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.     

Effect of crosslinking density on biaxial relaxation of SBR by using reduced variables

Use of reduced variables to account for the effect of crosslinking density ν_e in a styrene–butadiene rubber (SBR) system is demonstrated for general biaxial stress states. Recently published results from stress relaxation tests on five SBR vulcanizates crosslinked to different degrees by tetramethylthiuram disulfide were superposed by using ν_e as a reduction variable. The equilibrium shear modulus G_e calculated from the master relaxation curve at long reduced times was in satisfactory agreement with other results for SBR. The time-axis shifts were related in a linear logarithmic manner to the crosslinking density but had a slope slightly less than values previously reported for elastomer systems.     

Energy spectrum of extended Hubbard model with spin‐dependent hopping and related spin ladder model

We studied the energy spectrum of the 1‐D extended Hubbard model with spin‐dependent hopping and related spin ladder system formed by two coupled XXZ spin 1/2 chains with the interchain interaction of Ising type. It was proved that the model excitation spectrum has no gap excepting some special values of z‐projection of the ground‐state total spin. The thorough analytic consideration of two‐magnon states was given. The existence up to five bound states at specified value of quasimomentum of the pair of inverted spins was shown. We also present the results of density matrix renormalization group calculations that showed nonadequacy of the pair approximation for n‐magnon bound states of the extended model with the strong electron–electron interactions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Germanium,carbon‐germanium,and silicon‐germanium triangulenes

A series of germanium‐containing triangular molecules have been studied by density functional theory (DFT) calculations. The triangulene topology of the compounds provides for their high‐spin ground states and strong sign alternation of spin density and atomic charge distributions. High values of the exchange coupling constants witness ferromagnetic ordering of electronic structures of all studied triangulenes. The compounds bearing more electronegative atoms in a‐positions of the triangular networks possess higher aromatic character and stronger ferromagnetic ordering. © 2015 Wiley Periodicals, Inc.     

Information entropies of many-electron systems

The Boltzmann–Shannon (BS ) information entropy S_ρ = ∫ ρ(r)log ρ(r)dr measures the spread or extent of the one-electron density ρ(r), which is the basic variable of the density function theory of the many electron systems. This quantity cannot be analytically computed, not even for simple quantum mechanical systems such as, e.g., the harmonic oscillator (HO ) and the hydrogen atom (HA ) in arbitrary excited states. Here, we first review (i) the present knowledge and open problems in the analytical determination of the BS entropies for the HO and HA systems in both position and momentum spaces and (ii) the known rigorous lower and upper bounds to the position and momentum BS entropies of many-electron systems in terms of the radial expectation values in the corresponding space. Then, we find general inequalities which relate the BS entropies and various density functionals. Particular cases of these results are rigorous relationships of the BS entropies and some relevant density functionals (e.g., the Thomas–Fermi kinetic energy, the Dirac–Slater exchange energy, the average electron density) for finite many-electron systems. © 1995 John Wiley & Sons, Inc.     

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.     

Band structure and electronic properties of lithium azide (LiN3)

Ab initio Hartree–Fock band structure and molecular calculations have been performed to study the electronic structure of LiN₃ in a monoclinic C 2/m crystal structure. The total energy, band structure, density of states, and charge densities are computed. The calculated lattice energy (energy to separate the ions infinitely apart) of 8.6 eV agrees very well with 8.45 eV deduced from Madelung and London polarizability energies. The calculated split of the N 1s core bands of 5.0 eV compares favorably with the experimental X-ray photoelectron value of 4.4 eV. This good agreement is not contributed to crystalline environment effects as proposed in earlier MO studies of N where the best values obtained were 5.1, 5.8, and 6.3 eV, but to the quality of the nitrogen core basis set. The calculated valence density of states supports one of two competing interpretations that peak III observed in the X-ray photoelectron spectrum arises from contaminations or other extrinsic states.     

