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Oxide surfaces are technologically important in a range of applications, including catalysis, corrosion, gas sensors, ceramics and high-temperature superconductivity. In recent years, computer simulation methodologies and algorithms have developed to the stage where simulation can now play a complementary role with experiment, aiding in interpretation of experimental data and predicting surface behaviour. Several different approaches to the study of oxide surfaces have been developed and their use demonstrated. Static lattice simulations allow surfaces as well as point and extended defects in highly ionic materials to be investigated using an essentially classical model with simple interionic potentials. Comparison with experimental surface segregation studies shows the great predictive power of these calculations, and indeed much expensive experimental work could now be obviated. These classical models have also proved valuable in understanding the topology of non-planar surfaces. However, when an understanding of the electronic behaviour of the system is required, for example in studying reactivity, we turn instead to quantum mechanical methods. In recent years both cluster approaches (with a suitable cluster termination to represent the bulk lattice) and periodic treatments have been used with success. Particularly in the case of periodic treatments, it is possible to assess the predicted degree of ionicity and thus to confirm or disprove the validity of the static lattice approach for various different systems. With these developments, simulation is poised to make a valuable contribution as full partner to experiment in areas such as ceramics processing and catalyst design.

Ab initio cluster calculations are reported for the interaction of CO with non-defective planar and non-planar {001} surfaces of MgO and surfaces doped with Li+, Na+, Cu+, Cu2+, Zn2+ and Al3+. Fully relaxed surface structures are obtained from atomistic simulations. Of particular concern are the binding energies of CO to the surface and the calculated charge-transfer both of which are relevant to the formation of paramagnetic anionic species which have been observed experimentally.

Defect lattice calculations are presented for planar and non-planar surfaces of MgO and FeO. Fundamental defect energies are compared for the two oxides. The relaxed topography of irregularities at the {001} surface is presented together with the energies of substitution for Ca2+ and Li+ at various low coordination sites in MgO. Band-gap energy levels in MgO are given together with their modification at the {001} surface. Finally ad-atom binding and interaction energies at the surface of MgO and FeO are reported.

The vacuum ultra-violet photoelectron spectrum of the SiO(X1Σ+) molecule has been recorded and interpreted with the aid of both ab initio molecular orbital and multiple-scattering Xα calculations. Three bands have been observed with vertical ionization potentials of 11·61, 12·19 and 14·80 eV, corresponding to ionization to the X2Σ+, A2Π and B2Σ+ states of SiO+ respectively. Estimates of r e, and D e for these ionic states have been made.

Enthalpies of segregation for isovalent impurities in magnesium and calcium oxide as a function of surface concentration were calculated by using an atomistic computer simulation method. We have considered Be2+, Mg2+, Ca2+, Ba2+, and Ni2+, segregating to both (001) and (110) faces. The results obtained can be extrapolated to predict the behavior of other impurities including Mn2+, Fe2+, and Co2+, We find, for example, that Fe2+, Mn2+, Ca2+, Sr2+, and Ba2+ will concentrate at the (001) surface of MgO, while Ni2+ will be depleted. The enthalpy of segregation is found to vary substantially with coverage particularly for the larger impurities. The enthalpy becomes less negative with increasing impurity concentration due to the increasing lattice strain until the surface is nearly saturated. Then additional stabilization is obtained by restructuring of the surface layer. We predict reconstructed surfaces for both the (001) and (110) faces, which contain a high concentration of a larger impurity ion. The enthalpy of segregation shows a maximum at around 50% surface coverage implying a bimodal surface distribution of segregant. The influence of segregation on surface energy suggests two unusual effects. The (001) surface energy of the impure crystal becomes negative for surface concentrations of impurity greater than 10% Ba2+ or 75% Sr2+ in MgO. This implies a thermodynamic barrier to sintering. At high coverages of Ba2+ in MgO the (110) surface becomes more stable than the (001) face suggesting that facetting may occur.

The authors use a combination of lattice simulation calculations and ab initio quantum mechanical techniques to study the adsorption behavior of methanol in ZSM-5. We locate the low-energy adsorption sites for the methanol molecule inside the pores of the ZSM-5 zeolite using lattice simulation techniques. Electronic structure calculations are carried out on the cluster representing the adsorption complex, while an array of point charges are included to represent the long-range electrostatic effects. We propose a dissociation mechanism for methanol at the Broensted acid site of this zeolite.

