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Copper nanoclusters exhibit extraordinarily electronic, catalytic and optical properties different from bulk copper. Consistency between our bond order-length-strength induced nonbonding-electron-polarization (BOLS-NEP) theory and density functional theory (DFT) calculation of copper nanoclusters CuN(N=13~147) verifies that: i) interlayer Cu-Cu bond length contract from 0.2556 nm of bulk to 0.2414 nm of Cu13; ii) Cu 1s and 2p binding energy are trapped to larger energy by the deepened potential well around under-coordinated sites as the nanoparticle size decreases; iii) Charges are localized at surface rather than intinerate in nanoparticles; iv) Valence band shift upward to smaller energy opposite to core level due to the polarization of localized valence charge by the densely entrapped bonding electrons. The experiment and theory agreement by using the UPS and STM/S.
Metal nanoclusters have attracted numerous researches in experimental and theoretical analysis due to the extraordinary chemical and physical properties which cannot be seen from bulk materials, such as their unique applications in catalyst, optics, biology, magneto-electronics, biosensors, nanoscopic devices and thin film growth1-4.
The noble metal clusters (Cu, Ag, and Au) and alkali metal clusters have several resemblances in the electronic structure because of single s orbital and the d band below of Fermi level in bulk metals5,6. When reduced to nanoscale, Cu-Cu bond was reported to shrink spontaneously up to 12% compared with the bond length of bulk 7; the k-edge binding energy of Cu 1s was revealed to shift downward from 8975.5 to 8976.5eV as Cu island size decreases7; meanwhile, Cu valence charges shift upward to Fermi level as the size decreases revealed by ultraviolet photoelectron spectra (UPS)8, and from Cu nano chain interior to chain end by STM/S.9,10 The size and structure of metal nanoclusters play a unique role in catalyst that one of the significant catalysts is copper nanoclusters11-13. Observation catalyst application at metal clusters is related to agglomeration atoms and effected on size and structure14. Catalytic properties observed in Cu/ZnO base on methanol synthesis due to decrease Cu-Cu coordination, dynamic changes15, oxidizing by H2O and reducing by CO in gas composition3.
Copper nanocrystals with face-centered cubic (fcc) structures transit between multiply twinned particles (MTPs) and single crystals in nanoclusters. The MTPs structure assumes fivefold symmetric that at the copper nanoclusters start with seven atoms like a pentagonal bipyramid, and the stability is determined by the ratio of surface-volume to total energy16-19. The magic number of alkali clusters was established by Knight et al.20 and fullerene was discovered by Kroto et al. in 198521 cause to develop experimental in clusters fabrication. In 1882, the first copper fivefold was reported by von Lasaulx which shown a star-like shape and pentagonal dimples22,23. The pentagonal dendrites were observed by the vapor phase method for growing copper24. The stable copper clusters with 8, 18, 20 atoms are independent of the geometry at elevated temperatures due to the large band gap at the Fermi level25. The copper clusters with large atoms (1-410) was performed by UPS that was recommended as crystalline26.
The investigation of the geometrical structure and electrical properties of copper nanoclusters is considered by numerous theories. The analysis of critical size of copper clusters (13, 55, and 147 atoms) was achieved by a semi-empirical theory in 1993 that was compatible with previous experiments27. The first principle study of small copper clusters was reported by Mossobrio et al. in 199528. A DFT of small copper clusters (neutral, cationic and anionic) was investigated regarding to less than 5 atoms by using the linear combination of Gaussian-type orbital density functional theory (LCGTO-DFT) by Calaminici et al.29. The tight binding dynamic was used for copper clusters (2-55 atoms) with the icosahedral structure that was compared their results with ab-inito calculations and some experiments for geometry transition in n=4230,31. According to previous method, copper nanoclusters with n=40-44 have less stability and decahedron-icosahedrons-cuboctahedron structure whereas with n=45-55 icosahedrons-decahedron-cuboctahedron structure6. The investigation of structure and energy of copper clusters with 2-45 atoms by molecular dynamics simulation that was shown the copper clusters desire to figure three dimensional structure and the Cu26 is more stable than the others32.
In this study, we employed bond-order-bond-length-bond-strength (BOLS) correlation theory and DFT to calculate polarization and charge transfer in icosahedral (ICO) and truncated octahedral (TO) structures of copper nanoclusters.
Base on bond-order-bond-length-bond-strength (BOLS) correlation theory33, the coordination number (CN) has a key role in defects, disorder, dislocation, atomic vacancies and at the surface. The bonds become shorter and stronger compared with the bulk and the effect on CN reduction base on Goldschmit and Pulaing34. BOLS theory with the curvature K-1 (the number of atoms along the radius of a spherical dot), atomic coordination (zi), bond contraction coefficient (Ci), bond length (di), and charge density (ni) in the ith atomic layer and subscript b for bulk values as followed:
Bulk of Cu (3d104s1) has high electrical conductivity; due to the 3d states that provide the density of state at the Fermi level, whereas at copper nanoclusters the delocalized electrons in 4s-state allocates the happening of collective electronic excitation at relatively low energy, localized 3d-states affected at cluster properties such as surface and Fermi level close to the vacuum due to the expansion valance band with the size of nanoclusters 5,8,14,35.
Transition metals have a strong bond with s and p conduction electrons and an incompletely filled d shell. The delocalized conduction electrons observed in the s and p electrons, while the localized electrons are in the d electrons due to covalent bonds 36. The total bonding in this kind of metal has been able to vision since the sum of the s, p electrons (metallic bonding) and the d electrons (covalent bonding)36.