Revisiting superdelocalizability. Mathematical stability of reactivity indices

Superdelocalizability, S _r, defined by Fukui et al. as a variant of reactivity indices in the Hückel molecular orbital scheme for conjugated hydrocarbon molecules is reinvestigated with particular emphasis on its behavior for infinitely large π-electronic systems. Surprisingly, almost all the S _r values of polyacetylene are found to diverge with the size of molecule, while all the S _r values of comb polyene converge to certain values. Similarly, the S _r values of linear polyacene diverge, while those of zigzag polyacene converge. Whether the superdelocalizability for a series of periodic polymers converges or diverges can be predicted, respectively, if the density of states of the infinitely large π-electron network is shown to have non-zero or zero gap at the Fermi level. The behavior of atom-atom polarizability defined by Coulson et al. is also checked and discussed. Received: 27 July 1998 / Accepted: 9 September 1998 / Published online: 23 February 1999     

Inequalities for fermion density matrices

A partial trace over the occupation numbers of all but k states in the density matrix of an ensemble with an arbitrary number of single-particle states is defined as the (reduced) k-state density matrix. This matrix is used to obtain a complete, practical solution to the problem of determining the representability of the diagonal elements of the one- and two-particle (reduced) density matrices. This solution is expressed as a series of linear inequalities involving the density-matrix elements; the inequalities are identical with those derived previously by Davidson and McCrae by a different method. In addition, our method is used to obtain nonlinear, matrix inequalities on the off-diagonal elements of the density matrices.     

The sequential product of geminals and the ground states of some atoms

By means of the SPG function which is associated with an extreme point of the set of N-representable second-order reduced density matrices, an attempt is made to perform the calculations of the ground states of some atoms with four electrons such as Be. The results show that the SPG function is as suitable as the well-known AGP function for approximating the ground states of atoms and molecules.     

Triplet‐State Aromaticity of 4nπ‐Electron Monocycles: Analysis of Bifurcation in the π Contribution to the Electron Localization Function

The π contribution to the electron localization function (ELF) is used to compare 4nπ‐ and (4n+2)π‐electron annulenes, with particular focus on the aromaticity of 4nπ‐electron annulenes in their lowest triplet state. The analysis is performed on the electron density obtained at the level of OLYP density functional theory, as well as at the CCSD and CASSCF ab initio levels. Two criteria for aromaticity of all‐carbon annulenes are set up: the span in the bifurcation values ΔBV(ELF_π) should be small, ideally zero, and the bifurcation value for ring closure of the π basin RCBV(ELF_π) should be high (≥ 0.7). On the basis of these criteria, nearly all 4nπ‐electron annulenes are aromatic in their lowest triplet states, similar to (4n+2)π‐electron annulenes in their singlet ground states. For singlet biradical cyclobutadiene and cyclooctatetraene constrained to D_4h and D_8h symmetry, respectively, the RCBV(ELF_π) at the CASSCF level is lower (0.531 and 0.745) than for benzene (0.853), even though they have equal proportions of α‐ and β‐electrons.     

Electronic structures and optical properties of BiOX (X = F,Cl, Br,I) via DFT calculations

Based on the density functional theory (DFT), the lattice constants and atomic positions of BiOX (X = F, Cl, Br, I) species have been optimized, and the electronic and optical properties of the relaxed species have been calculated, with Bi 5d states considered or not. Relaxation generally results in the shrinkage in a and the expansion of c. Relaxed BiOCl, BiOBr, and BiOI present indirect band gaps, whereas BiOF exhibits a direct or somewhat indirect band‐gap feature corresponding to the relaxation and calculation with the Bi 5d states or not. The bottom of the conduction band is quite flat for relaxed BiOI, and apparently flat in BiOBr, and shows observable flatness in BiOCl as well when considering the Bi 5d states. The top of the valence band is rather even as well for some species. The obtained maximum gaps for relaxed BiOF, BiOCl, BiOBr, and BiOI are 3.34, 2.92, 2.65, and 1.75 eV, respectively. The density peak of X np states in the valence band shifts toward the valence band maximum with the increasing X atomic number. The bandwidths, atomic charges, bond orders, and orbital density have also been investigated along with some optical properties. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Inverting the external-potential-to-electron density map in systems of electrons by minimization of a least-squares fit functional for analytic potentials

