Molecular dynamics simulation of polarizable gold nanoparticles

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Condensed Matter, Interfaces, and Materials

Molecular dynamics simulation of polarizable gold nanoparticles interacting with sodium citrate Olga A. Perfilieva, Dmitrii V. Pyshnyi, and Alexander Anatolyevich Lomzov J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b00362 • Publication Date (Web): 21 Dec 2018 Downloaded from http://pubs.acs.org on December 23, 2018

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Journal of Chemical Theory and Computation

Molecular dynamics simulation of polarizable gold nanoparticles interacting with sodium citrate Olga A. Perfilieva a, Dmitrii V. Pyshnyi a,b, Alexander A. Lomzov a,b a

Institute of Chemical Biology and Fundamental Medicine, SB RAS, 8 Lavrentiev Avenue, Novosibirsk 630090, Russia b Novosibirsk State University, 2 Pirogova St., Novosibirsk 630090, Russia Abstract To study the structure of a citrate-capped gold nanoparticle and forces involved in citrate–gold interactions, we performed a molecular dynamics simulation of a truncated-octahedron nanoparticle containing Au(111) and Au(100) surfaces with sodium citrate. In this paper, we employed an approach to the modeling of interactions of a gold nanoparticle with citrate molecules taking into account the image charge effect in the metal. First, we built models of 6 and 14 nm nanoparticles, which can reproduce the polarization effects, based on a rigid-rod gold model and the GolP-CHARMM force field. To verify the simulation results, we analyzed density plots, radial distributions, distributions perpendicular to Au(111) and Au(100) surfaces, the electric potential of the system, and the dynamics of citrate crown formation. We observed formation of a stable citrate crown around the nanoparticle and detected nonuniform surface distribution of citrate ions with the preference for Au(111) facets over Au(100) ones. Testing of the model of the citrate-capped gold nanoparticle in a simulation at high concentrations of Na+ and Cl ions (0.8 M) showed incorporation of chloride anions into the citrate crown. We compared the results of citrate crown formation between polarizable and nonpolarizable gold models and noticed a difference in the citrate distribution on the surface of the gold nanoparticle. We found that polarization effects in the metal are involved in the mechanism of interaction of the gold nanoparticle and citrate ions. The obtained results are in good agreement with experimental data and computer simulations from a number of other studies, which prove the validity of the proposed model. Introduction The structure and properties of the gold nanoparticle coated with a citrate shell (also called a crown) or other ligands have been actively studied by different groups of researchers.1-9 Among the various procedures used in these studies, in silico research methods play an important role.10-16 In particular, such methods deal with the system at the nanoscale level and represent a useful tool for identifying the mechanisms of interaction of a citrate molecule with the surface of a gold nanoparticle and for determining the structure of the citrate crown around the nanoparticle. This type of simulation requires a special approach to parameterization of the interactions in an ensemble of molecules. Methods of quantum chemical calculations are employed to study the interaction of a surface with surrounding molecules in small systems (up to several hundred atoms). For example, ab initio Car–Parrinello molecular dynamics (MD) simulation of an aqueous Au(111) surface has revealed orientation of the water molecule on the atop site of gold atoms.17 Density functional theory (DFT) calculations of adsorbate-binding energy and of interaction geometry in vacuum are often carried out for parameterization of force fields, especially in the absence of experimental data.18-21 Quantum mechanical calculations enable a detailed study of a system at the atomic level, but the computational cost for such methods is high.22-23 The classical MD approach involving different force fields makes it possible to investigate large molecular assemblies (millions of atoms) for long periods (up to microseconds).23 This type of system consideration and representation is suitable for studies on

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large nanoparticles (larger than 10 nm), which can serve as a substrate platform for polymer molecules such as DNA or peptides. To analyze the interaction of a gold surface with other molecules using the MD approach, a number of special force fields have been developed. CHARMM-METAL24 is an example of a force field that does not take into account the polarization effect and is suitable for the simulation of peptide adsorption on gold. For uncharged molecules with a small dipole moment, the contribution of the polarization effect to the adsorption energy is often negligible, whereas for charged molecules, such as citrate, this effect should be taken into account.25-27 Polarization in a metal can be examined in different ways, for example, classically by introducing an imaginary plane behind which a charge of the opposite sign is located.27 The capacitance–polarizability interaction model and force field can serve as an example of another more complex approach that was successfully applied to describe interactions of an icosahedral gold nanoparticle (consisting of 309 atoms) and water.28 Recently, polarization effects have been introduced into the gold model using elements of a Drude oscillator.29 In this model, a dummy electron is added to a positively charged core of a gold atom forming a dipole with two opposite charges connected by a harmonic spring. Changing of bond lengths in the oscillator reproduces the image charge effect in the metal. Each atom of a gold dipole also has parameters for a van der Waals interaction. The model can be implemented with standard force fields for simulation of biological molecules without additional parametrization. In the rigid-rod model, gold atoms are represented by dipoles with a fixed bond length between charges.30,31 Dipoles can freely rotate around the mass center of a real atom, thus simulating polarization effects in the metal. The early force field used with the rigid-rod model was GolP,30 which is compatible with the OPLS-AA32 force field, developed to model interactions of a protein with a gold surface. Nonetheless, analysis of water molecules in this field predicts an incorrect adsorption geometry, with the hydrogen atom directed toward the surface; this arrangement did not match the data of quantum mechanical calculations.17 Then, GolP-CHARMM20,21 compatible with the CHARMM33 force field for Au(111) and Au(100) surfaces was developed and took into account the adsorption geometry of water and of small organic molecules. Application of the GolP-CHARMM field is limited to these two types of surfaces because the gold model includes virtual sites with a specific Lennard–Jones interaction for each type of the surface. The rigid-rod gold model has been successfully utilized to construct Au(111) and Au(100) slabs and to study the interactions of interface gold atoms with small organic molecules and proteins,34-36 but nanoparticle models of this type with Au(111) and Au(100) surfaces have not yet been devised. During studies on interactions of some molecules with gold nanoparticles, it is necessary to take into consideration that under experimentally observed conditions, gold nanoparticles are not naked but covered by various ligands to prevent aggregation. In the Turkevich method37 widely used for the synthesis of gold nanoparticles, sodium citrate acts as a stabilizing agent for gold colloids. Investigation of citrate interaction with the gold surface is an important field of research on nanoparticle properties. Recently, a citrate model with bonded force field parameters adapted for a simulation in water was developed.38 The same group of authors also developed the GolPCHARMM force field, which contains the parameters for a nonbonded interaction of citrate with Au(111) and Au(100) surfaces.20,21 The interaction of sodium citrate with the Au(111) surface in an explicit water shell has been simulated by means of the GolP-CHARMM force field.36 As a result, an amorphous, multilayer organization of citrate overlayers with common “stripe” and “islands” motifs was observed, as were more complex structures such as loops and straight and curved chains. It was found that Na+ ions play an important role in the structure of overlayers and participate in the formation of citrate bilayers on the surface of gold. Citrate has also been modeled with a 3 nm gold nanoparticle having (111), (100), and (110) facets in the ReaxFF39 force field, which takes into account events of chemical bond ACS Paragon Plus Environment

