# A DFTB-Based Molecular Dynamics Investigation of an Explicitly Solvated Anatase Nanoparticle
## 1 Introduction  
Of the fields of chemical physics, computational chemistry and atomistic simulations could be considered to be the fastest growing. The potential applications of the field are bound mostly by advances in computer hardware, which is (typically) outside the remit of the chemist's research. The growth in power, and consequent reduction in cost, of computational resources has historically doubled approximately every two years, a trend known as Moore's Law. In this way, computational chemists have been incredibly fortunate; over the course of ten years, the increase in available resources can reclassify a problem from \"impossible\", to \"cutting-edge\", to \"difficult\", to \"routine\".  
However, an infinite growth in computational resources should not be assumed. Already, chipset manufacturers are running up against hard physical limits in designing and manufacturing processors with higher transistor densities than the previous generation [1]. Therefore, it is becoming increasingly important for computational chemists to have knowledge of, and access to, a variety of efficient and reliable simulation methodologies to correspond with the nature and scale of the system they wish to examine.  
Herein, we present a description and some analyses of a self-consistent charge density functional tight-binding molecular dynamics (SCC DFTB-MD, or simply DFTB) simulation of an explicitly solvated, anatase-structured TiO\({}_{2}\) nanoparticle. The aim of this paper is not to provide an exhaustive or comprehensive description of the properties of such a system, but rather to showcase the application of a relatively under-utilised methodology in DFTB, and to perhaps inspire other computational chemists to consider expanding their repertoire of techniques to include this methodology for large-scale simulations.  
The core of the DFTB methodology is very similar to full DFT; the Kohn-Sham equations are solved numerically, using approximate parameters determined by the electronic density of the system. The key difference between the methods is the eponymous \"tight-binding\" approximation; electrons are tightly bound to the atomic orbitals they occupy at the beginning of the simulation, although they are permitted to become as dispersedor localised as is necessary to minimise the energy of the system. Thus, the electronic Hamiltonians are parameters of the method, similar to the pseudopotentials of DFT. The tight-binding approximation means that the method is not inherently suited to metallic systems, although the careful construction of parameters can go some way towards offsetting this. However, the lack of widely available DFTB parameter sets is likely the largest problem faced by those who wish to employ it. A more complete description of the DFTB methodology is provided by [PERSON] and [PERSON] [2].  
The motivation for this study stems from the authors' previous research of systems containing TiO2. Previous publications from the authors have examined planar systems of TiO2 under a variety of different conditions, such as various surface terminations, with and without applied electric fields, and diverse simulation methodologies from force-field MD to ab initio MD [3; 4; 5; 6; 7]. Hitherto this publication, we had not considered the use of DFTB-based methodologies for simulations of this kind of system; however, following the publication of a series of articles concerning SCC DFTB calculations of TiO2 systems by [PERSON] and colleagues [8; 9], we became aware of the potential power of the method. By including electronic structure data (with a few caveats, as will be described), DFTB has many of the advantages of full Density-Functional Theory (DFT), while requiring less resources by orders of magnitude. This means that the systems studied can be larger and/or MD trajectories can be longer for the same resource allocation.