This paper reports fundamental defect energies in CsF, β-CsCl, CaBr 2 , CaI 2 , Ga 2 O 3 , Ti 2 O 3 , Rh 2 O 3 and V 2 O 3 obtained by simple extrapolation procedures, and in CaCl 2 by direct atomistic simulation. It is suggested that CsF, β-CsCl and CaBr 2 will exhibit mixed lattice disorder, and that in Ti 2 O 3 , Rh 2 O 3 and V 2 O 3 Schottky and anion Frenkel energies differ by less than 1 eV. The implications of mixed disorder for the interpretation of Arrhenius energies of diffusion are examined. For CsF and β-CsCl these are shown to be of the usual type, whereas the temperature dependence of the diffusion coefficients in CaBr 2 is predicted to be more complicated.

The present paper is concerned with calculated energies of lattice and electronic disorder in thoria. From these we deduce the fundamental defect structure, electronic energy levels and oxidation-reduction potentials. This enables us to re-assess the reported diffusion and electrical conductivity data and to suggest alternative defect mechanisms for these processes.

A theoretical study of the segregation of titania (TiO2) at the (001) surface of magnesium oxide (MgO) based on atomistic simulation methods is reported. It is suggested that titanium ions in MgO exist almost exclusively as neutral impurity-vacancy pairs. The stability of those at the surface relative to the bulk is estimated, and from this the effective enthalpy of segregation is deduced. Finally the segregation behaviour of TiO2 in MgO is compared with that of CaO.

Atomistic simulation methods have been used to calculate the energetics of substitution and segregation of calcium ions near and at the {001} and {110}¦ surfaces of magnesium oxide at thermal equilibrium. Defect clusters and complete planes of segregating ions have been considered, thereby including impurity-impurity interaction terms. Calculated enthalpies of segregation of −0.42 and −0.78 eV, derived from different interatomic potentials, are in good agreement with the experimental heat of segregation of −0.78±0.22 eV reported recently by Wynblatt and McCune. A simple statistical mechanical theory leads to an Arrhenius expression for large crystals and the deviation from this behaviour expected in microcrystallites.

In this paper we report a theoretical calculation of vibration-rotation transition wavenumbers and transition moments for HD + , HT + , and DT + for v , N ≤ 5. The results for HD + agree with the experimental results to within 0.015 cm −1 .

Existing theories of the relative dipole moments in singlet and triplet states have been re-examined, and calculations are presented for NH, CH2 and a fictitious molecule with nuclear charges 1.1 and 0.9 au. The usual assumption that electrons are farther apart in the triplet is found to be questionable. Changes in inner molecular orbitals are also more important than was believed previously.

The form of the effective Hamiltonian for a diatomic molecule in an electronic state intermediate between Hund's cases (a) and (b) is reexamined. The derivation is performed in three stages: (i) an electronic contact transformation removes the effects of matrix elements which couple different electronic states; (ii) a vibrational contact transformation removes matrix elements coupling different vibrational states; and (iii) a spin-rotational contact transformation removes indeterminacies in the final Hamiltonian. Expressions for the effective parameters resulting from these transformations are presented. The Hamiltonian is in a convenient form for fitting to experimental data, and the formulas for the parameters assist in the comparison with ab initio calculations. The relations between the present parameters and those employed in the computer program of Zare, Schmeltekopf, Harrop, and Albritton [J. Mol. Spectrosc. 46, 37–66 (1973)] are given, and make it possible to correct a previous misunderstanding regarding the value of the spin-rotation parameter γe in the X2Π state of HCl+. The parameters obtained for this state are compared with ab initio calculations which take account of first-order perturbations within the state and second-order perturbations from the A2Σ+ state and from the four states of the configuration … σ 2 π 2 σ ∗ . The A2Σ+ state is the dominant perturber, but the contributions from the other states are not negligible. For example, their contribution to γe is larger than the first-order contribution.

The vacuum ultraviolet photoelectron spectra of BrF (X1Σ+) and IF (X1 Σ+) have been recorded and interpreted with the aid of both MS — Xα — SCF calculations and ab initio calculations. For both BrF and IF the first band is split by spin—orbit coupling into two components corresponding to ionization to the X2Π 3 2 Phytochemistry and X2Π 1 2 ionic states. Estimates of re, ḡwe and De for these states have been made.

The influence of impurity polarisability and surface unit cell size are examined in relation to the segregation of Ca2+, Sr2+ and Ba2+ at the (001) surface of MgO. It is shown that the inclusion of polarisability increases the calculated heat of segregation for all three impurities. Increasing the unit cell size from that previously used leads to a more extensive surface reconstruction for monolayer coverage by Ba2+ but essentially the same structures for Ca2+ and Sr2+.

It is shown that for H+2 and its isotopes, the electronic Schrodinger equation involving the electron rest mass me can be related in a simple way to that involving the electron reduced mass μe = me(ma + mb)/(me + ma + mb) by a straight-forward scaling of all distances in the first of these equations by μe/me. A numerical comparison of the two approaches is made at the adiabatic level of approximation for HD+, and it is seen that any differences would have only a negligible effect on the calculated vibration-rotation spectrum.

