Search

DFT calculations of the Li substitutional defect in diamond based on the B3LYP functional and a 64-atom supercell indicate that (i) the quartet (Sz = 3/2) state is lower in energy than the doublet (Sz = 1/2) state by 0.07 eV (810 K) for fully relaxed static structures and by 0.09 eV (1045 K) with the inclusion of zero-point vibrations, (ii) the effective charges at the Li and four neighbouring C sites are similar in the two spin states, but there are substantial differences in the corresponding spin distributions, and (iii) there are unprecedented differences in the Raman spectra of the two spin states, in terms of both frequency distributions and intensities, that can most reasonably be attributed to strong spin-phonon coupling, in view of the very similar charge distributions in the two states. These differences are an order of magnitude greater than those reported previously for any bulk transition metal or rare-earth compound. The basis sets and functional used in these calculations predict many of the relevant constants (a0, c11, c44) of diamond mostly to within 1% of the experimental values, most notably the TO(X) Raman frequency and the phonon density of states. Comparisons with the calculated Raman spectra of the quintet (Sz = 2) and singlet (Sz = 0) spin states of the neutral vacancy defect, which have similar spin distributions at the four neighbouring C atoms (Cn) to the vacancy site as those at the corresponding Cn sites in the quartet and singlet states of the Li defect, show that the differences in the two Raman spectra of the latter defect are closely related to those in the former.

EPR data of the positively charged N2 defect (N+2) are reported from all-electron calculations based on the B3LYP hybrid functional using a local (Gaussian type) basis set, within a supercell scheme, as implemented in the CRYSTAL code. The Fermi contact Aiso term, the components of the hyperfine coupling tensor, , and the electric field gradient (only P‖ is available) are all in excellent agreement with two independent sets of experimental data, with errors of less than 4%. The equilibrium geometry, electronic structure, and IR and Raman spectra are also computed, where the two spectra are compared with those of the neutral N2 and double positive N++2, both of which have closed shell ground states. In particular the IR and Raman spectra of the three species exhibit important differences. Information on the charge, spin and geometry of defective species derived from experimental EPR data are based mostly on relatively simple models; here they are obtained directly from rigorous quantum mechanical simulations. It is shown that the extrapolation from the experimental EPR data can lead to relatively serious errors.

The local geometry, electronic structure, and vibrational features of three vicinal double interstitial defects in diamond, ICIC, ICIN, and ININ, are investigated and compared with those of three "simple" ⟨100⟩ interstitial defects, ICC, ICN, and INN, previously reported by Salustro et al. [Phys. Chem. Chem. Phys. 20, 16615 (2018)], using a similar quantum mechanical approach based on the B3LYP functional constructed from Gaussian-type basis sets, within a supercell scheme, as implemented in the CRYSTAL code. For the first time, the Fermi contact term and hyperfine coupling tensor B of the four open shell structures, ICIC, ICIN, ICC, and ICN, are evaluated and compared with the available experimental EPR data. For the two double interstitial defects, the agreement with experiment is good, whereas that for the single interstitials is found to be very poor, for which a likely reason is the incorrect attribution of the EPR spectra to uncertain atomic details of the micro-structure of the samples. The infrared spectra of the three double interstitial defects exhibit at least two peaks that can be used for their characterization.

The lattice structures, electronic characteristics and spectroscopic features of the three vicinal substitutional, spin zero defects, Ns-Ns (A-centre), Bs-Bs, and Bs-Ns in diamond are reported. They are derived from all-electron B3LYP calculations based on Gaussian basis sets, within a periodic supercell scheme, including both 64- and 216-atom cells. The local geometry reflects the differences between the strong C-C bond of the host lattice and the weaker impurity-impurity bonding in the defective systems. The band structures show two occupied bands 1.06 eV above the VBE for Ns-Ns, and empty bands 3.36 eV and 0.25 eV below the CBE for Bs-Bs and for Bs-Ns respectively. The IR spectra of Bs-Bs and Ns-Ns contain sharp peaks at 631 cm−1, 692 cm−1 and 1373 cm−1, and 451 cm−1, 571 cm−1 and 1276 cm−1, respectively, which might reasonably be considered as ‘finger prints’ for these systems. For Bs-Ns, a set of medium intensity absorptions are predicted at 890 cm−1, 945 cm−1, 1018 cm−1, 1078 cm−1 and 1281 cm−1. However, numerous peaks in this region have been predicted for other defective systems, so that the firm identification of Bs-Ns based on these frequencies is much less certain than Bs-Bs and Ns-Ns.

