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Dialogue(s): problems-and-solutions-concerning-first-principles Sections: Damascius - Problems and Solutions Concerning First Principles [Thanks to Marty and Yoni for videotaping and editing/production, and to StefanR for title and cataloguing info.] More Info Pierre Grimes and Philosophical Midwifery The Noetic Society The Pierre Grimes and the Noetic Society collection here on archive.org.

Applying our first UU principle.

Rep. Adam Kinzinger (R-IL) spoke at the "Principles First" Summit, a gathering in Washington, DC of Republicans who oppose former President Donald Trump. He talked about Russia's invasion of Ukraine as a possible watershed moment in the Republican Party and American politics. He also discussed the issues he believes are most pressing in the country as well as the legacy of January 6, 2021. Sponsor: Principles First

Rep. Adam Kinzinger (R-IL) spoke at the "Principles First" Summit, a gathering in Washington, DC of Republicans who oppose former President Donald Trump. He talked about Russia's invasion of Ukraine as a possible watershed moment in the Republican Party and American politics. He also discussed the issues he believes are most pressing in the country as well as the legacy of January 6, 2021. Sponsor: Principles First

Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.

This article is from Sensors (Basel, Switzerland) , volume 14 . Abstract Micro-cantilever sensors are widely used to detect biomolecules, chemical gases, and ionic species. However, the theoretical descriptions and predictive modeling of these devices are not well developed, and lag behind advances in fabrication and applications. In this paper, we present a novel multiscale simulation framework for nanomechanical sensors. This framework, combining density functional theory (DFT) calculations and finite element method (FEM) analysis, is capable of analyzing molecular adsorption-induced deformation and stress fields in the sensors from the molecular scale to the device scale. Adsorption of alkanethiolate self-assembled monolayer (SAM) on the Au(111) surface of the micro-cantilever sensor is studied in detail to demonstrate the applicability of this framework. DFT calculations are employed to investigate the molecular adsorption-induced surface stress upon the gold surface. The 3D shell elements with initial stresses obtained from the DFT calculations serve as SAM domains in the adsorption layer, while FEM is employed to analyze the deformation and stress of the sensor devices. We find that the micro-cantilever tip deflection has a linear relationship with the coverage of the SAM domains. With full coverage, the tip deflection decreases as the molecular chain length increases. The multiscale simulation framework provides a quantitative analysis of the displacement and stress fields, and can be used to predict the response of nanomechanical sensors subjected to complex molecular adsorption.

We show that any {\em quasi-particle} or GW approximation to the self-energy does not capture excitonic features in time-resolved (TR) photoemission spectroscopy. In this work we put forward a first-principles approach and propose a feasible diagrammatic approximation to solve this problem. We also derive an alternative formula for the TR photocurrent which involves a single time-integral of the lesser Green's function. The diagrammatic approximation applies to the {\em relaxed} regime characterized by the presence of quasi-stationary excitons and vanishing polarization. The main distinctive feature of the theory is that the diagrams must be evaluated using {\em excited} Green's functions. As this is not standard the analytic derivation is presented in detail. The final result is an expression for the lesser Green's function in terms of quantities that can all be calculated {\em ab initio}. The validity of the proposed theory is illustrated in a one-dimensional model system with a direct gap. We discuss possible scenarios and highlight some universal features of the exciton peaks. Our results indicate that the exciton dispersion can be observed in TR {\em and} angle-resolved photoemission.

The magnetic order of the localized Eu$^{2+}$ spins in optimally-doped Eu(Fe$_{1-x}$Ir$_{x}$)$_{2}$As$_{2}$ ($\mathit{x}$ = 0.12) with superconducting transition temperature $\mathit{T_{SC}}$ = 22 K was investigated by single-crystal neutron diffraction. The Eu$^{2+}$ moments were found to be ferromagnetically aligned along the $\mathit{c}$-direction with an ordered moment of 7.0(1) $\mu_{B}$ well below the magnetic phase transition temperature $\mathit{T_{C}}$ = 17 K. No evidence of the tetragonal-to-orthorhombic structural phase transition was found in this compound within the experimental uncertainty, in which the spin-density-wave (SDW) order of the Fe sublattice is supposed to be completely suppressed and the superconductivity gets fully developed. The ferromagnetic groud state of the Eu$^{2+}$ spins in Eu(Fe$_{0.88}$Ir$_{0.12}$)$_{2}$As$_{2}$ was supported by the first-principles density functional calculation. In addition, comparison of the electronic structure calculations between Eu(Fe$_{0.875}$Ir$_{0.125}$)$_{2}$As$_{2}$ and the parent compound EuFe$_{2}$As$_{2}$ indicates stronger hybridization and more expanded bandwith due to the Ir substitution, which together with the introduction of electrons might work against the Fe-SDW in favor of the superconductivity.

