Angular aspects of exchange correlation and the fermi hole

The complete (nonreduced) αα probability density functions evaluated from the Hartree–Fock and simple Hartree product wavefunctions have been used to elucidate the angular features of spin correlation and the Fermi hole in the 2³S state of helium and the ground state of beryllium. This approach shows that the local Fermi holes in these two cases are very similar and that the Fermi hole is essentially spherically symmetric when the reference electron is close to the nucleus. As the reference electron is removed to larger radial distances, appreciable polarization of the Fermi hole is observed. The polarization is greater in the direction of the nucleus than away from the nucleus, contrary to the situation in the Coulomb hole of the helium ground state where the polarization is greater away from the nucleus than toward the nucleus. Several other differences between the He 2³S Fermi hole and the He 1¹S Coulomb hole are noted.     

稀土对ZA27合金晶间腐蚀影响的电子理论研究

通过自行开发的计算机软件构造了ZA27合金中α相大角度晶界析出η相及稀土元素的原子集团模型. 采用递归法计算了Al, Zn, La, Y的局域态密度, 计算并分析了α相、η相的总态密度和费米能级, 及稀土对态密度和费米能级的影响. 计算表明: 稀土元素的局域态密度形状与Zn相近, 其与Zn结合的能力大; 稀土元素降低η相的费米能级, 减小Zn, Al电极电位差, 具有抑制晶间腐蚀的作用; 稀土元素不改变α相、η相的总态密度形状, 但使η相的态密度增大, 改变η相的电子结构; 晶格结构对原子的态密度有一定的影响, 掺杂原子的态密度趋于与基体原子态密度相同.     

Fermi and Coulomb holes of molecules in excited states

Correlation holes of electrons with the same (Fermi hole) and different (Coulomb hole) spins in the ground (X¹Σ⁺), first (A¹Σ⁺) and second (B¹II) excited states of LiH were constructed from full configuration interaction (CI ) wave functions. It was found that the shapes of both the Fermi and Coulomb holes in these states are dependent on the location of the reference electron. When the reference electron is chosen to be close to the Li nucleus, the Fermi correlation results in a large negative hole for all three states. However, the A¹Σ⁺ excited state is further characterized by displaying a second hole around the H nucleus, and in the B¹II state, the hole is elongated along the molecular axis. Coulomb correlation shows up strongly in the A¹Σ⁺ state and, in addition, there is clearly correlation of electrons at the two nuclei. These features of the correlation holes were compared with those from a two-Slater-determinant model wave function. The Hartree, Fermi, and Coulomb screening potentials in these states were also studied in the light of possible modeling of the correlation functionals for the excited states. © 1995 John Wiley & Sons, Inc.     

Brillouin zone double integrals

A semianalytic scheme is proposed for the evaluation of Brillouin zone (BZ ) double integrals such as are met in the evaluation of Compton profiles (CPS ) and the angular distribution of annihilation photons (ADAPS ) obtained in single-slit positron annihilation experiments. The difficulty that arises due to the jump discontinuities in the momentum density at the generalized Fermi surfaces (FS +HMC ), p_F = k_F + g, where k_F is the electron Fermi momentum vector and g is a reciprocal lattice vector, is addressed.     

Electronic structure of beryllium

The electronic energy bands in beryllium have been recalculated. The earlier work of Terrell [1] was found to contain a systematic error in the form of overlapping muffin tins. The new band structures give a density of states with the Fermi surface lying in the hole like portion, consistent with Hall measurements. All existing calculations misplaced the Fermi surface. As a further check on the new bands, the Hall coefficient A_H was calculated. We obtained A_H = (7.6 ± 0.8) × 10^?24 cgs units for the easy axis or c direction, in excellent agreement with the experimental value of A_H = 8.56 × 10²⁴ cgs units.     