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formation and breakage.40 It was shown that citrate is highly reactive with the gold surface and can form strong complexes with gold adatoms by capturing them from the surface of the nanoparticle. It was concluded that a fully deprotonated form of citrate is preferable and important for the interaction with the gold surface. The starting point of the present study includes building of a gold nanoparticle with polarization effects because electrostatic interaction of the charged citrate molecule with the metal may affect the adsorption process and energy. Another key parameter is the nanoparticle size suitable for a comparison with a typical nanoparticle used in experiments (usually ~5–20 nm in diameter [d]). Therefore, we consider a simple way to simulate polarization in the gold model; this approach does not dramatically change the standard MD formalization of force fields. Thus, the main purpose of our research was to study the interactions of a polarizable model of a gold nanoparticle with sodium citrate by the classical method of MD simulation. We chose the approach proposed for formalization of the image charge effect in gold via the rigidrod model.30,31 The main steps of our study are listed below: • gold nanoparticle morphology that can be realized in a simulation force field (GolP-CHARMM) was determined; • a rigid-rod model of a gold nanoparticle with virtual sites for Au(111) and Au(100) surfaces was built; • the obtained gold nanoparticle in an aqueous medium with sodium citrate was simulated, and the results were analyzed. Methods MD simulation The MD simulations were carried out using Gromacs41 package version 5 in the GolPCHARMM force field. The nanoparticle was placed in the center of the cuboid simulation cell with the size of 13.0 × 13.0 × 13.0 nm3 for a 6 nm nanoparticle and 22.84 × 22.84 × 22.84 nm3 for a 14 nm nanoparticle. Citrate anions (fully deprotonated C6H5O73) were added into the system in the amount of 451 and 2756 molecules (0.34 and 0.39 M) for nanoparticles with d of 6 and 14 nm, respectively. These values were chosen to promote formation of a local concentrated layer around the nanoparticles that is sufficient for assembly into a crown structure (with 84% of the surface coverage for d = 6 nm and 100% for d = 14 nm). The percentage of coverage and the number of citrate molecules were calculated according to data reported by Park et al. (the density of citrate ligands was 2.8  1010 mole/cm2, which was 45% of the surface coverage).1 For the neutralization charge of the simulation cell, sodium ions were added into the system in an amount of three Na+ cations per citrate molecule. The simulations were performed in explicit water in the NVT ensemble with three-dimensional (3D)-periodic boundary conditions by means of a Nosé Hoover thermostat.42,43 The cutoff Verlet scheme44 was used with particle mesh Ewald (PME)45 electrostatic summation and was truncated at 11 Å for Lennard–Jones and Coulomb interactions. During the simulations, all real atoms and virtual sites were fixed in space and only dipole particles were free to rotate. Citrate was modeled by bonded38 and nonbonded20,21 GolPCHARMM force field parameters. A modified TIP3P46,47 water model and nonbonded parameters for the Na+ ion were also taken from the GolP-CHARMM force field. The system was first equilibrated by slow heating from 0 to 300 K with a reduced time step of 0.5 fs for 1 ns. A productive simulation was conducted via at least 10 cycles of annealing with a time step of 1 fs in a manner similar to that mentioned by other authors36 testing the same model of gold. Such a simulation method speeds up the process of cell equilibration. The temperature of gold was maintained at 300 K, while the rest of the system including water, citrate ions, and Na+ ions followed a temperature cycle (300, 400, 500, 600, 500, 400, and 300 K) of 700 ps with time checkpoints (0, 200, 225, 425, 625, 650, and 700 ps).



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An additional simulation was performed with sodium citrate and a nonpolarizable gold nanoparticle model (d = 6 nm), which consisted only of real atoms with van der Waals interactions. The Lennard–Jones parameters for gold were borrowed from the CHARMMMETAL24 force field. The rest of the conditions in the simulation, e.g., the temperature regime, the citrate model, and the amount of citrate in the system, were the same as those for the polarizable gold model as described above. For simulation of the interaction of a citrate-capped nanoparticle with Na and Cl ions, the results of crown modeling for the polarizable nanoparticle with d = 6 nm were employed. A snapshot of the MD trajectory obtained after a 7 ns simulation without a chloride ion served as an initial structure for modeling. Na+ and Cl were added to a concentration of 0.8 M each (1323 Na+ ions and the same number of Cl ions) into the enlarged 14.0 × 14.0 × 14.0 nm simulation cell. The simulation protocol was the same as that of the modeling system without the salt. Nonbonded interaction parameters of chloride ions with gold were calculated according to 𝜎𝑖 + 𝜎𝑗 Lorentz–Berhelot mixing rules48 ( 𝜎𝑖𝑗 = ,𝜀𝑖𝑗 = (𝜀𝑖 ∗ 𝜀𝑗)) based on GolP-CHARMM force 2

field parameters of Au–Au interaction. The parameters obtained for Cl were as follows: σ = 0.362 nm and ε = 0.9033 kJ/mol for the Au(111) surface; σ = 0.372 nm and ε = 1.3256 kJ/mol for Au(100). Calculation and visualization of the electrostatic potential in the system The electric field potential was visualized as a 3D grid with intensity of the potential at nodes placed inside the analyzed ensemble. The magnitude of the electrostatic potential was revealed by the concentration of points corresponding to certain intensity. The obtained result includes a method for taking into consideration the periodicity of a given ensemble, a method for optimizing the calculation and visualization of the potential intensity, and a procedure for presenting the results in .gro format. The electric potential at each grid point i (Vi) is calculated as the sum of the potentials from atomic charges of all molecules: 𝑞𝑗 𝑽𝒊 = ∑𝑗, 𝑗 ≠ 𝑖𝑟 (1) 𝑖𝑗

where 𝑞𝑗 is the charge of the jth atom, 𝑟𝑖𝑗 denotes the distance from the charge of the jth atom to the ith point of the grid in which the potential is being considered. Because modeling by the method of MD was carried out under periodic conditions, it was necessary to take into account the influence of atoms from neighboring cells during calculation of the potential. This is especially important for the atoms located at corners of the cell. Under 3D-periodic conditions, each simulation cell is surrounded by its 26 copies. For a large system, the inclusion of all atoms from the cell in question and from neighboring cells during calculation of the total field potential at each grid node requires large computational resources. Because the potential from a given charge decreases with distance as 1/r, at a given node of the grid, the nearest charges from a neighboring cell make a greater contribution to the intensity than do distant charges from the same cell. To optimize the calculation process, only those charges that fall into a cube with a side equaling to half of the cell size and centered at the given node are taken into account during estimation of the total electric field potential of a node; this strategy is consistent with the Coulomb cutoff of 11 Å (see the section MD simulation). The obtained values of the electric field potential at the grid nodes were visualized by means of the points randomly distributed near a given node and not overlapping with neighboring nodes. Intensity of the potential was determined via the concentration of points by means of a filter system. Filters were the values from the absolute values of the intensity, which determine the number of points to be placed near the node. The system of filters forms a profile of the electric potential intensity. The results of calculating the 3D potential distribution were transformed into .gro format by representing the points of the grid as oxygen and nitrogen atoms. The sign of the potential is ACS Paragon Plus Environment

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indicated by different colors of the nitrogen and oxygen atoms. When viewed in the VMD software,49 the red color corresponds to the positive potential, and the blue color corresponds to the negative potential. This way of representation enables readers to visualize a given ensemble of molecules together with the 3D potential in the VMD software. Computation of the distribution of citrate ions perpendicular to the surfaces of the nanoparticle and geometrical radial distribution To determine the distribution of molecules around a nanoparticle, we considered the position of their mass centers in the simulation cell. For distribution perpendicular to the surfaces, we investigated the space above Au(111) and Au(100) surfaces (see Figure S1). The number of molecules N (centers of mass) located in the current volume was determined by going from the surface of the nanoparticle along the normal to the plane with specified distance step dr. The concentration of molecules at a specific distance c(r) = N(r)/V was obtained by normalization of the number of molecules N(r) to volume V = dr  S, where S is an area of the surface under consideration [Au(111) or Au(100)]. To calculate the graphs of dynamics (Figures S15–S18), each time point was averaged over the temperature interval 300–340 K. The graphs of 0 and 28000 ps were calculated using seven and three frames of the trajectory, respectively; for all other time points, 10 frames were averaged. A geometrical radial distribution was computed according to the same principles as those for the distribution perpendicular to the surface. The concentration of molecules was determined via the formula c(r) = N(r)/V(r), where N(r) is the number of centers of mass dropped onto the spherical layer with thickness of distance step dr, in a thin spherical layer of volume V(r). The starting point (zero value) for distance r was the center of the nanoparticle. Density map calculations were carried out by means of AmberTools17 package.50 Results and discussion Choosing a shape of the gold nanoparticle To construct a gold nanoparticle for simulation, it is necessary to determine common morphological features of the nanoparticle. Depending on the experimental conditions for obtaining nanoparticles and their sizes, the dominant equilibrium shape of the nanoparticle can change.51 By means of theoretical models, researchers attempt to predict and explain the structure of a nanoparticle under given conditions on the basis of experimental data (e.g., direct images of a nanoparticle obtained by microscopic techniques).52 The morphological diversity of nanoparticles can be subdivided into two types: nanoparticles having a single face-centered cubic (FCC) crystal lattice and twinned nanoparticles.51,53 The simple FCC shapes formed by {111} and {100} crystal planes include a truncated octahedron, cuboctahedron, cube, and truncated cube. Twinned nanoparticles are polycrystalline and consist of single crystal units connected by a mirror plane. An icosahedron and decahedron are typical examples of twinned nanoparticle shapes. A multitwinned icosahedral nanoparticle exposes 20 surfaces with an arrangement of atoms similar to the {111} crystal plane. A decahedron possesses fivefold symmetry with 10 surfaces of the {111} type. Ino and Marks decahedral nanoparticles also include {100} facets. Various theoretical approaches are used to determine the equilibrial dominant form, e.g., DFT calculations and thermodynamic and kinetic approaches.52-62 From the thermodynamic point of view, an equilibrium nanoparticle of a given diameter has such a ratio of {111}, {110}, and {100} surfaces (with different surface energies) that minimizes the total energy. For FCC, this shape corresponds to a truncated octahedron.55,60,63 Nevertheless, if we consider the kinetic approach,53 the most rapidly formed and kinetically stable is the icosahedral shape. Due to the combined effects of thermodynamic and kinetic influences, the shape of the decahedron is stabilized at greater diameters of nanoparticles. As for the size 14 nm, which we will consider in our simulation, it can be concluded54 that such nanoparticles are in a transition region from the ACS Paragon Plus Environment


