Highly accurate coupled-cluster singlet and triplet pair energies from explicitly correlated calculations in comparison with extrapolation techniques

Coupled-cluster singles and doubles (CCSD) valence shell correlation energies of the systems CH₂ (<¹A₁ state), H₂O, HF, N₂, CO, Ne, and F₂ are computed by means of standard calculations with correlation-consistent basis sets of the type cc-pVxZ (x = D, T, Q, 5, 6) and by means of explicitly correlated coupled-cluster calculations (CCSD-R12/B) with large uncontracted basis sets of the type 19s14p8d6f4g3h for C, N, O, F, and Ne and 9s6p4d3f for H. These CCSD-R12/B calculations provide reference values for the basis set limit of CCSD theory. The computed correlation energies are decomposed into singlet and triplet pair energies. It is established that the singlet pair energies converge as X^?3 and the triplet pair energies as X^?5 with the cardinal number of the correlation-consistent basis sets, and an extrapolation technique is proposed that takes into account their different convergence behaviour. Applied to the cc-pV5Z and cc-pV6Z results, this new extrapolation yields pair energies with a mean absolute deviation of 0.02 mE_h from the CCSD-R12/B reference values. For the seven systems under study, the extrapolated total valence shell correlation energies agree to within 0.2 mE_h with the CCSD-R12/B benchmark data.     

Electronic structure of PbI2 from photoelectron spectra and the exciton problem

The valence band density of states for PbI₂ is determined from X-ray and u.v. induced photoelectron spectra. It is shown that the band derived from Pb 6s states is at 8 eV binding energy and not at the top of the valence bands as suggested by band structure and charge density calculations. A rigid shift in the predominantly iodine 5p derived bands to lower binding energy brings the band structure calculations into essential agreement with experiment. Pb 5d core level binding energies determined here are used to derive core level exciton energies of 0.7 eV from published reflectivity spectra.     

The electronic structures of Mg,Al and Si in octahedral coordination with oxygen from SCF Xα MO calculations

Molecular orbital calculations performed using the SCF Xα Scattered Wave Cluster method are presented for the octahedral oxyanions MgO₆^?10, AlO₆^?9 and SiO₆^?8. The AlO₆^?9 results are used to assign and interpret the X-ray photoelectron spectra (XPS), X-ray emission (XES) and u.v. spectra of Al₂O₃. Agreement between calculation and experiment is good for valence band and fair for conduction band orbitais. The SCF Xα results for MgO₆^?10 are also in good agreement with observed valence band energies in MgO, but in this case the lowest energy features in the u.v. spectrum are not assignable in terms of either the calculations or the X-ray spectral results. The substantial increase in covalency expected between the Mg and Si oxides is evidenced in the calculations by an increase in valence region width from 2.6 to 5.3 eV and an increase in valence-conduction band separation from 5.2 to 10.0 eV. The calculated trends are in reasonable agreement with u.v. spectral data and with absolute valence orbital binding energies derived from X-ray spectra. A comparison of the SiO₆^?8 calculation with the analogous tetrahedral SiO₄^?4 calculation shows the valence band in the octahedral oxyanion to be much simpler in structure and somewhat narrower than that in the tetrahedral oxyanion. Using the orbital structure calculated for the valence bands of tetrahedral and octahedral oxides, a method is presented for calculating atomization energies directly from X-ray spectral data for SiO₂, Al₂O₃ and MgO. Results are in good agreement with experiment but the method involves an empirical parameter which is not presently understood in detail. Studies of trends in p-type bonding orbital binding energies derived from experimental data provide a qualitative explanation for the preferred coordination numbers in the Mg, Al and Si oxides.     

Study of the band edge in CdIn2S4 by photovoltaic effect

Photovoltaic spectra were measured at 300 and 100 K on AuCdIn₂S₄ Schottky barriers in the spectral range near the band edge of the compound. Analysis of the spectra gives the values of the direct and indirect gaps at both temperatures together with the associated phonon energies. The results are compared with the predictions of the most recent band calculations on CdIn₂S₄.     

