligand exchange dynamics evaluated for a series of monatomic ions in aqueous solution, carbon dioxide in aqueous and dichloromethane solutions, and pure liquid water has been investigated. In the case of the monatomic ions, the RAD approach is superior in achieving a well separated definition of the first solvation layer. In contrast, the MV algorithm provides a better separation of the NNs from a molecular point of view, leading to better results in the case of solvated CO2. When analyzing the coordination environment in pure water, the cutoff-based GC framework was found to be the most reliable approach. By comparison of the number of ligand exchange reactions and the associated mean ligand residence times (MRTs) with the properties of the coordination number autocorrelation functions, it is shown that although the average coordination numbers are sensitive to the different definitions of the first solvation shell, highly consistent estimates for the associated MRT of the solvated system are obtained in the majority of cases.

The effect of polymer coating on nanoparticles' interaction with lipid membranes studied by coarse-grained molecular dynamics simulations

Nanoparticles' (NPs) permeation through cell membranes, whether it happens via passive or active transport, is an essential initial step for their cellular internalization. The NPs' surface coating impacts the way they translocate through the lipid bilayer and the spontaneity of the process. Understanding the molecular details of NPs' interaction with cell membranes allows the design of nanosystems with optimal characteristics for crossing the lipid bilayer: computer simulations are a powerful tool for this purpose. In this work, we have performed coarse-grained molecular dynamics simulations and free energy calculations on spherical titanium dioxide NPs conjugated with polymer chains of different chemical compositions. We have demonstrated that the hydrophobic/hydrophilic character of the chains, more than the nature of their terminal group, plays a crucial role in determining the NPs' interaction with the lipid bilayer and the thermodynamic spontaneity of NPs' translocation from water to the membrane. We envision that this computational work will be helpful to the experimental community in terms of the rational design of NPs for efficient cell membrane permeation.

Exploring Molecular Energy Landscapes by Coupling the DFTB Potential with a Tree-Based Stochastic Algorithm: Investigation of the Conformational Diversity of Phthalates

Exploring the global energy landscape of relatively large molecules at the quantum level is a challenging problem. In this work, we report the coupling of a nonredundant conformational space exploration method, namely, the robotics-inspired iterative global exploration and local optimization (IGLOO) algorithm, with the quantum-chemical density functional tight binding (DFTB) potential. The application of this fast and efficient computational approach to three close-sized molecules of the phthalate family (DBP, BBP, and DEHP) showed that they present different conformational landscapes. These differences have been rationalized by making use of descriptors based on distances and dihedral angles. Coulomb interactions, steric hindrance, and dispersive interactions have been found to drive the geometric properties. A strong correlation has been evidenced between the two dihedral angles describing the side-chain orientation of the phthalate molecules. Our approach identifies low-energy minima without prior knowledge of the potential energy surface, paving the way for future investigations into transition paths and states.

Mechanism of RGD-conjugated nanodevice binding to its target protein integrin αVβ3 by atomistic molecular dynamics and machine learning

Active targeting strategies have been proposed to enhance the selective uptake of nanoparticles (NPs) by diseased cells, and recent experimental findings have proven the effectiveness of this approach. However, no mechanistic studies have yet revealed the atomistic details of the interactions between ligand-activated NPs and integrins. As a case study, here we investigate, by means of advanced molecular dynamics simulations (MD) and machine learning methods (namely equilibrium MD, binding free energy calculations and training of self-organized maps), the interaction of a cyclic-RGD-conjugated PEGylated TiO2 NP (the nanodevice) with the extracellular segment of integrin αVβ3 (the target), the latter experimentally well-known to be over-expressed in several solid tumors. Firstly, we proved that the cyclic-RGD ligand binding to the integrin pocket is established and kept stable even in the presence of the cumbersome realistic model of the nanodevice. In this respect, the unsupervised machine learning analysis allowed a detailed comparison of the ligand/integrin binding in the presence and in the absence of the nanodevice, which unveiled differences in the chemical features. Then, we discovered that unbound cyclic RGDs conjugated to the NP largely contribute to the interactions between the nanodevice and the integrin. Finally, by increasing the density of cyclic RGDs on the PEGylated TiO2 NP, we observed a proportional enhancement of the nanodevice/target binding. All these findings can be exploited to achieve an improved targeting selectivity and cellular uptake, and thus a more successful clinical outcome.