International audience; 97 Total downloads11 citation on Dimensions.Turn on MathJaxGet permission to re-use this articleShare this article Share this content via email Share on Facebook Share on Twitter Share on Google+ Share on MendeleyArticle informationAbstractThis paper reports calculated energies and electronic structures of O(2p), O(2s) and Al(2p) excited states in bulk -Al2O3, at the and surfaces and in the presence of O vacancy defects, obtained from all-electron HF, B3LYP, GGA and LDA calculations based on a recently described direct -SCF approach (Mackrodt et al 2018 J. Phys.: Condens. Matter 30 495901). The closely related frequency-dependent optical constants derived from B3LYP calculations within the CPHF/DF framework are also reported, where both sets of results are shown to compare favourably with the experimental spectra. The differences between the directly calculated excited state energies, which in -Al2O3 are equal to the leading excitation edges, based on the four functionals, are substantially less than the differences between the corresponding (ground state) band gaps, as reported previously for AFII NiO (Mackrodt et al 2018 J. Phys.: Condens. Matter 30 495901). For the B3LYP functional, these energies are 8.7 eV, 12.5 eV and 73.7 eV for the O(2p), O(2s) and Al(2p) excitations respectively. The O(2p) edge is predicted to be degenerate, with distinct excitations from O(2p) states that are parallel to and perpendicular to the c-axis, in agreement with the reported spectra (Tomiki et al 1993 J. Phys. Soc. Japan 62 573). Detailed analyses of the charge and spin distributions in the four bulk excited states indicate that these are essentially charge-transfer excitonic, with acceptor sites at the nearest neighbour positions. Despite the close proximity of the O() and O(2p) excited state energies, the charge and spin distributions are predicted to be quite different.

This paper reports calculated energies and electronic structures of nineteen excited states in NiO based on a Δ-SCF approach reported previously for the [Formula: see text] transitions in NiO and Sr2CuO2Cl2. They are the spin-flip: [Formula: see text]; eight [Formula: see text]: (one electron) 3A2g → 3 T 2g , (two electron) 3A2g → 3 T 1g , 3A2g → a 1 E g , 3A2g → 1 T 2g , 3A2g → 1 T 1g , 3A2g → b1 E g , 3A2g → b1 T 2g ; two O(2p) → Ni(3d); seven Ni(3d) → O(2p) (including two spin-flip) and the O(2s) → Ni(3d) charge transfer excitations, which span an energy range from 0.25 eV to 17.53 eV, and include the fundamental band gap associated with an excitonic O(2p) → Ni(3d) transition at 4.23 eV. These are compared to absorption and emission spectra, and previous calculations. In the case of the O(2p) → Ni(3d) excitations, comparisons are given for gap and Γ-point energies derived from HF, PBE0, HSE06, B3LYP, B1WC, GGA and LDA one-electron approximations. Finally, the directly calculated Stokes shifts and associated luminescence energies for the two O(2p) → Ni(3d) transitions are reported, where the excitonic value is found to be in good agreement with the recently reported experimental value.

This paper reports the calculated relaxed lattice configurations and corresponding electronic and magnetic structures, and Raman frequencies of two divacancies in diamond, $$V_2$$ and VC=CV, in which the vacancies are first and third neighbours, respectively. The calculations are formulated within a supercell approach to local defects in crystalline solids, here 64- and 128-atom unit cells and based largely on the B3LYP one-electron approximation constructed from an all-electron Gaussian basis set. Three important findings are first, that, of the four possible spin states, $$S_z=$$ 0, 1, 2, 3, the singlet is predicted to be lowest in energy for both divacancies; second, that the singlet state of $$V_2$$ is $$\sim$$ 1.7 eV lower in energy than that in VC=CV; and third, that the Raman peak at 1628 cm $$^{-1}$$ in defective diamond can be ascribed to the presence of a C=C double bond, as in the singlet state of VC=CV.

This paper reports the fully-relaxed lattice and electronic structures, vibrational spectra, and hyperfine coupling constants of the substitutional Ns defect in diamond, derived from B3LYP calculations constructed from all-electron Gaussian basis sets and based on periodic supercells. Mulliken analyses of the charge and spin distributions indicate that the defect comprises a single unpaired electron distributed very largely over both the negatively-charged substituted site and one of the four nearest-neighbour carbon sites, which relaxes away from the impurity. This leads to a local C3v symmetry, with the nitrogen ‘lone pair’ lying along the C3 axis and pointed towards the ‘dangling’ bond of the shifted carbon neighbour. The calculated band gap is 5.85 eV, within which a singly-occupied, majority spin donor band is found ∼2.9 eV above the valence band, and an unoccupied, minority spin acceptor band ∼0.9 eV below the conduction band. Atom-projected densities of states of the donor and acceptor levels show that, contrary to a widespread description, ∼30% only of the donor band derives from nitrogen states per se, with the majority weight corresponding to states associated with the shifted carbon atom. The defect formation energy is estimated to be ∼3.6 eV. The calculated IR spectrum of the impurity centre shows several features between 800 and 1400 cm−1, all of which are absent in the perfect crystal, for symmetry reasons. These show substantial agreement with recent experimental observations. The calculated hyperfine constants related to the coupling of the unpaired electron spin to the N and C nuclei, for which the Fermi contact terms vary from over 200 MHz to less than 3 MHz, are generally in good agreement with the largest experimental values, both in terms of absolute magnitudes and site assignments. The agreement is less good for the smallest two values, for which the experimental assignments are less certain. The results lend support to previous suggestions that some of the weaker lines in the observed spectra, notably those below ∼7 MHz, which are difficult to assign unambiguously, might result from the overlap of lines from different sites.

