On transition rates in surface hopping

Trajectory surface hopping (TSH) is one of the most widely used quantum-classical algorithms for nonadiabatic molecular dynamics. Despite its empirical effectiveness and popularity, a rigorous derivation of TSH as the classical limit of a combined quantum electron-nuclear dynamics is still missing. In this work, we aim to elucidate the theoretical basis for the widely used hopping rules. Naturally, we concentrate thereby on the formal aspects of the TSH. Using a Gaussian wave packet limit, we derive the transition rates governing the hopping process at a simple avoided level crossing. In this derivation, which gives insight into the physics underlying the hopping process, some essential features of the standard TSH algorithm are retrieved, namely (i) non-zero electronic transition rate ("hopping probability") at avoided crossings; (ii) rescaling of the nuclear velocities to conserve total energy; (iii) electronic transition rates linear in the nonadiabatic coupling vectors. The well-known Landau-Zener model is then used for illustration. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770280]

Recoil-induced electronic excitation and ionization in one-and two-electron ions

The electronic redistribution of an ion or atom induced by a sudden recoil of the nucleus occurring during the emission or capture of a neutral particle is theoretically investigated. For one-electron systems, analytical expressions are derived for the electronic transition probabilities to bound and continuum states. The quality of a B-spline basis set approach is evaluated from a detailed comparison with the analytical results. This numerical approach is then used Io study the dynamics of two-electron systems (neutral He and Ne ) using correlated wavefunctions for both the target and daughter ions. The total transition probabilities to discrete states, autoionizing states and direct single- and double-ionization probabilities are calculated from the pseudospectra. Sum rules for transition probabilities involving an initial bound state and a complete final series are discussed.

A further investigation of the kinetic demixing/decomposition of La0.6Sr0.4Co0.2Fe0.8O3- δ oxygen separation membranes

Kinetic demixing and decomposition were studied on three La_0.6Sr_0.4Co_0.2Fe_0.8O_{3- δ} oxygen-separation hollow fibre membrane modules, which were operated under a 0.21/0.009bar oxygen partial pressure difference at 950°C for 1128, 3672 and 5512h, respectively. The post-operation membranes were characterized by Secondary Ion Mass Spectrometry, Scanning Electronic Microscope, Energy Dispersive Spectrum and X-ray Diffraction. The occurrence of kinetic demixing and decomposition was confirmed through the microstructural evolution of the membranes. Secondary-phase grains were found on the air-side surface of the membranes after the long-term operation and Co and Fe enrichment as well as La depletion was found on the surface and in the bulk at the air side. Cation diffusivities were found to be in the order Co>Fe>Sr>La. Kinetic demixing and decomposition rates of the membranes at the air side were found to be self-accelerating with time; the role of A-site deficiency in the perovskite lattice in the bulk near the air side surface is implicated in the mechanism. The oxygen permeability was not affected by the kinetic demixing and decomposition of the material during long-term operation (up to 5512h), however, we may expect permeability to be affected by secondary phase formation on the air-side surface at even longer operational times. © 2010 Elsevier B.V.

The near-edge structure in energy-loss spectroscopy: many-electron and magnetic effects in transition metal nitrides and carbides

We investigate the ability of the local density approximation (LDA) in density functional theory to predict the near-edge structure in electron energy-loss spectroscopy in the dipole approximation. We include screening of the core hole within the LDA using Slater's transition state theory. We find that anion K-edge threshold energies are systematically overestimated by 4.22 +/- 0.44 eV in twelve transition metal carbides and nitrides in the rock-salt (B1) structure. When we apply this 'universal' many-electron correction to energy-loss spectra calculated within the transition state approximation to LDA, we find quantitative agreement with experiment to within one or two eV for TiC, TiN and VN. We compare our calculations to a simpler approach using a projected Mulliken density which honours the dipole selection rule, in place of the dipole matrix element itself. We find remarkably close agreement between these two approaches. Finally, we show an anomaly in the near-edge structure in CrN to be due to magnetic structure. In particular, we find that the N K edge in fact probes the magnetic moments and alignments of ther sublattice.

