First-principles theory of the EPR g tensor in solids: defects in quartz

Identification of paramagnetic centers in irradiated Sn-doped silicon dioxide by first-principles

We present a first-principles investigation of Sn paramagnetic centers in Sn-doped vitreous silica based on calculations of the electron paramagnetic resonance (EPR) parameters. The present investigation provides evidence of an extended analogy between the family of Ge paramagnetic centers in Ge-doped silica and the family of Sn paramagnetic centers in Sn-doped silica for SnO2concentrations below phase separation. We infer, also keeping into account the larger spin-orbit coupling of Sn atoms with respect to Ge atoms, that a peculiar and highly distorted three-fold coordinated Sn center (i.e. the Sn forward-oriented configuration) should give rise to an orthorhombic EPR signal of which we suggest a fingerprint in the EPR spectra recorded by Chiodiniet al(2001Phys. Rev.B64073102). Given its structural analogy with theEα'and Ge(2) centers, we here name it as the 'Sn(2) center'. Moreover, we show that the single trapped electron at a SnO4tetrahedron constitutes a paramagnetic center responsible for the orthorhombic EPR signal reported in Chiodiniet al(1998Phys. Rev.B589615), confuting the early assignment to a distorted variant of the Sn-E' center. We hence relabel the latter orthorhombic EPR signal as the 'Sn(1) center' due to its analogy to the Ge(1) center in Ge-doped silica.

Deep Levels and Electron Paramagnetic Resonance Parameters of Substitutional Nitrogen in Silicon from First Principles

Nitrogen is commonly implanted in silicon to suppress the diffusion of self-interstitials and the formation of voids through the creation of nitrogen-vacancy complexes and nitrogen-nitrogen pairs. Yet, identifying a specific N-related defect via spectroscopic means has proven to be non-trivial. Activation energies obtained from deep-level transient spectroscopy are often assigned to a subset of possible defects that include non-equivalent atomic structures, such as the substitutional nitrogen and the nitrogen-vacancy complex. Paramagnetic N-related defects were the object of several electron paramagnetic spectroscopy investigations which assigned the so-called SL5 signal to the presence of substitutional nitrogen (NSi). Nevertheless, its behaviour at finite temperatures has been imprecisely linked to the metastability of the NSi center. In this work, we build upon the robust identification of the SL5 signature and we establish a theoretical picture of the substitutional nitrogen. Through an understanding of its symmetry-breaking mechanism, we provide a model of its fundamental physical properties (e.g., its energy landscape) based on ab initio calculations. Moreover by including more refined density functional theory-based approaches, we calculate EPR parameters (↔g and ↔A tensors), elucidating the debate on the metastability of NSi. Finally, by computing thermodynamic charge transition levels within the GW method, we present reference values for the donor and acceptor levels of NSi.

Graphite-like Charge Storage Mechanism in a 2D π-d Conjugated Metal-Organic Framework Revealed by Stepwise Magnetic Monitoring

Quasi-two-dimensional (2D) fully π-d conjugated metal-organic frameworks (MOFs) have been widely employed as active materials of secondary batteries; however, the origin of their high charge storage capacity is still unknown. Some reports have proposed a mechanism by assuming the formation of multiple radicals on one organic ligand, although there is no firm evidence for such a mechanism, which would run counter to the resonance theory. In this work, we utilized various magnetometric techniques to monitor the formation and concentration of paramagnetic species during the electrochemical process of 2D π-d conjugated Cu-THQ MOF (THQ = tetrahydroxy-1,4-benzoquinone). The spin concentration of the fully reduced (discharged 1.5 V) electrode was estimated to be around only 0.1 spin-1/2 per CuO₄ unit, which is much lower than that of the expected "diradical" form. More interestingly, a significant elevation of the temperature-independent paramagnetic term was simultaneously observed, which indicates the presence of delocalized π electrons in this discharged state. Such results were corroborated by first-principles density functional theory calculations and the electrochemically active density of states, which reveal the microscopic mechanism of the charge storage in the Cu-THQ MOF. Hence, a graphite-like charge storage mechanism, where the π-electron band accepts/donates electrons during the charge/discharge process, was suggested to explain the excessive charge storage of Cu-THQ. This graphite-like charge storage mechanism revealed by magnetic studies can be readily generalized to other π-d conjugated MOFs.