Molecular Dynamics for the Optimal Design of Functionalized Nanodevices to Target Folate Receptors on Tumor Cells

Atomistic details on the mechanism of targeting activity by biomedical nanodevices of specific receptors are still scarce in the literature, where mostly ligand/receptor pairs are modeled. Here, we use atomistic molecular dynamics (MD) simulations, free energy calculations, and machine learning approaches on the case study of spherical TiO2 nanoparticles (NPs) functionalized with folic acid (FA) as the targeting ligand of the folate receptor (FR). We consider different FA densities on the surface and different anchoring approaches, i.e., direct covalent bonding of FA γ-carboxylate or through polyethylene glycol spacers. By molecular docking, we first identify the lowest energy conformation of one FA inside the FR binding pocket from the X-ray crystal structure, which becomes the starting point of classical MD simulations in a realistic physiological environment. We estimate the binding free energy to be compared with the existing experimental data. Then, we increase complexity and go from the isolated FA to a nanosystem decorated with several FAs. Within the simulation time framework, we confirm the stability of the ligand-receptor interaction, even in the presence of the NP (with or without a spacer), and no significant modification of the protein secondary structure is observed. Our study highlights the crucial role played by the spacer, FA protonation state, and density, which are parameters that can be controlled during the nanodevice preparation step.

Solvent Effects in Ligand Stripping Behavior of Colloidal Nanoparticles

Inorganic colloidal nanoparticle (NP) properties can be tuned by stripping stabilizing ligands using a poor solvent. However, the mechanism behind ligand stripping is poorly understood, in part because in situ measurements of ligand stripping are challenging at the nanoscale. Here, we investigate ethanol solvent-mediated oleylamine ligand stripping from magnetite (Fe₃O₄) NPs in different compositions of ethanol/hexane mixtures using atomistic molecular dynamics (MD) simulations and thermogravimetric analysis (TGA). Our study elucidates a complex interplay of ethanol interactions with system components and indicates the existence of a threshold concentration of ∼34 vol % ethanol, above which ligand stripping saturates. Moreover, hydrogen bonding between ethanol and stripped ligands inhibits subsequent readsorption of the ligands on the NP surface. A proposed modification of the Langmuir isotherm explains the role of the enthalpy of mixing of the ligands and solvents on the ligand stripping mechanism. A good agreement between the MD predictions and TGA measurements of ligand stripping from Fe₃O₄ NPs validates the simulation observations. Our findings demonstrate that the ligand coverage of NPs can be controlled by using a poor solvent below the threshold concentration and highlight the importance of ligand-solvent interactions that modulate the properties of colloidal NPs. The study also provides an approach for a detailed in silico study of ligand stripping and exchange from colloidal NPs that are crucial for applications of NPs spanning self-assembly, optoelectronics, nanomedicine, and catalysis.

Metadynamics simulations for the investigation of drug loading on functionalized inorganic nanoparticles

Inorganic nanoparticles show promising properties that allow them to be efficiently used as drug carriers. The main limitation in this type of application is currently the drug loading capacity, which can be overcome with a proper functionalization of the nanoparticle surface. In this study, we present, for the first time, a computational approach based on metadynamics to estimate the binding free energy of the doxorubicin drug (DOX) to a functionalized TiO₂ nanoparticle under different pH conditions. On a thermodynamic basis, we demonstrate the robustness of our approach to capture the overall mechanism behind the pH-triggered release of DOX due to environmental pH changes. Notably, binding free energy estimations align well with what is expected for a pH-sensitive drug delivery system. Based on our results, we envision the use of metadynamics as a promising computational tool for the rational design and in silico optimization of organic ligands with improved drug carrier properties.

An Efficient Way to Model Complex Iron Carbides: A Benchmark Study of DFTB2 against DFT

Iron carbides have attracted increasing attention in recent years due to their enormous potential in catalytic fields, such as Fischer-Tropsch synthesis and the growth of carbon nanotubes. Theoretical calculations can provide a more thorough understanding of these reactions at the atomic scale. However, due to the extreme complexity of the active phases and surface structures of iron carbides at the operando conditions, calculations based on density functional theory (DFT) are too costly for realistically large models of iron carbide particles. Therefore, a cheap and efficient quantum mechanical simulation method with accuracy comparable to DFT is desired. In this work, we adopt the spin-polarized self-consistent charge density functional tight-binding (DFTB2) method for iron carbides by reparametrization of the repulsive part of the Fe-C interactions. To assess the performance of the improved parameters, the structural and electronic properties of iron carbide bulks and clusters obtained with DFTB2 method are compared with the previous experimental values and the results obtained with DFT approach. Calculated lattice parameters and density of states are close to DFT predictions. The benchmark results show that the proposed parametrization of Fe-C interactions provides transferable and balanced description of iron carbide systems. Therefore, spin-polarized DFTB2 is valued as an efficient and reliable method for the description of iron carbide systems.