The vibrational Infrared and Raman spectra of six interstitial oxygen defects in silicon containing a Si-O-Si bridge between adjacent Si atoms are obtained from all-electron B3LYP calculations within a supercell scheme, as embodied in the CRYSTAL code. Two series of defects have been considered, starting from the single interstitial defect, O1. The first consists of four defects, O1,n, in which two O1 defects are separated by (n - 1) Si atoms, up to n = 4. The second consists of four defects, On, in which nO1 defects surround a single Si atom, with n = 1-4, where O4 has the same local nearest neighbor structure as α-quartz. For both series of defects, the equilibrium geometries, charge distributions, and band structures are reported and analyzed. The addition of 1-4 oxygen atoms to the perfect lattice generates 3-12 new vibrational modes, which, as a result of the lighter atomic mass of O with respect to Si, are expected to occur at wavenumbers higher than 521 cm-1, the highest frequency of pristine silicon, thereby generating a unique new Raman spectrum. However, only a small subset of these new modes is found in the spectrum. They appear at 1153 cm-1 (O1), at 1049 cm-1 and 1100 cm-1 (O1,2), at 1108 cm-1 (O1,3), at 1130 cm-1 and 1138 cm-1 (O1,4), and 773 cm-1, 1057 cm-1, and 1086 cm-1 (O4), and can be considered "fingerprints" of the respective defects, as they are sufficiently well separated from each other. Graphical animations indicate the nature and intensity of each of the observed modes which are not overtones or combinations.

Ordered BaO overlayers have been grown on MgO(001) by successive cycles of Ba deposition, oxygen exposure and high temperature annealing. XPS was used to quantify the Ba coverage. The overlayers adopt the lattice spacing characteristic of bulk BaO for coverages in excess of 3 monolayers. Owing to the near equality between a 0 (BaO) and 2 a 0 ( MgO ) the {20} LEED spots from BaO lie close to {11} spots from the substrate. Ionic model calculations confirm that the surface structure proposed for BaO on MgO is energetically favoured with respect to alternative configurations.

The basic approaches to the computer simulation of ionic solids are briefly reviewed, leading to a strategy for the calculation of the heat of segregation of cation dopants in metal oxides. It is shown that equilibrium surface coverages of dopant cations can be derived from simulation studies if due account is taken of the variation of segregation energy with surface coverage. Isovalent dopants in MgO are considered in detail and comparison is made with experimental work on Ca/MgO(001) and Ba/MgO(001). The behaviour of isovalent dopants in Al2O3 is more complex owing to major surface relaxation effects in the pure material and the existence of several different low index surfaces of comparable energy. However comparison with experimental work on Y/Al2O3 is encouraging. The behaviour of aleovalent dopants is illustrated with respect to Ti in MgO and Mg in Al2O3. In both cases the simulation studies treat a neutral dopant-vacancy complex.

Direct calculations are reported of the one-electron d(xy)→d(x 2 − y 2) and d(xy)→d(z 2) and two-electron d(xz, yz)→d(z 2, x 2 − y 2) crystal-field excitations in NiO based on first principles calculations within the B3LYP hybrid scheme. It is shown that within this scheme, calculations at the limit of exact exchange lead to the most satisfactory overall agreement with the experimental spectra, and that for the localized basis set used in this study the stability limit of the excited states is between 30% and 40% exact exchange for the AF2 and ∼20% for the FM spin alignments. A mapping of the crystal-field Hamiltonian suggested by Kanamori onto the directly calculated ground and excited state total energies leads to values of the crystal-field, ΔCF, and the Racah B parameters which are close to those obtained previously from spectroscopic and theoretical studies. There is also close agreement between the two-electron excitation energy obtained from the Kanamori Hamiltonian and that calculated directly. It...