A method to calculate the NMR spectra of paramagnetic species using thermalized electronic relaxation

For paramagnetic species, it has been long understood that the hyperfine interaction between the unpaired electrons and the nucleus results in a nuclear magnetic resonance (NMR) peak that is shifted by a paramagnetic shift, rather than split by the coupling, due to an averaging of the electronic magnetic moment caused by electronic relaxation that is fast in comparison to the hyperfine coupling constant. However, although this feature of paramagnetic NMR has formed the basis of all theories of the paramagnetic shift, the precise theory and mechanism of the electronic relaxation required to predict this result has never been discussed, nor has the assertion been tested. In this paper, we show that the standard semi-classical Redfield theory of relaxation fails to predict a paramagnetic shift, as does any attempt to correct for the semi-classical theory using modifications such as the inhomogeneous master equation or Levitt-di Bari thermalization. In fact, only the recently-introduced Lindbladian theory of relaxation in magnetic resonance [J.Magn.Reson., 310, 106645 (2019)] is able to correctly predict the paramagnetic shift tensor and relaxation-induced linewidth in pNMR. Furthermore, this new formalism is able to predict the NMR spectra of paramagnetic species outside the high-temperature and weak-order limits, and is therefore also applicable to dynamic nuclear polarization. The formalism is tested by simulations of five case studies, which include Fermi-contact and spin-dipolar hyperfine couplings, g-anisotropy, zero-field splitting, high and low temperatures, and fast and slow electronic relaxation.

Numerical study of disorder on the orbital magnetization in two dimensions

The modern theory of orbital magnetization (OM) was developed by using Wannier function method, which has a formalism similar with the Berry phase. In this manuscript, we perform a numerical study on the fate of the OM under disorder, by using this method on the Haldane model in two dimensions, which can be tuned between a normal insulator or a Chern insulator at half filling. The effects of increasing disorder on OM for both cases are simulated. Energy renormalization shifts are observed in the weak disorder regime and topologically trivial case, which was predicted by a self-consistentT-matrix approximation. Besides this, two other phenomena can be seen. One is the localization trend of the band orbital magnetization. The other is the remarkable contribution from topological chiral states arising from nonzero Chern number or large value of integrated Berry curvature. If the fermi energy is fixed at the gap center of the clean system, there is an enhancement of |M| at the intermediate disorder, for both cases of normal and Chern insulators, which can be attributed to the disorder induced topological metal state before localization.

GIAO versus GIPAW: Comparison of Methods To Calculate 11B NMR Shifts of Icosahedral Closo-Heteroboranes toward Boron-Rich Borides

In this work, we perform first-principle density functional theory calculations with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional to compare the results of the gauge-including atomic orbital (GIAO) method with the gauge-including projector-augmented wave (GIPAW) approach for isotropic ¹¹B nuclear magnetic resonance shifts. GIPAW had been used successfully for the theoretical calculation of nuclear magnetic parameters of ¹¹B species in strong ionic solid-phase compounds such as borates but had been applied very rarely to structures where boron is mainly involved in complex covalent bonding situations, for example, in icosahedra of boron-rich borides. Thus, we investigate the accuracy of both well-known methods and reliability of the effective treatment of core electrons on a test set containing 16 experimentally known closo-(hetero)dodecaboranes. In general, we find very good agreement between GIAO and GIPAW when compared to experimental observations. However, accidental degeneracies of the shift values are better predicted by GIPAW. The optimized molecular geometries on the PBE level agree well with gaseous electron diffraction data and lead to theoretical isotropic chemical ¹¹B shifts with root-mean-square errors of 2.1 and 1.0 ppm depending on the used model of converting absolute shieldings to chemical shifts. The comparison with results from hybrid functionals (B3LYP, B3LYP-D2, and PBE0) shows a minor improvement in accuracy, which is in agreement with ¹³C shifts of sp³-hybridized species. In order to prove the reliability of the conversion parameters obtained by PBE, we report the calculated ¹¹B shifts of 1,2-, 1,7-, and 1,12-PCB₁₀H₁₁ with GIAO and GIPAW to our knowledge for the first time. Additionally, Bader's analysis is carried out on the converged electron density for all boron species within the molecular test set, yielding no simple direct relation between charge and isotropic shifts.