Multi-scale modeling of folic acid-functionalized TiO2 nanoparticles for active targeting of tumor cells

Strategies based on the active targeting of tumor cells are emerging as smart and efficient nanomedical procedures. Folic acid (FA) is a vitamin and a well-established tumor targeting agent because of its strong affinity for the folate receptor (FR), which is an overexpressed protein on the cell membranes of the tumor cells. FA can be successfully anchored to several nanocarriers, including inorganic nanoparticles (NPs) based on transition metal oxides. Among them, TiO₂ is extremely interesting because of its excellent photoabsorption and photocatalytic properties, which can be exploited in photodynamic therapy. However, it is not yet clear in which respects direct anchoring of FA to the NP or the use of spacers, based on polyethylene glycol (PEG) chains, are different and whether one approach is better than the other. In this work, we combine Quantum Mechanics (QM) and classical Molecular Dynamics (MD) to design and optimize the FA functionalization on bare and PEGylated TiO₂ models and to study the dynamical behavior of the resulting nanoconjugates in a pure water environment and in physiological conditions. We observe that they are chemically stable, even under the effect of increasing temperature (up to 500 K). Using the results from long MD simulations (100 ns) and from free energy calculations, we determine how the density of FA molecules on the TiO₂ NP and the presence of PEG spacers impact on the actual exposure of the ligands, especially by affecting the extent of FA-FA intermolecular interactions, which are detrimental for the targeting ability of FA towards the folate receptor. This analysis provides a solid and rational basis for experimentalists to define the optimal FA density and the more appropriate mode of anchoring to the carrier, according to the final purpose of the nanoconjugate.

Molecular dynamics simulations of cRGD-conjugated PEGylated TiO2 nanoparticles for targeted photodynamic therapy

The conjugation of high-affinity cRGD-containing peptides is a promising approach in nanomedicine to efficiently reduce off-targeting effects and enhance the cellular uptake by integrin-overexpressing tumor cells. Herein we utilize atomistic molecular dynamics simulations to evaluate key structural-functional parameters of these targeting ligands for an effective binding activity towards α_Vβ₃ integrins. An increasing number of cRGD ligands is conjugated to PEG chains grafted to highly curved TiO₂ nanoparticles to unveil the impact of cRGD density on the ligand's presentation, stability, and conformation in an explicit aqueous environment. We find that a low density leads to an optimal spatial presentation of cRGD ligands out of the "stealth" PEGylated layer around the nanosystem, favoring a straight upward orientation and spaced distribution of the targeting ligands in the bulk-water phase. On the contrary, high densities favor over-clustering of cRGD ligands, driven by a concerted mechanism of enhanced ligand-ligand interactions and reduced water accessibility over the ligand's molecular surface. These findings strongly suggest that the ligand density modulation is a key factor in the design of cRGD-targeting nanodevices to maximize their binding efficiency into over-expressed α_Vβ₃ integrin receptors.

Analyzing the TiO2surface reactivity based on oxygen vacancies computed by DFT and DFTB methods

Titanium dioxide is a key material in many fields, including technological, industrial and biomedical applications. Many of these applications are related to the surface reactivity of TiO₂and involve its reducibility properties. Recently titania has been banned as a food additive due to its (nano)toxicity, and the release of reactive oxygen species plays a crucial role in many toxicological mechanisms. Determining chemical descriptors that account for the extension of reduction is necessary to understand such processes and necessary for predicting the reactivity of an unknown system. In the present work, we compute a set of chemical descriptors for selected surfaces of anatase and rutile TiO₂. The aim is twofold: we want to provide chemically meaningful information on the surface reactivity, and benchmark the descriptors for twoab initioschemes. To do so, we compute the oxygen vacancy formation energy, and the corresponding electronic structure, in four slab models with two different computational schemes (DFT+Uand DFTB). In this way, we characterize the robustness of the dataset, with the purpose of scaling up to more realistic model systems such as nanoparticles or explicit solvent, which are too computationally demanding for state-of-the-art density functional theory approaches.

Effect of dopamine-functionalization, charge and pH on protein corona formation around TiO2 nanoparticles

Inorganic nanoparticles (NPs) are gaining increasing attention in nanomedicine because of their stimuli responsiveness, which allows combining therapy with diagnosis. However, little information is known about their interaction with intracellular or plasma proteins when they are introduced in a biological environment. Here we present atomistic molecular dynamics (MD) simulations investigating the case study of dopamine-functionalized TiO₂ nanoparticles and two proteins that are overexpressed in cancer cells, i.e. PARP1 and HSP90, since experiments proved them to be the main components of the corona in cell cultures. The mechanism and the nature of the interaction (electrostatic, van der Waals, H-bonds, etc.) is unravelled by defining the protein residues that are more frequently in contact with the NPs, the extent of contact surface area and the variations in the protein secondary structures, at different pH and ionic strength conditions of the solution where they are immersed to simulate a realistic biological environment. The effects of the NP surface functionalization and charge are also considered. Our MD results suggest that less acidic intracellular pH conditions in the presence of cytosolic ionic strength enhance PARP1 interaction with the nanoparticle, whereas the HSP90 contribution is partly weakened, providing a rational explanation to existing experimental observations.

