Muffin-tin Orbital Theory Research Articles

Scaling of Transition State Vibrational Frequencies and Application of d-Band Theory to the Brønsted–Evans–Polanyi Relationship on Surfaces

Semiempirical energy relations provide a means of estimating thermodynamic properties. Specifically, linear scaling relationships (LSRs) and Brønsted–Evans–Polanyi (BEP) relationships correlate adsorption energies between adsorbates across surfaces and reaction energies with activation barriers, respectively. Although vibrational scaling relations (VSRs) exist between adsorbates at identical sites, scaling between vibrational frequencies of adsorbed local minima and transition states is lacking. Here, we present density functional theory calculations for AHX (A = C, N, O) diffusions on transition metal surfaces and reveal linear scaling between frequencies of local minima and the transition state between those minima. Using d-band theory and linear muffin tin orbital theory (LMTO), we derive the slopes of these transition state vibrational scaling relations (TSVSRs) and, in so doing, provide a rigorous theory extending the original BEP relations developed for solution chemistry to surface chemistry. With a single reference DFT calculation, we predict the slopes and quantify uncertainty in the predictions.

Active learning with non-ab initio input features toward efficient CO2 reduction catalysts.

In a conventional chemisorption model, the d-band center theory (augmented sometimes with the upper edge of the d-band for improved accuracy) plays a central role in predicting adsorption energies and catalytic activity as a function of the d-band center of solid surfaces, but it requires density functional calculations that can be quite costly for the purposes of large scale screening of materials. In this work, we propose to use the d-band width of the muffin-tin orbital theory (to account for the local coordination environment) plus electronegativity (to account for adsorbate renormalization) as a simple set of alternative descriptors for chemisorption which do not require ab initio calculations for large-scale first-hand screening. This pair of descriptors is then combined with machine learning methods, namely, neural network (NN) and kernel ridge regression (KRR). We show, for a toy set of 263 alloy systems, that the CO adsorption energy on the (100) facet can be predicted with a mean absolute deviation error of 0.05 eV. We achieved this high accuracy by utilizing an active learning algorithm, without which the accuracy was 0.18 eV. In addition, the results of testing the method with other facets such as (111) terrace and (211) step sites suggest that the present model is also capable of handling different coordination environments effectively. As an example of the practical application of this machine, we identified Cu3Y@Cu* as an active and cost-effective electrochemical CO2 reduction catalyst to produce CO with an overpotential ∼1 V lower than a Au catalyst.

Scaling relationships and theory for vibrational frequencies of adsorbates on transition metal surfaces

Adsorbate vibrational excitations are an important fingerprint of molecule/surface interactions, affecting temperature contributions to the free energy and impacting reaction rate and equilibrium constants. Furthermore, vibrational spectra aid in identifying species and adsorption sites present in experimental studies. Despite their importance, knowledge of how adsorbate frequencies scale across materials is lacking. Here, by combining previously reported experimental data and our own density-functional theory calculations, we reveal linear correlations between vibrational frequencies of adsorbates on transition metal surfaces. Through effective-medium theory, linear muffin-tin orbital theory, and the d-band model, we rationalize the squares of the frequencies to be fundamentally linear in their scaling across transition metal surfaces. We identify the adsorbate-binding energy as a descriptor for certain molecular vibrations and rigorously relate errors in frequencies to errors in adsorption energies. We also discuss the impact of scaling on surface thermochemistry and adsorbate coverage.

Alloying effect on the ideal tensile strength of ferromagnetic and paramagnetic bcc iron

Using ab initio alloy theory formulated within the exact muffin-tin orbitals theory in combination with the coherent potential approximation, we investigate the ideal tensile strength (ITS) in the [001] direction of bcc ferro-/ferrimagnetic (FFM) and paramagnetic (PM) Fe1−xMx​ (M = Al, V, Cr, Mn, Co, or Ni) random alloys. The ITS of ferromagnetic (FM) Fe is calculated to be 12.6 GPa, in agreement with available data, while the PM phase turns out to posses a significantly lower value of 0.7 GPa. Alloyed to the FM matrix, we predict that V, Cr, and Co increase the ITS of Fe, while Al and Ni decrease it. Manganese yields a weak non-monotonic alloying behavior. In comparison to FM Fe, the alloying effect of Al and Co to PM Fe is reversed and the relative magnitude of the ITS can be altered more strongly for any of the solutes. All considered binaries are intrinsically brittle and fail by cleavage of the (001) planes under uniaxial tensile loading in both magnetic phases. We show that the previously established ITS model based on structural energy differences proves successful in the PM Fe-alloys but is of limited use in the case of the FFM Fe-based alloys. The different performance is attributed to the specific interplay between magnetism and volume change in response to uniaxial tension. We establish a strong correlation between the compositional effect on the ITS and the one on the shear elastic constant C' for the PM Fe-alloys and briefly discuss the relation between hardenability and the ITS.