In the race towards high-performance ultra-scaled devices, two-dimensional materials offer an alternative paradigm thanks to their atomic thickness suppressing short-channel effects. It is thus urgent to study the most promising candidates in realistic configurations, and here we present detailed multiscale simulations of field-effect transistors based on arsenene and antimonene monolayers as channels. The accuracy of first-principles approaches in describing electronic properties is combined with the efficiency of tight-binding Hamiltonians based on maximally-localised Wannier functions to compute the transport properties of the devices. These simulations provide for the first time estimates on the upper limits for the electron and hole mobilities in the Takagi's approximation, including spin-orbit and multi-valley effects, and demonstrate that ultra-scaled devices in the sub-10 nm scale show a performance that is compliant with industry requirements.

The momentum distribution function (MDF) bands of iron-group transition metals from Sc to Cu have been investigated on the basis of the first-principles momentum dependent local ansatz wavefunction method. It is found that the MDF for $d$ electrons show a strong momentum dependence and a large deviation from the Fermi-Dirac distribution function along high-symmetry lines of the first Brillouin zone, while the $sp$ electrons behave as independent electrons. In particular, the deviation in bcc Fe (fcc Ni) is shown to be enhanced by the narrow $e_{g}$ ($t_{2g}$) bands with flat dispersion in the vicinity of the Fermi level. Mass enhancement factors (MEF) calculated from the jump on the Fermi surface are also shown to be momentum dependent. Large mass enhancements of Mn and Fe are found to be caused by spin fluctuations due to $d$ electrons, while that for Ni is mainly caused by charge fluctuations. Calculated MEF are consistent with electronic specific heat data as well as the recent angle resolved photoemission spectroscopy data.

We have calculated the adsorption energy of carbon monoxide on a monolayer of copper adsorbed on the (111) face of cubic zirconia. We investigate the structural parameters of three phases of bulk zirconia (cubic, tetragonal, and monoclinic) and find excellent agreement with experiment. We have also analyzed the structural relaxation of both the stoichiometric and reduced (111) surfaces of cubic zirconia ($c$-ZrO$_2$). For adsorption of copper on $c$-ZrO$_2$, we find that the preferred binding site is atop the terminal oxygen atom, favored by 0.3 eV over other high symmetry sites. We compare CO adsorption on zirconia-supported copper to the results of carbon monoxide on copper (100) (S. P. Lewis and A. M. Rappe, J. Chem. Phys. {\bf 110}, 4619,(1999).) and show that adsorption on oxide-supported copper is over 0.2 eV more stable than adsorption on the bare surface.

We describe, within an ab-initio approach, the stabilization of the tetragonal phase vs. the monoclinic one in Yttrium-doped Zirconia. The process is believed to be influenced from different mechanisms. Indeed we show that there is a delicate balance between the change in electrostatic and kinetic energy and exchange-correlation effects. In the tetragonal phase the perturbation induced by doping is better screened at the price of sacrificing correlation energy. Our work opens the opportunity to use the same approach to predict the tetragonal phase stabilization of materials like Zirconia or Hafnia, with different and less characterized dopants.

Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

555 p. 19 cm

555 p. 20 cm

Book digitized by Google from the library of Oxford University and uploaded to the Internet Archive by user tpb.

Book digitized by Google from the library of Oxford University and uploaded to the Internet Archive by user tpb.

A superhard boron nitride phase dubbed as Z-BN is proposed as possible intermediate phase between h-BN and zinc blende BN (c-BN), and investigated using first-principles calculations within the framework of the density functional theory. Although the structure of Z-BN is similar to that of bct-BN containing four-eight BN rings, it is more energy favorable than bct-BN. Our study reveals that Z-BN, with a considerable structural stability and high density comparable to c-BN, is a transparent insulator with an indirect band gap about 5.27 eV. Amazingly, its Vickers hardness is 55.88 Gpa which is comparable to that of c-BN. This new BN phase may be produced in experiments through cold compressing AB stacking h-BN due to its low transition pressure point of 3.3 GPa.