Thomas–Fermi–Dirac models of atoms constrained by nuclear cusp and long-range conditions

The traditional Thomas–Fermi–Dirac model of the electronic structure for a neutral atom is deficient in that it predicts an infinite electron density at the nucleus and a sharp cutoff of the electron density at a finite radius. This study was carried out to remedy these faults in the model. Extending an idea used earlier in Thomas–Fermi (TF ) theory [Proc. Natl. Acad. Sci. U.S.A. 83 , 3577 (1985)], the Thomas–Fermi–Dirac (TFD ) energy functional is minimized under constraints ∫ρ( r ) d r = N, ∫e^?2kr▽²ρ( r )d r < ∞ and ∫(1 ? e^?k′r)ρ^4/3( r )d r < ∞, with k and k′ determined by the nuclear cusp condition and the correct asymptotic behavior. Optimum coordinate scaling also is considered. It is found that the TFD model is substantially improved by constraining the minimization search domain of the energy functional in this way. Energies are given for five noble gas atoms, and Compton profiles for these atoms are calculated. The behavior of electrons in momentum space is improved in both this modified TFD model and in the corresponding modified TF model.     

原子簇NixFe和NiFex(x=1-5)电子性质的DFT研究

More than one hundred models were designed to reflect the local structure and electronic property of Ni-Fe amorphous alloys. After calculating by DFF method, a series of configurations of clusters NixFe and NiFex （x = 1 - 5） were gained. The configurations, which possessed the lowest energies and non-imaginary frequencies, were considered the most stable optimized structures. The catalytic activity, charge and magnetic properties were analyzed and discussed. The different Fe content changed the catalytic properties of clusters through altering the value of Fermi level of every cluster. However the density of state （DOS） nearby Fermi level and average 3d orbital population of atom Ni, which were also important properties related to the catalytic activation, were little changed. Based on the Fermi level, the activity of catalyst toward hydrogenation reaction would be considered best when the ratio of Ni to Fe was close to 1. The Fermi level of clusters was far distant to the level of nitrogen in singlet state. It would be the reason why the reaction condition in ammonia synthesis and nitrogen fixation process was rigorous. When Fe atom contents were higher than 75% （NiFe3）, the electrons transferred from atom Fe to Ni, but when the ratio was decreased, the transfer was reversed. The ratio of atoms of local structure also played an important role in the aspect of electron transition. On the average 3d orbital population of atom Fe, the average magnetic moments of Fe atoms in clusters were calculated. When Fe atom contents were 50% nearly, the average magnetic moment achieved the highest point.     

Direct current conductivity studies on poly(3-methyl thiophene)

The direct current (dc) conductivity of poly(3-methyl thiophene) was measured in the temperature range of 77–300 K. The observed dc conductivity data were analyzed in the light of Mott’s variable range hopping model. Different Mott’s parameters such as characteristic temperature (T ₀), average hopping distance (R), average hopping energy (W), and density of states at the Fermi level (N [E _F ]) were evaluated. By taking the inverse of the coefficient of exponential decay of the localized states involved in the hopping process as 0.5 nm, a realistic value of density of states at the Fermi level (N [E _F ]) was obtained that agrees well with the values reported earlier for other conjugated polymers.     

Thomas–Fermi theory from a perturbative treatment of the hydrogenic limit energy density functional: A possible link to local density functional theory

A perturbation expansion which connects the hydrogenic limit energy density functional to the Thomas–Fermi functional is discussed. This perturbation series, where the Coulomb energy density functional is treated as the perturbation to the hydrogenic limit functional, is, in fact, the q = (N/Z) expansion of Thomas–Fermi theory. A truncated form of the first-order correction to the functional provides further insight into the model which treats the ground state energy as a local functional of the electron density.     

Energy‐Level Alignment for Single‐Molecule Conductance of Extended Metal‐Atom Chains

The use of single‐molecule junctions for various functions constitutes a central goal of molecular electronics. The functional features and the efficiency of electron transport are dictated by the degree of energy‐level alignment (ELA), that is, the offset potential between the electrode Fermi level and the frontier molecular orbitals. Examples manifesting ELA are rare owing to experimental challenges and the large energy barriers of typical model compounds. In this work, single‐molecule junctions of organometallic compounds with five metal centers joined in a collinear fashion were analyzed. The single‐molecule i–V scans could be conducted in a reliable manner, and the E_FMO levels were electrochemically accessible. When the electrode Fermi level (E_F) is close to the frontier orbitals (E_FMO) of the bridging molecule, larger conductance was observed. The smaller |E_F?E_FMO| gap was also derived quantitatively, unambiguously confirming the ELA. The mechanism is described in terms of a two‐level model involving co‐tunneling and sequential tunneling processes.     