Disordered magnetic multilayers: Electron transport within the coherent potential approximation

We develop an efficient technique for ab initio calculations of the current-perpendicular-to-plane (CPP) electron transport in disordered magnetic multilayers. The method is based on the tight-binding linear muffin-tin orbital theory and the coherent potential approximation (CPA) to treat the substitutional randomness in an effective-medium approach. A formulation of the CPA vertex corrections, giving rise to an incoherent part of the CPP conductance, is described in detail and the numerical implementation is discussed. The developed approach is illustrated on several disordered systems derived from fcc Co-Cu-Co trilayers and its results are compared to those of a supercell technique simulating the randomness in terms of two-dimensional lateral supercells. The overall good agreement of the two techniques proves reliability of the CPA for a number of specific features encountered in disordered multilayers. As another example, results for layered diluted ferromagnetic (Ga, Mn)As semiconductors are reported, including a brief discussion of spin-resolved and incoherent CPP conductances and a comparison to bulk residual resistivities.

Thermoelastic properties of random alloys from first-principles theory

We present a first-principles description of the temperature-dependent elastic constants in random alloys. The substitutional disorder is treated using the coherent potential approximation implemented within the frameworks of exact muffin-tin orbitals theory. The temperature effects are approximated as the sum of electronic and thermal expansion contributions. Calculations on pure Nb demonstrate that this approach correctly accounts for the main temperature dependence of cubic elastic constants. When extended to Nb-Zr solid solution, the theoretical results show good agreement with experiments at temperatures $\ensuremath{\lesssim}300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

Chemical composition–elastic property maps of austenitic stainless steels

Despite a tremendous development during the last decades, both as regards computer power and methodology, it has remained impossible to treat steel at a fundamental atomic level. However, recently we have shown [L. Vitos, P.A. Korzhavyi, B. Johansson, Phys. Rev. Lett. 88 (2002) 155501] that the most efficient theories of random substitutional alloys combined with advanced numerical techniques have made possible to establish a theoretical insight to the electronic structure of stainless steels. Here a detailed description of the quantum-mechanical modeling of austenitic stainless steels is presented. We adopt an ab initio electronic structure calculation method based on the coherent potential approximation, implemented within the framework of the exact muffin tin orbitals theory, to map the chemical composition distributions of austenitic stainless steels into the elastic property distributions. The so generated database can be fruitfully used in the design of new class of steel alloys.

Elastic anomalies in Ag-Zn alloys

Ab initio total energy calculations, based on the exact muffin-tin orbitals theory, are used to determine elastic properties of ${\mathrm{Ag}}_{1\ensuremath{-}c}{\mathrm{Zn}}_{c}$ random alloys in the face-centered and body-centered cubic crystallographic phases. The compositional disorder is treated within the framework of the coherent potential approximation. The cubic elastic constants B, ${C}^{\ensuremath{'}},$ and ${C}_{44}$ and the Debye temperatures are calculated for the whole range of concentrations, $0l~cl~1.$ Experimental data are in very good agreement with the present results. Rapid variations of ${C}^{\ensuremath{'}}$ and ${C}_{44}$ are observed at high Zn concentrations, which contradicts the common empirical observation that alloying has only minor effects on elastic properties.

High-pressure structure of ScAlO3perovskite

Total energy calculations performed for ScAlO 3 perovskite, using the global parametrization method (GPM) in conjunction with the exact muffin-tin orbitals theory, show that the orthorhombic Pbnm structure remains stable relative to the cubic structure for pressures up to 150 GPa. The slightly larger compressibility of AlO 6 octahedra relative to the ScO 12 polyhedra is reflected in increasing polyhedral volume ratio, V Sc /V Al and in a moderate reduction of the orthorhombic distortion with hydrostatic pressure. This observation indicates limitations in the structural analogy between ScAlO 3 and the geophysically important MgSiO 3 perovskite.