Formation Gibbs free energy of point defects and oxygen clusters in uranium dioxide at high-pressure high-temperature conditions are calculated from first principles, using the LSDA+U approach for the electronic structure and the Debye model for the lattice vibrations. The phonon contribution on Frenkel pairs is found to be notable, whereas it is negligible for the Schottky defect. Hydrostatic compression changes the formation energies drastically, making defect concentrations depend more sensitively on pressure. Calculations show that, if no oxygen clusters are considered, uranium vacancy becomes predominant in overstoichiometric UO2 with the aid of the contribution from lattice vibrations, while compression favors oxygen defects and suppresses uranium vacancy greatly. At ambient pressure, however, the experimental observation of predominant oxygen defects in this regime can be reproduced only in a form of cuboctahedral clusters, underlining the importance of defect clustering in UO2+x. Making use of the point defect model, an equation of state for non-stoichiometric oxides is established, which is then applied to describe the shock Hugoniot of UO2+x. Furthermore, the oxidization and compression behavior of uranium monoxide, triuranium octoxide, uranium trioxide, and a series of defective UO2 at zero Kelvin are investigated. The evolution of mechanical properties and electronic structures with an increase of the oxidation degree are analyzed, revealing the transition of the groundstate of uranium oxides from metallic to Mott insulator and then to charge-transfer insulator due to the interplay of strongly correlated effects of 5f orbitals and the shift of electrons from uranium to oxygen atoms.

In this study we investigated by means of density functional theory calculations the adsorption geometry and bonding mechanism of a single thymine (C$_5$H$_6$N$_2$O$_2$) molecule on Cu(110) surface. In the most stable energetic configuration, the molecular plane is oriented perpendicular to substrate along the $[1\bar{1}0]$ direction. For this adsorption geometry, the thymine molecule interacts with the surface via a deprotonated nitrogen atom and two oxygen ones such that the bonding mechanism involves a strong hybridization between the highest occupied molecular orbitals (HOMOs) and the d-states of the substrate. In the case of a parallel adsorption geometry, the long-range van der Waals interactions play an important role on both the molecule-surface geometry and adsorption energy. Their specific role was analyzed by means of a semi-empirical and the seamless methods. In particular, for a planar configuration, the inclusion of the dispersion effects dramatically changes the character of the adsorption process from physisorption to chemisorption. Finally, we predict the real-space topography of the molecule-surface interface by simulating scanning tunneling microscopy (STM) images. From these simulations we anticipate that only certain adsorption geometries can be imaged in STM experiments.

The structural, elastic and electronic properties of ReN are investigated by first-principles calculations based on density functional theory. Two competing structures, i.e., CsCl-like and NiAs-like structures, are found and the most stable structure, NiAs-like, has a hexagonal symmetry which belongs to space group P63/mmc with a=2.7472 and c=5.8180 \AA. ReN with hexagonal symmetry is a metal ultra-incompressible solid and has less elastic anisotropy. The ultra-incompressibility of ReN is attributed to its high valence electron density and strong covalence bondings. Calculations of density of states and charge density distribution, together with Mulliken atomic population analysis, show that the bondings of ReN should be a mixture of metallic, covalent, and ionic bondings. Our results indicate that ReN can be used as a potential ultra-incompressible conductor. In particular, we obtain a superconducting transition temperature T$_c$=4.8 K for ReN.

The lattice dynamic properties and spin-phonon coupling in DyMn$_2$O$_5$ are studied by using the density-functional theory. The calculated phonon frequencies are in very good agreement with experiments. We then compare the phonon modes calculated from different spin configurations. The results show that the phonon frequencies change substantially in different spin configurations, suggesting that the spin-phonon coupling in this material is very strong. Especially, the short range spin ordering has drastic effects on the highest Raman and IR phonon modes that might be responsible for the observed phonon anomalies near and above the magnetic phase transitions.

