Muffin-tin Approximation Research Articles

MS-Xα calculation of the barrier to internal rotation in ethylene

Calculations for ethylene using the multiple-scattering Xα method in the muffin-tin approximation are reported. Comparison of the calculated twisting potentials of both the singlet ground state and the first excited triplet with experimental values show about the same agreement as ab initio calculations including configuration interaction. In addition, the use of overlapping spheres is shown not to improve the Xα results.

Future prospects for the Xα method

Recent work to eliminate the effect of the muffin-tin approximation has shown that this makes an important improvement in Xα results for diatomic molecules, though it is less important for atoms with many neighbors. Various aspects of the Xα method itself, not involving the muffin-tin approximation, are discussed. It is pointed out that for the Hellmann Feynman and virial theorems to hold for the Xα method, with α's varying from one atom to another, it is sufficient if the α's change values from those appropriate to one atom to those for another on the surfaces of spheres small enough so that the charge density is practically constant over the surface of such a sphere. This means that the spheres should be smaller than those usually used for the muffin-tin method. It is shown that one can get approximately the correct exchange correlation for any atom, except the very lightest ones, if a value of α equal to 0.7772 is used within a sphere of radius rα, somewhat smaller than the radius of maximum radial charge density in the L shell, and a value of 2/3 is used everywhere outside these spheres. Except for the very light atoms, this would fulfill the requirements for the Hellmann Feynman and virial theorems to hold. There is a discussion of spin polarization in molecules. The value of 0.7772 for hydrogen would imply that it is to be treated in a spin-polarized way, which would imply that an antiferromagnetic type of structure for the H2 molecule, somewhat similar to that proposed many years ago by Coulson and Fischer, should be used. Some magnetic problems are discussed, and in particular a procedure is outlined for using the Xα method to find the Heisenberg exchange integral in an antiferromagnetic substance like NiO. Calculations of this quantity have not yet been completed.

Dependence of transition metal energy bands on hubbard parameters

Band calculations carried out for all fee and bcc transition metals by the Hubbard method show a strong linear dependence of their features on two characteristic energies of the method which are easily calculated from the muffin-tin potential used. As an example the density-of-states curve has been predicted for β-Mn, for which a direct band calculation would be very laborious, by the use of this information.

A ms-Xα-mt study of cyclobutane

The multiple-scattering Xα method with the muffin-tin potential approximation (MS-Xα-MT) was studied for its application in a somewhat strenuous conformational analysis test. The ring-puckering potential for cyclobutane experimentally is of the double-well type with a barrier of 1.44 kcal/mole. However, this study did not show the out-of-plane form to be energetically favored. Two sets of calculations were performed to determine something of the geometry sensitivity of this method and it appears too insensitive to geometry changes in the model. It seems that the muffin-tin potential leads to significant errors in the total energy which preclude the technique in its present form from conformational analysis studies.

The electronic structure of octahedral transition metal halides as calculated by the multiple scattering method

The multiple scattering formalism with Xα exchange and muffin-tin potentials is used in a study of the electronic structure of several octahedral transition metal complexes. The calculated orbital energies are ordered in agreement with the traditional opinion with antibonding orbitals of ee and t2g symmetry as highest occupied molecular orbitals. The splittings in orbital energies agree well with measured 10Dq values. Calculated spin densities are in fair agreement with experiments. The role of spin polarization is found to be greater than believed previously. The 3s splitting in the x-ray photoelectron spectra has been examined. For d5 systems a larger reduction of the splitting for more covalent bonding was obtained in agreement with experiments, whereas for d3 systems the opposite result was found, contrary to experimental evidence. Mossbauer isomer shifts have been studied. The pressure shift is found to be crucially dependent on the choice of muffin-tin sphere radii. The shifts between Fe3+, Fe2+, and Fe+ agree with other calculations and with experiments, provided a calibration constant α = 0.35a30, mm/sec is used.

Application of the method of tight binding for determining the excited bands of sodium and potassium

An accurate determination of the energy bandstructure of sodium and potassium has been performed by extending the basis set to include Bloch sums of single Gaussian orbitals of s, p, d, and f type. The results obtained using this extended basis set offer improvement over the results obtained using only Bloch sums of atomic orbitals. This increased variational freedom affected the bottom of the conduction band very little (about 0.01 a.u.) but affected the high energy bands in potassium by as much as 0.06 a.u. Comparison of energy bands using muffin-tin potential and overlapping atomic potential is also presented.

Calculation of dipole moments for diatomic molecules with multiple-scattering Xα wave functions

The dipole moments for LiH, BH, and CH are calculated with the multiple-scattering-Xα (MS-Xα) wave functions. The integral over the intersphere region is reduced to a one-dimensional integral by use of prolate spheroidal coordinates. The results show that it is adequate to use the MS-Xα wave functions for such calculations and that there is an improvement over the use of the muffin-tin charge density approximation.