The delocalized valance 4s electrons are dependent on the shape and surface size of clusters and the surface of clusters related to 3d electrons with corelike behavior in copper nanoclusters which proved by UPS8. The electrons were shifted by the cluster size due to electrostatic effect and detected the electronic level cluster structure. The best feature of UPS spectra detected the 3d band narrows which is proportional to rise size of clusters. The large copper clusters in UPS spectra are similar to the 3d band of bulk structure. In the experiment, the top of occupied 3d band was observed as a sharp peak in the density of states by Smith 37. The long bond of copper bulk is 2.556Å 18,38. Here, we considered copper nanoclusters with different number of atoms which have icosahedral and truncated octahedral structures in Figure 1.
The bond length and charge transfer using the Mulliken population analysis 39,40 and Hirshfeld partitioning of electron density distribution 41 (116,135 and147 atoms) calculated which shown in Table 1. The DFT (semi-core pseudopotential 42) calculation with DMol3 code 43 localized density approximation in PWC 44. The tolerance energy, forces and displacement in geometry optimization were arranged at 10-5 Hartree, 0.002 Hartree/Å and 0.005Å.
Results and Discussion:
Shell-resolved Bond Contraction and charge transfer:
The calculation revealed the Cu-Cu bond in bulk (2.55 nm) is longer than the nanoclusters in DFT calculation. In O-Cu bond shrink 4-12% of the O-Cu (100), Au-Au bond 30% reduces, and diamond (111) also decrease to 30% 45,46. The increase of bond energy density per unit volume in the relaxed surface causes to contract CN-imperfection induce spontaneous bond and reduce the associated binding energy47. The negative and positive charge shown charge gain and loss which transfer electrons from inner to outer shell in nanoclusters. The bond contraction coefficient is less than one and the value is between 0.85-0.9 in noble metal clusters (Cu, Ag, and Au) regarding to the bond contracts and agree with the results in Table 148,49.
Core level Quantum entrapment:
X-ray absorption fine structure technique (EXAFS) spectra study the k-edge threshold which is dependent on cluster size and shift the core-level energy up to the Fermi level. The binding energy enhances in small copper and nickel cluster due to a net binding energy between free atom and bulk metal value 7. XPS experiments showed that Cu 2p binding energy shifts downward from 932eV of 50 nm size to 934eV of 1nm nanoclusters 50. Moreover, the Cu 1s binding energy was also revealed to shift downward from 8975.5 to 8976.5eV as Cu island size decreases.7 (state the reason here??)
Valence charges polarization:
In Figure 2, the electrons in outer shell have a high LDOS toward inner shell, which are polarized by inner electrons. DFT calculations exhibit occupied and unoccupied localized state and was investigated by using Scanning Tunneling Microscopy/Spectroscopy (STM/S) technique in some experiments such as silver clusters and chain on Ag(111) 51,52, Cu chains on Cu(111) 10, carbon magnetism53, Pd monomer on Al2O3 layer 54, Au chain on Si(111)55 and Au adatomic on NiAl (110) 56. STM investigates the metal surface whereas STS probes the electronic properties. For tunneling electron, the tunneling conductance (dI/dV) evaluates the existed local density of state. In gold monomer, the increase in conductance is related to tunneling into an empty state in Au atom and in second Au observes the double peaks due to strong coupling. The resonance of conductance could not detect more than three Au atom because of overlap the neighbor. The conductivity results shown two effects i) 1D quantum well with infinite walls analysis and while one of the energy levels is similar to sample bias, the tunneling conductance measure is high, and ii) the conductivity in the length of chain axis verifies with the squared wave function which illustrate the density of state in the matching state En. The nodes of wave function observe the minimum conductivity along of chain axis 9.
The dI/dV of a monomer and dimer of copper is around 3.3 V and 2.6 V sample bias which show the increase in the number of atoms effect the decrease in energetic positions and separation. The Cu chain results agree with Pd monomers on Al2O354 and Au on NiAl (110)56 which confirm symmetry of eigenstates due to quantum confinement in 1D potential well and state localized in end of the chain. There are two occupied below the Fermi level and one unoccupied state in Γ point of copper chain. The tight-binding demonstrate the wave function of the unoccupied state in STM experiments. The localized in occupied states with d-wave nature prove quasi-1D confinement compares to the unoccupied state.
The probability of local density of electrons in level En and near the Fermi energy is associated the slope of dI/dV near zero-bias for instance, 4 peaks or states observe in copper with seven atoms9,10,57. what's the result? Red shift?)
In Figure 3, the peak shifts from -2.07 (Cu147) to -1.36 eV (Cu13) in icosahedral structure, which Cu13 included Cu147 and from -1.86 (Cu38) to -2.01 eV (Cu116) truncated octahedral structure. Polarization occurs in the localized states near to the Fermi energy. The polarization observes in the end and edge of nanolcusters and agrees with the tunneling conductance (dI/dV) versus distance for different copper chain 10.
In this study, we calculated DFT in copper nanoclusters and use BOLS correlation theory for obtaining charge transfer and bond contraction coefficient. The size, shape and surface of nanoclusters depend on 4s and 3d electrons. The delocalized electrons have a key role in polarization. In small copper nanoclusters has a higher binding energy related to UPS and STM/S experimental which confirm our results.