Investigation of room temperature ferromagnetism in transition metal doped BiFeO3

Spintronic functionality in ferromagnetic materials is a next-generation technique, to be used in data storage, high-frequency communications, and logic devices with minimum energy consumption. Ultra-low energy consumption in high-speed logic devices can be envisioned by inducing ferromagnetic behavior into room temperature multiferroic materials. However, there is a scarcity of room temperature multiferroic materials which have a definite spin degree of freedom. To fully exploit these technological challenges, we introduce the induced ferromagnetism in bismuth ferrite (BiFeO₃, BFO) by doping transition metal (Cr, Ni, Co) elements. Our investigation initiates with the experimental study on chemically synthesized BiFe_(1-x)M _x O₃ samples where x  =  0.0625 (6.25%) and M  =  Cr, Ni and Co. Experimental findings are verified by theoretical simulation using density functional theory (DFT  +  U) and gauge including projector augmented wave (GIPAW) based calculation. All the experimental studies are done at room temperature while the theoretical verification using DFT is carried to understand the underlying mechanism behind the magnetic behavior of doped BiFeO₃. It is done by optimizing the structural parameters comparable to the room temperature values. Microstructural and magnetic properties are studied using x-ray diffraction (XRD), transmission electron microscopy (TEM) and Vibrating sample magnetometer (VSM). All these experimental studies confirm the structural changes and induced ferromagnetism with doping. X-ray photoelectron spectroscopy (XPS) verified the reason behind this ferromagnetic property on the basis of oxygen vacancy content. Electron paramagnetic resonance (EPR) spectroscopy shows the tuning of Δg values due to enhanced magnetization. The density of states (DOS) calculations were performed on BFO (band-gap 1.89 eV) after structural optimization using DFT  +  U method, confirm our experimental findings. Magnetic moment values change drastically with doping elements (M), i.e. almost negligible for BFO (antiferromagnetic) to maximum (2.85 μ _B/f.u.) for Ni-doped sample. We also compute the EPR g-tensor using GIPAW method to confirm the tuning of Δg values due to enhanced magnetization. These results can highlight the impact and importance of suitable transition element doping to induce the room temperature ferromagnetism in BiFeO₃.

v-P2O5 micro-clustering in P-doped silica studied by a first-principles Raman investigation