Dynamics of Heterogeneous Catalytic Processes at Operando Conditions

The rational design of high-performance catalysts is hindered by the lack of knowledge of the structures of active sites and the reaction pathways under reaction conditions, which can be ideally addressed by an in situ/operando characterization. Besides the experimental insights, a theoretical investigation that simulates reaction conditions-so-called operando modeling-is necessary for a plausible understanding of a working catalyst system at the atomic scale. However, there is still a huge gap between the current widely used computational model and the concept of operando modeling, which should be achieved through multiscale computational modeling. This Perspective describes various modeling approaches and machine learning techniques that step toward operando modeling, followed by selected experimental examples that present an operando understanding in the thermo- and electrocatalytic processes. At last, the remaining challenges in this area are outlined.

The Mystery of Black TiO2: Insights from Combined Surface Science and In Situ Electrochemical Methods

Titanium dioxide (TiO₂) is often employed as a light absorber, electron-transporting material and catalyst in different energy and environmental applications. Heat treatment in a hydrogen atmosphere generates black TiO₂ (b-TiO₂), allowing better absorption of visible light, which placed this material in the forefront of research. At the same time, hydrogen treatment also introduces trap states, and the question of whether these states are beneficial or harmful is rather controversial and depends strongly on the application. We employed combined surface science and in situ electrochemical methods to scrutinize the effect of these states on the photoelectrochemical (PEC), electrocatalytic (EC), and charge storage properties of b-TiO₂. Lower photocurrents were recorded with the increasing number of defect sites, but the EC and charge storage properties improved. We also found that the PEC properties can be enhanced by trap state passivation through Li⁺ ion intercalation in a two-step process. This passivation can only be achieved by utilizing small size cations in the electrolyte (Li⁺) but not with bulky ones (Bu₄N⁺). The presented insights will help to resolve some of the controversies in the literature and also provide rational trap state engineering strategies.

Tempering stochastic density functional theory

We introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density as a sum of a "warm" component complemented by "colder" correction(s). Since the warm component is larger in magnitude but faster to evaluate, we use many more stochastic orbitals for its evaluation than for the smaller-sized colder correction(s). This results in a significant reduction in the statistical fluctuations and systematic deviation compared to sDFT for the same computational effort. We demonstrate the method's performance on large hydrogen-passivated silicon nanocrystals, finding a reduction in the systematic deviation in the energy by more than an order of magnitude, while the systematic deviation in the forces is also quenched. Similarly, the statistical fluctuations are reduced by factors of ≈4-5 for the total energy and ≈1.5-2 for the forces on the atoms. Since the embedding in t-sDFT is fully stochastic, it is possible to combine t-sDFT with other variants of sDFT such as energy-window sDFT and embedded-fragmented sDFT.

Exploring the drug loading mechanism of photoactive inorganic nanocarriers through molecular dynamics simulations

Inorganic nanoparticles are gaining increasing attention as drug carriers because they respond to external physical stimuli, allowing therapy to be combined with diagnosis. Their drawback is low drug loading capacity, which can be improved by proper and efficacious functionalization. In this computational study, we take TiO2 spherical nanoparticles as prototype photoresponsive inorganic nanoparticles and we fully decorate them with two different types of bifunctional ligands: TETTs and DOPACs, which present different surface anchoring groups (silanol or catechol) but the same drug tethering COOH group, although in different concentrations (3 vs. 1), thus causing different steric hindrances. Then, we put these two types of nanocarriers in bulk water and in the presence of several DOX molecules and let the systems evolve through molecular dynamics (MD) simulations, clearly observing drug loading on the nanocarriers. This comparative MD study allows the investigation of the loading mechanism, performance of a conformational analysis and establishment of the guiding interactions through an energy decomposition analysis. We learn that DOX mostly interacts with the functionalized NPs through electrostatics, as a consequence of the protonated amino group, although several H-bonds are also established both with the ligands and with the oxide surface. Different ligands induce a different electrostatic potential around the NP; therefore, those which lead to the formation of more negative hotspots (here TETTs) are found to favour DOX binding. The leading role of electrostatics can provide a rational explanation for a pH-dependent drug release mechanism that is often invoked for DOX when reaching diseased cells because under anomalous acidic conditions both the NP surface and the carboxylate groups of the ligands are expected to get protonated, which of course would weaken, if not totally quench, the interaction of the nanocarrier with protonated DOX.