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decahedral shape to FCC shapes. The choice of truncated-octahedron morphology can be made on the basis of the findings that this shape is the most thermodynamically stable52,53,64 and retains its structure the best with increasing temperature.64 When the shape of a nanoparticle is being determined, the ratio of {111} and {100} surfaces is an important parameter. It is known that a nanoparticle tends to increase the presence of a lower-energy facet {111} for its stabilization.63 According to thermodynamic reconstruction52,60 in vacuum for the 14 nm nanoparticle, facets {111} should constitute 90.5% of the total surface area. In contrast, with the increasing temperature and taking into account some kinetic factors in the model,53,54 the theory predicts an increasing percentage of the {100} surface area, followed by the transformation of a truncated octahedron into a cuboctahedron. Via this approach and a phase diagram54 for a gold nanoparticle with d of 14 nm at 300 K, the proportions of the {111} and {100} planes will be approximately 66% and 34%, respectively. In our simulation, we also consider a smaller nanoparticle (6 nm) sharing the morphology of a truncated octahedron as a useful system for calculations involving moderate numbers of atoms, although nanoparticles of such diameters may be stabilized in an icosahedral shape.54 Building of the gold nanoparticle model To create a gold nanoparticle, we chose a model of gold that takes into consideration the polarization effect. The model was developed for Au(111) and Au(100) surfaces but has not been previously applied to construction of a gold nanoparticle. In the Gromacs software, this gold model was used with GolP30,31 and GolP-CHARMM force fields20,21 (based on the CHARMM force field33) for proteins and with GolDNA-AMBER19 (based on the AMBER force field65) for DNA and the Au(111) surface. The special features of this model deal with representation of gold atoms in the form of dipoles that can rotate around a real center of an atom simulating the induced charges. This group of atoms is responsible for electrostatic interactions. In addition, there are virtual atoms on the surface that determine the van der Waals interaction of gold atoms with other molecules. Virtual sites are introduced into the model in such a way that they lead to a correct position of an adsorbed molecule relative to a gold atom (atop, bridge, and hollow sites). All these features greatly complicate the model because instead of one type of gold atom, there are several types: real gold atoms, virtual dipoles associated with them, and virtual sites of (111) and (100) surfaces with their own van der Waals parameters. The process of setting up a model is represented by the following steps:  construction and multiplication of the unit cell (with real atoms and virtual sites) to form a cubic crystal of the required size;  obtaining a nanoparticle from a crystal by cutting off excess atoms with eight planes (111) and then six planes (100) and determination of surfaces Au(111) and Au(100) and types of gold atoms for surfaces;  construction of the final model of the nanoparticle by specifying it in 3D geometrical space, addition of virtual atomic dipoles to real gold atoms, and preparation of files for MD simulations. Construction of the unit cell and its multiplication The cubic crystal from which the nanoparticle will be derived can be considered a set of points in 3D space with a definite position. This set of points can be described by a 3D array of (nx + 1) × (ny + 1) × (nz + 1) size, where nx, ny, and nz are numbers of unit cell blocks along the x-, y-, and z-axis.


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Face-centered cubic (FCC) unit cell

Virtual sites for {100} six planes 12 virtual sites

Virtual sites for {111} eight planes 32 virtual sites

Figure 1. The unit cell of the face-centered cubic lattice (FCC) with additional virtual sites for {100} and {111} planes (four sites shown). Real atoms of the lattice are represented by orange balls. Virtual sites are shown as red and blue stars for {100} and {111} planes, respectively. Examples of {100} and {111} planes are yellow. An elementary cell can also be initiated as a 3D array, which in turn can be considered geometrically analogous to an elementary FCC unit cell. Virtual sites for all the {100} and {111} planes were added to the real atoms of the unit cell (Figure 1). Virtual sites for {100} surfaces were set in the middle of the cube edges. For the {111} surface, 4  8 virtual site points were defined as centers of triangles on the corresponding plane. If we have a unit cell with the side equal to 1, then the coordinates of virtual atoms for {100} are as follows: (0.5; 0; 0), (0; 0.5; 0), (1; 0.5; 0), (0.5; 1; 0), (1; 0; 0.5), (1; 1; 0.5), (0; 0; 0.5), (0; 1; 0.5), (0.5; 0; 1), (0; 0.5; 1), (1; 0.5; 1), and (0.5; 1; 1). Taking into account the denominator of every virtual site (111) and (100) inside the unit cell, it is reasonable to represent each elementary cell in the form of a 6 × 6 × 6 3D-array (du = 6) in accordance with the position of virtual sites. Table 1. The positions of (111) virtual sites in the unit cell. The header shows different types of {111} crystallographic planes. Coordinates of virtual sites in a column belong to the corresponding plane (unit cell size is 1 × 1 × 1). (111)

(111)

(111)

(111)

(111)

(111)

(111)

(111)

(16;16;46) (26;26;26) (16;46;16) (46;16;16)

(16;16;26) (26;26;46) (16;46;56) (46;16;56)

(56;56;46) (46;46;26) (56;26;16) (26;56;16)

(56;56;26) (46;46;46) (56;26;56) (26;56;56)

(16;56;46) (26;46;26) (16;26;16) (46;56;16)

(16;56;26) (26;46;46) (16;26;56) (46;56;56)

(56;16;46) (46;26;26) (56;46;16) (26;16;16)

(56;16;26) (46;26;46) (56;46;56) (26;16;56)

According to the proposed structural organization, the unit cell can be easily extended to a cuboid crystal of any size. By multiplying a unit cell, a researcher can create a large cubic crystal (nx = ny = nz = n) of (du*n + 1)3 size in the form of a 3D array. Instead of a continuous list of atoms with coordinates, the array can be used to describe the crystal structure. The array contains only numbers that denote the types of atoms. To label a real atom in the array, the number “2” was employed, virtual atoms for {100} and {111} planes were represented by numbers “5” and “7,” respectively. The array initialization consisted of filling it out with zeros ACS Paragon Plus Environment


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(“0”), which means that there was no atom in any unit cell node. If we denote the array as [a], then each element of the array is designated as a(i,j,k). The maximum number of elements in each dimension of the array is (6  n) + 1. The array can be considered a 3D grid of an unknown geometric scale size with real or virtual atoms that can be located in its node. On the basis of visual representation of a unit cell, each atom is exposed in the array. This method of data organization is effective and visually representative for solving the problem of nanoparticle construction. At a later stage, the array can be transformed into a geometric structure according to the lattice parameters of a gold crystal unit cell. Obtaining a nanoparticle from a cubic crystal and determining the surfaces The next step was to cut off redundant atoms in the cube with planes to produce the truncated-octahedron geometry. For this purpose, we analyzed an atom’s position relative to the planes of the nanoparticle surface. The equations for all 14 planes (eight planes of the {111} type and six planes of the {100} type) for the truncated octahedron should be defined (see Figure 2 and Supporting Information, section “Symmetric equation for {111} and {100} planes”). The diameter d and a ratio of total (111) and (100) surface areas (𝑆𝛴{111}:𝑆𝛴{100}) can be used to identify the positions of the planes when building a nanoparticle model.