Synthetic vitreous silica is currently the preferred material for the production of optical fibres because of the several excellent properties of this glass, e.g. high transmission in the visible and IR domains, high mechanical strength, chemical durability, and ease of doping with various materials. For instance, fiber lasers and amplifiers exploit the light amplification properties provided by rare-earth ions employed as dopants in the core of silica-based optical fibers. The structure and composition of the nearest neighbor shell surrounding rare-earth ions in silica-based optical fibers and amplifiers have been intensively debated in the last decade. To reduce aggregation effects between rare-earth ions, co-dopants such as phosphorus and aluminium are added as structural modifiers; phosphorus-doping, in particular, has proved to be very efficient in dissolving rare-earth ions. In this work, we provide further insights concerning the embedding of P atoms into the silica network, which may be relevant for explaining the ease of formation of a phosphorus pentoxide nearest-neighbor shell around a rare-earth dopant. In particular, by means of first-principles calculations, we discuss alternative models for an irradiation (UV, x-, γ-rays) induced paramagnetic center, i.e. the so called room-temperature phosphorus-oxygen-hole center, and its precursors. We report that the most likely precursor of a room-temperature phosphorus-oxygen-hole center comprises of a micro-cluster of a few (at least two) neighboring phosphate tetrahedra, and correspondingly that the occurrence of isolated [(O-)2P(=O)2]- units is unlikely even at low P-doping concentrations. In fact, this work predicts that the symmetric stretching of P=O bonds in isolated [(O-)2P(=O)2]- units appears as a Raman band at a frequency of ~1110 cm-1, and only by including at least another corner-sharing phosphate tetrahedron, it is shown to shift to higher frequencies (up to ~40 cm-1) due to the shortening of P=O bonds, thereby leading to an improved agreement with the observed Raman band located at ~1145 cm-1.

Paramagnetic NMR in solution and the solid state

The field of paramagnetic NMR has expanded considerably in recent years. This review addresses both the theoretical description of paramagnetic NMR, and the way in which it is currently practised. We provide a review of the theory of the NMR parameters of systems in both solution and the solid state. Here we unify the different languages used by the NMR, EPR, quantum chemistry/DFT, and magnetism communities to provide a comprehensive and coherent theoretical description. We cover the theory of the paramagnetic shift and shift anisotropy in solution both in the traditional formalism in terms of the magnetic susceptibility tensor, and using a more modern formalism employing the relevant EPR parameters, such as are used in first-principles calculations. In addition we examine the theory first in the simple non-relativistic picture, and then in the presence of spin-orbit coupling. These ideas are then extended to a description of the paramagnetic shift in periodic solids, where it is necessary to include the bulk magnetic properties, such as magnetic ordering at low temperatures. The description of the paramagnetic shift is completed by describing the current understanding of such shifts due to lanthanide and actinide ions. We then examine the paramagnetic relaxation enhancement, using a simple model employing a phenomenological picture of the electronic relaxation, and again using a more complex state-of-the-art theory which incorporates electronic relaxation explicitly. An additional important consideration in the solid state is the impact of bulk magnetic susceptibility effects on the form of the spectrum, where we include some ideas from the field of classical electrodynamics. We then continue by describing in detail the solution and solid-state NMR methods that have been deployed in the study of paramagnetic systems in chemistry, biology, and the materials sciences. Finally we describe a number of case studies in paramagnetic NMR that have been specifically chosen to highlight how the theory in part one, and the methods in part two, can be used in practice. The systems chosen include small organometallic complexes in solution, solid battery electrode materials, metalloproteins in both solution and the solid state, systems containing lanthanide ions, and multi-component materials used in pharmaceutical controlled-release formulations that have been doped with paramagnetic species to measure the component domain sizes.

Electronic orbital response of regular extended and infinite periodic systems to magnetic fields. I. Theoretical foundations for static case

A theoretical treatment for the orbital response of an infinite, periodic system to a static, homogeneous, magnetic field is presented. It is assumed that the system of interest has an energy gap separating occupied and unoccupied orbitals and a zero Chern number. In contrast to earlier studies, we do not utilize a perturbation expansion, although we do assume the field is sufficiently weak that the occurrence of Landau levels can be ignored. The theory is developed by analyzing results for large, finite systems and also by comparing with the analogous treatment of an electrostatic field. The resulting many-electron Hamilton operator is forced to be hermitian, but hermiticity is not preserved, in general, for the subsequently derived single-particle operators that determine the electronic orbitals. However, we demonstrate that when focusing on the canonical solutions to the single-particle equations, hermiticity is preserved. The issue of gauge-origin dependence of approximate solutions is addressed. Our approach is compared with several previously proposed treatments, whereby limitations in some of the latter are identified.

Advanced capabilities for materials modelling with Quantum ESPRESSO

Quantum EXPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. Quantum EXPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.

