ReaxFF and Density Functional Theory Studies of Structural and Electronic Properties of Copper Oxide Clusters

Copper oxide clusters have been used in many areas, such as solar cells,¹ organic light emitting diodes (OLED),² photo-catalysis,³ and electrochemical applications.⁴ Copper oxide clusters are very useful in industries, being a very well-known the catalyst in promoting the formation of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs). Copper oxide clusters have had their structural and electronic properties studied in experiments.^5-18 However, theoretical studies of copper oxide clusters are not much. Small copper oxide clusters have been researched using density functional theory (DFT). CuO₂,¹⁹ CuO₃,²⁰ CuO₄,²¹ CuO₅,²¹ CuO₆ clusters^22,23 and their several isomers are calculated with DFT. Cu_nO_n clusters with n = 1 - 8 have been examined using Monte Carlo (MC) simulations and DFT.²⁴ Also, Cu₃O_n clusters with n = 1 - 6 have been examined using ab initio MC simulations and DFT.²⁵

In general, DFT calculations need many resources such as CPU time and memory for large molecules. For finding the global minimum energy structures, if the structures of many initial copper oxide clusters need to be calculated using DFT, these procedures are very expensive computationally. Fortunately, the ReaxFF for Cu/O/H interaction were developed by Adri van Duin in 2010.²⁶ ReaxFF is a bond based force field in Molecular Dynamics simulations. ReaxFF energy terms in the system are in equation (1)

ReaxFF describes chemical bonding without expensive quantum mechanics (QM) calculations. Therefore, the local energy structures of copper oxide clusters can be calculated with ReaxFF inexpensively. Then, the lowest structures of each copper oxide clusters are optimized using DFT. In this article, we investigate the structures and electronic properties of copper oxide clusters (Cu_nO_n, n = 9 - 15) using ReaxFF and DFT.

For finding local minimum energy of copper oxide clusters, we made about 200 initial copper oxide clusters by turning Cu₉O₉ clusters to Cu₁₅O₁₅ clusters. We attached a Cu-O unit to an optimized Cu₈O₈ cluster,²⁴ studied previously for making initial Cu₉O₉ structures. By this process, we made each initial copper oxide clusters from Cu₉O₉ and Cu₁₅O₁₅ clusters. All initial structures were calculated using ReaxFF. The LAMMPS program was used for ReaxFF calculations. We used parameters for the Cu-O system.^26,27 The NVE-MD simulations on copper and oxygen were relaxed to 0 K with 100 Å 100 Å × 100 Å. After ReaxFF calculations, we calculated single point calculations using DFT for all initial copper oxide clusters structures to obtain ReaxFF calculations, then, decided the lowest energy structure of each copper oxide cluster. We put single point calculation energies of initial Cu₉O₉ clusters in Table S1. We used the B3LYP/LANL2DZ model chemistry to optimize copper oxide cluster calculations, because this model is in very good agreement with experimental data.²⁴ We also calculated the lowest spin-state energy of copper oxide clusters structures. All calculations were done using the Gaussian 09 program.²⁸

The copper oxide clusters, Cu_nO_n (n = 1 - 8), were studied in the previous investigation using ab initio Monte Carlo simulations and DFT.²⁴ Figure 2 shows the optimized neutral Cu_nO_n clusters with n = 9 - 15 using the B3LYP/LANL2DZ model chemistry. The numbers of each atom of copper oxide clusters are Bader charges.²⁹ We calculated doublet and quartet spin states for odd-numbered copper oxide clusters and singlet and triplet spin states for even-numbered copper oxide clusters in neutral copper oxide clusters. Table 1 shows the spin states of the lowest energy structures of copper oxide clusters. In neutral copper oxide clusters, odd-numbered copper oxide clusters have quartet spin states and even-numbered copper oxide clusters have triplet spin states. In cationic and anionic copper oxide clusters, odd-numbered copper oxide clusters have triplet spin states and even-numbered copper oxide clusters have quartet spin states.