An XPS study of hafnium nitride films

XPS spectra are presented from films of different stoichiometry: HfN_1.0 made by CVD and reactive sputtering and HfN_1.09 made by ion plating. They support the existing theoretical calculations where the valence band comprises a strong Hf 5d band immediately below E_F and a band of mainly N 2p character some 6 eV below E_F. The core levels are shifted to larger binding energies by about 1.5 eV indicating electron transfer from hafnium to nitrogen. The effect of substoichiometry on the spectra is very small.     

Electronic and optical properties of pure and Mo doped anatase TiO2 using GGA and GGA+U calculations

Comparative GGA and GGA+U calculations for pure and Mo doped anatase TiO₂ are performed based on first principle theory, whose results show that GGA+U calculation provide more reliable results as compared to the experimental findings. The direct band gap nature of the anatase TiO₂ is confirmed, both by using GGA and GGA+U calculations. Mo doping in anatase TiO₂ narrows the band gap of TiO₂ by introducing Mo 4d states below the conduction band minimum. Significant reduction of the band gap of anatase TiO₂ is found with increasing Mo doping concentration due to the introduction of widely distributed Mo 4d states below the conduction band minimum. The increase in the width of the conduction band with increasing doping concentration shows enhancement in the conductivity which may be helpful in increasing electron–hole pairs separation and consequently decreases the carrier recombination. The Mo doped anatase TiO₂ exhibits the n-type characteristic due to the shifting of Fermi level from the top of the valence band to the bottom of the conduction band. Furthermore, a shift in the absorption edge towards visible light region is apparent from the absorption spectrum which will enhance its photocatalytic activity. All the doped models have depicted visible light absorption and the absorption peaks shift towards higher energies in the visible region with increasing doping concentration. Our results describe the way to tailor the band gap of anatase TiO₂ by changing Mo doping concentration. The Mo doped anatase TiO₂ will be a very useful photocatalyst with enhanced visible light photocatalytic activity.     

Band structure and optical functions of ternary chain TlInSe2

The band structure of ternary chain TlInSe₂ is calculated by a pseudo-potential method with allowance for non-locality of ionic pseudo-potentials. In the obtained band structure the symmetry and forbidden character of the direct transitions at band gap are ascertained to be the same as reported earlier from the results of the empirical pseudo-potential calculations. The imaginary part of the components parallel and perpendicular to the c-axis of the dielectric function tensor of TlInSe₂ is calculated at photon energies up to 10 eV. The real part of these components is obtained by extrapolation of the imaginary part to higher energies and subsequent Kramers–Kronig transformation. The obtained dielectric function is compared with the one obtained ellipsometrically in the range 0.85–6.5 eV. The results of comparison are rather favorable.     

Tailoring the photocatalytic activity of WO3 by Nb-F codoping from first-principles calculations

In this letter, the electronic structure properties of Nb, F monodoping and Nb-F codoping are explored by first-principles calculations. Our results show that Nb-F codoping can reduce the band gap notably. The band edge analysis indicates that both conduction band maximum (CBM) and valence band minimum (VBM) move to higher energies, which is desirable for water splitting. The formation energy and pair binding energy calculation shows that this anion-cation codoping is easy to realize in both O-rich and O-poor conditions. The calculated optical absorption spectra indicate that the visible light absorption can be significantly improved by Nb-F codoping in WO₃. Therefore, Nb-F co-doped WO₃ is predicted to be a promising visible light photocatalyst for water splitting.     

Electronic structure of spin-chain compounds: common features

The incommensurate composite systems M₁₄Cu₂₄O₄₁ (M = Ca, Sr, La) are based on two fundamental structural units: CuO₂ chains and Cu₂O₃ ladders. We present electronic structure calculations within density functional theory in order to address the interrelations between chains and ladders. The calculations account for the details of the crystal structure by means of a unit cell comprising 10 chain and 7 ladder units. It turns out that chains and ladders can be treated independently, which allows us to introduce a model system based on a reduced unit cell. For the CuO₂ chains, we find two characteristic bands at the Fermi energy. Tight binding fits yield nearest and next-nearest neighbour interactions of the same order of magnitude.     