Electron energy-loss near-edge shape as a probe to investigate the stabilization of yttria-stabilized zirconia

The electron energy-loss near-edge structure (ELNES) at the O K edge has been studied in yttria-stabilized zirconia (YSZ). The electronic structure of YSZ for compositions between 3 and 15 mol % Y2O3 has been computed using a pseudopotential-based technique to calculate the local relaxations near the O vacancies. The results showed phase transition from the tetragonal to cubic YSZ at 10 mol % of Y2O3, reproducing experimental observations. Using the relaxed defect geometry, calculation of the ELNES was carried out using the full-potential linear muffin-tin orbital method. The results show very good agreement with the experimental O K-edge signal, demonstrating the power of using ELNES to probe the stabilization mechanism in doped metal oxides.

Free energy and molecular dynamics calculations for the cubic-tetragonal phase transition in zirconia

The high-temperature cubic-tetragonal phase transition of pure stoichiometric zirconia is studied by molecular dynamics (MD) simulations and within the framework of the Landau theory of phase transformations. The interatomic forces are calculated using an empirical, self-consistent, orthogonal tight-binding model, which includes atomic polarizabilities up to the quadrupolar level. A first set of standard MD calculations shows that, on increasing temperature, one particular vibrational frequency softens. The temperature evolution of the free-energy surfaces around the phase transition is then studied with a second set of calculations. These combine the thermodynamic integration technique with constrained MD simulations. The results seem to support the thesis of a second-order phase transition but with unusual, very anharmonic behavior above the transition temperature.

Effect of relaxation on the oxygen K-edge electron energy-loss near-edge structure in yttria-stabilized zirconia

The electron energy-loss near-edge structure (ELNES) at the oxygen K-edge has been investigated in a range of yttria-stabilized zirconia (YSZ) materials. The electronic structure of the three polymorphs of pure ZrO2 and of the doped YSZ structure close to the 33 mol %Y2O3 composition have been calculated using a full-potential linear muffin-tin orbital method (NFP-LMTO) as well as a pseudopotential based technique. Calculations of the ELNES dipole transition matrix elements in the framework of the NFP-LMTO scheme and inclusion of core hole screening within Slater's transition state theory enable the ELNES to be computed. Good agreement between the experimental and calculated ELNES is obtained for pure monoclinic ZrO2. The agreement is less good with the ideal tetragonal and cubic structures. This is because the inclusion of defects is essential in the calculation of the YSZ ELNES. If the model used contains ordered defects such as vacancies and metal Y planes, agreement between the calculated and experimental O K-edges is significantly improved. The calculations show how the five different O environments of Zr,Y,O, are connected with the features observed in the experimental spectra and demonstrate clearly the power of using ELNES to probe the stabilization mechanism in doped metal oxides.

Energy levels and transition probabilities for nitrogen-like Fe xx

Energies of the 700 lowest levels in Fe XX have been obtained using the multiconfiguration Dirac-Fock method. Configuration interaction method on the basis set of transformed radial orbitals with variable parameters taking into account relativistic corrections in the Breit-Pauli approximation was used to crosscheck our presented results. Transition probabilities, oscillator and line strengths are presented for electric dipole (E1), electric quadrupole (E2) and magnetic dipole (M1) transitions among these levels. The total radiative transition probabilities from each level are also provided. Results are compared with data compiled by NIST and with other theoretical work.

Dirac-Fock energy levels and transition probabilities for oxygen-like Fe XIX

Multiconfigurational Dirac-Fock calculations are reported for 656 energy levels and the 214 840 electric dipole (E I), electric quadrupole (E2) and magnetic dipole (M1) transition probabilities in oxygen-like Fe xix. The spectroscopic notations as well as the total transition probabilities from each energy level are provided. Good agreement is found with data compiled by NIST.

Electronic structure of the nitrogen-vacancy center in diamond from first-principles theory

The nitrogen-vacancy (NV) center is a paramagnetic defect in diamond with applications as a qubit. Here, we investigate its electronic structure by using ab initio density functional theory for five different NV center models of two different cluster sizes. We describe the symmetry and energetics of the low-lying states and compare the optical frequencies obtained to experimental results. We compute the major transition of the negatively charged NV centers to within 25–100 meV accuracy and find that it is energetically favorable for substitutional nitrogens to donate an electron to NV0. The excited state of the major transition and the NV0 state with a neutral donor nitrogen are found to be close in energy.