Ab initio calculations of the effective spin-spin parameter λ, and of electric dipole intensities for the forbidden 1Σ+-3Σ- transition, are reported for NH, NF, PH, PF, NCl and SO, and values of λ alone are calculated for O2 and S2. In general the values of λ agree to within 10 per cent with the experimental values, and the calculations enable the apparently irregular variation of λ within this class of molecules to be explained. The effect on λ of several approximations has been investigated, and it is found that the simplest model considered gives reasonable agreement with experiment, as others have found in comparable cases. This model employs single configuration wavefunctions in which the 3Σ- orbitals are used to represent the isoconfigurational 1Σ+ state; only the interaction with this one 1Σ+ state is included, and only one-centre spin-orbit integrals are retained. Values of λ were calculated at three internuclear separations bracketing the experimental equilibrium separation, so that the vibration...

This paper describes the study of the -OH group in ZSM-5 zeolite. The importance of zeolite ZSM-5 and the advantages in studying the OH groups by computer simulation techniques are highlighted. The methodology followed in the present study, which is a combination of classical and quantum-chemical calculations, is briefly described. The basis set SV3-21G has been chosen following trial calculations performed with different standard sets of basis functions. Results of geometrical optimizations carried out to determine the position of hydrogen in the ZSM-5 lattice are reported. The size of the point-charge (PC) cluster is varied and its effect on the calculated properties of the hydroxyl group is discussed. Calculations on a larger quantum-chemical (QC) cluster containing the hydroxyl group in both normalized and experimental structures reveal that geometry is an important factor for electronic properties. The procedure for generation of a suitable PC cluster to represent the rest of the lattice is described. Results of a calculation for a cluster model of 82 ions (PC cluster) in which a Si 2 O 7 (QC cluster) entity is explicitly treated by ab initio procedures, are discussed. The reported parameters include the O-H vibrational frequency, the proton binding energy and the aluminium substitution energy and we discuss their implications for the catalytic properties.

Alkali metal trapped hole centres are usually unstable species, but there is experimental evidence that spectroscopically identical, stable centres can be formed in alkaline earth oxides. The “microgalaxy” model has been proposed to explain the stability of these centres. We have used static lattice modelling procedures to investigate several features of alkali metal doped alkaline earth oxides and in particular the nature of the impurity-hole interaction. We have calculated solution energies for a range of alkali metal oxides in alkaline earth oxides. The results indicate systems which, thermodynamically at least, are easier to form than those studied experimentally so far. It seems, however, that microgalaxy formation is controlled more by kinetic effects, and preliminary ionic migration calculations bear this out. We have also studied the stabilities of isolated trapped hole defects with respect to the free hole (calculated to be a large polaron) in alkaline earth oxides. These results, and calculated barrier heights to decay of the centre, are in qualitative agreement with experiment. The stabilities of a range of small clusters of alkali metal trapped hole centres were studied and indicated greater thermodynamic stability with increasing size.

Calculations of the thermal band gap, ionisation energy and O(2p) valence band width are reported based on defect lattice methods. From these it is estimated that the large polaron is the preferred hole state in α-Al2O3 by about 0.4 eV. Theoretical values for the optical and thermal energy levels of Ti3+ in α-Al2O3 are also reported.

A quantum chemical cluster (QCC) is treated explicitly by an ab initio technique, and is embedded in a point charge cluster (PCC). The latter is chosen to represent the long-range electrostatic terms in the zeolite lattice. Calculations have been carried out on a series of zeolite clusters namely, Zeolite-A(LTA), ZSM-11(MEL), ZSM-5(MFI), Offretite(OFF), Mordenite(MOR), Faujasite(FAU) and Zeolite-L(LTL). The predicted acidic properties of these zeolites, the effect of the substitution of silicon by aluminium or boron and the values of the vibrational frequency are reported and compared with experimental data.

For the most part the atomistic simulation of ceramics has been concerned with bulk material and, in particular, with structural features and defect properties that are well-established, at least in principle, if not always known in quantitative detail [1]. The simulation of ceramic surfaces on the other hand, in most cases breaks new ground, for here knowledge and understanding at an atomic level are still both sparse and rudimentary [2]. For example, it is only very recently that information on the crystal structure and relative stability of the lowest index surfaces of α-alumina has become available, solely from simulation studies [3], although the (bulk) properties of alumina have been investigated extensively for many years. The same is true for impurities. They are known to exert an important, often controlling, influence on the properties of ceramics, yet phenomena such as surface segregation remain largely unexplored. The present chapter, then, gives a brief review of some recent atomistic simulations of impurity segregation at the lowest index surfaces of MgO and CaO. The aim here is to illustrate the variety of behaviour, the level of detail and the unexpected nature of the results that such studies can sometimes reveal. In so doing it might also prompt futher experimental investigation into this important aspect of ceramic materials.