Figure 2. Geometry of the nanoparticle obtained from the cube crystal (thin black lines). Cutting planes {111} (thick black lines) form an octahedron in the center of the cube. The truncated octahedron is obtained by removing excess atoms by means of {100} planes (pink lines). Changing the cutting position of {100} planes relative to the center of the cube results in a different ratio of (111) and (100) surface areas and can lead to different shapes of the nanoparticle (an octahedron, truncated octahedron, cuboctahedron, or cube). For cutting off excess atoms, the cube was assumed to be placed in a Cartesian coordinate system with the origin in the center of the cube. Each element of the array a(i,j,k) was centered by shifting all coordinates by half of the cube side (3  n) to use a symmetric equation for {111} and {100} planes. An octahedron was obtained from the cube by changing the array of elements according to their positions relative to eight planes {111}. For the selected plane and each element of array [a], the status of the point in the cube was redetermined: if point a(i,j,k) was beyond plane {111} forming an octahedron, then a(i,j,k) was redefined by zeros (“0”). Then the parameter of {100} equations (see Supporting Information, section “Symmetric equation for {111} and {100} planes”) determines at what position the {100} planes are settled and enables precise cutting of excess atoms. Thus, varying the ratio of (100) and (111) planes, one can obtain ACS Paragon Plus Environment

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nanoparticles of different shapes (an octahedron, truncated octahedron, cuboctahedron, truncated cube, or cube). The next step was to detect the surface in the nanoparticle model. A surface of the nanoparticle was considered for each plane and nonzero element of array [a]. Elements in an array that belong to cutting planes also lie on the surface of the nanoparticle. We define these elements as surface atoms and change the status of an element in array [a] according to the plane type: {111} or {100}. For example, instead of values “2,” “5,” and “7” in the array, we inserted others: “3” and “37” for the real and virtual atom of surface (111), respectively, and “4” and “47” for the real and virtual surface atoms of (100). The usage of different numbers for different surfaces enabled us to give atoms of the surface their own interaction parameter if necessary. After that, array [a] containing zeros where there are no nanoparticle atoms and containing numbers where the atoms are present was subjected to the following modification: internal virtual atoms were deleted from the array (in our case they are denoted by the values “5” and “7”) by setting them to “0.”. Making of a geometrical space model with a unique topology taking into account polarization effects The information from 3D array [a] (containing representation of nanoparticles in the form of zeros and numbers in space coordinates (i,j,k) of array [a]) had to be transformed into 3D geometric coordinates (x,y,z) and into certain types of gold atoms used in the rigid-rod gold model.20,30,31 The real atoms and virtual sites of a (111) surface indicated by values “3” and “37” of the array become AUS and AUI atom types of gold, respectively, in the model. For a (100) surface, the real atoms “4” and virtual sites “47” should be redefined as AUSS and AUII, respectively. All internal real atoms “2” were renamed to the AUB type. Each type of gold atom had its own mass and charge according to the rigid-rod model, which is useful for making system topology files.20,30,31 A fixed distance between elements of the array [a] 3D grid was denoted as the scale factor (sf) variable: 𝑢𝑠 (2) 𝑠𝑓 = 𝑑𝑢 where us = 0.40782 nm is a unit cell size parameter of the Au lattice,66 and du = 6 is the number of unit cell partitions (see Construction of the unit cell and its multiplication) Using sf as the scale factor of the grid, we were able to calculate Cartesian coordinates of all real gold atoms and virtual sites. If a(i,j,k) is an element of array [a], then x = i  sf, y = j  sf, and z = k  sf. Nonetheless, array [a] did not contain dipoles. Dipoles were added to the model during determination of the Cartesian coordinates of atoms. Atoms AUC with the charge 0.3e were added to each real atom at the distance of 0.07 nm along the x-axis to build a gold dipole in accordance with the rigid-rod model of gold.20,30,31 The rigid-rod dipole with the AUC atom was fixed in the topology of the system to take into account the polarization effect during simulation. Topology of the system also contained information about charges and masses of different gold atom types. Finally, output files were converted to such a format that enables using them in the simulation of the nanoparticle in the Gromacs package: a .gro file with coordinates; a file of the molecule topology (.itp) with correct atom types, charges, masses, and dipole constraints; and an index file (.ndx) in which some atoms that had to be fixed during the simulation were listed.



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Figure 3. Illustration of the typical structure of the truncated octahedron nanoparticle model (d = 3 nm). Facets, edges, and vertices of the nanoparticle are shown. Colors represent different types of gold atoms: white and red are (111) and (100) virtual sites, whereas blue and gold are real atoms. Dipole atoms are not shown. As a result, we built the nanoparticle with surfaces (111) and (100) for which the surface atoms were defined: virtual sites responsible for short van der Waals interactions [white for (111) and red for (100)] and the real atoms with dipoles [gold for (111) and blue for (100)] responsible for electrostatic interactions. Inside the nanoparticle there were only real atoms with dipoles. Figure 3 depicts the typical structure of the truncated-octahedron gold nanoparticle. Two gold nanoparticle models with d = 6 and 14 nm and the surface ratio 𝑆𝛴{111}:𝑆𝛴{100} of 66%:34% were constructed for simulation. Because the truncated-octahedron nanoparticle is not spherical, we defined d of the nanoparticle as a distance between two opposite (100) planes. For simulation stability, the vertex atoms were removed (see Supporting Information, section “Preparing the nanoparticle system for simulation”). Given that our attention was focused on binding to the metal surface, and Au(111) and Au(100) facets occupy most of the nanoparticle interface, we did not consider in detail van der Waals interactions at the edges and vertices. In GolP-CHARMM,20,21 such parameters for corners are absent. Perhaps for a more careful analysis of the effects of edges and vertices, these interactions should be parameterized separately. In principle, the proposed algorithm of nanoparticle construction makes it possible to redefine the types of gold atoms for edges and give them special values if necessary. Simulation of gold nanoparticles with sodium citrate The simulation of gold nanoparticles with d = 6 and 14 nm in an explicit water shell with sodium citrate was performed for 21 and 28 ns, respectively. Formation of a stable sodium citrate coverage was observed during the simulation for both 6 and 14 nm nanoparticles. This finding can be easily illustrated by the analysis of radial geometrical distribution for different molecules (Figures 4 and 5). The analysis of radial distribution dynamics for citrate and sodium ions reveals the formation of narrowing peaks around the nanoparticle. The maxima of peaks reach a plateau at the same time for citrate and sodium ions; this situation corresponds to the formation of a stable sodium citrate crown. It formed faster for the 6 nm nanoparticle (after ~10 ns) and took twice the time for the 14 nm nanoparticle (~20 ns); these data are consistent with the size of ACS Paragon Plus Environment

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the analyzed systems. The maxima and standard deviation of the citrate and sodium ions radial distributions averaged over the last 3 ns of the simulation were the same: 4.3 ± 0.45 nm and 8.6 ± 0.85 nm from the center of the small and big nanoparticle, respectively (see also Supporting information, section “The estimation of citrate crown thickness”). Dynamics of water molecules along the MD trajectory indicated a replacement of water around the nanoparticle by citrate and sodium ions (Figures 4C and 5C). The water radial distribution curve for the small nanoparticle consists of a peak, then a valley, followed by an increase to the plateau. The depth of the valley correlated with the growth of ion distribution peaks with time. A similar time trend was observed for the big nanoparticle, but the first peak of water was absent due to the extended surface of the nanoparticle on radial distribution graphs (see Supporting Information section “The estimation of citrate crown thickness”). The presence of water near the surface of both nanoparticles was confirmed by density maps (see Figure 8 below).

Figure 4. Dynamics of radial distributions of citrate (A), Na+ ions (B), and water (C) for the nanoparticle of d = 6 nm. The 21 ns trajectory (with a time step of 200 ps, and a radial distance step of 0.1 nm) was smoothed using a moving average of five time points. The position of the origin of the coordinates is at the center of the nanoparticle.

Figure 5. Dynamics of radial distributions of citrate (A), Na+ ions (B), and water (C) for the nanoparticle of d = 14 nm. The 28 ns trajectory (with a time step of 200 ps and a radial distance step of 0.1 nm) was smoothed using moving average of five time points. The position of the origin of the coordinates is at the center of the nanoparticle.