Coulomb effects in the organic charge transfer salt TTT2I3

Madelung energy and simple band structure calculations on different models of the TTT₂I₃ complex indicate, that the iodine chains do not play an active role in the conduction process. The relatively small Coulomb coupling of the iodine chains to the crystal obtained by the Madelung calculations rationalizes the structural findings about the ordering of these chains at low temperatures. The Madelung energy difference between the localized model (with TTT^o and TTT⁺ ions) and delocalized model (with partly charged $\text{TTT}{}^{\mathrm{<mtext>1</mtext><mtext>2+</mtext>}}$ stacks) is large enough to stabilize the former.     

Binding energy analysis of solid hydrogen fluoride

Ab initio energy band structure calculations of infinite single and double HF chains are performed. Interaction energies within and between the linear macromolecules are deduced. As an alternative way for the decomposition of the binding energy tetrameric HF clusters are investigated. Second order perturbation theory is applied to calculate the correlation energy contributions. The interaction of the elementary cell with its neighboring cells in the same layer is repulsive. A binding energy is obtained for the interaction with cells in different layers. The cohesive energy is about - 2 kcal mol^-1 with respect to a single HF dimer. The results show that the binding energy in molecular crystals can be determined with the help of molecular cluster calculations.     

The electronic structure of Fe1+xNb3-xSe10

Fe_1+xNb_3-xSe₁₀ has a crystal structure consisting of prismatic niobium chains and iron/niobium octahedral chains. A Charge Density Wave (CDW) has been observed at low temperatures, as might be expected from the similarity of the prismatic niobium chains to those present in NbSe₃. Here we report tight binding band structure calculations which indicate that the electrons responsible for conduction and the CDW reside primarily on the prismatic chains. The effects of disorder and stoichiometry in the iron/niobium octahedral chains on the electronic structure and CDW wave vector are discussed.     

Yrast states in the doubly-odd nucleus100Tc

High spin states up toJ=14 and excitation energy up toE ^*=3076 keV have been observed in the odd-odd nucleus¹⁰⁰Tc with the reaction⁹⁶Zr(⁷Li, 3n), at bombarding energies between 21 and 31 MeV, by in-beam γ spectroscopy and conversion-electron measurements. A ΔJ=1 negative parity band similar to that observed in theN=57 isotone¹⁰²Rh, and based on the 8^?, 708 keV state has been identified. The observed band can be interpreted in terms of collective core excitations based on a two-quasiparticle state of(πg_9/2 ? νh_11/2) configuration. Comparison with IBFM-2 calculations have been performed.     