Homogeneous Fermi liquid with ‘artificial’ repulsive inverse square law interparticle potential energy

A good deal is known by now on the so-called jellium model of the homogeneous electron liquid. However, much of the quantitative progress at experimentally realizable densities has come from quantal computer simulation. Therefore, we here consider a homogeneous Fermion liquid with ‘artificial’ repulsive interaction λ/(r_ij )² between Fermions i and j at separation r_ij . We discuss first of all the way the static structure function S(q), essentially the Fourier transform of the pair correlation function, is changed because of non-zero λ from the ‘Fermi hole’ form due entirely to Pauli principle effects between parallel spin Fermions. Unlike jellium with e ²/r_ij repulsive interactions, S(q) is proportional to q at long wavelengths, whereas the plasmon in jellium annulls the q term and S(q) is quadratic in q as q tends to zero. However for λ/(r_ij )² interactions, the coefficient of q appearing in the Fermi hole structure factor, is renormalized by particle repulsions. Then some discussion is given of Fermion quasiparticle lifetimes τ as the Fermi surface is approached. Arguments are presented that τ^?1 is proportional to |E???E _F| as E tends to the Fermi energy. This is already interesting, in fact, in connection with the jellium model and therefore an approximate analytic form of τ is finally derived.     

Relationship between oxygen content and superconductivity of Tl0.5Pb0.5Sr2CuOy(y≈5)

The electronic energy band structures of the Tl_0.5Pb_0.5Sr₂Cu0_y (y5) superconductor were calculated and the effect of the oxygen content on its electronic structures was studied in the present paper. The results show that the oxygen content has a great influence on its electronic structures. The moderate oxygen content causes the number of bands near the Fermi surface to increase and results in a sudden change in the densities of states at the Fermi level E _f. The influence of the oxygen content on the electronic structures is mainly due to the peroxide pairs in the unit cell. The lower or higher oxygen content results in the decrease in the number of bands near E _f and the densities of states at E _f, which is of no advantage to superconductivity.     

19F NMR of five polyfluoronaphthalenes. Inter-ring FF coupling constants

Analyses of the ¹⁹F and ¹H spectra of 1,2,3,4,5-pentafluoro-, 1-bromo-4,5,6,7,8-pentafluoro-, 1,2,3,4,5,6-hexafluoro-, and 1-bromo-3,4,5,6,7,8-hexafluoro-naphthalene are presented, and it is observed that the Fermi contact mechanism does not, simply, account for the long range couplings. Calculations of the carbon-carbon polarizability part of the Fermi contact term do, however, imply that inter-ring F,F couplings should be almost constant from difluoro- to heptafluoro-naphthalene. Within the limits of this study, the inter-ring F,F couplings, excluding peri F,F couplings, do not vary substantially. The steric effect of substituting an α-hydrogen with bromine, at a peri position and adjacent to fluorine, is to increase the F,F coupling at the opposed peri position by 20 Hz, an unusually high increase in J(FF)peri.     

Tamm states in zigzag carbon nanotubes: Analytic estimates in the Hückel approximation

The frontier molecular orbitals of [C _n ] _q hydrocarbons, fragments of (n, 0) nanotubes, were considered. Asymptotic estimates for two different sets of frontier molecular orbitals were obtained in the Hückel approximation. The problem was shown to be equivalent to the search for model polyene levels with alternating resonance parameters (β and β′ = γβ). The γ parameter was determined by the symmetry type of molecular orbitals and took on values from 0 to 2. The problem was reduced to an analysis of a regular linear polyene with a modified terminal atom by taking alternant symmetry into account. The states of the system were classified according to quasi-momentum Θ values, which could be complex. Solutions with a complex Θ value were localized at tube ends and could be interpreted as Tamm states. The criterion of the appearance of Tamm solutions for the problem under consideration was formulated, γ < 1 − 1/(q + 2). The conclusion was drawn that these states for an arbitrary [C _n ] _q fragment lied close to the Fermi level, and their energies were described by the asymptotic equation α ± βρ^{(q + 1)}. Delocalized levels were always situated farther from the Fermi level than Tamm states.     