Photoactivated processes in optical fibers: generation and conversion mechanisms of twofold coordinated Si and Ge atoms

In this work we present an extensive investigation of nanoscale physical phenomena related to oxygen-deficient centers (ODCs) in silica and Ge-doped silica by means of first-principles calculations, including nudged-elastic band, electron paramagnetic resonance parameters calculations, and many-body perturbation theory (GW and Bethe-Salpeter equation) techniques. We show that by neutralizing positively charged oxygen monovacancies we can obtain model structures of twofold Si and Ge defects of which the calculated absorption spectra and singlet-to-triplet transitions are in excellent agreement with the experimental optical absorption and photo-luminescence data. In particular we provide an exhaustive analysis of the main exciton peaks related to the presence of twofold defects including long-range correlation effects. By calculating the reaction pathways and energy barriers necessary for the interconversion, we advance a double precursory origin of the [Formula: see text] and Ge(2) centers as due to the ionization of neutral oxygen monovacancies (Si-Si and Ge-Si dimers) and as due to the ionization of twofold Si and Ge defects. Furthermore two distinct structural conversion mechanisms are found to occur between the neutral oxygen monovacancy and the twofold Si (and Ge) atom configurations. Such conversion mechanisms allow to explain the radiation induced generation of the ODC(II) centers, their photobleaching, and also their generation during the drawing of optical fibers.

Atomic structure of interface states in silicon heterojunction solar cells

Combining orientation dependent electrically detected magnetic resonance and g tensor calculations based on density functional theory we assign microscopic structures to paramagnetic states involved in spin-dependent recombination at the interface of hydrogenated amorphous silicon crystalline silicon (a-Si:H/c-Si) heterojunction solar cells. We find that (i) the interface exhibits microscopic roughness, (ii) the electronic structure of the interface defects is mainly determined by c-Si, (iii) we identify the microscopic origin of the conduction band tail state in the a-Si:H layer, and (iv) present a detailed recombination mechanism.

Identification of the nitrogen split interstitial (N-N)(N) in GaN

Combining electron paramagnetic resonance, density functional theory, and positron annihilation spectroscopy (PAS), we identify the nitrogen interstitial defect in GaN. The isolated interstitial is unstable and transforms into a split interstitial configuration (N-N)(N). It is generated by particle irradiation with an introduction rate of a primary defect, pins the Fermi level at E(C)-1.0 eV for high fluences, and anneals out at 400 °C. The associated defect, the nitrogen vacancy, is observed by PAS only in the initial stage of irradiation.

Pulsed electrically detected magnetic resonance for thin film silicon and organic solar cells

In thin film solar cells based on non-crystalline thin film silicon or organic semiconductors structural disorder leads to localized states that induce device limiting charge recombination and trapping. Both processes frequently involve paramagnetic states and become spin-dependent. In the present perspectives article we report on advanced pulsed electrically detected magnetic resonance (pEDMR) experiments for the study of spin dependent transport processes in fully processed thin film solar cells. We reflect on recent advances in pEDMR spectroscopy and demonstrate its capabilities on two different state of the art thin film solar cell concepts based on microcrystalline silicon and organic MEH-PPV:PCBM blends, recently studied at HZB. Benefiting from the increased capabilities of novel pEDMR detection schemes we were able to ascertain spin-dependent transport processes and microscopically identify paramagnetic states and their role in the charge collection mechanism of solar cells.

