Molecular Cluster Model Research Articles

Microscopic models for Cu, Ag and Au cationic substitutional impurities and the metal vacancy in ZnSe

Rigorous self-consistent field electronic structure calculations have been carried out for the substitutional Cu, Ag, Au and for the metal vacancy in cubic ZnSe. The multiple-scattering X α molecular cluster model utilized in the calculations reproduces the main features of the band structure of the perfect crystal. According to our ca 1 culations Cu Zn introduces e (d) and T 2 (d) resonant atomic-like levels close to the bottom of the uppermost valence band. Ag Zn and Au Zn introduce similar e (d) and t 2 (d) hyppe r deep levels. Dangling-bond-like t 2 acceptor states are introduced in the band gap by the IB group impurities as well as by the metal vacancy (single acceptors in the former case and a double acceptor in the later case).

Electronic structure of the Au-Mn pair complex in silicon

The electronic structure of the substitutional goldin-terstitial-manganese pair complex in silicon has been studied using the multiple-scattering Xα molecular cluster model. A 25Si + Au sMn i cluster is adopted and the boundary condition problem was solved according to the Watson-sphere terminated cluster model. The calculations indicate that the Au-Mn complex has a spin S=2 in the neutral charge state and S= 3 2 in the positive and negative charge states. These values are compared with the results obtained from EPR experiments.

Soliton defects in polyacetylene: Local‐density functional results

AbstractWe report local‐density functional results for the electronic structure of neutral soliton defects in polyacetylene. The results were obtained using a modified version of the discrete variational method Xα molecular cluster model. For defect‐free chains the calculated X‐ray and ultraviolet photoelectron spectra are in good agreement with experiment. For chains with low concentrations of solitons, we find the forbidden gap broadens slightly, and two nearly dispersionless bands, split by several tenths of eV, are introduced into the gap. The predicted splitting is in accord with recent experimental results for this defect.

The noble gas atoms as impurities in silicon

Ground state one-electron energies have been calculated for the substitutional and interstitial helium, neon, and argon impurities in silicon by use of the self-consistent-field multiple-scattering Xα method within the framework of the Watson-sphere-terminated molecular cluster model. The substitutional noble gas atoms are found to inhibit the rebonding of the first neighbor's dangling bonds through orthogonality repulsion. The interstitial nobel gas atoms induce empty shallow levels close to the bottom of the conduction band. We tentatively relate these levels to the emission bands observed for silicon crystals implanted with helium, neon, and argon.

A b i n i t i o calculations of 29Si NMR chemical shifts for some gas phase and solid state silicon fluorides and oxides

A b initio coupled Hartree–Fock perturbation theory (CHFPT) employing near Hartree–Fock basis sets has been used to calculate the 29Si NMR chemical shifts of SiF4(Td), SiF−5 (D3h), SiF−26 (Oh), and SiO−44 (in both Td and C3v geometries). The increase in the shielding constant, σ, from SiF4 to SiF−26 is calculated to be 114 ppm, compared to an experimental value of about 75 ppm, while the decrease in σ between SiF4 to SiO−44 is calculated to be 43 ppm, compared to an experimental value of about 40 ppm. These results indicate that CHFPT applied to properly chosen molecular cluster models for solids can accurately reproduce experimental trends in solid state NMR chemical shifts. Calculations on SiF4 and SiO−44 for different internuclear distances also establish that the chemical shift is very weakly dependent on distance, suggesting that observed correlations between chemical shift and average Si–O distance in silicates arise indirectly, through the relationship between degree of polymerization and the average Si–O bond distance. By contrast, a C3v distorted SiO−44 tetrahedron (one bond 1.584 Å long and three bonds 1.651 Å long) gives an anisotropy in the chemical shift tensor of 54 ppm, with the larger value of σ occurring along the direction of the short Si–O bond, in reasonable agreement with available experiment. The calculations also support the use of the simple superimposed free atom approximation for the diamagnetic contribution to σ. For the Td species the paramagnetic contribution is shown to be dominated by excitations from the t2 σ orbitals to the σ* orbitals, as suggested previously on qualitative grounds. It may therefore be possible to interpret trends in σ by focusing on the energies and compositions of the t2 σ orbitals.

Theoretical Studies of Defects in Binary and Ternary Oxides

In the past decade, there has been an explosive development of computational techniques utilizing high-speed computers to study the electronic and atomic structural properties of solids. These techniques form an important compliment to laboratory experiments for providing a better understanding of spectroscopic properties, as well as the energetics of the solid systems. For ideal metallic and semiconducting crystal lattice with translational symmetry, the conventional energy band structure approaches are capable to provide a good degree of precision in both electronic structure and system energies. On the other hand the molecular-cluster model represents a convenient method of studying those properties that are primarily a function of the local environment of the system, such as vacancy, substitutional and interstitial defects.