We present a first-principles density functional study of the structural, electronic and magnetic properties of the ferroelectric domain walls in multiferroic BiFeO3. We find that domain walls in which the rotations of the oxygen octahedra do not change their phase when the polarization reorients are the most favorable, and of these the 109 degree domain wall centered around the BiO plane has the lowest energy. The 109 degree and 180 degree walls have a significant change in the component of their polarization perpendicular to the wall; the corresponding step in the electrostatic potential is consistent with a recent report of electrical conductivity at the domain walls. Finally, we show that changes in the Fe-O-Fe bond angles at the domain walls cause changes in the canting of the Fe magnetic moments which can enhance the local magnetization at the domain walls.

We present a first-principles density functional study of the structural, electronic and magnetic properties of the ferroelectric domain walls in multiferroic BiFeO3. We find that domain walls in which the rotations of the oxygen octahedra do not change their phase when the polarization reorients are the most favorable, and of these the 109 degree domain wall centered around the BiO plane has the lowest energy. The 109 degree and 180 degree walls have a significant change in the component of their polarization perpendicular to the wall; the corresponding step in the electrostatic potential is consistent with a recent report of electrical conductivity at the domain walls. Finally, we show that changes in the Fe-O-Fe bond angles at the domain walls cause changes in the canting of the Fe magnetic moments which can enhance the local magnetization at the domain walls.

To explore the electronic structure of the first aromatic superconductor, potassium-doped solid picene which has been recently discovered by Mitsuhashi et al with the transition temperatures $T_c=7 - 20$ K, we have obtained a first-principles electronic structure of solid picene as a first step toward the elucidation of the mechanism of the superconductivity. The undoped crystal is found to have four conduction bands, which are characterized in terms of the maximally localized Wannier orbitals. We have revealed how the band structure reflects the stacked arrangement of molecular orbitals for both undoped and doped (K$_3$picene) cases, where the bands are not rigid. The Fermi surface for K$_3$picene is a curious composite of a warped two-dimensional surface and a three-dimensional one.

The construction of a reliable potential for GeO2, from first-principles, is described. The obtained potential, which includes dipole polarization effects, is able to reproduce all the studied properties (structural, dynamical and vibrational) to a high degree of precision with a single set of parameters. In particular, the infrared spectrum was obtained with the expression proposed for the dielectric function of polarizable ionic solutions by Weis et al. [J.M. Caillol, D. Levesque and J.J. Weis, J. Chem. Phys. 91, 5544 (1989)]. The agreement with the experimental spectrum is very good, with three main bands that are associated to tetrahedral modes of the GeO2 network. Finally, we give a comparison with a simpler pair-additive potential.

The construction of a reliable potential for GeO2, from first-principles, is described. The obtained potential, which includes dipole polarization effects, is able to reproduce all the studied properties (structural, dynamical and vibrational) to a high degree of precision with a single set of parameters. In particular, the infrared spectrum was obtained with the expression proposed for the dielectric function of polarizable ionic solutions by Weis et al. [J.M. Caillol, D. Levesque and J.J. Weis, J. Chem. Phys. 91, 5544 (1989)]. The agreement with the experimental spectrum is very good, with three main bands that are associated to tetrahedral modes of the GeO2 network. Finally, we give a comparison with a simpler pair-additive potential.

The early Church, the Church of the First Century, moved with power, the likes of which has rarely, if ever been witnessed since. If the Church today is to see that same power of God in operation, it needs to employ the same principles, the same Word of God that the early Church did, of which there were seven major principles.

The early Church, the Church of the First Century, moved with power, the likes of which has rarely, if ever been witnessed since. If the Church today is to see that same power of God in operation, it needs to employ the same principles, the same Word of God that the early Church did, of which there were seven major principles.

Book digitized by Google from the library of the New York Public Library and uploaded to the Internet Archive by user tpb.

Book digitized by Google from the library of the New York Public Library and uploaded to the Internet Archive by user tpb.

Book digitized by Google from the library of the New York Public Library and uploaded to the Internet Archive by user tpb.

Book digitized by Google from the library of the New York Public Library and uploaded to the Internet Archive by user tpb.

Book digitized by Google from the library of the New York Public Library and uploaded to the Internet Archive by user tpb.