The electronic structures of the core and valence ion states of metal oxides

SCF-Xα SW MO calculations on metal core ion hole states and X-ray emission (XES) and X-ray photoelectron (XPS) transition states of the non- transition metal oxidic clusters MgO₆^10?, AlO₄^5? and SiO₄^4? show relative valence orbital energies to be virtually unaffected by the creation of valence orbital or metal core orbital holes. Accordingly, valence orbital energies derived from XPS and XES are directly comparable and may be correlated to generate empirical MO diagrams. In addition, charge relaxation about the metal core hole is small and valence orbital compositions are little changed in the core hole state. On the other hand, for the transition metal oxidic clusters FeO₆^10?, CrO₆^9? and TiO₆^8? relative valence orbital energies are sharply changed by a metal core orbital or crystal field orbital hole, the energy lowering of an orbital increasing with its degree of metal character. Consequently O 2p nonbonding → M 3d-O 2p antibonding (crystal field) energies are reduced, while M 3d bonding → O 2p nonbonding and M 3d-O 2p antibonding → M 4s,p-O 2p antibonding (conduction band) energies increase. Charge relaxation about the core hole is virtually complete in the transition metal oxides and substantial changes are observed in the composition of those valence orbitals with appreciable M 3d character. This change in composition is greater for e _g than for t_2g orbitals and increases as the separation of the e_g crystal field (CF) orbitals and the O 2p nonbonding orbital set decreases. Based on the hole state MO diagrams the higher energy XPS satellite in TiO₂ (at about 13 eV) is assigned to a valence → conduction band transition. The UV PES satellites at 8.2 eV in Cr₂O₃ and 9.3 eV in FeO are tentatively assigned to similar transitions to conduction band orbitals, although the closeness in energy of the crystal field and O 2p nonbonding orbitals in the valence orbital hole state prevents a definite assignment on energy criteria alone. However the calculations do clearly show that charge transfer transitions of the e_g bonding → e_g crystal field orbital type would generally occur at lower energy than is consistent with observed satellite structure.A core electron hole has little effect upon relative orbital energies and is only slightly neutralized by valence electron redistribution for MgO and SiO₂. For the transition metal oxides a core hole lowers the relative energies of M3d containing orbitals by large amounts, reducing O → M charge transfer and increasing M 3d crystal field → conduction band energies. Large and sometimes overcomplete neutralization of the core hole is observed, increasing from CrO₆^9? to FeO₆^10? to TiO₆^8?. as the O → M charge transfer energy declines.High energy XPS satellites in TiO₂ may be assigned to O 2p nonbonding → conduction band transitions while lower energy UV PES satellites in FeO and Cr₂O₃ arise from crystal field or O 2p nonbonding → conduction band excitations. Our “shake-up” assignment for FeO₆^10?, CrO₆^9? and TiO₆^8? are less than definitive because no procedure has yet been developed to calculate “shake-up” intensities resulting from transitions of the type described. However the results do allow a critical evaluation of earlier qualitative predictions of core and valence hole effects. First, we find that the comparison of hole or valence state ionic systems with equilibrium distance systems of higher nuclear and/or cation charge (e.g. the comparison of the FeO₆^10? Fe 2p core hole state to Co₃O₄) is dangerous. For example, larger MO distances in the ion states substantially reduce crystal field splittings. Second, core and CF orbital holes sharply reduce O → M charge transfer energies, giving 2e_g → 3e_g energy separations which are generally too small to match observed satellite energies. Third, highest occupied CF-conduction band energies are only about 4–5 eV in the ground states, but increase to about 7–11 eV in the core and valence hole states of the transition metal oxides studied. The energetic arguments presented thus support the idea of CF and/or O 2p nonbonding → conduction band excitations as assignments for “shake-up” satellites, at least in oxides of metals near the beginning of the transition series.     

Crystal structures and band gap characters of h-BN polytypes predicted by the dispersion corrected DFT and GW method

Geometry optimizations are performed for three polytypes of h-BN using density functional theory with dispersion correction for the van der Walls interaction. Quasiparticle band structure calculations are carried out to solve the controversy on band gap type of h-BN. Band energies are corrected by GW method. The h-BN with B_k structure has an indirect band gap of 5.840 eV. Two kinds of h-BN polytypes are shown to be mechanically stable and have quasi-direct band gap type.     

Ab initio study of SrTiO3 surfaces

We present first-principles total-energy calculations of (001) surfaces of SrTiO₃. Both SrO-terminated and TiO₂-terminated surfaces are considered, and the results are compared with previous calculations for BaTiO₃ surfaces. The major differences are in the details of the relaxed surface structures. Our calculations argue against the existence of a large ferroelectric relaxation in the surface layer, as had been previously proposed. We do find some indications of a weak surface ferroelectric instability, but so weak as to be easily destroyed by thermal fluctuations, except perhaps at quite low temperatures. We also compute surface relaxation energies and surface electronic band structures, obtaining results that are generally similar to those for BaTiO₃.     

Microwave emulations and tight-binding calculations of transport in polyacetylene

A novel approach to investigate the electron transport of cis- and trans-polyacetylene chains in the single-electron approximation is presented by using microwave emulation measurements and tight-binding calculations. In the emulation we take into account the different electronic couplings due to the double bonds leading to coupled dimer chains. The relative coupling constants are adjusted by DFT calculations. For sufficiently long chains a transport band gap is observed if the double bonds are present, whereas for identical couplings no band gap opens. The band gap can be observed also in relatively short chains, if additional edge atoms are absent, which cause strong resonance peaks within the band gap. The experimental results are in agreement with our tight-binding calculations using the nonequilibrium Green's function method. The tight-binding calculations show that it is crucial to include third nearest neighbor couplings to obtain the gap in the cis-polyacetylene.     