Calculations are reported of the enthalpies of mixing of MnO/MgO and NiO/MgO based on temperature-dependent lattice statics and dynamics and ab initio periodic Hartree-Fock methodology with a posteriori corrections for electron correlation derived from density-functional theory. For MnO/MgO both methodologies predict enthalpies of mixing that are close to those reported by Hahn and Muan (J. Phys. Chem. Solids, 1961, 19, 338). For NiO/MgO, on the other hand, classical simulations predict positive deviations from ideality in contrast to Hartree-Fock calculations which predict small negative deviations in agreement with the experimental data of Davies and Navrotsky (J. Solid State Chem., 1981, 38, 264).

Hybrid spin unrestricted Hartree?Fock density functional theory (UHF-DFT) calculations of LixNi1?xO indicate that within the range of exact exchange for which the electronic structures of the associated point defects, , and are insulating, is a largely inert defect with negligible effect on the electronic, magnetic and excitonic properties of the NiO host lattice. Over this range of exact exchange the free hole, , is essentially d8L in nature, or O? in chemical terms, with strong spatial and spin polaronic character. The differences in the electronic properties of the free, , and bound, , hole, notably the d8L?d9 gap, are minimal so that their separate identification would seem to be unlikely.

First-principles, periodic, spin-unrestricted Hartree-Fock (UHF) calculations predict the ground state of Immm ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ to be a highly ionic ${(d}^{9})$ insulator with strong coupling of antiferromagnetically aligned ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ spins within the corner-sharing ${\mathrm{CuO}}_{4}$ units. The distribution of ground-state valence-band states is in good agreement with He I and He II photoemission spectra with $\mathrm{O}(p)$ states occupying the upper part of the band and $\mathrm{Cu}(d)$ states the lower part. The conduction-band lower edge consists largely of $\mathrm{Cu}(d)$ states leading to essentially a charge-transfer classification. Compared with the experimental values, the local Cu spin moment is grossly overestimated and the (Ising model) coupling constant grossly underestimated, due, it is suggested, to zero-point fluctuations. Local $\stackrel{\ensuremath{\rightarrow}}{d}d$ excitons obtained directly from variationally minimized excited states are found between \ensuremath{\sim}1.2 and \ensuremath{\sim}2.2 eV, of which the lowest-energy state, ${d}_{\mathrm{xy}}\ensuremath{\rightarrow}{d}_{{x}^{2}\ensuremath{-}{y}^{2}},$ is predicted to occur within the optical gap of \ensuremath{\sim}1.5 eV. Hole states are found to be strongly polaronic, of essentially $\mathrm{O}(p)$ character and confined (at low temperature) to non-corner-sharing oxygen sites. Taking account of electron correlation, the lowest-energy hole state is predicted to be locally singlet with an unpaired O ${p}_{y}$ electron aligned antiferromagnetically to ${(d}_{{x}^{2}\ensuremath{-}{y}^{2}}{)}^{1}$ in the form of a modified (two-center) Zhang-Rice singlet. Antiferromagnetic alignment is predicted to persist (at zero Kelvin) even for hole densities of 50%.

The work of Taylor et al. [Phys. Rev. B 56, 14 380 (1997)], which calculates the free energy of three-dimensional periodic crystals and its analytic derivatives with respect to all the external and internal degrees of freedom using lattice statics and lattice dynamics in the quasiharmonic approximation, is extended to lattices which are periodic in only two dimensions. Derivatives are calculated by means of first-order perturbation theory and detailed expressions for all the lattice sums required are presented. The method is used to calculate the temperature variation of the surface free energy, surface structure, and density of states of some representative oxide surfaces. These include the {100} and {110} surfaces of MgO, the {100} surface of NiO, the {111} surface of ${\mathrm{Li}}_{2}\mathrm{O}$ and the microfaceted {110} surface of MgO. For these systems, surface free energies decrease slightly over the range of temperatures for which the quasiharmonic approximation holds.

Recent developments in the growth of ultra-thin epitaxial layers of oxides and the fabrication of a diversity of nanostructures has led to current interest in, and much speculation about, the properties of low dimensional systems. In this paper we report recent calculations for low dimensional NiO on MgO(100) surfaces both from first principles electronic structure calculations and free energy calculations based on surface lattice dynamics. The results include surface structures and dynamics at a range of temperatures and electronic structures of ground, excited, ionised, d→d and charge–transfer excitonic states in different spin alignments.

This study presents a comparison of the experimental O K-edge absorption spectrum of haematite (α-Fe2O3) with a theoretical spectrum obtained from all-electron ab initio periodic Hartree-Fock calculations of the antiferromagnetic R3 structure. There is good overall accord between the two spectra and agreement to within about 0.2eV for the major peak-to-peak separations. From a consideration of the empty p density of states (DOS), calculations predict the first 20eV of the absorption to result almost entirely from excitations of the type |O 1s〉 → |O np〉 with negligible participation of the Fe p states. The lower part of the spectrum is attributed to O p states hybridized with Fe d states while, at energies greater than 5eV above the absorption edge, in the region of the broad absorption at about 11 eV, calculations suggest that the predominant hybridization is with the Fe s states. Important differences are found between the near-edge empty p DOS of the antiferromagnetic R3 and ferromagneti...

