PDF document: (file:AuNanoParticles.pdf not found)
Objective
This laboratory is intended to introduce the student to the use of semiempirical electronic structure methods. In particular, the semiempirical methods will be applied to the study of metallic clusters and the interaction of the clusters with discrete molecular systems such as pyridine. The reactivity of the metallic systems will be rationalized in terms the electron population of the atoms in the cluster. The metal-ligand affinity will be quantitatively estimated.
Introduction
The noble metals nanoparticles (Cu, Ag and Au) exhibit physical properties that make them unique for scientific and technological applications: electronics, catalysis, biotechnology, spectroscopy, etc. These properties may be modulated by specific chemical treatment of the particles during their synthesis. Hence, the geometrical and electronic characterization of their structures is crucial to understand the mechanisms that control such properties.
In this exercise, we will use a theoretical approach to study nanoparticles of gold, including their structural and optical properties and the changes in these properties that arise from chemical functionalization. In order to assess the quality of our calculations it is common to contrast the results with other theoretical studies based on similar models. Thus, we will consider structures of tetrahedral/pyramidal shape whose geometries-–interatomic distances and angles–-have been taken from their natural crystal lattices.
The affinity of the metal particles for other chemical species will be calculated by the difference in energy between the isolated molecules and the aggregate. The Figure 1 shows a schematic representation of the two binding modes of interaction between pyridine and a metal particle of pyramidal shape. In this respect, we will identify the reactive sites of the metal particles and study which mechanism is thermodynamically favored. The formation of the aggregate molecule/cluster will be also characterized by its optical properties (absorption spectrum) and how they correlate with the structure and composition of the complex.
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Figure 1: Representation of the two binding modes of a donor ligand (pyridine) to a metal particle of tetrahedral shape. In the S mode the pyridine attaches to a face of the particle while in the V mode it reacts by the vertices.
Procedure
For this particular exercise we will use the program CNDO/INDO accessible at NanoHUB (www.nanohub.org). The atomic coordinates of the species that we will study are available as separate attachments.
__1.- The CNDO/INDO program interface. __
After logging into !nanoHUB, select the option My HUB (see Figure 2). On the menu My Tools select the tab All Tools and locate the application CNDO/INDO. If you click on the star next to the name, the application will be marked as Favorite and placed on this folder.
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Figure 2: NanoHUB window showing My HUB. The programs are listed on the tab All Tools of the menu My Tools. Selecting the (Image(Fig2h.jpg) failed - File not found) next to the name of the desired tool, marks it as Favorite and a link to it is placed in the Favorites folder. The button (Image(Fig2a.jpg) failed - File not found) launches the application.
At this point you may start the application by clicking on the Launch Tool button. The window with the program’s GUI will appear as illustrated in Figure 3. The Popout feature of the tool (located on the upper right hand side of the window) may be activated by clicking on the button; it will create a dedicated window to the tool on your local computer that facilitates the work.
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Figure 3: Initial window of the CNDO/INDO program interface on the web browser.
If you wish to continue working on the current project from a different location an computer, you may close the browser and even shut down the computer; when you log back in the NanoHUB all be as you left it. Even if a job was running, it will continue running on the background or, most likely, it will have finished the calculation in the meantime. Do not however click on the Close button; it will terminate the current CNDO/INDO session for good.
2.- Definition of the model.
2a.- Molecular geometry, electric charge, and spin multiplicity.
To illustrate the selection of a molecular model, lets consider for instance the clusters Au20 as model of a gold nanoparticle of pyramidal shape. The structure, extracted from the experimental, X-ray structure of the material, is given in Cartesian coordinates in the file Au20.xyz. Download the file to your computer and then upload the coordinates to the CNDO/INDO program: on the CNDO Job menu, located on main window of the tool (see Figure 4), select Upload… and follow the instructions to pass the Au20.xyz file to the CNDO/INDO program. The Cartesian coordinates of the cluster will appear on the text box Atomic Positions. The interatomic distances are in Angstroms so the Units option must be set accordingly. During the computation, we will ignore the symmetry of the system so select option “C1” on the Point Group menu.
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Figure 4: Defining the chemical model: atomic coordinates, charge and spin multiplicity.
Once the structure has been entered, the electric charge and the spin multiplicity of the system must be specified. Enter the appropriate values on the Charge and Multiplicity records. In the case of the Au20 cluster we will assume that the particles are neutral (Charge=0) and all the electrons are paired with opposite spins.
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Figure 5: Structural model for a neutral Au20 cluster.
To complete the description of the system, we have to provide the theoretical approach that we will utilize in the computation. In our study we will calculate the wave function by solving the Schrödinger equation using the approximate, semiempirical method INDO (Intermediate Neglect of Differential Overlap).
2c.– Simulation parameters.
The Schrödinger equation is solved iteratively using the Self-Consistent Field (SCF) method. The Error! Reference source not found shows the parameters that control the calculation. In the SCF method, the wave function is recomputed cyclically until the associated energy converges that is, the difference in energy between two consecutive iterations drops below a predefined threshold. The limit is specified by the parameter Convergence in the Control Parameters tab. In this exercise, we will use 10-5 eV as energy threshold and SCF Iterations: 200. This means that if the energy has not converged in 200 SCF iterations, the program will stop. It is a good practice to keep this parameter small, run the calculation and observe the SCF trend: if in the first few iteration it oscillates, stop the calculation and increase the SCF dumping factor (Parameter Shift in Control Parameters). Then rerun the calculation. For small systems, the solution is generally found in fewer steps. If the SCF procedure is converging but it needs more iteration steps, it is possible to restart the calculation. See the section Restarting Computation below.