Reactive molecular dynamics simulations of hydration shells surrounding spherical TiO2 nanoparticles: implications for proton-transfer reactions

In many potential applications, nanoparticles are typically in an aqueous medium. This has strong influence on the stability, optical properties and reactivity, in particular for their functionalization. Therefore, the understanding of the chemistry at the interface between the solvent and the nanoparticle is of utmost importance. In this work, we present a comparative ReaxFF reactive molecular dynamics investigation on spherical TiO2 nanoparticles (NSs) of realistic size, with diameters from 2.2 to 4.4 nm, immersed in a large drop of bulk water. After force field validation for its use for a curved anatase TiO2 surface/water interface, we performed several simulations of the TiO2 nanoparticles of increasing size in a water drop. We found that water can be adsorbed jointly in a molecular and dissociative way on the surface. A Langmuir isotherm indicating an adsorption/desorption mechanism of water on the NS is observed. Regarding the dissociative adsorption, atomistic details reveal two different mechanisms, depending on the water concentration around the NS. At low coverage, the first mechanism involves direct dissociation of a single water molecule, whereas, at higher water coverage, the second mechanism is a proton transfer reaction involving two water molecules, also known as Grotthuss-like mechanism. Thermal annealing simulations show that several water molecules remain on the surface in agreement with the experimental reports. The capacity of adsorption is higher for the 2.2 and 3.0 nm NSs than for the 4.4 nm NS. Finally, a comparative investigation with flat surfaces indicates that NSs present a higher water adsorption capacity (undissociated and dissociated) than flat surfaces, which can be rationalized considering that NSs present many more low-coordinated Ti atoms available for water adsorption.

Design of iso-material heterostructures of TiO2via seed mediated growth and arrested phase transitions

Stabilization of different morphologies of iso-material native/non-native heterostructures is important for electron-hole separation in the context of photo-electrochemical and opto-electronic devices. In this regard, we explore the stabilities of different morphologies of rutile ("native", ground state phase) and anatase ("non-native" phase) TiO₂ heterostructures through (1) seed-mediated growth and (2) a thermally induced arrested phase transition synthesis protocol. Furthermore, the experimental results are analyzed through a combination of Density Functional Tight Binding (DFTB) and Finite Element Model (FEM) methods. During the seed-mediated growth, anatase is grown over a polydispersed and polycrystalline rutile core through thermal treatment yielding core-shell, Janus and yolk-shell iso-material heterostructures as observed from HRTEM. The arrested phase transition of anatase to rutile at different annealing temperatures yields rutile crystals in the subsurface region of the anatase and rutile/core-thin anatase/shell heterostructures but does not yield a Janus structure. Small particles that can be modeled via DFTB computations suggest that: (1) a heterostructure of the rutile/core-anatase/shell is energetically more stable than the anatase/core-rutile/shell or any other Janus configuration, (2) the off-centered rutile/core-anatase shell is more favorable to the mid-centered rutile/core-anatase shell and (3) Janus heterostructures can be stabilized when the mass ratio of the rutile seed to anatase overgrowth is high. FEM simulations, performed to evaluate the importance of stress relaxation in bicrystalline materials without defects, suggest that Janus structures can be stabilized in larger particles. The present studies add to the heuristics available for synthesizing iso-material heterostructures.

Dopamine-Decorated TiO2 Nanoparticles in Water: A QM/MM vs an MM Description

Nanoparticle functionalization is a modern strategy in nanotechnology to build up devices for several applications. Modeling fully decorated metal oxide nanoparticles of realistic size (few nanometers) in an aqueous environment is a challenging task. In this work, we present a case study relevant for solar-light exploitation and for biomedical applications, i.e., a dopamine-functionalized TiO₂ nanoparticle (1700 atoms) in bulk water, for which we have performed an extensive comparative investigation with both MM and QM/MM approaches of the structural properties and of the conformational dynamics. We have used a combined multiscale protocol for a more efficient exploration of the complex conformational space. On the basis of the results of this study and of some QM and experimental data, we have defined strengths and limitations of the existing force field parameters. Our findings will be useful for an improved modeling and simulation of many other similar hybrid bioinorganic nanosystems in an aqueous environment that are pivotal in a broad range of nanotechnological applications.