Total-energy method based on the exact muffin-tin orbitals theory

I present a total-energy method based on the exact muffin-tin orbitals (EMTO) theory and the full charge density (FCD) technique. The FCD-EMTO method combines the accuracy of the full-potential method and the efficiency of the muffin-tin potential method. The one-electron Kohn-Sham equations are solved exactly for the overlapping muffin-tin potential and from the self-consistent solutions the full charge density is constructed. The EMTO kinetic energy, combined with the Coulomb and exchange-correlation terms calculated from the total density, yields the FCD-EMTO total energy. The accuracy of the FCD-EMTO method is demonstrated through several test calculations.

Application of the exact muffin-tin orbitals theory: the spherical cell approximation

We present a self-consistent electronic structure calculation method based on the exact muffin-tin orbitals (EMTO) theory developed by O.K. Andersen, O. Jepsen and G. Krier [in: V. Kumar, O.K. Andersen, A. Mookerjee (Eds.), Lectures on Methods of Electronic Structure Calculations, Word Scientific, Singapore, 1994, pp. 63–124] and O.K. Andersen, C. Arcangeli, R.W. Tank, T. Saha-Dasgupta, G. Krier, O. Jepsen and I. Dasgupta [Mater. Res. Soc. Symp. Proc. 491 (1998) 3–34]. The EMTO theory can be considered as an improved screened KKR (Korringa–Kohn–Rostoker) method which is able to treat large overlapping potential spheres. Within the present implementation of the EMTO theory the one-electron equations are solved exactly using Green's function formalism, and Poisson's equation is solved within the spherical cell approximation (SCA). To demonstrate the accuracy of the SCA–EMTO method, test calculations have been carried out.

Three-dimensional electron momentum density of aluminum by(γ,eγ)spectroscopy

We report on the measurement of the three-dimensional electron momentum density (EMD) of aluminum. 150 keV photons with an intensity of $2\ifmmode\times\else\texttimes\fi{}{10}^{11}$ photons/s from a multipole wiggler of the European Synchrotron Radiation Facility have been scattered at a 100 nm thin self-supporting aluminum foil and measured in coincidence with their recoil electrons. To improve the agreement with a full potential linear muffin-tin orbital theory, electron correlation effects have been incorporated via the so-called Lam-Platzman correction [Phys. Rev. B 9, 5122 (1974)]. A comparison with two-dimensional angular correlation of annihilation radiation has been made and demonstrates the strong influence of the positron wave function on the EMD. In analogy to these experiments, we used the first derivative of the EMD as an indication of the Fermi breaks.

Atomistic simulation of thermodynamic and mechanical properties of metals

This paper reviews the atomistic simulation of thermodynamic and mechanical properties of prototype metals using first-principles density-functional methods. Electronic-structure techniques developed from linear muffin-tin orbital theory can yield accurate cold and electron-thermal contributions to the equation of state, pressure-induced structural phase transitions, phonons, elastic moduli, and ideal shear strength to ultrahigh pressures. Complementary interatomic-potentials methods developed from generalized pseudopotential theory can provide in addition the ion-thermal equation of state, high-pressure melting curve, and temperature–pressure phase diagram, as well as the atomic structure and energetics of point and extended defects including vacancies, grain boundaries, and dislocations. The latter represent essential atomistic input into the rigorous multiscale modeling of mechanical properties such as plastic flow. Applications to the metals magnesium, molybdenum, and tantalum are discussed.

Ab initio total-energy calculations for iron-acceptor pairs in silicon

We present ab initio total-energy calculations for trigonal and orthorhombic iron-acceptor pairs in silicon. The total-energy calculations have been performed in the general framework of the density-functional theory treating many-particle effects in the local spin-density approximation. We use a Green's-function approach based on the linear muffin-tin orbitals theory using the atomic-sphere approximation (which unfortunately prohibits the inclusion of any lattice-relaxation effects). Our total-energy calculations lead to a model for the electronic structure of both orthorhombic and trigonal pairs that is dominated by ionic binding of the interstitial iron to the acceptor on a substitutional site and does not predict a significant covalent binding of the pair. This is in contrast to the case of ${\mathrm{Fe}}_{\mathrm{i}}$-${\mathrm{Au}}_{\mathrm{Si}}$ and ${\mathrm{Fe}}_{\mathrm{i}}$-${\mathrm{Ag}}_{\mathrm{Si}}$ pairs for which there is a strong covalent pair binding for any position of the Fermi energy. In agreement with the ionic-binding model, we do not find pairing in n-type material for any iron-acceptor pairs. We find, however, that in n-type material there is moderately strong pairing of iron with shallow donors (${\mathrm{P}}_{\mathrm{Si}}^{+}$ for example), again in agreement with an ionic model for the pair formation.