Ab initio SCF MO and modified electron gas studies of electron deficient anions and ion pairs in mineral structures

Ab initio SCF MO calculations on small molecular cluster models of solids have recently yielded equilibrium bond distances and angles with an accuracy rivaling that of analogous calculations on small gas phase molecules. Modified electron gas (MEG) calculations also yield accurate bond distances although they give much larger errors in cohesive energy than do the ab initio calculations. The MEG method has been mainly used to calculate the interaction energies of closed shell atoms and ions. However, recent work suggests that non-closed shell electron-deficient anions such as CO30 may occur in minerals. Similarly, IR studies on CO2 dissolved in silicates suggests the presence of ion pairs such as MgO2CO. Such species are here studied using both ab initio SCF and MEG methods.

Comment on ‘‘A proposal for the proper use of pseudopotentials in molecular orbital cluster model studies of chemisorption’’

In recent SCF calculations for M5CO clusters (M=Cu, Ni, Al), Bagus et al. found that serious errors arise when pseudopotentials are introduced for the Cu and Ni atoms. Using the Cu pseudopotential and basis set given by Bagus et al., in SCF/CI calculations for Cu2, we find that serious errors arise indeed, but that the bulk of these errors can be eliminated by (i) a proper account of core–core interaction and (ii) enlargement of the basis set.

Bonding Character of β-LiAl Crystal Containing Li Vacancy

The electronic structure and bonding character of β-LiAl has been studied by a molecular cluster model to clarify the electronic effects on the Li diffusion. The interactions of Li–Li, Li–Al and Al–Al are discussed using the Mulliken population analysis. It is found that the Li–Al and the Al–Al bonds are relatively strong, compared with the Li–Li one. The Li–Al bond is considered unfavorable for the Li diffusion. A formation of Li vacancy causes a redistribution of electron density which effectively contributes to the stabilization of the system. It is also found that the electron distribution in the Li–Al bond changes into a favorable one for the Li diffusion when the vacancy is formed.

Vibrations of CO chemisorbed on metal surfaces: Cluster model studies

The molecular orbital cluster model has been used to study the vibrations of CO interacting with metal surfaces. In all cases the equilibrium CO geometry is taken normal to the surface with C directly above a metal atom; SCF and correlated CI wave functions have been obtained. For CO/Cu(100), we have studied the C–O and Cu–C stretch modes. The C–O frequency ωe and effective charge e* have been analyzed in terms of σ and π contributions; the adsorption site metal π, 3dπ, and 4pπ, donation to CO 2π* contributes in a major way to e*. The ωe and e* for the C–O stretch have been compared for one metal atom–CO clusters of Cu, Ni, and Fe. The ωe decrease in the order Cu, Ni, and Fe; the e* increase in the same order. This is to be expected from the order of the metal dπ to CO 2π* donation and bonding which is Fe>Ni>Cu.

Self-consistent cluster calculation of binding energy and potential for positive muons in copper and copper-impurity systems.

The binding energy, potential profile, and electronic structure for positive muons in copper are calculated with the use of a molecular-cluster model in the framework of the self-consistent local-density theory. Spin polarization was considered in calculations on finite clusters including ${\mathrm{Cu}}_{14}$ and an interstitial positive muon. Different positions of the muon along the body diagonal [111], and slightly displaced from the diagonal, covering the path between octahedral O to tetrahedral T sites were considered. Both the binding energy \ensuremath{\Delta}${E}_{\mathrm{tot}(\mathrm{r}\ensuremath{\rightarrow})}$ and the muon potential ${V}^{\ensuremath{\mu}}$(r\ensuremath{\rightarrow}) exhibit a double minimum, with the O site more stable. The effects of Cu vacancies and Ni impurities on the muon in copper are considered also. Binding-energy curves show the attraction of the Cu vacancy and Ni impurity for the muon. Valence-charge-density distribution profiles for different positions of a muon along the [111] direction in \ensuremath{\mu}-${\mathrm{Cu}}_{14}$, \ensuremath{\mu}-${\mathrm{Cu}}_{13}$, and \ensuremath{\mu}-Ni-${\mathrm{Cu}}_{13}$ clusters are calculated.

Electronic Structure of Mercury, Gold and Platinum Impurities in Silicon

AbstractThe electronic structures of substitutional and tetrahedral-site interstitial Hg+, Auo and Pt− isoelectronic impurities in silicon have been analysed. The centers are theoretically described by the Watson-sphereterminated molecular cluster model within the framework of the multiplescattering Xa formalism. At the substitutional sites the centers are related to the “vacancy” model recently proposed to describe the properties of the elements at the end of the transition-metal series. At the interstitialsites the impurities introduce a hyperdeep s-like level close to the bottom of the valence band and, in agreement with experiments, do not show shallow donor activities. For all the analysed centers the d-states remain fully occupied below, or within, the valence band.