TETT-functionalized TiO2 nanoparticles for DOX loading: a quantum mechanical study at the atomic scale

In this work, we present a quantum mechanical investigation, based on the self-consistent charge density functional tight-binding (SCC-DFTB) method, of the functionalization with silane-type ligands (TETT) of a spherical TiO₂ nanoparticle of realistic size (2.2 nm containing 700 atoms) to create an efficient nanosystem for simultaneous photodynamic therapy and drug transport. We determine the mechanism of the TETT ligand anchoring and its stability under thermal treatment, through molecular dynamics simulations at 300 K. Then, we build a medium and a full coverage model (22 and 40 TETTs, respectively) and analyze the interaction among TETT ligands and between the ligands and the surface. Finally, on the fully covered nanoparticle, we succeed in localizing two minimum energy structures for an attached doxorubicin anticancer molecule (DOX) and provide the atomistic details for both the covalent and the non-covalent (electrostatic) types of interaction. A future development of this work will be the investigation of the loading capacity of this drug delivery system and of the pH effect of the surrounding aqueous environment.

Recent Advancements in the Understanding of the Surface Chemistry in TiO2 Photocatalysis

Surface chemistry plays a major role in photocatalytic and photoelectrochemical processes taking place with the participation of TiO2. The synthesis methods, surface characterizations, theoretical research methods, and hardware over the last decade generated opportunities for progress in the surface science of this photocatalyst. Very recently, attention was paid to the design of photocatalysts at the nanoscale level by adjusting the types of exposed surfaces and their ratio, the composition and the surface structure of nanoparticles, and that of individual surfaces. The current theoretical methods provide highly detailed designs that can be embodied experimentally. The present review article describes the progress in the surface science of TiO2 and TiO2-based photocatalysts obtained over the last three years. Such aspects including the properties of macro- and nano-scale surfaces, noble-metal-loaded surfaces, doping with Mg and S, intrinsic defects (oxygen vacancies), adsorption, and photoreactions are considered. The main focus of the article is on the anatase phase of TiO2.

Density-functional tight-binding: basic concepts and applications to molecules and clusters

The scope of this article is to present an overview of the Density Functional based Tight Binding (DFTB) method and its applications. The paper introduces the basics of DFTB and its standard formulation up to second order. It also addresses methodological developments such as third order expansion, inclusion of non-covalent interactions, schemes to solve the self-interaction error, implementation of long-range short-range separation, treatment of excited states via the time-dependent DFTB scheme, inclusion of DFTB in hybrid high-level/low level schemes (DFT/DFTB or DFTB/MM), fragment decomposition of large systems, large scale potential energy landscape exploration with molecular dynamics in ground or excited states, non-adiabatic dynamics. A number of applications are reviewed, focusing on -(i)- the variety of systems that have been studied such as small molecules, large molecules and biomolecules, bare orfunctionalized clusters, supported or embedded systems, and -(ii)- properties and processes, such as vibrational spectroscopy, collisions, fragmentation, thermodynamics or non-adiabatic dynamics. Finally outlines and perspectives are given.

Theoretical study of the surface structure of anatase nanoparticles: effect on dye adsorption and photovoltaic properties

The properties of TiO₂ can vary greatly, depending on the size and morphology of the particles used.

Shaping Magnetite Nanoparticles from First Principles

Iron oxide magnetic nanoparticles (NPs) are stimuli-responsive materials at the forefront of nanomedicine. Their realistic finite temperature simulations are a formidable challenge for first-principles methods. Here, we use density functional tight binding to open up the required time and length scales and obtain global minimum structures of Fe_{3}O_{4} NPs of realistic size (1400 atoms, 2.5 nm) and of different shapes, which we then refine with hybrid density functional theory methods to accomplish proper electronic and magnetic properties, which have never been accurately described in simulations. On this basis, we develop a general empirical formula and prove its predictive power for the evaluation of the total magnetic moment of Fe_{3}O_{4} NPs. By converting the total magnetic moment into the macroscopic saturation magnetization, we rationalize the experimentally observed dependence with shape. We also reveal interesting reconstruction mechanisms and unexpected patterns of charge ordering.

Optimizing PEGylation of TiO2 Nanocrystals through a Combined Experimental and Computational Study

PEGylation of metal oxide nanoparticles is the common approach to improve their biocompatibility and in vivo circulation time. In this work, we present a combined experimental and theoretical study to determine the operating condition that guarantee very high grafting densities, which are desirable in any biomedical application. Moreover, we present an insightful conformational analysis spanning different coverage regimes and increasing polymer chain lengths. Based on 13C NMR measurements and molecular dynamics simulations, we show that classical and popular models of polymer conformation on surfaces fail in determining the mushroom-to-brush transition point and prove that it actually takes place only at rather high grafting density values.