We study the thermodynamics, mechanism, and kinetic aspects of the $B1$-$B2$ phase transition in alkali halides and alkaline-earth oxides, using both two-body potentials and first-principles periodic Hartree-Fock theory, including a posteriori correlation corrections and self-consistent density functional calculations. Both the Buerger and Watanabe-Tokonami-Morimoto mechanisms are shown to be operable, for the activation energies of the two mechanisms are very close. The activation energies predicted by the potential model are always smaller than those from first-principles electronic structure calculations. Transition paths based on both approaches show marked variations with pressure and can be used to rationalize the pressure hysteresis observed experimentally. We discuss the effects of changing cation and anion size and charge on the transition pressures and activation energies and volumes.

First-principles periodic Hartree-Fock calculations of MnO are reported which suggest that the phase transition recently observed under shock compression at ∼90GPa is not a simple B1-to-B2 transiti...

This paper describes Shell, a program which uses lattice statics and quasiharmonic lattice dynamics to calculate analytically the free energy of a crystal, and its derivatives with respect to both internal and external strains, at a given temperature and pressure. These quantities can be used to perform efficient fully dynamic structure optimisation of unit cells containing hundreds of ions. Interactions are via short-ranged spherically symmetric pairwise and three-body potentials as well as the usual Coulomb terms, and polarizability effects may be accounted for by use of the shell model. Application of the code to the rutile phase of MgF2 is briefly described.

First-principles periodic spin-unrestricted Hartree-Fock calculations of C2/m and Pnmn LiMnO2 are reported which indicate that the ground-state valence configuration is essentially d5 with a local moment close to 4μB in an antiferromagnetic (AF3) spin arrangement. Calculations for unrelaxed 25% periodic Li-Mn antisite disordered C2/m and Pnmm structures are entirely consistent with a value of about 10% disorder reported for the C2/m phase. For the system LixMnO2 in the region 1 ≤ x ≤ ½, where the C2/m structure is apparently retained and the discharge voltage associated with Li removal is constant, Mulliken analyses and spin-density distributions indicate that the valence configuration of Mn is essentially unaltered with the formation of localized holes on the 0 sites with strong spin polaron character as in MnO. Both the Fermi and the LI removal energies are calculated to change by only a few per cent. In this region, new empty O(p) states are created below the conduction-band edge of LiMnO2, fr...

First principles periodic Hartree-Fock calculations of Li:MnO, Li x M n O 2 and CaMnO 3 are reported from which direct evidence is presented to indicate that the valence state of Mn remains essentially d 5 throughout the series. The net spin moment on Mn, on the other hand, follows that convential change from ∼ 5μ B to ∼ 3 μ B associated with the valence states Mn(ll), Mn(III), Mn(lV).

First-principles periodic Hartree - Fock calculations of the first ionized (hole) state of MnO in both the ferromagnetic and antiferromagnetic spin configurations are reported. Mulliken populations, charge and spin distributions and atom-projected densities of valence band states provide direct evidence of O(p) holes in agreement with recent experimental and theoretical studies of NiO. Calculations find the energy of the self-trapped hole to be lower than that of the delocalized hole which suggests small-polaron behaviour, in agreement with recent observations. Three different spin arrangements of the hole with respect to the lattice are reported from which the magnetic contributions to the energy are obtained in addition to the lattice relaxation energy associated with an increase in the separation. The relaxation energy is close to the reported activation energy for hole conductivity, which further supports small-polaron behaviour of holes in MnO. An excited configuration of the hole state has been determined from broken-symmetry calculations which Mulliken population and direct charge and spin distribution analyses suggest is . Also reported are similar calculations of the first electron addition state of MnO which indicate that this is essentially a state. Unlike that of the hole state, the energy of the self-trapped electron is found to be higher than that of the delocalized carrier which suggests intermediate- or large-polaron behaviour of the free carrier. However, a localized state is predicted in the presence of an substitutional impurity.

First principles periodic Hartree-Fock calculations of the first ionised state of Fe 0.125 Ni 0.875 are reported from which the Mulliken populations, charge and spin distributions and atom projected densities of valence band states provide direct evidence of Fe(3d) holes in complete agreement with recent conductivity measurements on materials with approximately the same composition. This is in marked contrast to the self-trapped hole in NiO, also reported here, and the bound hole in Li-doped NiO where both experiment and a recently reported calculation find holes of predominantly O(2p) character.