Neutral Cu₉O₉ cluster, Cu₁₀O₁₀ cluster, and Cu₁₁O₁₁ cluster have the CuO₄ group at the bottom of each cluster as does the Cu₈O₈ cluster. The copper atoms of CuO₄ groups have a large positive charge. (1.07 for the Cu₉O₉ cluster, 1.10 for the Cu₁₀O₁₀ cluster, and 1.11 for the Cu₁₁O₁₁ cluster) A neutral Cu₉O₉ cluster was made by adding a Cu-O unit at the bottom of a neutral optimized Cu₈O₈ cluster. The structures of neutral, cationic and anionic Cu₉O₉ clusters are the same (Figures 2 - 4). Three isomers are found in the neutral Cu₉O₉ clusters in Figure 1. The relative energies of the second and third most stable structures are 1.83 and 19.16 kcal/mol, respectively.

Figure1.

Optimized structures of neutral Cu₉O₉ clusters using the B3LYP/LANL2DZ model chemistry. The numbers in parentheses indicate the relative energies in kcal/mol. Copper/oxygen atoms colored yellow/red.

Figure2.

Optimized structures of neutral Cu_nO_n clusters (n = 9 - 15) using the B3LYP/LANL2DZ model chemistry. The numbers of atoms are Bader charges. Copper/oxygen atoms colored yellow/red.

Figures 3 and 4 shows the optimized structures of cationic and anionic copper oxide clusters (Cu_nO_n with n = 9 - 15), respectively.

Figure3.

Optimized structures of cationic Cu_nO_n clusters (n = 9 - 15) using the B3LYP/LANL2DZ model chemistry. The numbers of atoms are Bader charges. Copper/oxygen atoms colored yellow/red.

Figure4.

Optimized structures of anionic Cu_nO_n clusters (n = 9 - 15) using the B3LYP/LANL2DZ model chemistry. The numbers of atoms are Bader charges. Copper/oxygen atoms colored yellow/red.

Next, a neutral Cu₁₀O₁₀ cluster was formed by attaching a Cu-O unit to the top of the neutral optimized Cu₉O₉ cluster. The structure of the neutral Cu₁₀O₁₀ cluster is different from that of cationic and anionic Cu₁₀O₁₀ clusters. However, the structures of cationic and anionic Cu₁₀O₁₀ clusters are the same, and these clusters are made by adding a Cu-O unit at the bottom of the CuO₄ group. Therefore, the CuO₄ group was broken.

In Cu₁₁O₁₁ clusters, a Cu-O unit was added at the top of neutral, cationic, and anionic optimized Cu₁₀O₁₀ clusters, respectively. The structures of cationic Cu₁₁O₁₁ cluster is the same with the structure of anionic Cu₁₁O₁₁ cluster. In Cu₁₂O₁₂ clusters, the CuO₄ group of the neutral Cu₁₂O₁₂ cluster was destroyed, because a Cu-O unit is attached. Cationic and anionic Cu₁₂O₁₂ clusters were made by adding a Cu-O unit to the bottom side of the optimized cationic and anionic Cu₁₁O₁₁ clusters, but the CuO₄ group still remains for a cationic Cu₁₂O₁₂ cluster and is broken for an anionic Cu₁₂O₁₂ cluster

A Cu-O unit is attached to the middle of the back of a neutral Cu₁₂O₁₂ cluster to make a Cu₁₃O₁₃ cluster, and the structures of neutral, cationic, and anionic Cu₁₃O₁₃ clusters are very similar. Neutral Cu₁₄O₁₄ was constructed by adding a Cu-O unit to the lower part of the back of neutral optimized Cu₁₃O₁₃ clusters. Like Cu₁₃O₁₃ clusters, neutral, cationic, and anionic Cu₁₄O₁₄ clusters are very similar structurally each other. A neutral Cu₁₅O₁₅ cluster was made by attaching the side of a neutral optimized Cu₁₄O₁₄ cluster. However, the structure of a neutral Cu₁₅O₁₅ cluster is somewhat different from that of cationic and anionic Cu₁₅O₁₅ clusters.

Table 2 shows the HOMO-LUMO gaps of neutral (CuO)_n clusters with n = 9 - 15. The Cu₉O₉ cluster has the largest HOMO-LUMO gap (2.10 eV) and the average value of HOMO-LUMO gaps (from Cu₁₀O₁₀ to Cu₁₅O₁₅ clusters) is 1.54 eV.