Rational design of nanosystems for simultaneous drug delivery and photodynamic therapy by quantum mechanical modeling

Drug delivery systems are based on reversible interactions between carriers and drugs. Spacers are often introduced to tailor the type of interaction and to keep drugs intact. Here, we model a drug delivery system based on a functionalized curved TiO₂ nanoparticle of realistic size (700 atoms - 2.2 nm) by the neurotransmitter dopamine to carry the anticancer chemotherapeutic agent doxorubicin (DOX). The multiscale quantum chemical study aims at unraveling the nature and mechanism of the interactions between the components and the electronic properties of the composite system. We simulate the temperature effect through molecular dynamics runs of thermal annealing. Dopamine binds preferentially to low coordinated Ti sites on the nanoparticle through dissociated bidentate and chelate modes involving the diol groups. DOX is tethered by H-bonds, π-π stacking, dipole-dipole interactions and dispersion forces. Comparing different coverage densities of the spacer on the nanoparticle surface, we assess the best conditions for an effective drug transport and release: only at full coverage, DOX does not slip among the dopamine molecules to reach the nanoparticle surface, which is crucial to avoid the formation of stable coordinative bonds with under-coordinated Ti atoms. Finally, given the strong absorption properties and fluorescence of DOX and of the TiO₂ photocatalyst, we model the effect of light irradiation through excited state calculations to localize excitons and to follow the charge carrier's life path. This fundamental study on the nature and mechanism of drug/carrier interaction provides a solid ground for the rational design of new experimental protocols for a more efficient drug transport and release and its combination with photodynamic therapy.

TiO2-SrTiO3 Biphase Nanoceramics as Advanced Thermoelectric Materials

The review embraces a number of research papers concerning the fabrication of oxide thermoelectric systems, with TiO2-SrTiO3 biphase ceramics being emphasized. The ceramics is particularly known for a two-dimensional electron gas (2DEG) forming spontaneously on the TiO2/SrTiO3 heterointerface (modulation doping), unlike ordinary 2DEG occurrence on specially fabricated thin film. Such effect is provided by the SrTiO3 conduction band edge being 0.40 and 0.20 eV higher than that for anatase and rutile TiO2, respectively. That is why, in the case of a checkered arrangement of TiO2 and SrTiO3 grains, the united 2D net is probably formed along the grain boundaries with 2DEG occurring there. To reach such conditions, there should be applied novelties in the field of ceramics materials science, because it is important to obtain highly dense material preserving small (nanoscale) grain size and thin interface boundary. The review also discusses some aspects of reactive spark plasma sintering as a promising method of preparing perovskite-oxide TiO2-SrTiO3 thermoelectric materials for high-temperature applications.

Understanding the interplay between size, morphology and energy gap in photoactive TiO2 nanoparticles

Anatase TiO2 nanoparticles (NPs) have the potential to photocatalyse water splitting using UV light, to thus provide hydrogen fuel in a clean and sustainable manner. Such NPs have optical gaps covering a small range of relatively high energy solar photons, giving rise to low photo-efficiencies. Although anatase NPs with 10-20 nm diameters thermodynamically prefer crystalline faceted morphologies, application of physico-chemical procedures can produce more rounded NPs with amorphous shells. Such engineered metastable core-shell NPs (so-called black TiO2 NPs) have reduced band gaps due to shell-induced band edge broadening, resulting in higher photoactivities. For <5 nm diameters, TiO2 NPs typically exhibit spherical-like NP morphologies, which also display enhanced photoactivity. For smaller NPs it is difficult to experimentally determine their thermodynamic stability and internal atomic structure, to help rationalise their higher photoactivities. Employing accurate electronic structure calculations, we establish the relative stability of spherical and faceted stoichiometric TiO2 NPs with 1-3.4 nm diameters. Mirroring experimental preparation, simulated thermal annealing is found to significantly stabilise relaxed spherical cut anatase NPs. We find that the smallest spherical NPs become amorphized by annealing, but, for diameters >2 nm, annealing yields NPs with anatase-cores and amorphous-shells. Like larger black TiO2 core-shell NPs, we confirm that our core-shell NPs are metastable relative to faceted anatase NPs and have significantly smaller optical gaps than faceted NPs. Our calculated gaps are in excellent agreement with experimental data, strongly supporting the validity of our NP models. Energy gap narrowing in these core-shell NPs is found to be due to broadening of valence band states induced by the amorphous shell, analogous to the mechanism proposed for black TiO2 NPs. Our stoichiometric NPs also show that this band narrowing effect does not require the disordered shells to be non-stoichiometric or for incorporation of other atom types. Instead, we find that this effect mainly arises from 4-coordinated Ti atoms in the amorphous shell. Our careful and systematic computational investigation, using NP models of unprecedented realism, thus provides direct confirmation that the enhanced photoactivity in small spherical TiO2 NP observed in experiment is due to the formation of metastable core-shell NPs with 4-coordinated Ti centres.