Ground-state properties of isolated interstitial iron in silicon: Electronic structure and hyperfine interactions.

We have performed ab initio total energy calculations for interstitial iron in silicon with particular emphasis on the matrix elements for the hyperfine interactions with the iron nucleus and with several silicon ligand nuclei. The total energy calculations have been performed in the general framework of the density functional theory (DFT) treating many-particle effects in the local spin-density approximation (LSDA). We use a Dyson's equation approach to solve the Kohn-Sham equation of the density functional theory and calculate the Green's function with the help of the linear muffin-tin orbital theory using the atomic-spheres approximation (ASA). Unfortunately the use of the ASA prohibits the inclusion of lattice relaxation effects. Our total energy calculations lead to a model for the electronic structure which is dominated by covalent hybridization of iron d states with silicon p states. From the results of our calculations we can easily explain the reaction of the electronic system when passing from ${\mathrm{Fe}}_{\mathit{i}}^{0}$ to ${\mathrm{Fe}}_{\mathit{i}}^{+}$. To this aim we slightly modify the Ludwig-Woodbury model: In a first step we consider the exchange splitting of the iron d states which in a second step are further split by the crystal field. The hyperfine matrix elements for Si:${\mathrm{Fe}}_{\mathit{i}}^{0}$ are calculated directly from the magnetization density obtained by the LSDA-DFT calculation and show excellent agreement with data from electron nucleus double resonance (ENDOR) experiments. For Si:${\mathrm{Fe}}_{\mathit{i}}^{+}$ we have to take into account the spin-orbit interaction of the iron d orbitals. Since our total energy calculations neglect spin-orbit interactions, we switch to a description which uses symmetry-adapted many-particle wave functions. With these functions we calculate the matrix elements for the hyperfine interaction with the iron nucleus and with several silicon ligand nuclei. We use the localization properties of our magnetization density to determine the many-particle wave function and to obtain data for the hyperfine interactions. We show that the covalent hybridization of the iron d states with iron p states and with silicon orbitals alone cannot explain the discrepancy between calculated and measured data for the hyperfine interaction with the iron nucleus. However, the additional consideration of a dynamical Jahn-Teller effect as a Ham effect leads to consistent data. The calculated data for the ligand hyperfine interaction allow one to definitely assign ligand shells to the measured ENDOR data. \textcopyright{} 1996 The American Physical Society.

Van Hove singularity scenario and hole density in CaCuO2: Pressure effects.

A first-principles self-consistent full-potential linear muffin-tin orbital theory has been employed to investigate the effect of hydrostatic pressure on the location of the van Hove singularity (vHs) and the concentration of holes in the parent superconductor ${\mathrm{CaCuO}}_{2}$. One finds the pinning of the vHs at the Fermi level for a critical relative volume (V/${\mathit{V}}_{0}$)=0.68, ${\mathit{V}}_{0}$ being the volume at normal pressure. This critical volume corresponds to a pressure of about 40 GPa, which should show up in a large value of ${\mathit{T}}_{\mathit{c}}$ in the experiment. The nested area in the Brillouin zone is maximum for the critical volume. The hole concentration increases with the pressure.

Extended muffin-tin orbital theory applied to the reaction of CO+H2on Ni(001)

The method using energy bands from a linear combination of muffin-tin orbitals has been extended so that the unit cell is now divided into muffin-tin and non-muffin-tin regions, instead of atomic Wigner-Seitz cells. The full potential including the nonspherical contribution to the potential is still included throughout the unit cell. The new method has been applied to the interaction of CO+${\mathrm{H}}_{2}$ on Ni(001) surface. Through use of three-dimensional charge-density plots, we show that CO forms C+C${\mathrm{O}}_{2}$ through disproportionation. We also show that the Ni(001) surface can break the carbon-oxygen bond of formaldehyde, but not carbon monoxide.