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Snapshots of final frames for both nanoparticles are presented in Figure 6. Almost all citrate ions were involved in the formation of the shell around the nanoparticle at the end of the simulation, thus indicating that the process of crown formation ran successfully (100% of the initial citrate amount was in the crown for d = 6 nm and 93% for d = 14 nm).

Figure 6. The final snapshot of citrate crown formation after 28 and 21 ns simulations of gold nanoparticles of d = 14 nm (A) and d = 6 nm (B), respectively. Atoms are colored according to elements: red corresponds to oxygen, green to carbon, white to hydrogen, ochre to real gold atoms, yellow to virtual gold sites, and blue to sodium ions. Water molecules and gold dipoles are not shown. In general, we can conclude that not all the nanoparticle surface is covered by citrate, thus resulting in heterogeneity of the citrate crown.1,3 Citrate is organized as a multilayered shell that is consistent with the experimentally estimated thickness of citrate coverage1 and a study on high-resolution microscopic images of nanoparticles.3 The overall distribution of citrate ions above the nanoparticle surface has a nontrivial structure (see Figures 7B–E and S3–S10 for more details). Nevertheless, in the composition of the crown, readers can see motifs of citrate corresponding to simulation data obtained by Wright et al. for a polarizable Au(111) surface: linear and branched chains and bilayers connected through Na+ ions.36 In the same paper, those authors identified three adsorption states of citrate in the amorphous overlayers: “directly adsorbed” citrate had close van der Waals contacts with gold (up to 5 Å from the surface), “indirectly adsorbed” formed a bilayer through a sodium ion with adsorbed species (approximately 5–8 Å), and the “third layer”. Lee et al. obtained a clearcut image of citrate layers around a 10 nm nanoparticle by transmission electron microscopy techniques and also concluded that the citrate shell around the 10 nm nanoparticle consists of 2– 3 layers with the estimated distance between them equal to 3-3.5 Å.3 The final result on citrate distribution curves perpendicular to the surface of the nanoparticle indicates a layered structure of the citrate crown too (see Figure 7A). The graph is averaged over all eight Au(111) and all six Au(100) facets. The distributions of citrate ions above Au(111) look similar between 6 and 14 nm nanoparticles. The first peak at a distance of ACS Paragon Plus Environment

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0.5 nm from the surface can be attributed to the directly adsorbed citrate layer. The next highmagnitude point appears at 0.7 nm which probably corresponds to indirectly adsorbed citrates according to reference data.36 We also noticed a large so-called “third layer,” which accounted for an asymmetrical form of distribution. According to our data, the third layer is diffuse and merges with the previous layer, in agreement with complex 3D structural organization of citrate ions (see Figures S3–S10). Averaged distributions above the Au(100) surface reveal a significant difference from Au(111) because of a decreased number of adsorbed citrate ions and a more extended diffuse layer. The analysis of the visual model of citrate overlayers on the Au(100) surface revealed that in a typical case, citrate ions hung over the middle part of the surface without binding to it. On average, citrates were closer to the Au(100) surface of the 14 nm nanoparticle and had a greater number of direct contacts with the surface area. Moreover, in the case of the 14 nm nanoparticle, some surfaces Au(100) (namely 010) were populated by citrate ions (see Figures S9 and S10).

Figure 7. A) An average normalized distribution of citrate mass centers perpendicular to the surface: for the nanoparticle with d = 6 nm (solid curves) and for the 14 nm nanoparticle (dashed curves). Blue and red curves denote Au(111) and Au(100) surfaces, respectively. The graph distance step is 0.1 nm, the position of zero is at the surface level. Typical structures of citrate overlayers above the surface of Au (100) for d = 14 nm (B), for d = 6 nm (D), and Au(111) for d = 14 nm (C) and for d = 6 nm (E). Citrate is represented by blue lines, and red balls indicate centers mass of citrate ions. Higher magnitude of the distribution perpendicular to the Au(111) surface as compared to the Au(100) surface (Figure 7A) means a preference of the citrate shell for Au(111), in line with the data reported by Park and coauthors.1 In that paper, a model of a protonated citrate form (H2Citrate) was analyzed on Au(111), Au(100), and Au(110) surfaces to fit experimental results including microscopy images of citrate layers. It was concluded that the preference for Au(111) ACS Paragon Plus Environment


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is due to the possible binding of the terminal carboxyl group of citrate to the bridge site of the Au(111) surface. On the other hand, according to the arrangement of gold atoms on different surfaces, formation of a citrate network is possible on both Au(100) and Au(111) surfaces in contrast to the Au(110) surface.1 Differential affinity to facets of a gold nanoparticle has also been demonstrated for other capping ligands.10-13 It is well known that surfactant cetyltrimethylammonium bromide (CTAB) has uneven density at side and end surfaces of a gold nanorod. MD simulations showed that structural organization of CTAB on the Au(111) surface resulted in more open water-ion channels which provided additional transport of growth components to nanorod ends.10-12 Accordingly, elongation of a gold nanorod is probably associated with heterogeneity of surface coverage, namely with high density of CTAB at the side facets ({100}, {110}) and lower binding efficiency to the end facets of the {111} type. We then used the distribution perpendicular to the surface to estimate the number of citrate molecules directly adsorbed on the surface of a nanoparticle. The criterion for evaluation of citrate molecules in close contact with the surface was the distance on distribution graphs less than or equal to 0.5 nm. Similar geometric principles were applied in calculations for citrate molecules on the Au(111) surface.36 Table 2 shows that only ~5% of citrate molecules in the simulation cell were located directly on the surface of the 6 and 14 nm nanoparticles. Most citrate molecules adsorb indirectly on the surface through Na+ ions.36 The percentage of citrate molecules being analyzed above the surface was ~60% for both nanoparticles (see Figure S1). The rest of citrate molecules were associated with the edge volume of each nanoparticle. Table 2. Analysis of direct contacts of citrate ions with the surface of a nanoparticle from the distribution perpendicular to the surface of the nanoparticle for the last three frames of the MD trajectory (see Methods). The molecule is regarded as directly adsorbed if the distance between a citrate mass center and gold atoms is less than or equal to 0.5 nm. 6 nm {100}

surface type {111} average number of directly adsorbed 21 1 molecules average number of molecules above surface 159 94 number of molecules in cell 451 451 % of direct contacts with surface 4.7% 0.2% 35.3 % of analyzed molecules 20.8% %

total

14 nm {111} {100} Total

22

142

14

156

253 451 4.9% 56.1 %

1404 2756 5.2% 51.0 %

279 2756 0.5% 10.1 %

1683 2756 5.7% 61.1 %

To complete the analysis of the distribution perpendicular to the surface of a nanoparticle, we estimated the thickness of the citrate crown and compared it with the values from radial distribution graphs (see Supporting Information, section “The estimation of citrate crown thickness” for details). The overall result of 1.0–1.2 nm is close to experimentally measured values of 0.6–1.2 nm.1,3 To detail the localization of different molecules and atoms in the simulation cells, an analysis of the density distribution was performed next. For both nanoparticles (6 and 14 nm), the picture looks very similar. According to our results, the citrate ions concentrate mainly near nanoparticle edges and vertices, as proposed by Park et al.1 on the basis of measurements of citrate shell thickness (see Figure 8A). Sodium ions are tightly bound to the negatively charged citrate ions. The arrangement of Na+ ions in the structure (Figure 8A) indicates their major participation in the assembling and stabilization of the crown, including the possibility of formation of citrate motifs. The analysis of citrate ion orientations relative to the gold surface revealed a preferential interaction of CH2 groups with gold atoms. Our results match the ACS Paragon Plus Environment

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adsorption geometry of citrate on a Au(111) surface reported by Wright et al.,36 because we study the same model of citrate (Cit3 with optimized parameters for an aqueous medium38), the rigid-rod model of polarization in gold,30,31 and the same GolP-CHARMM force field.20,21