Importance of electronegativity differences and surface structure in molecular dissociation reactions at transition metal surfaces

The dissociative adsorption of N-2 has been studied at both monatomic steps and flat regions on the surfaces of the 4d transition metals from Zr to Pd. Using density functional theory (DFT) calculations, we have determined and analyzed the trends in both straight reactivity and structure sensitivity across the periodic table. With regards to reactivity, we find that the trend in activation energy (Ea) is determined mainly by a charge transfer from the surface metal atoms to the N atoms during transition state formation, namely, the degree of ionicity of the N-surface bond at the transition state. Indeed, we find that the strength of the metal-N bond at the transition state (and therefore the trend in Ea) can be predicted by the difference in Mulliken electronegativity between the metal and N. Structure sensitivity is analyzed in terms of geometric and electronic effects. We find that the lowering of Ea due to steps is more pronounced on the right-hand side of the periodic table. It is found that for the early transition metals the geometric and electronic effects work in opposition when going from terrace to step active site. In the case of the late 4d metals, however, these effects work in combination, producing a more marked reduction in Ea.

Electronic structure and total energy of interstitial hydrogen in iron: Tight-binding models

An application of the tight binding approximation is presented for the description of electronic structure and interatomic force in magnetic iron, both pure and containing hydrogen impurities. We assess the simple canonical d-band description in comparison to a non orthogonal model including s and d bands. The transferability of our models is tested against known properties including the segregation energies of hydrogen to vacancies and to surfaces of iron. In many cases agreement is remarkably good, opening up the way to quantum mechanical atomistic simulation of the effects of hydrogen on mechanical properties.

Shell Model Study of Local and Global Energy Barriers in KDP

We perform a study of the energetics of KH2PO4 (KDP) by using a shell model (SM) which was constructed by adjusting the interaction parameters to ab initio calculations, and was fitted to reproduce phonons, polarization-inversion energies and structural properties. We calculate the energy profiles by performing global displacements and local distortions following the ferroelectric (FE) mode pattern in clusters of different sizes embedded in a paraelectric (PE) phase matrix. These properties are expected to be relevant to the PE-FE phase transition. The obtained SM results are compared to corresponding ab initio (AI) data. The global instabilities are found in good agreement for both KDP and DKDP. We also find qualitative good agreement in the KDP structure and even quantitative agreement in the expanded DKDP structure for the local distortions. The SM results reproduce well different trends like increasing instabilities as the cluster sizes grows, as the heavier atoms are included, and as the volume is increased, in accordance with the corresponding data from AI calculations.

Modelling Transition Due to Backward Facing Steps Using the Laminar Kinetic Energy Concept

Boundary layer transition estimation and modelling is essential for the design of many engineering products across many industries. In this paper, the Reynolds-averaged Navier–Stokes are solved in conjunction with three additional transport equations to model and predict boundary layer transition. The transition model (referred to as the kTkT–kLkL–ωω model) is based on the kk–ωω framework with an additional transport equation to incorporate the effects low-frequency flow oscillations in the form of a laminar kinetic energy (kLkL). Firstly, a number of rectifications are made to the original kTkT–kLkL–ωω framework in order to ensure an appropriate response to the free-stream turbulence level and to improve near wall predictions. Additionally, the model is extended to incorporate the capability to model transition due to surface irregularities in the form of backward-facing steps with maximum non-dimensional step sizes of approximately 1.5 times the local displacement thickness of the boundary layer where the irregularity is located (i.e k/δ∗⪅1.5k/δ∗⪅1.5) at upstream turbulence intensities in the range 0.01<Tu(%)<0.80.01<Tu(%)<0.8. A novel function is proposed to incorporate transition sensitivity due to aft-facing steps. This paper details the rationale behind the development of this new function and demonstrates its suitability for transition onset estimation on a flat plate at zero pressure gradient.