We calculate the probability of DNA loop formation mediated by regulatory proteins such as Lac repressor (LacI), using a mathematical model of DNA elasticity. Our model is adapted to calculating quantities directly observable in Tethered Particle Motion (TPM) experiments, and it accounts for all the entropic forces present in such experiments. Our model has no free parameters; it characterizes DNA elasticity using information obtained in other kinds of experiments. [...] We show how to compute both the "looping J factor" (or equivalently, the looping free energy) for various DNA construct geometries and LacI concentrations, as well as the detailed probability density function of bead excursions. We also show how to extract the same quantities from recent experimental data on tethered particle motion, and then compare to our model's predictions. [...] Our model successfully reproduces the detailed distributions of bead excursion, including their surprising three-peak structure, without any fit parameters and without invoking any alternative conformation of the LacI tetramer. Indeed, the model qualitatively reproduces the observed dependence of these distributions on tether length (e.g., phasing) and on LacI concentration (titration). However, for short DNA loops (around 95 basepairs) the experiments show more looping than is predicted by the harmonic-elasticity model, echoing other recent experimental results. Because the experiments we study are done in vitro, this anomalously high looping cannot be rationalized as resulting from the presence of DNA-bending proteins or other cellular machinery. We also show that it is unlikely to be the result of a hypothetical "open" conformation of the LacI tetramer.

We investigate the electron transfer from a dissociatively adsorbed H2 molecule to a Au(111) surface using the first-principles methods. A fractional electron transfers from a molecule to a substrate, and potential energy increases during the process. The initial energy increase coincides with that of the isolated, separated, and positively charged H2 molecule calculated by the real-space density functional method. The barrier formation is due to the destabilization of the molecule induced by the electron transfer. The electronegativity difference between the adsorbate and the substrate determines the direction of the electron transfer.

We report on a first-principles investigation of the electronic structure and of the magnetic properties of the quasi-two-dimensional Mott insulator SrCu$_{2}$(BO$_{3}$)$_{2}$. Based on the hopping integrals and Coulomb interactions calculated with LDA and LSDA+U, we provide a microscopic explanation of the symmetric Heisenberg and antisymmetric Dzyaloshinskii-Moriya exchange integrals of SrCu$_{2}$(BO$_{3}$)$_{2}$. The intra-atomic exchange interaction of oxygen is shown to strongly contribute to the intra-dimer isotropic exchange. The results are in good agreement with those derived from experimental data, both regarding the orientation of the Dzyaloshinskii-Moriya vectors and the magnitude of all exchange integrals. The microscopic analysis is confirmed by the results of Green function's and total energies difference methods.

The ground state structural, electronic and magnetic properties of multiferroic TbMn$_2$O$_5$ are investigated via first-principles calculations. We show that the ferroelectricity in TbMn$_2$O$_5$ is driven by the non-centrosymmetric magnetic ordering, without invoking the spin-orbit coupling and non-collinear spins. The {\it intrinsic} electric polarization in this compound is calculated to be 1187 $nC\cdot$ cm$^{-2}$, an order of magnitude larger than previously thought.

The "Principles First" summit was held in Washington, DC, which brought together conservative centrists and pro-democracy advocates and provided an alternative to the Conservative Political Action Conference. In this portion of the conference, a panel discussed the state of the U.S. economy and the long-term challenges of federal deficits and debt. Also, former Republican National Committee Chair Michael Steele delivered a speech on U.S. founding principles in light of "the tyranny of Donald Trump." Sponsor: Principles First

Lots of two-dimensional (2D) materials have been predicted theoretically, and further confirmed in experiment, which have wide applications in nanoscale electronic, optoelectronic and thermoelectric devices. Here, the thermoelectric properties of ATeI (A=Sb and Bi) monolayers are systematically investigated, based on semiclassical Boltzmann transport theory. It is found that spin-orbit coupling (SOC) has important effects on electronic transport coefficients in p-type doping, but neglectful influences on n-type ones. The room-temperature sheet thermal conductance is 14.2 $\mathrm{W K^{-1}}$ for SbTeI and 12.6 $\mathrm{W K^{-1}}$ for BiTeI, which are lower than one of most well-known 2D materials, such as transition-metal dichalcogenide, group IV-VI, group-VA and group-IV monolayers. By analyzing group velocities and phonon lifetimes, the very low sheet thermal conductance of ATeI (A=Sb and Bi) monolayers is mainly due to small group velocities. It is found that the high-frequency optical branches contribute significantly to the total thermal conductivity, being obviously different from usual picture with little contribution from optical branches. According to cumulative lattice thermal conductivity with respect to phonon mean free path (MFP), it is difficulty to further reduce lattice thermal conductivity by nanostructures. Finally, possible thermoelectric figure of merit $ZT$ of ATeI (A=Sb and Bi) monolayers are calculated. It is found that the p-type doping has more excellent thermoelectric properties than n-type doping, and at room temperature, the peak $ZT$ can reach 1.11 for SbTeI and 0.87 for BiTeI, respectively. These results make us believe that ATeI (A=Sb and Bi) monolayers may be potential 2D thermoelectric materials, and can stimulate further experimental works to synthesize these monolayers.