Figure 8. Density maps of different atoms in systems along the last 7 ns of the MD trajectory: A) citrate O carboxyl atom (red) and Na+ ions (blue) for the nanoparticle of d = 14 nm; B) a water oxygen atom (O) for the nanoparticle of d = 14 nm; C) a water oxygen atom (green) and water hydrogen atoms (red) above Au(100) for the nanoparticle of d = 6 nm. Real gold atoms are shown as yellow spheres. Water molecule density maps calculated during the last 7 ns of 28 ns MD trajectories uncovered their strong interaction and specific orientation near the gold surfaces (Figure 8B). The water density map outlines the contours of a nanoparticle surface, most sharply for the Au(100) surfaces (Figure 8B). Detailed consideration of the water oxygen density map with the gold surfaces showed a preferential orientation of water molecules relative to the gold atoms. For the Au(111) surface, the plane of water molecules was preferentially parallel to the gold surface (see Figure S19B and S19D). In the case of the Au(100) surface, parallel and, less likely, perpendicular orientations were observed (see Figures 8С, S19A, and S19C). The orientation of water on different surfaces and the preference for Au(100) over Au(111) are in agreement with quantum chemical calculations.20,67 The presence of more tightly interacting water may influence the binding of citrate to the Au(100) surface in comparison with Au(111). It can make an additional contribution to the predominant adsorption of citrate on the Au(111) surface. In addition, water is most tightly interacting with nanoparticle edges via the oxygen atom without preferential orientation of the hydrogens. We propose that the orientation of water on edges of a nanoparticle originates from tight interactions of the positively charged dipole atoms AUC with a negatively charged O atom (see below). In summary, as a result of simulation, a structure of the citrate crown around a gold nanoparticle with d = 6 nm or d = 14 nm was successfully formed. We characterized the final citrate distribution, dynamics of its formation, and final citrate distribution for both nanoparticles. The main features of citrate coverage (such as heterogeneity, the presence of free gold surfaces, and the thickness) were consistent with experimental results. Analysis of the electrostatic-potential distribution The resulting distribution of the citrate crown around a gold nanoparticle is difficult to explain without consideration of the forces governing the interaction between a metal nanoparticle and surrounding molecules. It seems that electrostatic forces arising from polarization effects in the nanoparticle model could have a considerable influence on a charged citrate molecule during the simulation. To reveal the possible mechanism behind the crown formation process, intensity of the electric potential was analyzed for the gold nanoparticles in different environments. We compared the electrostatic field potentials of the 14 nm gold nanoparticle between vacuum, ACS Paragon Plus Environment


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water, and the citrate-capped model system simulated in the periodic cuboid cell. The electrostatic potential of the nanoparticle was visualized in all cases as described in Methods.

Figure 9. The electric potential of a gold nanoparticle of d = 14 nm in vacuum (A) and in aqueous media: with only water molecules (B) or in the presence of citrate (C). The negative potential is blue, and the positive potential is red. In vacuum, the nanoparticle had no distinguishable charge distribution profile at the surface or corners (Figure 9A). The analysis of the potential of a gold nanoparticle in a water box revealed the development of heterogeneity. The Au(100) surface carried a stronger negative potential above the surface than Au(111) did (Figure 9B). To compensate the potential near the uncharged nanoparticle, the field potential near the edges became positive. When a nanoparticle from the system with sodium citrate was evaluated (Figure 9C), a similar potential distribution was observed: the nanoparticle edges acquired a positive charge, while the surfaces became negatively charged with higher magnitude for {100} as compared to {111}. This finding can probably explain the origin of citrate concentration near the edges of a nanoparticle. Because water density maps (Figure 9B) uncovered the presence of water molecules near surfaces and edges of a citrate-capped nanoparticle and a possibility of parallel water orientation near Au(100) (Figures 8C and S19), we assumed that these data are in agreement with the electrostatic potential distribution. We believe that small water molecules could get close to more open atoms at the edges and vertices and induce a positive charge at these sites under the influence of the negatively charged oxygen atom of water. After that, gold dipoles are oriented according to the geometry of a nanoparticle and affect water adsorption on different surfaces. Nevertheless, it is worth mentioning that citrate forms the crown structure through sodium ions; therefore, more complex electrostatic interactions with the surface are possible. In addition, the arrangement of gold atoms on the surface can affect the binding to different surfaces of the nanoparticle via van der Waals forces. On the basis of all these results, we can propose a mechanism of formation of a nonisotropic citrate crown near a nanoparticle. First, the closest water molecules cause redistribution of gold nanoparticle dipoles. Then, the negatively charged citrate ions get attracted to the positively charged edges through the long-range electrostatic interactions and form a network around the nanoparticle. After citrate reaches the surface of the nanoparticle, the van der Waals interactions orient the molecule on the surface in addition to electrostatic forces. It can be assumed in the first approximation that citrate prefers to interact with the Au(111) surface over Au(100) owing to a weaker negative field above Au(111). Similar observations related to the presence of a positive electrostatic potential on nanoparticle corners with a low coordination number have been obtained for gold and platinum clusters.68 This observation explains the high catalytic activity of these sites toward Lewis bases. It seems that the nanoparticle morphology itself determines the charge distribution and offers an additional opportunity for electrostatic interactions with the surrounding molecules. ACS Paragon Plus Environment

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Comparison of simulation results between the polarizable and nonpolarizable model of a gold nanoparticle To clarify the involvement of the polarization effect in the process of citrate crown formation, we performed simulation of the nonpolarizable model of a gold nanoparticle (d = 6 nm) with sodium citrate. When only van der Waals interactions with gold were considered, the citrate crown also completely formed after 21 ns of the simulation (Figure S21A). Moreover, the coverage had a heterogeneous multilayer structure with the presence of naked gold surfaces as in the case of the polarizable nanoparticle model. In contrast, the patterns of arrangement of citrate molecules above the surface of the nanoparticle were significantly different. The main difference, which is clearly seen in the distribution graphs perpendicular to the surface of a nanoparticle, is the number of close van der Waals contacts with the gold surface (32% of all citrate molecules in the case of the nonpolarizable model versus 5% in the case of the polarizable model; see Table S1, Figure S21C, and Table 2). We can propose a possible explanation of these results on the basis of electrostatic-potential analysis of the polarizable gold nanoparticle (see above). Inclusion of gold dipoles in the nanoparticle model caused changes in the charge distribution, with the negative field potential being on the surfaces and the positive field potential near edges and vertices of the nanoparticle. During the process of crown formation, negatively charged citrate is affected by repulsive forces from a surface having a negative electrostatic field in the model with polarization. On the other hand, in the simulation of the nonpolarizable gold model, a citrate molecule could easily bind to the center of nanoparticle facets, thereby resulting in an increasing number of close van der Waals contacts with the gold surface. Another feature of the simulation of the nonpolarizable model of gold is comparable affinity of citrate for both types of nanoparticle surfaces with no significant preference for Au(111) (see Figure S21B–D). It should be noted that the simulation was conducted under conditions of periodically rising temperature, which increased the number of collision events between citrate molecules and the gold surface. Nonetheless, in the case of a nanoparticle with polarization, especially the small nanoparticle (d = 6 nm), the Au(100) surface area was virtually unpopulated by citrate. We assume that the negative electrostatic field above Au(100) in the polarizable gold model strongly hinders the efficiency of landing on the Au(100) surface of the nanoparticle. The orientations of citrate with respect to the surface of the polarizable and nonpolarizable gold model were similar, with CH2 groups being preferentially exposed to the nanoparticle surface, and the COOH group pointed away. Apparently, this binding mode of citrate facilitated the assembly of “linear chains,” “bilayers,” and “island” structural motifs, which have been described for a polarizable Au(111) surface.36 In summary, a citrate crown was formed in both cases (in the simulation with and without the image charge effect in the metal). Nevertheless, the necessity of including the polarization effects in the nanoparticle model is based on theoretical principles because citrate is a charged molecule (see Introduction). Testing of the citrate-capped nanoparticle model with sodium chloride One of methods for testing and studying gold nanoparticles is salt-induced aggregation. It is known that at a high salt concentration, gold nanoparticles aggregate with a visible color change of the solution from red to blue.69 The aggregation mechanism is often associated with the removal of the negatively charged citrate crown from a nanoparticle under the influence of electrostatic forces and uncovering of the hydrophobic gold surface for van der Waals interactions with the surface of another nanoparticle.70 To study the suitability of the newly developed gold model for investigation of nanoparticle properties, we carried out a simulation of the citrate-capped nanoparticle of d = 6 with ions Na+ and Cl at a concentration of 0.8 M for 35 ns. We chose a 7 ns snapshot of the MD ACS Paragon Plus Environment


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trajectory as a starting point of the simulation. This snapshot corresponds to 95% of citrate ions located near the nanoparticle when the formation of the crown is clearly detectable but is not fully completed. This choice was governed by the necessity of decreasing the simulation time to observe possible citrate shell reorganization. During the simulation, we observed numerous changes in the structure of the citrate crown. Typical processes along the MD trajectory were as follows: repeating rearrangement of the structure, detachment of a small number of citrate ions from the surface, and clustering of citrates into new groups (compare Figure S22A and S22B). After 32 ns, a large group of citrate ions (28) separated from the shell (Figure 10A). In the absence of NaCl, we never observed the detachment of citrate clusters of such size from the crown during the simulation.