MS-Xα calculations of polyhedral boron compounds

MS-Xα calculations have been carried out for B6H-26, B5H9, and 1,6-B4C2H6. Even with the simple muffin-tin approximation, the agreement of the transition state orbital energies with the measured photoelectron spectral ionization potentials for B5H9, and 1,6-B4C2H6 is as good or better than that found with previous ab initio minimum STO basis LCAO-MO-SCF calculations. The undesirable brittleness of the refractory borides is due to boron polyhedra being joined together in three-dimensional networks by unpaired outpointing electrons at the apices of the polyhedra. It is suggested that a way to ameliorate this brittleness would be to replace some of the boron atoms by carbons (or nitrogens or oxygens) to cut down on the outpointing unpaired electrons and thus to cut down on three dimensional network bonding. It is further hypothesized that such “carborides” or related congeneric species might also have an excellent possibility of being high-temperature superconductors.

Band structure calculation for realistic (non-muffin-tin) potentials based on the rigorous cellular method

Altmann's cellular method in which the Bloch states are determined by minimizing the mean square mismatch of a finite partial wave expansion at the cell boundaries, is shown to be readily adaptable to non-muffin-tin potentials. As a first test, the new method is applied to a nonspherically symmetric potential of aluminum and checked against a self-consistent muffin-tin potential, the former chosen such that its spherical average coincides with the latter. The non-muffin-tin effects turn out to be very small, as is expected for face-centered cubic lattices.

The MS potential from a set of overlapping densities

It is shown that the usual overlapping spheres method must include, in the monoelectronic potential, some overlap terms which are not present in the functional form of the muffin-tin potential. A new truncated spheres approximate projection is presented and compared with other projections which make use of muffin-tin-like potentials. Results are presented for the potential corrections in the atomic region of the H2 molecule and for some transition metal dihalides, where a comparison between the calculated transition state eigenvalues and the experimental photoelectron spectra is presented.

Analysis of the Ni K-edge X-ray absorption near edge structure in Ni((C2H5O)2PS2)2

The Ni((C2H5O)2PS2)2 complex has been investigated using the X-ray absorption near edge structure (XANES) analysis. Nickel K-edge XANES spectra of the complex have been measured and theoretical calculations of the spectra have been carried out using the finite difference method; the calculation of molecular potential has been carried out both in the full potential and in the muffin-tin approximation. The analysis of results obtained has shown that a good agreement between theoretical and experimental spectra in the low-energy region is achieved only in the case of full potential calculations (beyond the muffin-tin approximation for the potential shape).

Small copper clusters: Study of the local atomic and electronic structure by the XANES and DFT methods

The Cu L3 edge X-ray absorption spectra of free Cun clusters containing 5–15 atoms were obtained for the first time. It is shown that the geometry of small clusters, including the bond length and bond angle, can be studied by analyzing the X-ray absorption spectra. The experimental X-ray absorption spectra of Cu13 clusters were theoretically interpreted using the self-consistent method of full multiple scattering, the finite difference method in the muffin-tin potential approximation, and the full potential method for the icosahedral cluster structure. Good agreement between the theoretical and experimental spectra is achieved for the calculation in the full potential approximation.

Application of XANES spectroscopy to study local structure of photoexcited Cu complex

A new technique for the analysis of transient X-ray absorption (also known as pump-and-probe XAS) and extraction of 3D structural information for photoexcited molecules is proposed. It is applied to metal-to-ligand-charge-transfer state of [Cu(dmp) 2] + (dmp=2,9-dimethyl-1,10-phenanthroline) in acetonitrile solution. Theoretical approach combines fitting of XANES spectra with a multidimensional interpolation approximation and calculating theoretical XANES with molecular potentials beyond the muffin-tin approximation. The results of the study show that the best fit of the experimental XANES data includes a solvent molecule binding to the Cu with Cu–N distance of 2.00 Å, average distance Cu–N of dmp groups is 2.04 Å and that photoexcited state is characterized by significant rocking distortions of the dmp ligands.

Full-potential multiple scattering for core electron spectroscopies

We present a rigorous derivation of a real space full-potential multiple-scattering theory(FP-MST), valid both for continuum and bound states, that is free from the drawbacksthat up to now have impaired its development, in particular the need to use cell shapefunctions and rectangular matrices. In this connection we give a new scheme togenerate local basis functions for the truncated potential cells that is simple,fast, efficient, valid for any shape of the cell and reduces to the minimum thenumber of spherical harmonics in the expansion of the scattering wavefunction. Thisapproach provides a straightforward extension of MST in the muffin-tin (MT)approximation, with only one truncation parameter given by the classical relationlmax = kRb, wherek is the photo-electronwavevector and Rb the radius of the bounding sphere of the scattering cell. Some numerical applications of thetheory are presented, both for continuum and bound states.