First-principles periodic Hartree–Fock calculations of the ground and first ionised and electron-addition states of rutile MnO 2 are reported from which the integrated charge- and spin-density distributions provide direct evidence that the charge state of Mn is essentially d5, as it is in MnO, and remains so with electron removal or addition. The net spin moment on Mn, on the other hand, is ca. 3 µ B , which is that normally associated with the Mn IV valence state, indicating that the unpaired d5 electron density is delocalised. This, together with the sign and magnitude of the overlap population, suggests strong covalency in this system in terms of p–d hybridisation.

A more exact method than hitherto available, based on lattice statics and quasi-harmonic lattice dynamics, is presented for the direct minimisation of the free energies of periodic solids with very large unit cells. This is achieved via the calculation of analytic derivatives of the vibrational frequencies with respect to all external and internal variables. The method, together with large defective supercells, is used to calculate the free energies of defects in MgO as a function of temperature. A major advantage of the supercell approach is that constant-volume and constant-pressure quantities are calculated independently. This allows a critical appraisal of the common approximations used for many years: (i) to convert constant-volume defect parameters to constant-pressure and (ii) to justify the use of static calculations at constant volume in the interpretation of experimental data obtained at constant pressure and at high temperatures. Defect enthalpies show only a small variation with temperature and differ by ca. 2% from the internal energy change in the static limit. An assessment is also made of the commonly used ZSISA approximation, in which the free energy at each temperature is minimised with respect to external strains only, simultaneously determining the internal strains by minimising the static lattice energy.

Ab initio periodic Hartree–Fock calculations are reported of normal and inverse spinel MnFe2O4. From Mulliken population analyses and net spin density distributions at Mn and Fe in both these structures, it is concluded that the charge states of Mn and Fe in the ground state are very similar to those in MnO and α-Fe2O3, with no evidence of the putative charge transfer leading to Fe2+ at A sites and Mn3+ at B sites in the inverse structure. For the latter an insulating spin polarised band comparising Mn and O states is found above the O(p) band of the normal structure.

We examine the performance of hybrid (HF-DFT) exchange functionals within Density Functional Theory (DFT) in describing the properties of crystalline solids. Recent applications are reviewed, and an extensive set of new results presented on transition metal compounds.

A brief review is presented of how density functional theory has been used to obtain interionic potentials in solids. The advantage and also the limitations of this approach are stressed. Functionals based on the uniform electron gas are much more successful than might have been anticipated from the underlying assumptions of the model.

MgO at high temperatures and pressures is studied by means of lattice dynamics in the quasi-harmonic approximation, and by molecular-dynamics simulation. The shell model is used to represent the polarizability of the oxygen ion. The two methods give very similar predictions for thermal expansion. However, the lattice dynamics fails at temperatures above 1500 K at atmospheric pressure, though not at high pressure (100 GPa). The predicted thermal expansion, using the Stoneham-Sangster and Lewis-Catlow potentials, is less than that observed experimentally. Predicted volumes at high pressure are too large. Shell-model molecular dynamics simulation can be used to study the dynamics at temperatures close to the melting point. A small anharmonic shift of vibrational frequencies is observed.

Ab initio Hartree-Fock calculations are reported of the electronic structures of CaO, VO, MnO and NiO. They are found to be essentially ionic in nature with ground states that are insulating, and, in the case of VO, MnO and NiO, high-spin antiferromagnetic. Calculated lattice parameters, binding energies and bulk moduli compare in accuracy with those for closed-shell oxides such as Li2O, MgO and Al2O3. Differences are found in the upper part of the valence band between VO and MnO and NiO. In VO it is predominantly V(3d) in character, whereas in both MnO and NiO it is O(2p). In the case of NiO this seems to be in accord with oxygen K-edge data for LixNi1−xO.

X-Ray diffraction measurements are reported of ceramic samples of the mixed-oxide system Ce1–xLaxO2–x/2 for 0

Classical simulations are described of the fully relaxed surface lattice structures of the five lowest-index planes of α-Al 2 0 3 and the resulting crystal morphology. The surface coverage by yttrium and magnesium as a function of temperature is evaluated on the basis of a non-Arrhenius isotherm and calculated heats of surface segregation. The calculated morphology, surface coverages and heats of segregation are compared with experiment. A quantum simulation of a relaxed {0001} surface is presented and the surface structure and energy compared with the classical results. Estimates are made of the adsorption energy of HF at the {0001} surface.

Periodic ab initio Hartree-Fock calculations are used to obtain two-body potential parameters for alpha -Al2O3. The approach, which is generally applicable to crystalline solids, yields potential models that are superior to empirical parameterizations.

Atomistic simulation techniques are used to obtain an equation of state for NaF at elevated temperatures and high pressures: phases with the NaCl and CsCl structures are considered. Two-body potentials and a simple shell model are employed within the quasiharmonic approximation. Calculated and theoretical isotherms and Hugoniots are compared, and other important thermodynamic properties are examined.

