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Systematic Optimization of a Force Field for Classical Simulations of TiO2−Water Interfaces Erik G. Brandt and Alexander P. Lyubartsev* Department of Materials and Environmental Chemistry, Stockholm University, SE 106 91, Stockholm, Sweden S Supporting Information *
ABSTRACT: Atomistic force field parameters were developed for the TiO2−water interface by systematic optimization with respect to experimentally determined crystal structures (lattice parameters) and surface thermodynamics (water adsorption enthalpy). Optimized force field parameters were determined for the two cases where TiO2 was modeled with or without covalent bonding. The nonbonded TiO2 model can be used to simulate different TiO2 phases, while the bonded TiO2 model is particularly useful for simulations of nanosized TiO2 and biomatter, including protein− surface and nanoparticle−biomembrane simulations. The procedure is easily generalized to parametrize interactions between other inorganic surfaces and biomolecules.
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generalized to develop force field parameters for other inorganic surfaces and biomolecules. In an accompanying paper,13 we use the optimized force field parameters to address the other long-standing problem in nanobio simulationsaccurate sampling of biomolecules near inorganic surfacesand to compute binding free energies of amino acid side chain analogues and a peptide to the TiO2 surface. TiO2 is one of the most common materials forming interfaces with biomatter, and is found in consumer products such as paints, sunscreens, and food coloring.14 Bulk TiO2 is believed to be inert with respect to biomaterials, but its role in nanotoxicity is still unclear. There has been considerable interest in developing models for TiO2 under ambient conditions, because of its abundant presence in biological environments. The most widely used classical model is due to Matsui and Akaogi15 (MA), which was parametrized to reproduce the bulk structure of TiO2 (not any surface properties). Later efforts extended the MA model with water interactions16−18 but were based on pairwise models that are difficult to unite with the standard force fields for biomolecular simulations already available in the literature (e.g., AMBER,19 CHARMM,20 OPLS21), and/or requires new parametrizations for every additional atom type that is to be simulated together with TiO2. Other simulations of the TiO2/water interface combined force field parameters from solid (TiO2) and liquid (water) state, in which case solid bulk atoms had to be fixed to keep the bulk structure of TiO2 intact.22 More complex TiO2 force fields offer the possibility to model surface reactions23 and adsorption24 but at the cost of
INTRODUCTION Biomolecules interacting with inorganic objects are fundamental in nanobiotechnological applications such as surfaceattached biomolecules for target delivery of drug molecules,1 protein adsorption to medical implants,2 protein−nanoparticle interactions3 and, not least, to understand the molecular mechanisms of nanotoxicity.4 The contact points between inorganic surfaces and biomatter (the nanobio interface5) can be tracked with experimental techniques like dynamic light scattering (DLS),6−8 chromatography9,10 and/or spectroscopy,11,12 but only by indirect measurements. On the other hand, computer simulations can in principle be used to directly calculate interactions at the nanobio interface, covering system sizes ∼1000 Å and time scales ∼1000 ns. These windows are highly relevant when modeling the nanobio interface, but outside the realm of quantum mechanics. This calls for “classical” models with atomistic or semiatomistic (atoms being grouped into effective interaction centers) representations in computer simulations of nanobio interactions, parametrized to reproduce properties relevant to the nanobio interface. Substantial effort has been invested during the last decades to develop classical molecular models for biomolecules (proteins, lipids, nucleic acids, carbohydrates, etc.), but there has been no comparable endeavor to include inorganic materials into the models. The state of classical models aimed to describe the nanobio interface remains underdeveloped, largely because of the difficulties involved with representing the electronic structure of the inorganic material by interacting point particles. The present work is an attempt to close this modeling gap by developing atomistic force field parameters for the TiO2−water interface. We use an automated algorithm that is extended to accept arbitrary experimental data as targets in the parameter fitting. The method can easily be © 2015 American Chemical Society
Received: March 19, 2015 Revised: June 27, 2015 Published: July 16, 2015 18110
DOI: 10.1021/acs.jpcc.5b02669 J. Phys. Chem. C 2015, 119, 18110−18125
Article
The Journal of Physical Chemistry C
i.e., parametrized at specific temperatures and pressures, and not necessarily accurate at other state points. The energy expression in eq 1 has been chosen to ensure transferability with the widespread AMBER force field,19 which includes interactions parameters for lipids, proteins, nucleic acids, and other common organic molecules. New compounds can also be added to AMBER with relatively small effort. We note that the energy functions for the other common force fields in the simulation community (CHARMM,20 OPLS21) are very similar. Finally, biological relevance and experimental basis were met by parametrizing the TiO2 force field to the adsorption enthalpy of water at room temperature and normal pressures. DFT Geometry Optimizations of Water Molecules on TiO2 Surfaces. The Materials Studio27 (MS) program was used to prepare and run the periodic density functional theory (DFT) calculations. The rutile TiO2 unit cell belongs to space group P42/mnm, with lattice parameters a = b = 4.594 Å and c = 2.959 Å (the unit cell angles are all 90°). The unit cell was replicated and cleaved either along the (100) plane or along the (110) plane. Water molecules were placed in random (unfavorable) orientations close to the surface. Periodicity was enforced in all dimensions, and the simulation cell was elongated to 15 Å in the direction normal to the surfaces. The sizes of the final TiO2 slabs were 9.1874 × 5.9174 Å2 (100 surface) and 5.9174 × 6.4965 Å2 (110 surface). The CASTEP28 module as implemented in MS was used for geometry optimizations with DFT using the Perdew−Wang 91 exchange-correlation functional29 and ultrasoft pseudopotentials in reciprocal space representation. There were in total 200 electrons in the (100) system and 176 electrons in the (110) system. The cell size and the positions of the surface atoms were held fixed during the optimization to avoid excessive rearrangements of surface atoms. The optimal geometries were determined self-consistently by the BFGS solver in CASTEP, which took about 100 iterations with tight convergence criteria (energy change per atom