The PAW/GIPAW approach for computing NMR parameters: a new dimension added to NMR study of solids

In 2001, Mauri and Pickard introduced the gauge including projected augmented wave (GIPAW) method that enabled for the first time the calculation of all-electron NMR parameters in solids, i.e. accounting for periodic boundary conditions. The GIPAW method roots in the plane wave pseudopotential formalism of the density functional theory (DFT), and avoids the use of the cluster approximation. This method has undoubtedly revitalized the interest in quantum chemical calculations in the solid-state NMR community. It has quickly evolved and improved so that the calculation of the key components of NMR interactions, namely the shielding and electric field gradient tensors, has now become a routine for most of the common nuclei studied in NMR. Availability of reliable implementations in several software packages (CASTEP, Quantum Espresso, PARATEC) make its usage more and more increasingly popular, maybe indispensable in near future for all material NMR studies. The majority of nuclei of the periodic table have already been investigated by GIPAW, and because of its high accuracy it is quickly becoming an essential tool for interpreting and understanding experimental NMR spectra, providing reliable assignments of the observed resonances to crystallographic sites or enabling a priori prediction of NMR data. The continuous increase of computing power makes ever larger (and thus more realistic) systems amenable to first-principles analysis. In the near future perspectives, as the incorporation of dynamical effects and/or disorder are still at their early developments, these areas will certainly be the prime target.

Electrically detected electron-spin-echo envelope modulation: a highly sensitive technique for resolving complex interface structures

We show that the electrical detection of electron-spin-echo envelope modulation (ESEEM) is a highly sensitive tool to study interfaces. Taking the Si/SiO2 interface defects in phosphorus-doped crystalline silicon as an example, we find that the main features of the observed echo modulation pattern allow us to develop a microscopic model for the dangling-bond-like P(b0) center by comparison with the results of ab initio calculations. The ESEEM spectrum is found to be far more sensitive to the defect characteristics than the spectrally resolved hyperfine splitting itself.

First-principles calculation of parameters of electron paramagnetic resonance spectroscopy in solids

The hyperfine A-tensor and Zeeman g-tensor parameterize the interaction of an 'effective' electron spin with the magnetic field due to the nuclear spin and the homogeneous external magnetic field, respectively. The A- and g-tensors are the quantities of primary interest in electron paramagnetic resonance (EPR) spectroscopy. In this paper, we review our work [E.S. Kadantsev, T. Ziegler, J. Phys. Chem. A 2008, 112, 4521; E. S. Kadantsev, T. Ziegler, J. Phys. Chem. A 2009, 113, 1327] on the calculation of these EPR parameters under periodic boundary conditions (PBC) from first-principles. Our methodology is based on the Kohn-Sham DFT (KS DFT), explicit usage of Bloch basis set made up of numerical and Slater-type atomic orbitals (NAOs/STOs), and is implemented in the 'full potential' program BAND. Our implementation does not rely on the frozen core approximation. The NAOs/STOs basis is well suited for the accurate representation of the electron density near the nuclei, a prerequisite for the calculation of highly accurate hyperfine parameters. In the case of g-tensor, our implementation is based on the method of Van Lenthe et al. [E. van Lenthe, P. E. S. Wormer, A. van der Avoird, J. Chem. Phys. 1997, 107, 2488] in which the spin-orbital coupling is taken into account variationally. We demonstrate the viability of our scheme by calculating EPR parameters of paramagnetic defects in solids. We consider the A-tensor of 'normal' and 'anomalous' muonium defect in IIIA-VA semiconductors as well as the S2 anion radical in KCl host crystal lattice.