Electronic structure of gold substitutional impurity in silicon

The electronic structure of Au+, Au0 and Au-substitutional impurities in silicon are calculated within the framework of the self-consistent-field multiple-scattering molecular cluster model. The results show that centres behave basically as a 'perturbed' silicon vacancy with a filled gold-derived atomic d level localised below the bottom of the crystal valence band.

A proposal for the proper use of pseudopotentials in molecular orbital cluster model studies of chemisorption

The interaction of CO with Cu5, Ni5, and Al4 are treated as model systems for molecular adsorption on metal surfaces. The effect of the use of pseudopotentials for the metal atoms is studied by considering three types of clusters. In the first case, all of the metal electrons are explicitly included in the wave function; an all electron (AE) treatment. In the second case, the metal atom which directly interacts with the CO is described by as AE but the remaining metal atoms include a pseudopotential for their core electrons. Finally, in the third case, all of the metal atoms in the cluster have a pseudopotential treatment for the core electrons. The AE cluster results are taken as reference values for the two pseudopotential treatments. The mixed cluster results are in excellent agreement with those of the all AE clusters; however, the results for the all pseudopotential cluster of Ni5CO or of Cu5CO are qualitatively different. The pseudopotential treatment for all of the metal atoms often leads to results that contain serious errors and it is not a reliable approach.

Electronic structure of a single neutral ideal phosphorus vacancy in GaP

The multiple-scattering Xalpha molecular cluster model is used to carry out self-consistent calculations of the electronic states of an isolated P vacancy in GaP. A fully occupied singly degenerate a1 level and a threefold-degenerate t2 level occupied by one electron are found within the band gap. This configuration indicates that the centre is unstable with respect to Jahn-Teller distortions. The vacancy states a1 and t2 are quite extended showing an appreciable charge distribution in the next-nearest neighbours of the vacancy (P atoms). The role played by these results in the explanation of the properties of the GaP:O centre is discussed.

Electronic structure of the linear-chain solid KTCP

The recently proposed multiple-scattering generalized partitioning molecular cluster model is used to calculate the electronic states of the [Pt (CN) 4 2-] dimer units. The obtained results are related to the electronic structure of the tetracyanoplatinate precursor salt KTCP. The mechanism that places the d z 2 - like band at the Fermi level in KCP quasi-one-dimensional conducting solid is analysed.

The nature of the metal–CO interaction and bonding

The adsorption of CO on metal surfaces is represented by molecular orbital cluster models of CO at an on top site and adsorbed normal to the surface carbon end down. Ab initio SCF and MCSCF calculations are performed for several clusters. The new constrained space orbital variation CSOV approach is used to analyze the bonding and to compare CO adsorption on Al, representative of sp metals, with that on Cu, representative of transition metals. There is a large repulsion between the superposed free CO and metal charge distributions which is considerably smaller for Cu than for Al because there are fewer valence σ electrons for Cu than for Al. The CSOV analysis shows that the metal to CO π donation is much more important than the CO to metal σ donation. It is also shown that for Cu, the dπ contribution to the metal π donation is larger than the valence 4 pπ contribution. The dπ donation is compared between Fe, Ni, and Cu and this donation and the metal–CO interaction are found to be different in the order Fe>Ni>Cu.

Molecular orbital cluster model study of Cu(001)/Cl

The Cl-Cu metal chemisorption is studied using molecular orbital theory. The surface is represented by a Cu cluster. The Cu atoms are described by a relativistic effective core potential having only one (4s 1) valence electron. In particular, the Cl-Cu interlayer distance is calculated in order to complement the information obtained from recent LEED and SEXAFS studies and to calibrate the theoretical approach used.

Molecular orbital cluster model study of Cu(001)/Cl

The Cl-Cu metal chemisorption is studied using molecular orbital theory. The surface is represented by a Cu cluster. The Cu atoms are described by a relativistic effective core potential having only one (4s 1) valence electron. In particular, the Cl-Cu interlayer distance is calculated in order to complement the information obtained from recent LEED and SEXAFS studies and to calibrate the theoretical approach used.

Electronic structure calculation of V 2+O 2 complexes in silicon

The self-consistent field multiple-scattering Xα molecular cluster model is applied to calculate the electronic states of a divacancy plus two oxygen complex in silicon. The calculations were carried out for the undistorted configuration of the defect. The obtained results, which are in fairly good agreement with EPR measurements, confirm the main features of the accepted microscopic model for the Si - P2 center.