Decay Dynamics of 3‐methyl‐3‐pentene‐2‐one from the light absorbing S2(ππ*) state ‐ Resonance Raman Spectroscopy and CASSCF Study

The photophysics of 3‐methyl‐3‐pentene‐2‐one (3M3P2O) after excitation to the S₂(ππ*) electronic state were studied using the resonance Raman spectroscopy and complete active space self‐consistent field (CASSCF) method calculations. The A‐band resonance Raman spectra were obtained in cyclohexane, acetonitrile, and methanol with excitation wavelengths in resonance with the first intense absorption band to probe the structural dynamics of 3M3P2O. The B3LYP‐TD/6‐31++G(d, p) computation was carried out to determine the relative A‐band resonance Raman intensities of the fundamental modes, and the result was used to reproduce the corresponding fundamental band intensities of the 223.1 nm resonance Raman spectrum and thus to examine whether the vibronic‐coupling existed in Franck‐Condon region or not. CASSCF calculations were carried out to determine the minimal singlet excitation energies of S_{1, FC}, S_1,min (nπ*), S_{2, FC}, S_2,min (ππ*), the transition energies of the conical intersection points S_n/S_π, S_n/S₀, and the optimized excited state geometries as well as the geometry structures of the conical intersection points. The A‐band short‐time structural dynamics and the corresponding decay dynamics of 3M3P2O were obtained by the analysis of the resonance Raman intensity pattern and CASSCF computations. It was revealed that the initial structural dynamics of 3M3P2O was towards the simultaneous C₃=C₄ and C₂=O₇ bond elongation, with the C₃=C₄ bond length lengthening greater at the very beginning, whereas the C₂=O₇ bond length changing greater at the later evolution time before reaching the CI(S₂/S₁) conical intersection point. The decay dynamics from S₂(ππ*) to S₁(nπ*) via S₂(ππ*)/S₁(nπ*) in singlet realm and from S₁(nπ*) to T₁(nπ*) via ISC[S₁(nπ*)/T₂(ππ*)/T₁(nπ*)] in triplet realm are proposed. Copyright © 2014 John Wiley & Sons, Ltd.     

Persistent luminescence — Quo vadis?

The present status of the persistent luminescence mechanisms is reviewed and the remaining unsolved details are discussed. These details include the identification and role of defects in the Eu²⁺-doped and R³⁺ co-doped alkaline earth aluminates (MAl₂O₄) and disilicates (M₂MgSi₂O₇; M:Ca, Sr, Ba) which can be partly resolved by the thermoluminescence (TL) measurements. The use of the synchrotron radiation - presently only sparsely used in the studies of persistent luminescence - is introduced: the oxidation state of the presumed R²⁺/R³⁺/R^IV species occurring in the persistent luminescence materials during the luminescence processes were examined with synchrotron radiation XANES (and EXAFS) methods. The band gap energies (E_g), the defect-related luminescence as well as the 4f⁷→4f⁶5d¹ transition energies were derived from the synchrotron radiation excitation spectra of the materials. Subsequently, the early steps of the density functional theory (DFT) calculations involving the solution of the persistent luminescence mechanisms (band gap energies, position of the Eu²⁺ levels) are discussed. Some remaining challenges are eventually highlighted.     

Properties of the πh 9/2 ⊗ νi 13/2 band in odd-odd 188Au

A new rotational band has been identified and assigned to ¹⁸⁸Au for the first time using the ¹⁷³Yb(¹⁹F,4nγ) reaction at the beam energies of 86 and 90 MeV. This band is proposed to be built on the πh _9/2 ⊗ νi _13/2 configuration by comparing the band properties with known bands in neighboring nuclei. The prolate-to-oblate shape transition through triaxial shape has been proposed to occur around ¹⁸⁸Au for the ηh _9/2 ⊗ νi _13/2 bands in odd-odd Au isotopes on the basis of total Routhian surface (TRS) calculations.