Energy-band structure and charge distribution for BaC6

An ab initio self-consistent calculation has been carried out for the electronic properties of BaC₆. Energy bands and charge densities are presented for BaC₆ and compared with those of LiC₆. The results show that the band originating from Ba states has a mixture of s and d character and the d component hybridizes appreciably with the π bands of graphite. The Fermi level intersects this band as well as the graphite π bands, giving rise to a complicated Fermi surface with several types of carriers. Depending on the type of volumetric partitioning, the charge transfer from Ba to graphite layers is determined to be between 0.7 and 1.0 electron per Ba atom. The calculated results are consistent with available transport and optical measurements.     

Theoretical study of the νO–H IR spectra for the hydrogen bond dimers from the polarized spectra of glutaric and 1-naphthoic acid crystals: Fermi resonances effects

A full quantum theoretical model is proposed to study the ν_O–H experimental IR line shapes of polarized crystalline glutaric and 1-naphthoic acid dimer crystals at room and liquid nitrogen temperatures. This work is an application of a previous model [M. E-A. Benmalti, D. Chamma, P. Blaise, and O. Henri-Rousseau, J. Mol. Struct. 785 (2006) 27–31] by accounting for Fermi resonances. The approach is dealing with the strong anharmonic coupling, Davydov coupling, multiple Fermi resonances between the first harmonics of some bending modes and the first excited state of the symmetric combination of the two ν_O–H modes and the quantum direct and indirect relaxation.Numerical results show that mixing of all these effects allows to reproduce satisfactorily the main features of the experimental IR line shapes of crystalline hydrogenated and deuterated glutaric and 1-naphthoic acid crystals and are expected to provide efficient of Fermi resonances effects.     

C36填充单壁碳纳米管的结构和电子性质

The structures and electronic properties for C36 encapsulated in four single-wall armchair carbon nanotubes (C36@(n,n), n=6-9) were calculated using ab initio self-consistent field crystal orbital method based on density functional theory. The calculations show that the interwall spacing between the carbon nanotube and C36 plays an important role in the stabilities of resultant structures. The optimum interwall spacing is about 0.30 nm and the tubes can be considered as inert containers for the encapsulated C36. The Fermi levels and relative position of energy bands also have something to do with the interwall spacing. The shifts of Fermi level and C36-derived electron states modulate the electron properties of these structures. The extra electrons fill the bands of C36@(8,8) with the optimum interwall spacing almost in a rigid-band manner.     

Layered Monophosphate Tungsten Bronzes [Ba(PO4)2]WmO3m−3: 2D Metals with Locked Charge-Density-Wave Instabilities

Phosphate tungsten and molybenum bronzes represent an outstanding class of materials displaying textbook examples of charge-density-wave (CDW) physics among other fundamental properties. Here we report on the existence of a novel structural branch with the general formula [Ba(PO₄)₂][W_mO_3m−3] (m=3, 4 and 5) denominated ′layered monophosphate tungsten bronzes′ (L-MPTB). It results from thick [Ba(PO₄)₂]⁴⁻ spacer layers disrupting the cationic metal-oxide 2D units and enforcing an overall trigonal structure. Their symmetries are preserved down to 1.8 K and the compounds show metallic behaviour with no clear anomaly as a function of temperature. However, their electronic structure displays the characteristic Fermi surface of previous bronzes derived from 5d W states with hidden nesting properties. By analogy with previous bronzes, such a Fermi surface should result into CDW order. Evidence of CDW order was only indirectly observed in the low-temperature specific heat, giving an exotic context at the crossover between stable 2D metals and CDW order.