In a system of electrons, there is a map connecting any external potential v with its electron density ρ _v. In this work, we describe a procedure for inverting this potential-to-density map, so that potentials (if any) corresponding to a target density ρ_t can be obtained. We give the trial external potential v _α , an analytic expression depending on a number of parameters α = (α₁, …) and then minimize the least-squares integral ∫(ρ _α − ρ_t)² d r by the conjugate gradient method, where ρ _α is the density corresponding to v _α . The implementation takes advantage of the analytic nature of v _α . The procedure can be applied to any system and quantum chemistry model, and works both for ground and excited states, as well as for ensembles of states. The method is tested with some excited states of the particle-in-a-box model, confirming the lack of a Hohenberg–Kohn theorem for excited states. It is also applied to the first singlet excited state of the helium atom, where, apart from the nucleus–electron attraction potential, some generalized external potentials are found.     

CH3I low-n Rydberg states in supercritical atomic fluids near the critical point

Vacuum ultraviolet photoabsorption spectra of CH₃I 6s and 6s′ Rydberg states doped into supercritical argon, krypton, and xenon perturbers were measured from low density to the density of the triple point liquid at noncritical temperatures and on an isotherm near the perturber critical temperature. A full line shape analysis of these spectra was performed using a single set of intermolecular potential parameters for each dopant/perturber system. The resulting perturber induced shift of the simulated adiabatic transition of the 6s and 6s′ Rydberg states is presented as a function of perturber number density, and this shift illustrates a perturber critical point effect on the excitation energies of the molecular low-n Rydberg states.     

Shaping the density to fit one-electron properties: Constrained RHF calculations on N2, FH,CO, and LiH

The molecular density required to give the correct values for one-electron properties is rarely given by wave functions obtained from variation methods based on the total energy or the eigenvalues. Perhaps if we knew how the density should be shaped in any particular volume to fit a particular property, the whole molecular density might then be properly described to fit the whole volume. The secant-parametrization procedure is used to constrain minimum basis set RHF wave functions for N₂, FH, CO, and LiH to determine the effects of different constraints on RHF wave functions, and to see how constraints improve the quality of small basis set RHF wave functions. One-electron property expectation values, energies, and unweighted and property weighted populations and electron density difference profiles are used to analyze the constrained wavefunctions. With the information from the constrained wave functions it should be possible to select a LCAO -CI basis and states to give the correct density for all properties. This should map onto the constrained wave function in the region of the constraint and at the same time minimize the energy of the total molecular wave function. Such a density would be suitable for the density analyses favored by Bader and Nguyen-Dang [Adv. Quantum Chem. 14 , 113 (1981)], Mezey [Theor. Chim. Acta 54 , 95 (1980); 58 , 309 (1981); 59 , 321 (1981)], and March [Theoretical Chemistry (Royal Society of Chemistry, London, 1981), Vol. 4, p. 158], and show the real atom needed to generate the molecule.     

The origin of energy functional in Roothaan open shell SCF theory

Different methods of averaging of energy over the states of electronic configurations γ^N (n_γ = 1, 2, 3 and N = 1, 2, …, 2n_γ ? 1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients (VCC ) in energy functionals for various states as well as for average values of energy are presented. It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations t^N (N = 2–4) and e² there exist states for which VCC are dependent on the choice of basis set of degenerate open-shell molecular orbitals. The origin of such “non-Roothaan” terms and peculiarities of its calculation by the restricted Hartree–Fock method are discussed.     