Motivated by the recent realization of graphene sensors to detect individual gas molecules, we investigate the adsorption of H2O, NH3, CO, NO2, and NO on a graphene substrate using first-principles calculations. The optimal adsorption position and orientation of these molecules on the graphene surface is determined and the adsorption energies are calculated. Molecular doping, i.e. charge transfer between the molecules and the graphene surface, is discussed in light of the density of states and the molecular orbitals of the adsorbates. The efficiency of doping of the different molecules is determined and the influence of their magnetic moment is discussed.

A first-principles investigation of the electron-phonon interaction in the recently synthesized osmium dinitride (OsN$_2$) compound predicts that the material is a superconductor. Superconductivity in OsN$_2$ would originate from the stretching of covalently bonded dinitrogen units embedded in the transition-metal matrix, thus adding dinitrides to the class of superconductors containing covalently bonded light elements. The dinitrogen vibrations are strongly coupled to the electronic states at the Fermi level and generate narrow peaks in the Eliashberg spectral function $\alpha^2F(\omega)$. The total electron-phonon coupling of OsN$_2$ is $\lambda=0.37$ and the estimated superconducting temperature T$_c \approx 1$ K. We suggest that the superconducting temperature can be substantially increased by hole doping of the pristine compound and show that T$_c$ increases to 4 K with a doping concentration of 0.25 holes/OsN$_2$ unit.

A newly developed fast molecular-dynamics method is applied to BaTiO3 ferroelectric thin-film capacitors with short-circuited electrodes or under applied voltage. The molecular-dynamics simulations based on a first-principles effective Hamiltonian clarify that dead layers (or passive layers) between ferroelectrics and electrodes markedly affect the properties of capacitors, and predict that the system is unable to hop between a uniformly polarized ferroelectric structure and a striped ferroelectric domain structure at low temperatures. Simulations of hysteresis loops of thin-film capacitors are also performed, and their dependence on film thickness, epitaxial constraints, and electrodes are discussed.

The first-principles calculations have been performed to investigate the ground state properties of cubic scandium trifluoride (ScF$_3$) perovskite. Using modified hybrid exchange-correlation functionals within the density functional theory (DFT) we have comprehensively compared the electronic properties of ScF$_3$ obtained by means of the linear combination of atomic orbitals (LCAO) and projector augmented-waves (PAW) methods. Both methods allowed us to reproduce the lattice constant experimentally observed in cubic ScF$_3$ at low temperatures and predict its electronic structure in good agreement with known experimental valence-band photoelectron and F 1$s$ X-ray absorption spectra.

Interatomic potentials have been widely used in atomistic simulations such as molecular dynamics. Recently, frameworks to construct accurate interatomic potentials that combine a systematic set of density functional theory (DFT) calculations with machine learning techniques have been proposed. One of these methods is to use compressed sensing to derive a sparse representation for the interatomic potential. This facilitates the control of the accuracy of interatomic potentials. In this study, we demonstrate the applicability of compressed sensing to deriving the interatomic potential of ten elemental metals, namely, Ag, Al, Au, Ca, Cu, Ga, In, K, Li and Zn. For each elemental metal, the interatomic potential is obtained from DFT calculations using elastic net regression. The interatomic potentials are found to have prediction errors of less than 3.5 meV/atom, 0.03 eV/\AA\ and 0.15 GPa for the energy, force and the stress tensor, respectively, which enable the accurate prediction of physical properties such as lattice constants and the phonon dispersion relationship.

