Spherical Cell Approximation Research Articles

Exact muffin tin orbital based first-principles method for electronic-structure and electron-transport simulation of device materials

The exact muffin tin orbital (EMTO) method features high efficiency and accuracy for first-principles simulations with density functional theory. In this paper we report our implementation of the EMTO method for electronic-structure and quantum transport simulation of device materials. We consider a device-material structure with a central device region in contact with different semi-infinite electrodes. Based on the Green's function method, the infinite device, nonperiodic in transport direction, is transformed into a calculable finite material system by treating the semi-infinite electrodes with electrode self-energies, and the Green's function of the device region is calculated with an efficient recursive technique. In the present implementation we adopt the spherical cell approximation to treat the electrostatics, and we solve the electrostatic potential of the finite device region by enforcing the boundary conditions to the known potential of electrode materials. The coherent potential approximation is incorporated for treating the atomic disorders inevitable in realistic materials, and the effects of multiple disorder scattering on electron transport are accounted for by vertex correction for simulating disordered electronic devices. To demonstrate the capability of the present implementation, we calculate the monolayer two-dimensional material MoS2 and black phosphorus, and study the spin-dependent tunneling in the Fe/MgO/Fe magnetic tunneling junction. We find the EMTO electronic structures of the calculated systems agree well with the results of the projector augmented wave method. The EMTO transport simulation produces the important spin-filtering effect of the Fe/MgO/Fe junction and the important influence of the interfacial disorders on the spin-dependent tunneling, agreeing well with previous theoretical and experimental studies. The implementation of the EMTO based device simulator provides an effective simulation tool for simulating both ordered and disordered device materials, extending the capability for theoretical design of electronic devices from first principles.

First-principles calculation of the energy of compressed calcium

The energy of a calcium crystal with a simple cubic lattice as a function of the ratio (t/U) between two internal parameters of the Hubbard model has been calculated using the Hubbard model for the s bands, equations of motion, and direct algebraic method. The electronic spectra have been calculated for the 4s band of the crystal in two principal symmetry directions of the first Brillouin zone. The calculations have been performed at temperatures T1 = 0 K and T2 = 1000 K. All calculations have been carried out for different interaction energies U of s electrons, one angle, and their different concentrations n in the range 0 ≤ n ≤ 2. The calculations have demonstrated that the dependences of the energy and electronic spectra in this compressed state are very smooth. The occupation of the Ca 4s band is in good agreement with the results of the pioneering calculations of compressed Ca (and a number of other metals), which were carried out by Gandel’man and his colleagues in the Wigner-Seitz spherical cell approximation. It has been shown that the performed analysis accurately reproduces the data obtained on the superconductivity in terms of the Bardeen-Cooper-Schrieffer theory if the 4s band is half-occupied.

Application of the Cell Potential Method To Predict Phase Equilibria of Multicomponent Gas Hydrate Systems

We present the application of a mathematical method reported earlier by which the van der Waals-Platteeuw statistical mechanical model with the Lennard-Jones and Devonshire approximation can be posed as an integral equation with the unknown function being the intermolecular potential between the guest molecules and the host molecules. This method allows us to solve for the potential directly for hydrates for which the Langmuir constants are computed, either from experimental data or from ab initio data. Given the assumptions made in the van der Waals-Platteeuw model with the spherical-cell approximation, there are an infinite number of solutions; however, the only solution without cusps is a unique central-well solution in which the potential is at a finite minimum at the center to the cage. From this central-well solution, we have found the potential well depths and volumes of negative energy for 16 single-component hydrate systems: ethane (C2H6), cyclopropane (C3H6), methane (CH4), argon (Ar), and chlorodifluoromethane (R-22) in structure I; and ethane (C2H6), cyclopropane (C3H6), propane (C3H8), isobutane (C4H10), methane (CH4), argon (Ar), trichlorofluoromethane (R-11), dichlorodifluoromethane (R-12), bromotrifluoromethane (R-13B1), chloroform (CHCl3), and 1,1,1,2-tetrafluoroethane (R-134a) in structure II. This method and the calculated cell potentials were validated by predicting existing mixed hydrate phase equilibrium data without any fitting parameters and calculating mixture phase diagrams for methane, ethane, isobutane, and cyclopropane mixtures. Several structural transitions that have been determined experimentally as well as some structural transitions that have not been examined experimentally were also predicted. In the methane-cyclopropane hydrate system, a structural transition from structure I to structure II and back to structure I is predicted to occur outside of the known structure II range for the cyclopropane hydrate. Quintuple (L(w)-sI-sII-L(hc)-V) points have been predicted for the ethane-propane-water (277.3 K, 12.28 bar, and x(eth,waterfree) = 0.676) and ethane-isobutane-water (274.7 K, 7.18 bar, and x(eth,waterfree) = 0.81) systems.