Electrical polarization and orbital magnetization: the modern theories

Macroscopic polarization P and magnetization M are the most fundamental concepts in any phenomenological description of condensed media. They are intensive vector quantities that intuitively carry the meaning of dipole per unit volume. But for many years both P and the orbital term in M evaded even a precise microscopic definition, and severely challenged quantum-mechanical calculations. If one reasons in terms of a finite sample, the electric (magnetic) dipole is affected in an extensive way by charges (currents) at the sample boundary, due to the presence of the unbounded position operator in the dipole definitions. Therefore P and the orbital term in M--phenomenologically known as bulk properties--apparently behave as surface properties; only spin magnetization is problemless. The field has undergone a genuine revolution since the early 1990s. Contrary to a widespread incorrect belief, P has nothing to do with the periodic charge distribution of the polarized crystal: the former is essentially a property of the phase of the electronic wavefunction, while the latter is a property of its modulus. Analogously, the orbital term in M has nothing to do with the periodic current distribution in the magnetized crystal. The modern theory of polarization, based on a Berry phase, started in the early 1990s and is now implemented in most first-principle electronic structure codes. The analogous theory for orbital magnetization started in 2005 and is partly work in progress. In the electrical case, calculations have concerned various phenomena (ferroelectricity, piezoelectricity, and lattice dynamics) in several materials, and are in spectacular agreement with experiments; they have provided thorough understanding of the behaviour of ferroelectric and piezoelectric materials. In the magnetic case the very first calculations are appearing at the time of writing (2010). Here I review both theories on a uniform ground in a density functional theory (DFT) framework, pointing out analogies and differences. Both theories are deeply rooted in geometrical concepts, elucidated in this work. The main formulae for crystalline systems express P and M in terms of Brillouin-zone integrals, discretized for numerical implementation. I also provide the corresponding formulae for disordered systems in a single k-point supercell framework. In the case of P the single-point formula has been widely used in the Car-Parrinello community to evaluate IR spectra.

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

Relativistic two-component calculations of electronic g-tensors that include spin polarization

The first two-component relativistic density-functional approach for the calculation of electronic g-tensors is reported that includes spin polarization using noncollinear spin-density functionals. The method is based on the relativistic Douglas-Kroll-Hess Hamiltonian and has been implemented into the ReSpect program package. Using three self-consistent-field calculations with orthogonal orientations of total magnetization J, the full g-matrix may be obtained. In contrast to previous spin-restricted two-component treatments, results with the new approach agree excellently with spin-polarized one-component calculations for light-atom radicals. Additionally, unlike one-component approaches, the method also reproduces successfully the negative deltag(parallel)-values of heavy-atom 2sigma radicals and the negative deltag(perpendicular) components in cysteinyl. The new method removes effectively the dilemma existing up to now regarding the simultaneous inclusion of spin polarization and higher-order spin-orbit effects in g-tensor calculations. It is straightforwardly applicable to higher than doublet spin multiplicities and has been implemented with hybrid functionals.

Orbital magnetization in periodic insulators

Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation of bulklike Wannier functions in the interior, and an unexpected one arising from net currents carried by Wannier functions near the surface. Each contribution can be expressed as a bulk property in terms of Bloch functions in a gauge-invariant way. Our expression is verified by comparing numerical tight-binding calculations for finite and periodic samples.

Orbital Magnetization in Extended Systems

While the orbital magnetic dipole moment of any finite sample is well-defined, it becomes ill-defined in the thermodynamic limit as a result of the unboundedness of the position operator. Effects due to surface currents and to bulk magnetization are not easily disentangled. The corresponding electrical problem, where surface charges and bulk polarization appear as entangled, was solved about a decade ago by the modern theory of polarization, based on a Berry phase. We follow a similar path here, making progress toward a bulk expression for the orbital magnetization in an insulator represented by a lattice-periodic Hamiltonian with broken time-reversal symmetry. We therefore limit ourselves to the case where the macroscopic (i.e. cell-averaged) magnetic field vanishes. We derive an expression for the contribution to the magnetization arising from the circulating currents internal to the bulk Wannier functions, and then transform to obtain a Brillouin zone integral involving the occupied Bloch orbitals. A version suitable for practical implementation in discretized reciprocal space is also derived, and the gauge invariance of both versions is explicitly shown. However, tests on a tight-binding model indicate the presence of additional edge currents, and it remains to be determined whether these can be related to the bulk band structure.