Figure 10. A) The simulation results on the 6 nm citrate-capped gold nanoparticle interacting with NaCl. Na+ and Cl ions are not depicted for clarity. The arrow marks the place where a big group of citrate molecules lost the contact with the crown. B) The last frame of radial distribution graphs for citrate (CIT) in a system with and without NaCl (red and blue curves, respectively). The radial distance step is 0.1 nm, the position of zero is at the center of the nanoparticle. Although rearrangement of the crown clearly takes place in the structure along the trajectory, we cannot make a firm conclusion about the radical changes in the thickness of the crown during the simulation from the radial distribution dynamics (Figures 10B and S23). Analysis of density maps suggests that Cl ions interacted with the citrate shell and got incorporated into the crown (Figure 11A). Moreover, localization of chloride ions at the edges of the nanoparticle is detectable. We assume that this phenomenon originated from a tight interaction of the positively charged dipole atoms (AUC) with the negatively charged chloride ion, which has smaller size and higher mobility than the citrate ion does. It can be concluded from radial distribution graphs (Figures 11B and S23) that sodium and chloride ions reach the same plateau, which corresponds to the same bulk concentrations of ions in solution.


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Figure 11. A) The density map of Cl (yellow) and citrate O carboxyl atom (cyan) with the nanoparticle of d = 6 nm along last 7 ns of the MD trajectory. B) Radial distribution of the last trajectory frame for citrate (CIT: blue curve), Cl (CL: red curve), and Na+ ions (NA: yellow curve). The radial distance step is 0.1 nm, and the position of zero is at the center of the nanoparticle. As a result, it can be concluded that during the 35 ns simulation, we did not detect the complete removal of the citrate crown. Even though Cl ions are incorporated into the crown, Na+ ions are still located there, and apparently, maintain its structure (Figure S22D). Nevertheless, the results indicate that there are changes in the structure of the crown under the influence of NaCl. In summary, gold nanoparticles hold promise for various chemical and physical interactions and cause adsorption of а molecule from the surrounding medium. Besides, the presence of surfaces with different arrangements of atoms as well as specific sites with low coordination such as edges and vertices further complicates the modes of binding to a nanoparticle. It seems that depending on their functional groups and charges, molecules can interact with different regions of the nanoparticle. A study on displacement of oligonucleotides (noncovalently attached to a gold nanoparticle) by thiols points to the existence of various regimes involving only partial displacement of DNA from the surface of a gold nanoparticle by high-molecular-weight thiols and complete removal of DNA by low-molecular-weight thiols.71 A layer-by-layer approach applied to obtain the gold nanoparticles with multilayer coverage (consisting of positively and negatively charged ligands) indicates the possibility of mixing the layers and formation of a shell with heterogeneous mosaic structure.72 The existence of selective surface-capping agents63,73 as well production of nanostar structures during nanoparticle overgrowth74,75 also confirms the nontrivial nature of binding to the surfaces and edges of a nanoparticle. The MD method can serve as a useful tool for investigating the interactions with metal nanoparticles. Analysis of our simulation results uncovered formation of a citrate crown around the gold nanoparticle. This finding is in good agreement with experimental data on its thickness and structure. Conclusions We developed a gold nanoparticle model with the polarization effect using the original method of unit cell initiation, cutting a nanoparticle out of a crystal cube, and detecting the surfaces and different types of gold atoms. As a result of modeling of the gold nanoparticle with sodium citrate, a citrate-capped gold nanoparticle model was obtained for the first time. The model was verified according to the literature data. The model reproduces such important properties as the structure and thickness of the citrate crown and rearrangement of citrate ACS Paragon Plus Environment


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molecules under the influence of NaCl. It was demonstrated that taking into account the effects of polarization in the model of a gold nanoparticle influenced the simulation results concerning the distribution of citrate ions on the metal surface. On the basis of electric potential visualization, the mechanisms of interaction of polarizable gold nanoparticles and citrate molecules were proposed. We believe that it is possible to use this model as a starting simulation point to investigate the interactions of citrate-capped gold nanoparticles with other molecules, including proteins and nucleic acids. ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Preparing the nanoparticle system for simulation; symmetric equation for {111} and {100} planes; volumes above Au(111) (red balls) and Au(100) (Figure S1); the final result of radial distribution graphs (Figure S2); the estimation of citrate crown thickness; the structure of citrate overlayers above the surfaces of Au(111) for d = 6 nm from the side view (Figure S3); structure of citrate overlayers above the surfaces of Au(111) for d = 6 nm from the top view (Figure S4); structure of citrate overlayers above the surfaces of Au(100) for d = 6 nm from the side view (Figure S5); structure of citrate overlayers above surfaces of Au(100) for d = 6 nm from the top view (Figure S6); structure of citrate overlayers above the surfaces of Au(111) for d = 14 nm from a side view (Figure S7); the structure of citrate overlayers above the surfaces of Au(111) for d = 14 nm from the top view (Figure S8); structure of citrate overlayers above the surfaces of Au(100) for d = 14 nm from a side view (Figure S9); structure of citrate overlayers above the surfaces of Au(100) for d = 14 nm from the top view (Figure S10); a normalized distribution of citrate mass centers perpendicular to Au(111) surfaces of the nanoparticle with d = 14 nm (Figure S11); a normalized distribution of citrate mass centers perpendicular to Au(111) surfaces of the nanoparticle with d = 6 nm (Figure S12); a normalized distribution of citrate mass centers perpendicular to Au(100) surfaces of the nanoparticle of d = 14 nm (Figure S13), a normalized distribution of citrate mass centers perpendicular to Au(100) surfaces of the nanoparticle with d = 6 nm (Figure S14); citrate dynamics perpendicular to the surface of the nanoparticle; a normalized distribution of citrate mass centers perpendicular to Au(111) surfaces of the nanoparticle with d = 14 nm along the trajectory (Figure S15); a normalized distribution of citrate mass centers perpendicular to Au(100) surfaces of the nanoparticle of d = 14 nm with time (Figure S16); a normalized distribution of citrate mass centers perpendicular to Au(111) surfaces of the nanoparticle with d = 6 nm along the trajectory (Figure S17); a normalized distribution of citrate mass centers perpendicular to Au(100) surfaces of the nanoparticle of d = 6 nm with time (Figure S18); density maps of the water oxygen atom and water hydrogen atoms around the surface of the nanoparticle with d = 6 nm during the last 7 ns (Figure S19); visualization of the electric field potential on the surface of the nanoparticle and for different molecular ensembles of the gold nanoparticle having d = 14 nm, citrate molecules and Na+ ions (Figure S20); the results of simulation of the nonpolarizable gold nanoparticle model (Figure S21); analysis of direct contacts of citrate molecules with the nonpolarizable nanoparticle model at d = 6 nm (Table S1); density maps of different atoms along the last 7 ns of trajectories in a simulation of the nanoparticle with d = 6 nm with and without NaCl (Figure S22); dynamics of the system radial distribution along the 35 ns trajectory with NaCl for the nanoparticle with d = 6 nm (Figure S23). AUTHOR INFORMATION Corresponding Author * Tel.: +7 383-363-5134. Fax: +7 383-363-5134. E-mail address: [email protected] ** Tel.: +7 383-363-5134. Fax: +7 383-363-5134. E-mail address: [email protected] ACS Paragon Plus Environment