An equation of state for MgO is calculated for conditions of high pressure and temperature using atomistic simulations within the quasiharmonic approximation with two‐body potentials and a simple shell model. It is shown that experimental Hugoniot data can be reproduced accurately; other important properties are also examined including various quantities of geophysical interest. Results for the Helmholtz free energy and internal energy surfaces A(V,T) and U(V,T) are presented in parametrized form.

Atomistic lattice simulations are reported of the normalstate crystal properties of high-Tc oxides. Nonstoichiometry in La2CuO4 and Nd2CuO4 associated with oxygen interstitial defects is examined in some detail. The lattice structure and defect chemistry of Ca2CuO3, Sr2CuO3, La2SrCu2O6, and Sr2CuO4 are also considered. Finally, Jahn-Teller effects and bipolaron formation are addressed in relation to high-Tc behavior.

A review is presented of the ways in which electron gas theory has been used to obtain interionic potentials in solids. The strengths and limitations of such non-empirical potentials, and of the methods used to generate them, are emphasized. After minor modifications, many of the functionals derived from electron gas theory turn out to be much more successful and much more widely applicable than might have been expected, given their underlying assumptions.

First principles periodic Hartree-Fock calculations are reported of the electronic and magnetic structures and hole states in the T (La2CuO 4 ) phases of Sr 2 CuO 2 F 2 , Sr 2 CuO 2 F 2,5 and NaSrCuO 2 F 2 . Sr 2 CuO 2 F2 is predicted to be a highly ionic antiferromagnetic charge transfer insulator with Cu in a d 9 ((d x 2 -y 2) 1 ) configuration. Holes are predicted to be highly localised spin polarons which destroy the AF ordering at concentrations of 0.5 per formula unit.

In conclusion then, this brief survey has sought to bring together just some of the diverse problems that are now tractable from a computational point of view. In the forseeable future two areas stand out as ripe for further progress. They are: (i) The development of improved solid state potentials, including many body effects and refinements to the shell model (ii) The application of defect lattice methods to extended defects such as grain boundaries, stacking faults and shear planes.

We examine the performance of hybrid (HF-DFT) exchange functionals within Density Functional Theory (DFT) in describing the properties of crystalline solids. Recent applications are reviewed, and an extensive set of new results presented on transition metal compounds.

First-principles calculations of nondefective VO in the $\mathrm{Fm}3\ifmmode\bar\else\textasciimacron\fi{}m$ structure based on a range of single-particle Hamiltonians containing varying amounts of exact exchange indicate that the ground electronic state is that of a ${d}^{3}$ high spin, antiferromagnetic (AF), Mott-Hubbard insulator with an ${\mathrm{AF}}_{1}$ spin alignment of the local cation moments. This description remains essentially unchanged down to 10% exact exchange, and only for the pure density functional theory (DFT) potential is the ${\mathrm{AF}}_{1}$ phase found to be metallic. Strong spin-lattice interaction is predicted with differences in lattice constant of up to 1.6% between ${\mathrm{AF}}_{1}$ and FM (ferromagnetic) order. The ${\mathrm{AF}}_{1}$ lattice constant is predicted to be $\ensuremath{\sim}4.37\AA{},$ which is roughly 7% greater than the reported lattice constants for the defective material. The bulk modulus is comparable to those of CaO, MnO, and NiO. A mapping of total energies onto an Ising spin Hamiltonian containing both direct and superexchange interactions reveals the dominant magnetic interaction to be the direct coupling of antiferromagnetically aligned nearest-neighbor cation spins, which leads to the stability of the ${\mathrm{AF}}_{1}$ phase. Direct coupling energies are found in the range $\ensuremath{-}11.1$ to $\ensuremath{-}44.3\mathrm{meV}$ as the proportion of exact exchange is reduced, leading to an estimated critical disorder temperature in the range 300--450 K. However, the limitations of such mapping are exposed by a consideration of the relative stabilities of the ${\mathrm{AF}}_{1}$ and ${\mathrm{AF}}_{3}$ alignments. Orbital projected densities of states reveal filled to unfilled gaps which depend strongly on the proportion of exact exchange and for the B3LYP potential (20% exact exchange) are $\ensuremath{\sim}2.5\mathrm{eV}$ for the spin-forbidden $xy(\ensuremath{\uparrow})\ensuremath{\rightarrow}xy(\ensuremath{\downarrow})$ excitation, $\ensuremath{\sim}3.0\mathrm{eV}$ for $xy(\ensuremath{\uparrow})\ensuremath{\rightarrow}{z}^{2}(\ensuremath{\uparrow}),$ and $\ensuremath{\sim}3.5\mathrm{eV}$ for $\stackrel{\ensuremath{\rightarrow}}{V}\mathrm{O}$ charge transfer. Variationally stable, highly local crystal-field excited states ranging in energy from $\ensuremath{\sim}0.6$ to $\ensuremath{\sim}2.7\mathrm{eV}$ are predicted for exchange-correlation potentials down to 30% exact exchange and from comparisons with the corresponding band excitation estimates of $\ensuremath{\sim}1$ to $\ensuremath{\sim}2\mathrm{eV}$ are obtained for the localization energy of Frenkel excitons. From a mapping of the excited crystal-field energies onto a Kanamori Hamiltonian, values are obtained for the lattice Racah B and C parameters and the $d$-orbital averaged exchange and crystal-field energies. A comparison of mapped and directly calculated energies of the two-electron excitation $(xz,yz)\ensuremath{\rightarrow}{(z}^{2}{,x}^{2}\ensuremath{-}{y}^{2})$ confirms the validity of Kanamori mapping, notably in the limit of exact exchange.