Gauge invariance of the spin-other-orbit contribution to the g-tensors of electron paramagnetic resonance

The spin-other-orbit (SOO) contribution to the g-tensor (DeltagSOO) of electron paramagnetic resonance arises due to the interaction of electron-spin magnetic moment with the magnetic field produced by the orbital motion of other electrons. A similar mechanism is responsible for the leading term in nuclear magnetic-shielding tensors sigma. We demonstrate that analogous to sigma, paramagnetic DeltagSOO contribution exhibits a pronounced dependence on the choice of the magnetic-field gauge. The gauge corrections to DeltagSOO are similar in magnitude, and opposite in sign, to the paramagnetic SOO term. We calculate gauge-invariant DeltagSOO values using gauge-including atomic orbitals and density-functional theory. For organic radicals, complete gauge-invariant DeltagSOO values typically amount to less than 500 parts per million (ppm), and are small compared to other g-tensor contributions. For the first-row transition-metal compounds, DeltagSOO may contribute several thousand ppm to the g-tensor, but are negligible compared to the remaining deviations from experiment. With popular choices for the magnetic-field gauge, the individual gauge-variant contributions may be an order of magnitude higher, and do not provide a reliable estimation of DeltagSOO.

Efficient and accurate approximations to the molecular spin-orbit coupling operator and their use in molecular g-tensor calculations

Approximations to the Breit-Pauli form of the spin-orbit coupling (SOC) operator are examined. The focus is on approximations that lead to an effective quasi-one-electron operator which leads to efficient property evaluations. In particular, the accurate spin-orbit mean-field (SOMF) method developed by Hess, Marian, Wahlgren, and Gropen is examined in detail. It is compared in detail with the "effective potential" spin-orbit operator commonly used in density functional theory (DFT) and which has been criticized for not including the spin-other orbit (SOO) contribution. Both operators contain identical one-electron and Coulomb terms since the SOO contribution to the Coulomb term vanishes exactly in the SOMF treatment. Since the DFT correlation functional only contributes negligibly to the SOC the only difference between the two operators is in the exchange part. In the SOMF approximation, the SOO part is equal to two times the spin-same orbit contribution. The DFT exchange contribution is of the wrong sign and numerically shown to be in error by a factor of 2-2.5 in magnitude. The simplest possible improvement in the DFT-SOC treatment [Veff(-2X)-SOC] is to multiply the exchange contribution to the Veff operator by -2. This is verified numerically in calculations of molecular g-tensors and one-electron SOC constants of atoms and ions. Four different ways of handling the computationally critical Coulomb part of the SOMF and Veff operators are discussed and implemented. The resolution of the identity approximation is virtually exact for the SOC with standard auxiliary basis sets which need to be slightly augmented by steep s functions for heavier elements. An almost as efficient seminumerical approximation is equally accurate. The effective nuclear charge model gives results within approximately 10% (on average) of the SOMF treatment. The one-center approximation to the Coulomb and one-electron SOC terms leads to errors on the order of approximately 5%. Small absolute errors are obtained for the one-center approximation to the exchange term which is consequently the method of choice [SOMF(1X)] for large molecules.

On-the-fly localization of electronic orbitals in Car–Parrinello molecular dynamics

The ab initio molecular-dynamics formalism of Car and Parrinello is extended to preserve the locality of the orbitals. The supplementary term in the Lagrangian does not affect the nuclear dynamics, but ensures "on the fly" localization of the electronic orbitals within a periodic supercell in the Gamma-point approximation. The relationship between the resulting equations of motion and the formation of a gauge-invariant Lagrangian combined with a gauge-fixing procedure is briefly discussed. The equations of motion can be used to generate a very stable and easy to implement numerical integration algorithm. It is demonstrated that this algorithm can be used to compute the trajectory of the maximally localized orbitals, known as Wannier orbitals, in ab initio molecular dynamics with only a modest increase in the overall computer time. In the present paper, the new method is implemented within the generalized gradient approximation to Kohn-Sham density-functional theory employing plane wave basis sets and atomic pseudopotentials. In the course of the presentation, we briefly discuss how the present approach can be combined with localized basis sets to design fast linear scaling ab initio molecular-dynamics methods.