Using first-principles evolutionary simulations, we have systematically investigated phase stability in the Hf-O system at pressure up to 120 GPa. New compounds Hf5O2, Hf3O2, HfO and HfO3 are discovered to be thermodynamically stable at certain pressure ranges and a new stable high-pressure phase is found for Hf2O with space group Pnnm and anti-CaCl2-type structure. Both P62m-HfO and P4m2-Hf2O3 show semimetallic character. Pnnm-HfO3 shows interesting structure, simultaneously containing oxide O2- and peroxide [O-O]2- anions. Remarkably, it is P62m-HfO rather than OII-HfO2 that exhibits the highest mechanical characteristics among Hf-O compounds. Pnnm-Hf2O, Imm2-Hf5O2, P31m-Hf2O and P4m2-Hf2O3 phases also show superior mechanical properties, these phases can be quenched to ambient pressure and their properties can be exploited.

We have investigated Mg intercalation into orthorhombic V$_2$O$_5$, one of only three cathodes known to reversibly intercalate Mg ions. By calculating the ground state Mg$_x$V$_2$O$_5$ configurations and by developing a cluster expansion for the configurational disorder in $\delta$-V$_2$O$_5$, a full temperature-composition phase diagram is derived. Our calculations indicate an equilibrium phase separating behavior between fully demagnesiated $\alpha$-V$_2$O$_5$ and fully magnesiated $\delta$-V$_2$O$_5$, but also motivate the existence of potentially metastable solid solution transformation paths in both phases. We find significantly better mobility for Mg in the $\delta$ polymorph suggesting that better performance can be achieved by cycling Mg in the $\delta$ phase.

In this work we present theoretical calculations and analysis of the vibronic structure of the spin-triplet optical transition in diamond nitrogen-vacancy centres. The electronic structure of the defect is described using accurate first-principles methods based on hybrid functionals. We devise a computational methodology to determine the coupling between electrons and phonons during an optical transition in the dilute limit. As a result, our approach yields a smooth spectral function of electron-phonon coupling and includes both quasi-localized and bulk phonons on equal footings. The luminescence lineshape is determined via the generating function approach. We obtain a highly accurate description of the luminescence band, including all key parameters such as the Huang-Rhys factor, the Debye-Waller factor, and the frequency of the dominant phonon mode. More importantly, our work provides insight into the vibrational structure of nitrogen vacancy centres, in particular the role of local modes and vibrational resonances. In particular, we find that the pronounced mode at 65 meV is a vibrational resonance, and we quantify localization properties of this mode. These excellent results for the benchmark diamond nitrogen-vacancy centre provide confidence that the procedure can be applied to other defects, including alternative systems that are being considered for applications in quantum information processing.

We present a comprehensive set of first principles electronic structure calculations to study transition metal solutes and their interactions with point defects in austenite. Clear trends were observed across the series. Solute-defect interactions were strongly correlated to the solute size factors, consistent with local strain field effects. Strong correlations with results in ferrite show insensitivity to the underlying crystal structure in Fe. Oversized solutes act as strong traps for vacancy and self-interstitial defects and as nucleation sites for the development of proto-voids and small self-interstitial loops. The reduction in defect mobility and net defect concentrations explains the observed radiation-damage resistance in austenitic steels doped with oversized solutes. Oversized solutes remaining dissolved in oxide dispersion-strengthened (ODS) steels could contribute to their radiation-damage resistance. Ni and Co diffuse more slowly than Fe, along with any vacancy flux produced under irradiation below a critical temperature, which is 400 K for Co and their concentrations should be enhanced at defect sinks. Cr and Cu diffuse more quickly than Fe, against a vacancy flux and will be depleted at defect sinks. Oversized solutes early in the transition metal series form highly-stable solute-centred divacancy (SCD) defects with a nearest-neighbour vacancy. The vacancy-mediated diffusion of these solutes is dominated by the dissociation and reassociation of the SCDs, with a lower activation energy than for self-diffusion, which has important implications for the nucleation and growth of complex oxide nanoparticles containing these solutes in ODS steels. Interstitial-mediated solute diffusion is energetically disfavoured for all except Cr, Mn, Co and Ni. The central role that solute size plays in the results presented here means they should apply to other solvent metals and alloys.