Recent progress in the application of first principles theory to the electronic structure of transition metal materials is reviewed with particular emphasis on the use of the exact exchange interaction. The success of this approach is exemplified by calculations on a range of materials: simple monoxides, chromium cyanides and perovskite structure copper fluorides. The reliability of computed properties is established for lattice structures, spin–couplings, spin–lattice interactions, orbital ordering effects and the changes in the ground state induced by hole doping.

First-principles periodic Hartree-Fock calculations of the ground state electron distribution and empty oxygen p states in Li 0.125 Ni 0.875 O and Li 0.25 Ni 0.75 O are reported which provide direct evidence of oxygen p holes in Li-doped NiO. Calculated changes in the densities of empty oxygen p states are in good agreement with oxygen K -edge spectra. The empty states of the Li-doped materials provide a theoretical value of the band gap in NiO which, unlike previous estimates, is reasonably close to the observed value of 3.7 eV.

Three approaches to the modeling of ionic solids at elevated temperatures and high pressures are outlined and examples given in each case. We consider (i) atomistic simulation techniques using the ionic model and two‐body potentials (ii) the use of analytic equations of state above and below the Debye temperature and (iii) the use of ab initio, periodic Hartree‐Fock methods. Results are reported for CaO, MgO, NaCl, and LiF, and we also examine the rutile‐fluorite high pressure phase transition in MgF2.

The surface coverage of Sr on doped MgO ceramics has been measured by angle-resolved X-ray photoelectron spectroscopy (XPS) for bulk doping levels in the range 3–1000 ppm. The experimental data are compared with results derived from atomistic simulations of the doped surface. At low doping levels Sr segregates by substitutional replacement of Mg in the top-most ionic layer of the ceramic and good agreement is found betwen the experimental Sr 3d : Mg 2s intensity ratio and values derived from atomistic simulation. However, at higher Sr doping levels there is evidence for build-up of Sr multilayers and formation of SrO as a discrete surface phase.

Direct first principles calculations are conducted for the three spin-allowed excitations in pure and hole-doped antiferromagnetic Sr2CuO2Cl2. The results obtained for the pure system are close to the resonant x-ray Raman spectra reported by Kuiper et al (1998 Phys. Rev. Lett. 80 5204), most notably in respect of the state, which was not observed directly. The energy of 1.53 eV computed for this excitation is in good agreement with the value 1.5 eV deduced from the Raman experiment, and both of these lie well above the energy 0.5 eV suggested previously on the basis of the optical spectrum (Perkins et al 1993 Phys. Rev. Lett. 71 1621). The associated spin-flip energy of approximately 0.2 eV proposed by Kuiper et al is shown to be entirely consistent with the observed Neel temperature and with first principles calculations, and further, that it corresponds to the flip of an unpaired dx2−y2 spin in the ground state rather than a dz2 spin in the excited state. The two excitation energies in the current UHF calculations differ by approximately 0.25 eV from the Raman values, an amount ascribed to the difference in pair correlation energies. In addition, hybrid functional calculations incorporating varying contents of exact exchange are found to offer no systematic improvement. The presence of a nearest neighbour hole in the most stable O(p) configuration is shown to have no significant effect upon either the order or the stability of the states, with changes in excitation energy of 0.1–0.2 eV. A comparison with previous cluster calculations indicates that the latter do not capture fully the effect of the surrounding lattice on these highly local excitations. The generality of the direct approach to excitations is further established by calculations of the energies of three nearest neighbour charge-transfer states, which are placed in the range from 5.3 to 5.6 eV, as compared with values around 5 eV predicted previously (Tanaka and Kotani 1993 J. Phys. Soc. Japan 62 464). The and charge-transfer excitations produce extensive renormalization of the valence levels that lead to substantial reductions in energy from the rigid-band estimates based on the ground state eigenvalue spectrum.