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ORCID Dmitrii V. Pyshnyi: 0000-0002-2587-3719 Alexander A. Lomzov: 0000-0003-3889-9464 Notes The authors declare no competing financial interests. Acknowledgments This work was done in accordance with the State assignment by the Russian State funded budget project (VI.62.1.4, 0309-2016-0004), and the structural analysis of the interaction between citrate ions and a gold nanoparticle (A.A.L.) was in part supported by the Russian Science Foundation (grant No. 16-15-10156). REFERENCES: (1) Park, J.-W.; Shumaker-Parry, J. S. Structural study of citrate layers on gold nanoparticles: role of intermolecular interactions in stabilizing nanoparticles. J. Am. Chem. Soc. 2014, 136, 1907-1921. (2) Park, J.-W.; Shumaker-Parry, J. S. Strong resistance of citrate anions on metal nanoparticles to desorption under thiol functionalization. ACS Nano 2015, 9, 1665-1682. (3) Lee, Z.; Jeon, K.-J.; Dato, A.; Erni, R.; Richardson, T. J.; Frenklach, M.; Radmilovic, V. Direct imaging of soft-hard interfaces enabled by graphene. Nano Lett. 2009, 9, 3365−3369. (4) Piella, J.; Bastús, N. G.; Puntes, V. Size-controlled synthesis of sub-10-nanometer citratestabilized gold nanoparticles and related optical properties. Chem. Mater. 2016, 28, 1066– 1075. (5) Dinkel, R.; Braunschweig, B.; Peukert, W. Fast and Slow Ligand Exchange at the Surface of Colloidal Gold Nanoparticles. J. Phys. Chem. C 2016, 120, 1673–1682. (6) Carnerero, J. M.; Jimenez-Ruiz, A.; Castillo, P. M.; Prado-Gotor, R. Covalent and NonCovalent DNA-Gold-Nanoparticle Interactions: New Avenues of Research. ChemPhysChem 2017, 18, 17-33. (7) Zhang, X; Servos, M. R.; Liu, J. Surface Science of DNA Adsorption onto Citrate-Capped Gold Nanoparticles. Langmuir 2012, 28, 3896–3902. (8) Nelson, E. M.; Rothberg, L. J. Kinetics and Mechanism of Single-Stranded DNA Adsorption onto Citrate-Stabilized Gold Nanoparticles in Colloidal Solution. Langmuir 2011, 27, 1770−1777. (9) Mahmood, M.; Casciano, D.; Xu, Y.; Biris, A. S. Engineered nanostructural materials for application in cancer biology and medicine. J. Appl. Toxicol. 2012, 32, 10−19. (10) Meena, S. K.; Sulpizi, M. Understanding the Microscopic Origin of Gold Nanoparticle Anisotropic Growth from Molecular Dynamics Simulations. Langmuir 2013, 29, 14954−14961. (11) Meena, S. K.; Celiksoy, S.; Schäfer, P.; Henkel, A.; Sönnichsen,C.; Sulpizi, M. The role of halide ions in the anisotropic growth of gold nanoparticles: a microscopic, atomistic perspective. Phys. Chem. Chem. Phys. 2016, 18, 13246−13254. (12) Meena, S. K.; Sulpizi, M. From gold nanoseeds to nanorods: The microscopic origin of the anisotropic growth. Angew. Chem. Int. Ed. 2016, 55, 11960-11964. (13) Almora-Barrios, N.; Novell-Leruth, G.; Whiting, P.; Liz-Marzán, L. M.; López, N. Theoretical description of the role of halides, silver, and surfactants on the structure of gold nanorods. Nano Lett. 2014, 14, 871–875. (14) Tavanti, F; Pedonea, A.; Menziani, M. C. A closer look into the ubiquitin corona on gold nanoparticles by computational studies. New J. Chem. 2015, 39, 2474−2482. (15) Feng, J.; Slocik, J. M.; Sarikaya, M.; Naik, R. R.; Farmer, B. L.; Heinz, H. Influence of the shape of nanostructured metal surfaces on adsorption of single peptide molecules in aqueous solution. Small 2012, 8, 1049−1059. ACS Paragon Plus Environment


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Figure 1. The unit cell of the face-centered cubic lattice (FCC) with additional virtual sites for {100} and {111} planes (four sites shown). Real atoms of the lattice are represented by orange balls. Virtual sites are shown as red and blue stars for {100} and {111} planes, respectively. Examples of {100} and {111} planes are yellow. 156x57mm (300 x 300 DPI)


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Figure 2. Geometry of the nanoparticle obtained from the cube crystal (thin black lines). Cutting planes {111} (thick black lines) form an octahedron in the center of the cube. The truncated octahedron is obtained by removing excess atoms by means of {100} planes (pink lines). Changing the cutting position of {100} planes relative to the center of the cube results in a different ratio of (111) and (100) surface areas and can lead to different shapes of the nanoparticle (an octahedron, truncated octahedron, cuboctahedron, or cube). 76x76mm (300 x 300 DPI)



Figure 3. Illustration of the typical structure of the truncated octahedron nanoparticle model (d = 3 nm). Facets, edges, and vertices of the nanoparticle are shown. Colors represent different types of gold atoms: white and red are (111) and (100) virtual sites, whereas blue and gold are real atoms. Dipole atoms are not shown. 78x74mm (300 x 300 DPI)


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Figure 4. Dynamics of radial distributions of citrate (A), Na+ ions (B), and water (C) for the nanoparticle of d = 6 nm. The 21 ns trajectory (with a time step of 200 ps, and a radial distance step of 0.1 nm) was smoothed using a moving average of five time points. The position of the origin of the coordinates is at the center of the nanoparticle. 171x69mm (300 x 300 DPI)



Figure 5. Dynamics of radial distributions of citrate (A), Na+ ions (B), and water (C) for the nanoparticle of d = 14 nm. The 28 ns trajectory (with a time step of 200 ps and a radial distance step of 0.1 nm) was smoothed using moving average of five time points. The position of the origin of the coordinates is at the center of the nanoparticle. 164x62mm (300 x 300 DPI)


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Figure 6. The final snapshot of citrate crown formation after 28 and 21 ns simulations of gold nanoparticles of d = 14 nm (A) and d = 6 nm (B), respectively. Atoms are colored according to elements: red corresponds to oxygen, green to carbon, white to hydrogen, ochre to real gold atoms, yellow to virtual gold sites, and blue to sodium ions. Water molecules and gold dipoles are not shown. 171x104mm (300 x 300 DPI)



Figure 7. A) An average normalized distribution of citrate mass centers perpendicular to the surface: for the nanoparticle with d = 6 nm (solid curves) and for the 14 nm nanoparticle (dashed curves). Blue and red curves denote Au(111) and Au(100) surfaces, respectively. The graph distance step is 0.1 nm, the position of zero is at the surface level. Typical structures of citrate overlayers above the surface of Au (100) for d = 14 nm (B), for d = 6 nm (D), and Au(111) for d = 14 nm (C) and for d = 6 nm (E). Citrate is represented by blue lines, and red balls indicate centers mass of citrate ions. 78x124mm (300 x 300 DPI)


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Figure 8. Density maps of different atoms in systems along the last 7 ns of the MD trajectory: A) citrate O carboxyl atom (red) and Na+ ions (blue) for the nanoparticle of d = 14 nm; B) a water oxygen atom (O) for the nanoparticle of d = 14 nm; C) a water oxygen atom (green) and water hydrogen atoms (red) above Au(100) for the nanoparticle of d = 6 nm. Real gold atoms are shown as yellow spheres. 177x58mm (300 x 300 DPI)



Figure 9. The electric potential of a gold nanoparticle of d = 14 nm in vacuum (A) and in aqueous media: with only water molecules (B) or in the presence of citrate (C). The negative potential is blue, and the positive potential is red. 174x62mm (300 x 300 DPI)


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Figure 10. A) The simulation results on the 6 nm citrate-capped gold nanoparticle interacting with NaCl. Na+ and Cl- ions are not depicted for clarity. The arrow marks the place where a big group of citrate molecules lost the contact with the crown. B) The last frame of radial distribution graphs for citrate (CIT) in a system with and without NaCl (red and blue curves, respectively). The radial distance step is 0.1 nm, the position of zero is at the center of the nanoparticle. 157x73mm (300 x 300 DPI)



Figure 11. A) The density map of Cl- (yellow) and citrate O carboxyl atom (cyan) with the nanoparticle of d = 6 nm along last 7 ns of the MD trajectory. B) Radial distribution of the last trajectory frame for citrate (CIT: blue curve), Cl- (CL: red curve), and Na+ ions (NA: yellow curve). The radial distance step is 0.1 nm, and the position of zero is at the center of the nanoparticle. 148x65mm (300 x 300 DPI)


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Molecular dynamics simulation of polarizable gold nanoparticles

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