Equation of State of Tantalum and Plutonium in a Spherical Cell Approximation and at Extremely High Pressures

We first present the equation of state (EOS) of a relativistic homogeneous electron gas in the exchange only approximation. We then go on to use this result to determine approximately the EOS of the heavy metals Pu and Ta. An essential ingredient is the electron density at the boundary of the Wigner-Seitz polyhedron and we determine this density using relativistic Thomas-Fermi theory.

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.

Equation of state in metals and cold stars - Evaluation of statistical models

The Thomas-Fermi-Dirac (TFD) statistical model for electronic structures if refined by Weizsacker gradient and correlation energy corrections. The resulting FTD-λWc model is then used to calculate the nonrelativistic, cold matter equation of state (EOS) in the Wigner-Seitz spherical cell approximation. The correction terms are important mainly at low densities near matter equilibrium (i.e., zero pressure). Inclusion of the gradient term removes many of the unphysical features of the TFD model. Results are summarized for several elements of astrophysical and theoretical importance. The mass-radius relation of a low-mass white dwarf model is calculated using the TDF-λWc EOS.

First principles calculations of the volume dependence of the spin susceptibility for Li and Na

The new variational principle-density functional theory of the spin susceptibility has been used to calculate its volume dependence for Li and Na. The results are compared with recent experiments and previous theories. The exchange-correlation functionals are treated in the local spin density approximation. The single particle electron states are treated in the spherical cell approximation. The agreement between the new theory and experiment is very good for Na and quite acceptable for Li when OPW values of the single particle density of states are used. The results of the new theory are superior to those of the previous theories.

SOLID HARMONICS AS BASIS FUNCTIONS FOR CUBIC CRYSTALS

The various sets of basis functions useful in discussing cubic crystals must include sets of symmetrized combinations of powers of the co-ordinates ortho-gonalized over the cellular polyhedron. Such polynomials are here called solid harmonics. A study of the actual solid harmonics reveals the limitations of the spherical cell approximation. The solid harmonics can be used to develop a new method over the cellular polyhedron of the body-centered cubic lattice or of the face-centered cubic lattice.

An Application of the W.K.B. Method to the Cohesive Energy of Monovalent Metals

A new method is developed which, within the limits of the spherical cell approximation first presented by Wigner and Seitz, will permit the evaluation of the cohesive energy, lattice constant, and compressibility of a monovalent metallic solid without the explicit computation of a central field for the atom. Analytic formulas for approximate solid state wave functions are produced in the region outside the atomic core by utilizing Imai's form of the W.K.B. method with the phase constant determined explicitly in terms of the known quantum defect of the free atom. These wave functions are applied to the determination of the minimum ground state energy in the alkali metals and of the sphere radius at which this occurs as functions of the quantum defects of the free atoms. These functions, when applied to Fr\"ohlich's semi-empirical formula, yield a rapid and accurate method for the computation of the ground-state energy as a function of sphere radius.