Computations of the structural consequences of segregation of Ba 2+ at monolayer and submonolayer coverages on (001) surfaces of MgO indicate extensive reconstruction. The predicted reconstruction for Ba 2+ /MgO contrasts sharply with insignificant reconstruction reported for pure MgO surfaces. Results are described for experimental comparisons of the surface luminescence and surface reactivity of high surface area samples of Ba 2+ /MgO with MgO and BaO. Extent of agreement is assessed between the observed Ba 2+ -related effects and these working hypotheses: (i) that the Ba 2+ induces surface reconstruction of the type calculated, to yield surface anions and cations in positions of altered, but non-integral, coordination; (ii) that photoexcitation of electrons at such O 2- cus sites are responsible for enhanced luminescence: and (iii) that Ba 2+ cus sites are involved in enhanced reactivity towards N 2 O at 300K.

This paper describes a methodology used to study sorption properties of molecules in zeolites. The method involves a combination of computer simulation techniques and quantum chemical calculations. As a specific example, the results of the calculations for the adsorption of methanol molecule in ZSM-5 zeolite are reported. The interaction energy of the methanol molecule with the framework atoms of the zeolite is calculated, as the methanol moves along the straight channel. The favourable adsorption sites are deduced based on the calculated values of the interaction energy. Non-empirical quantum, chemical calculations have been performed on the ZSM-5: methanol adsorption complex and its dissociation mechanism is proposed based on the results.

We describe a computer simulation method involving the combination of lattice energy calculation and quantum chemical (ab initio) calculation to characterise the active sites in ZSM-5 zeolite. The position and charge of atoms in point charge (PC) clusters are modified to obtain the gradient of force and the Madelung energy on hydroxyl group appropriate to the infinite lattice. A detailed survey of the properties of the −OH group in ZSM-5 is reported.

Preliminary ab initio calculations at the SCF level and beyond are reported for the chemisorption of H2 and CO at the (001) surface of MgO. It is concluded that the dissociative chemisorption of H2 requires the presence of defects and that at anion vacancies, V− centres and self-trapped holes the overall process is exothermic in each case. It is predicted to be non-activated at anion vacancies and possibly the same at the other two defects. Binding energies are calculated for the interaction of CO with a non-defective (001) surface of MgO and at impurity ions therein. They range from 2.5 kcal/mole at Al3+ to 20.8 kcal/mole at Cu2+ and are shown to be highly sensitive to lattice relaxation of the defective surface.

Defect lattice and ab initio SCF calculations are reported for defective non-planar surfaces of MgO. It is suggested that the concentration of free vacancies and Ca2+ will be much lower at non-planar irregularities than at planar surfaces and in the bulk, whereas the level of Li+ and trapped holes will be higher. The binding of H atoms and CO to three-coordinated comer sites is found to be appreciably higher than to the five-coordinated {001} surface. Thus it is concluded that calcium doping of MgO will affect neither CO chemisorption nor the dissociative chemisorption of hydrogen whereas lithium doping will influence both.

The adsorption of a series of molecules at the (001) surface of MgO and at an impurity Cu + ion therein has been studied by means of a combination of ab initio molecular orbital and lattice defect methods. The molecular species investigated include CO, HCO, HOC, H 2 CO and HCOH, and CH 3 O and CH 2 OH, all of potential importance in CO/H 2 chemistry. Binding energies of each species adsorbing either through carbon or oxygen have been derived from SCF studies using split-valence basis sets throughout. Additional calculations involving more flexible basis sets, with incorporation of electron correlation have also been performed. Binding through oxygen leads to very similar relative stabilities of the minima on both [CH 2 O] and [CH 3 O] potential energy surfaces to those predicted for the “free” gas-phase species, and is in general the energetically preferred mode of interaction when binding with an Mg 2+ ion of the non-defective surface. Binding through carbon is the energetically preferred path in interactions with the Cu + dopant ion, however, leading to significant changes in the “free” species energetics. This enhanced binding is attributed to the contribution from π back-donation, an effect which is of importance only in interactions with the dopant ion and which is found to be sensitive to the incorporation of electron correlation.

Calculated activation energies for cation vacancy migration in the presence of Ca 2+ Mg , Al 3+ Mg , Sc 3+ Mg impurity substitution ions are reported. The results are related to the recent experimental observations of vacancy mobility by Sempolinski and Kingery.