Interface two-dimensional metallicity but lack of superconductivity in heterobonded semiconductors: ZnS/Si and GaP/Si

As a follow up to our finding that CuCl/Si superlattices exhibit metallicity at the interfaces and possibly superconductivity, we explore other semiconductor superlattices for the same properties and present here our results for ZnS/Si and GaP/Si superlattices. As found for the CuCl/Si superlattices, both the ZnS/Si and GaP/Si superlattices exhibit two-dimensional metallicity at their interfaces, as shown by their band structures, Fermi surfaces, and charge-density distributions. Furthermore, to gauge any possible superconductivity, the McMillan-Hopfield electron-phonon coupling constant, , is calculated using the rigid muffin-tin approximation. Electron-phonon coupling is observed mostly at the interfaces but it is not strong enough to cause superconductivity at a finite temperature as estimated using the McMillan formula for Tc. This contrasts greatly with the CuCl/Si superlattices, in which electron-phonon coupling is strong enough to indicate superconductivity.

The Overlapping Muffin-Tin Approximation

We present the formalism and demonstrate the use of the overlapping muffin-tin approximation. This fits a full potential to a superposition of spherically symmetric short-ranged potential wells plus a constant. For one-electron potentials of this form, the standard multiple-scattering methods can solve Schrodingers’ equation correctly to 1st order in the potential overlap. Choosing an augmented-plane-wave method as the source of the full potential, we illustrate the procedure for diamond-structured Si. First, we compare the potential in the Si-centered overlapping muffin-tin approximation with the full potential, and then compare the corresponding overlapping muffin-tin approximation N -th order muffin-tin orbital and full-potential linear augmented plane wave band structures. We find that the two latter agree qualitatively for a wide range of overlaps and that the valence bands have a root mean squared deviation of 20 meV/electron for 30% radial overlap. Smaller overlaps give worse potentials and larger overlaps give larger 2nd-order errors of the multiple-scattering method. To further remove the mean error of the bands for small overlaps is simple.

Electron–phonon coupling and spin fluctuations in 3d and 4d transition metals:implications for superconductivity and its pressure dependence

We have calculated the electron–phonon coupling for the complete 4d series and thenonmagnetic 3d transition metals using the linear response method and the linearmuffin-tin orbitals’ basis. A comparison of the linear response results and those obtainedvia the rigid muffin-tin approximation is provided. Based on the calculated values of theelectron–phonon coupling constants, band density of states and the measured values of theelectronic specific heat constants, we estimate the spin-fluctuation effects, i.e. theelectron–spin-fluctuation (electron–paramagnon) coupling constants in these systems. Forthe sake of comparison, several other metals, Cu, Zn, Ag, Cd, Al and Pb, are also studied.Alternative estimates of the electron–paramagnon coupling constants are obtainedfrom the values of the Stoner parameters and the band densities of states atthe Fermi level. Implications of these results on the superconductivity and itspressure dependence as well as the alloying effects of superconductivity in thesesystems are discussed. It is pointed out that spin fluctuations play an importantrole in the validity of the Matthias rule that in metallic systems the optimumconditions for (electron–phonon) superconductivity occur for 5 and 7 valenceelectrons/atom.

X-ray emission and absorption spectra of Cr(CO)6: A comparison of quantum-chemical and full multiple scattering calculations with experiment

The full multiple scattering procedure using the extended continuum approximation and the single semiempirical muffin-tin (MT) potential gave X-ray emission spectra and the CrK absorption spectrum of Cr(CO)6, which were in good agreement with experiment. The bound states above the MT zero become the resonance states corresponding to the poles of the Green function in the lower semi-plane of the complex plane of energy. A procedure for determining the parameters of the poles was developed. A group of poles close to the real line were isolated; their number equals the number of molecular orbitals generated by wellatomized atomic orbitals. These poles completely determine the fine structure of the emission spectra and the first narrow peak in the absorption spectrum. Their energies were close to those of molecular orbitals found at the DFT level of theory, but were in worse agreement with the results of Hartree-Fock calculations. The Hartree-Fock method gave worse agreement with the experimental emission spectra than full multiple scattering and DFT. The fine structure of the region after the first narrow peak in the absorption spectrum is also mainly determined by the contributions from the poles, but these poles are farther from the real line than the poles corresponding to molecular orbitals.

Electronic structure of isolated, embedded, and double-walled nanotubes

The results of study of the band structure of single-walled nanotubes, both isolated and embedded into a crystal matrix, and double-walled nanotubes are surveyed. The mathematical apparatus of the linear augmented cylindrical wave method is described, and its application to prediction of the electronic properties, semiconducting and metallic, of nanotubes is considered. The method uses the local density functional approximation and the muffin-tin approximation for the electron potential and is implemented as a quantum-mechanical program package.

A local-density approximation for the exchange energy functional for excited states: The band-gap problem

We present excited-state density functional theory (DFT) to calculate band gap for semiconductors and insulators. For the excited-state exchange-correlation functional, we use a simple local-density approximation (LDA) like functional and it gives the result which is very close to experimental results. The linear muffin-tin potential is used to solve the self-consistent Kohn–Sham equation.