Influence of deep energetic levels on charge densities and capacitance of semiconductor/electrolyte interface

Charge density and space charge layer capacitance of semiconductor/electrolyte interface are determined by computational method in the case of crystalline, polycrystalline and amorphous semiconductors with multiple deep energetic levels. These determinations are performed as a function of the difference of potential between the potential in the bulk of the electrode and the potential at a point x and especially at x = 0 which correspond to the potential at the SC/electrolyte interface. The investigation of the results allows proposing new and original relations describing the charge density for polycrystalline and amorphous semiconductors. The variation of the charge density is manifested by the existence of different regions where the ionization phenomenon of the donor states relative to the discrete and continuous levels is exhibited. The space charge layer capacitance determined from the charge density using Poisson’s equation is also analyzed as a function of the potential difference through the space charge layer for the different parameters characterizing the discrete and continuous levels in the case of the different semiconductors. For amorphous semiconductors, the charge density and the space charge layer capacitance are analyzed for two models of the density of states. The representation of the inverse square capacity shows a linear variation where straight lines with different slopes appear in low and high potential range indicating Mott-Schottky behaviour.     

Structural,Magnetic and Thermoelectric Properties of hp-Mn3Ge5

Mn₃Ge₅ was obtained by high-pressure, high temperature synthesis. The compound adopts a Nowotny-Chimney-Ladder type crystal structure [tetragonal, space group P4 n2, a = 5.7449(1) Å, c = 13.9096(4) Å, Z = 4]. Magnetic measurements reveal a ferromagnetic transition around 40 K and metallic conductivity in the temperature range from 3 K to 350 K. Despite a low thermal conductivity, the metallic character of the sample and the low Seebeck coefficient result in low values for the thermoelectric Figure of merit, ZT. Band-structure calculations show that the Fermi level is located slightly below a pseudo-gap in the electronic density of states. Chemical bonding analysis in position space discloses moderate charge transfer and two- as well as three-atomic directed, heteroatomic bonding involving both the manganese and the germanium atoms.     

Two-Way Catalysis in a Diels–Alder Reaction Limits Inhibition Induced by an External Electric Field

Oriented external electric fields (EEFs) act as catalysts that can induce selectivity in chemical reactions. The responses of the Diels–Alder (DA) reaction between butadiene and ethylene (BDE-DA) as well as cyclopentadiene and ethylene (CPDE-DA) towards EEF stimuli are investigated here using density functional theory (B3LYP) calculations. EEF is a vector that catalyzes the reaction in one direction while inhibiting it in the opposite direction. Here we report that the inhibitive direction becomes rate-enhancing after some increase in the EEF. The EEF value that brings about the maximum possible inhibition for the reaction is defined as the electrostatic resistance point (ERP). The possibility of both normal and inverse electron-demand DA reactions causes catalytic activity in both directions of the EEF starting at a unique ERP value. The C5 substituents of cyclopentadiene control the ERP values depending upon the resistance power that the functional group provides against the EEF. The endo and exo diastereomeric transition states of the DA reaction have distinct ERP values and the difference (ΔERP) provides the through-space electrostatic contribution to the stereoselectivity on a relative scale. Thus, the ERP values can be used as a gauge for the electrostatic interactions between substituent groups and external stimuli.     

Ab initio MO and approximate density functional theory studies on the lowest singlet and triplet states of s and as-indacene

The lowest singlet and triplet states of s- and as-indacene have been studied by means of high-level ab initio MO and approximate density functional methods. Among the geometrical and energetical details discussed are the equilibrium structure of s-indacene (C_2h or D_2h), the structures and energies of the low-lying s-indacene triplet states, and the stability and geometry of the singlet and triplet states of as-indacene. It is shown that single-determinant-based methods, such as Hartree-Fock or MP 2, are not suited to properly describe these molecules. Instead, methods are required which explicitly take into account nondynamical and dynamical electron correlation. The results obtained by density functional theory-based methods compare very well with the most elaborate ab initio MO data and seem to provide an economical alternative even for molecules with a complicated electronic structure such as s- and as-indacene. © 1995 John Wiley & Sons, Inc.