Calculated atomization energies per atom are shown in Figure 5. Atomization energies per atom are calculated by equation (2).

Figure5.

Atomization energies per atom of neutral Cu_nO_n clusters (n = 9 - 15) using the B3LYP/LANL2DZ model chemistry

The atomization energies per atom are increased as the cluster size increases. However, the atomization energies per atom increase very slowly from the Cu₁₁O₁₁ cluster to the Cu₁₂O₁₂ cluster. The values of atomization energies peratom of the Cu₁₁O₁₁ and the Cu₁₂O₁₂ clusters are 2.62 eV and 2.63 eV, respectively. The atomization energies per atom of copper oxide clusters (Cu_nO_n, n = 1 - 8) rise rapidly from n = 1 to n = 5 and then almost no change at about 2.5 eV.²⁴ Second difference in energies is calculated from equation (3).

Figure 6 shows the second difference in energies of neutral, cationic, and anionic copper oxide clusters. In general, the second difference in energies tells which a cluster is more stable than other clusters. In neutral copper oxide clusters, odd-numbered copper oxide clusters are more stable than even-numbered copper oxide clusters, except for the Cu₁₄O₁₄ cluster. In Cu_nO_n clusters with n = 1 - 8, the odd-numbered copper oxide clusters are more stable than even-numbered copper oxide clusters, because the stability of neutral copper oxide clusters is correlated with a Cu-O-Cu angle from a tetrahedral geometry.²⁴

Figure6.

Second difference in energies of neutral, cationic, and anionic copper oxide clusters (Cu_nO_n) with n = 9 - 15. using the B3LYP/LANL2DZ model chemistry.

However, in our investigation, the stability of neutral copper oxide clusters cannot be explained by Cu-O-Cu angels. Table 3 shows the average Cu-O-Cu angles of neutral copper oxide clusters. The average Cu-O-Cu angles have similar values of about 104.4 degree except for the average Cu-O-Cu angle of the Cu₁₃O₁₃ cluster.

We think that the structural stability is correlated with a six-membered ring in our study. Generally, a six-membered ring is more stable than other rings. From the calculated second difference in energies, we know that Cu₁₁O₁₁, Cu₁₃O₁₃, and Cu₁₄O₁₄ clusters are more stable than are the Cu₁₀O₁₀ and Cu₁₂O₁₂ clusters. The Cu₁₁O₁₁, Cu₁₃O₁₃, and Cu₁₄O₁₄ clusters have one or two six-membered rings, and the Cu₁₀O₁₀ and Cu₁₂O₁₂ clusters have no six-membered ring.

In cationic and anionic clusters, there is the odd-even oscillation. Even-numbered clusters are more stable than are odd-numbered clusters. It is interesting that an anionic Cu₁₂O₁₂ cluster is more stable than other anionic clusters.

Figure 7 shows the calculated adiabatic ionization potentials and electron affinities of copper oxide clusters. There are odd-even oscillations from Cu₉O₉ to Cu₁₃O₁₃ clusters. After the Cu₁₃O₁₃ cluster, ionization energies and electron affinities are decreased and increased, respectively.

Figure7.

Calculated adiabatic ionization energies and electron affinities of Cu_nO_n clusters (n = 9 - 15) using the B3LYP/LANL2DZ model chemistry

We use ReaxFF and DFT calculations for finding the lowest energy copper oxide clusters, Cu_nO_n with n = 9 - 15. Using ReaxFF, we calculated lots of initial copper oxide clusters quickly. Then, the lowest energy structures of neutral, cationic, and anionic copper oxide clusters can be found with DFT. The structures of neutral, cationic, and anionic copper oxide clusters are very similar. (Cu₉O₉, Cu₁₃O₁₃, and Cu₁₄O₁₄ clusters) From the second difference in energies, in neutral copper oxide clusters, the Cu₁₁O₁₁, Cu₁₃O₁₃, and Cu₁₄O₁₄ clusters are more stable than are other copper oxide clusters. These clusters have one or two six-membered rings. Whether or not these clusters have a six-membered ring determines their structural stability.