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Figure 6: Simulation Control Parameters. The default values are appropriate for most of the calculations so in general they do not need to be changed.
Analysis of the results
After the computation has finished, a new window will automatically appear showing the picture of the structure (atomic configuration) of the system under study (See Figure 7).
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Figure 7: Structure of the particle Au20 showing the atomic labels.
Total Energy
In order to verify that the calculation has been successfully completed we must make sure that the SCF procedure has converged. On the Result menu, select the option Output Log. The window contains the description of the system and the results of the calculation. You may either download its content to your local computer for further reference (advisable), or search for specific information on-line using the built-in ‘Find:’ button located at the lower part of the window. For instance, search for the text “total energy”; if the string is found, its first appearance will be highlighted (see Figure 8). In the example, the SCF took 10 iterations to find a solution for the semiempirical (INDO) Hartree-Fock equation. The total energy, sum of the electronic and nuclear energies, is –192.0721473 eV. A few lines below, it is the energy that separates the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals, 3.6775 eV.
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Figure 8. Output Log showing the converged SCF total energy (highlighted) after 10 SCF cycles and the HOMO/LUMO energy gap, 3.6775 eV.
Charge distribution
The reactivity of a molecule may be inferred from its electron density distribution. One way to quantify such distribution is by means of the charge population analysis. The charge at each atomic center is assigned by the sum of its nuclear charge (atomic number) and the number of electrons on the orbitals whose occupancy comes from such center. Figure 9 shows the resulting Orbital Occupancy upon converged wave function. The gold atoms with occupancy less than 1 in the valence atomic orbital 6s have ceded electron density to become part of the cluster and hence will bear a positive charge. If the occupancy is more than 1 electron, however, they will be assigned a partial negative charge. The numerical values obtained for the Au20 system are shown on column Charge, highlighted on Figure 9. On the log file window, the population analysis section may be located by searching, for instance, for the string charge.
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Figure 9: Atomic charge population analysis of the Au20 particle.
Based on the electron population analysis, we may establish an electrostatic criterion to predict what centers of the Au20 will likely react with nucleophilic species and what others will be prone to react with electrophilic species. Although the electrostatic interactions may seem to be a reasonable argument to predict the initiating step of a reaction, it may not be sufficient: electronic factors are also in effect; they may dominate in the overall mechanism and change the direction of the reaction predicted by electrostatic factors alone. In a chemical process, the total energy is the decisive stability criterion between reactants and product.
Optical properties
Although the absorption spectrum may be also analyzed numerically reading the log file (search for example the string wavelength), the tool provides a graphical representation of this data showing the simulated UV/Vis spectrum as function of the wavelength. On the ‘Result’ options menu, select “Absorption spectrum”. The result obtained on the Au20 cluster is shown on Figure 10.
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Figure 10: Calculated absorption spectrum of pyramidal, neutral Au20 particles.
Restarting Computations
It may happen that the energy does not converge in the specified number of SCF iterations. In these cases, it is possible to restart and continue the calculation from the end of the previous one. To do so, first locate in the Output Log the SCF steps and make sure that the energy shows a convergent trend. Then, click on the Input button, which will take you back to the input window, and open the Control Parameters dialog tag as shown in Figure 11. On the Restart option select YES and for MO Assign pick PREVIOUS.
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Figure 11: Restarting incomplete SCF calculations. Set Restart: YES and MO Assign: PREVIOUS.
At this point, the computation may be restarted by clicking on the Simulate button.
Questions
The Cartesian coordinates of the structures are available as separate attachments.
A Nanoparticles.
1.- Nucleation.
The files M4_Tetrahedral.xyz and M4_Planar.xyz (with M= Au) contain the respective coordinates for the M4 clusters. Using the semi-empirical method INDO, calculate the electronic structures and tabulate the total energies of the clusters as a function of the geometry and the nature of the metal M.
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Based on the results, propose the mechanism of nucleation of the atoms to form the nanoparticle.
B. Electrostatics:
2.- Calculate the electronic structure of the Au20 particle and determine the HOMO-LUMO gap.
3.- Using the population analysis, identify the atoms on the particle as electron-donors (nucleophilic sites) or acceptors (electrophilic). Based on these values, predict what sites (V or S) of the metal particles would most likely be attacked by nucleophilic and electrophilic substances.
4.- Take note of the calculated dipole moment of the particles (Search: moment) and discuss the how the values vary with the geometry of the metal clusters.
C.- Reactivity and stereochemistry.
5.- Write the thermodynamic equations that represent the formation of a complex between the nanoparticle and the ligand (pyridine) and complete to show the energetic of the association reactions. What conclusions can you make concerning the dependence of stereochemistry on the nature of the metal.
6.- Review the predictions proposed in question 3 concerning the thermochemistry of donor/acceptor interactions. Are electrostatic considerations a sufficient criterion to predict the reactivity of the reactants and stereochemistry of the products?
Other questions (if appropriate and time allows it):
In excess of solvent, the pyridine may saturate the metal particles by occupying all acceptor (electrophilic) sites.
Au20 + 4 Py → [Au20 ⋅ Py4{{{]}}}
The files Au20_Py_Vertex.xyz and Au20_Py_Surface.xyz contain the Cartesian coordinates of the structures that represent the V and S models for the saturated metallic species.
1.- Calculate the respective enthalpies of reaction and determine which of the two species is thermodynamically favored.
2.- Based on the theoretical predictions, use the optical properties to propose an experiment that allows the characterization and identification of Au nanoparticles in solutions of pyridine.
Auxiliary Files
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(file:Au20_Py_Surface.xyz not found)
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