An efficient way to model complex magnetite: Assessment of SCC-DFTB against DFT

Magnetite has attracted increasing attention in recent years due to its promising and diverse applications in biomedicine. Theoretical modelling can play an important role in understanding magnetite-based nanomaterials at the atomic scale for a deeper insight into the experimental observations. However, calculations based on density functional theory (DFT) are too costly for realistically large models of magnetite nanoparticles. Classical force field methods are very fast but lack of precision and of the description of electronic effects. Therefore, a cheap and efficient quantum mechanical simulation method with comparable accuracy to DFT is highly desired. Here, a less computationally demanding DFT-based method, i.e., self-consistent charge density functional tight-binding (SCC-DFTB), is adopted to investigate magnetite bulk and low-index (001) surfaces with newly proposed parameters for Fe-O interactions. We report that SCC-DFTB with on-site Coulomb correction provides results in quantitatively comparable agreement with those obtained by DFT + U and hybrid functional methods. Therefore, SCC-DFTB is valued as an efficient and reliable method for the description magnetite. This assessment will promote SCC-DFTB computational studies on magnetite-based nanostructures that attract increasing attention for medical applications.

Interfacing CRYSTAL/AMBER to Optimize QM/MM Lennard⁻Jones Parameters for Water and to Study Solvation of TiO₂ Nanoparticles

Metal oxide nanoparticles (NPs) are regarded as good candidates for many technological applications, where their functional environment is often an aqueous solution. The correct description of metal oxide electronic structure is still a challenge for local and semilocal density functionals, whereas hybrid functional methods provide an improved description, and local atomic function-based codes such as CRYSTAL17 outperform plane wave codes when it comes to hybrid functional calculations. However, the computational cost of hybrids are still prohibitive for systems of real sizes, in a real environment. Therefore, we here present and critically assess the accuracy of our electrostatic embedding quantum mechanical/molecular mechanical (QM/MM) coupling between CRYSTAL17 and AMBER16, and demonstrate some of its capabilities via the case study of TiO₂ NPs in water. First, we produced new Lennard–Jones (LJ) parameters that improve the accuracy of water–water interactions in the B3LYP/TIP3P coupling. We found that optimizing LJ parameters based on water tri- to deca-mer clusters provides a less overstructured QM/MM liquid water description than when fitting LJ parameters only based on the water dimer. Then, we applied our QM/MM coupling methodology to describe the interaction of a 1 nm wide multilayer of water surrounding a spherical TiO₂ nanoparticle (NP). Optimizing the QM/MM water–water parameters was found to have little to no effect on the local NP properties, which provide insights into the range of influence that can be attributed to the LJ term in the QM/MM coupling. The effect of adding additional water in an MM fashion on the geometry optimized nanoparticle structure is small, but more evident effects are seen in its electronic properties. We also show that there is good transferability of existing QM/MM LJ parameters for organic molecules–water interactions to our QM/MM implementation, even though these parameters were obtained with a different QM code and QM/MM implementation, but with the same functional.

Curved TiO2 Nanoparticles in Water: Short (Chemical) and Long (Physical) Range Interfacial Effects

In most technological applications, nanoparticles are immersed in a liquid environment. Understanding nanoparticles/liquid interfacial effects is extremely relevant. This work provides a clear and detailed picture of the type of chemistry and physics taking place at the prototypical TiO₂ nanoparticles/water interface, which is crucial in photocatalysis and photoelectrochemistry. We present a multistep and multiscale investigation based on hybrid density functional theory (DFT), density functional tight-binding, and quantum mechanics/molecular mechanics calculations. We consider increasing water partial pressure conditions from ultra-high vacuum up to the bulk water environment. We first investigate single water molecule adsorption modes on various types of undercoordinated sites present on a realistic curved nanoparticle (2-3 nm) and then, by decorating all the adsorption sites, we study a full water monolayer to identify the degree of water dissociation, the Brønsted-Lowry basicity/acidity of the nanoparticle in water, the interface effect on crystallinity, surface energy, and electronic properties, such as the band gap and work function. Furthermore, we increase the water coverage by adding water multilayers up to a thickness of 1 nm and perform molecular dynamics simulations, which evidence layer structuring and molecular orientation around the curved nanoparticle. Finally, we clarify whether these effects arise as a consequence of the tension at the water drop surface around the nanosphere by simulating a bulk water up to a distance of 3 nm from the oxide surface. We prove that the nanoparticle/water interfacial effects go rather long range since the dipole orientation of water molecules is observed up to a distance of 5 Å, whereas water structuring extends at least up to a distance of 8 Å from the surface.

UPS and UV spectroscopies combined to position the energy levels of TiO2 anatase and rutile nanopowders

Positioning of absolute energy levels and the quantitative description of occupied levels obtained for TiO₂ nanopowders, combining UPS and UV-Vis spectroscopies.