The dielectric and dynamical properties of zinc-blende BN, AlN and GaN from first-principle calculation

The ab initio calculations of the electronic structural, dielectric and lattice-dynamical properties of zinc-blende BN, AlN and GaN were presented. The ground-state properties, i.e., the lattice constant, the bulk modulus and band gap, were calculated using a plane-wave-pseudopotential method within the density-function theory. A linear-response approach to the density-function perturb theory was used to derive the Born effective charge, the high-frequency dielectric constants and interatomic force constants for these materials. The interatomic force contants (IFCs) are useful for interpolating the dynamical matrices through the whole Brillouin zone. Phonon frequencies along high-symmetry lines were also obtained by interpolating the dynamical matrices using the interatomic force constants. In this paper, we discussed the difference of dielectric and dynamical properties among zinc-blende BN, AlN and GaN, and meanwhile, also compared these properties with other experimental data available and theoretical values. Generally, the calculations were in good agreement with the other existing experimental data and theoretical values. Supported by the Hunan Provincial Natural Science Foundation of China (Grant No. 05JJ40135) and Xiangnan University Important Science Foundation (Grant No. 2007Z010)     

Theoretical modelling of infrared spectra of the twinned lead zirconate

The THz-frequency range dispersion of the complex dielectric permittivity tensor of antiferroelectric lead zirconate, associated with its multiple weak infrared active phonon modes, is modelled by the oscillator formula with parameters fully determined from the recently developed atomistic shell model. The resulting realistic dielectric function is used to estimate the far-infrared reflectivity spectra of a twinned lead zirconate crystal in the limit of narrow and wide domains. It is shown that in case of the sufficiently narrow domain widths, the effective-medium average permittivity shows additional modes identified as geometric resonances (i.e. extraneous excitations created by material interfaces), possibly distinguishable in suitable experiments.     

A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency ω. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.     

Origin of the multiferroicity in BiMn2O5 from first-principles calculations

Electronic structure, Born effective charges, and spontaneous polarization of multiferroic single crystal BiMn₂O₅ have been investigated in the framework of density functional theory. The relative stability of the ground state and the origin of multiferroicity for magnetism and ferroelectricity are addressed. The results reveal that the stability of antiferromagnetic (AFM) state is better than the ferromagnetic (FM) and ferrimagnetic configurations. The Born effective charge tensors (Z^?) have been calculated for this compound using a Berry-phase approach, compared to their nominal ionic values, the Z^* of Mn atoms show anomalous difference. By investigating the electric structure of BiMn₂O₅, there exists obviously hybridization between Bi 6s and O 2p states, our calculations indicate that the 6s² lone pair on the formally trivalent Bi ion plays an important role in inducing the ferroelectric distortion.     

Density functional theory calculations of photophysical properties of linear 2, 7-carbazole derivatives as solar cell materials

A theoretical study has been performed to explore the optical and electronic properties on a series of linear 2, 7-carbazole derivative (PCDTBT) by introducing vinyl (v) as linkage and/or benzene (B) as end-capped group for solar cell materials. The PBE0/6-31G(d) method was employed to calculate the frontier molecular orbital (FMO) and energy gap of all derivatives. The values of energy gap change less than 0.28?eV depending on v as linkage and/or B as end-capped group. The absorption spectra was evaluated using the TD-PBE0/6-31?+?G(d,p) level on the basis of the optimized geometries. The absorption spectrum has a red shift along with the increasing of molecular chain. The results of ionization potential (IP), electron affinity (EA), and reorganization energy (λ) reveal that, v as linkage and/or B as end-capped group both lead to the increase of charger transfer rates for PCDTBT. Moreover, v as linkage and/or B as end-capped group have slight effects on the stability property of PCDTBT.     

Density-functional theory investigation of electronic structure,elastic properties,optical properties,and lattice dynamics of Ba_2Zn WO_6

The electronic structures,optical dielectric functions,elastic properties,and lattice dynamics of Ba2ZnWO6 have been investigated by using the generalized gradient approximation.The density of states and distributions of charge density show that O and Ba tend toward ionic bond,but O and W or Zn display the covalent bond character.The calculated energy band structure shows that Ba2ZnWO6 is a wide indirect band gap semiconductor.The static value 2.28 of the refractive index is attained.The analysis of the elastic properties of Ba2ZnWO6 indicates a rather weak elastic anisotropy.The phonon dispersion is calculated,suggesting no structural instability,which is agreement with the recent low temperature neutron diffraction experiments.The mensurability C v(phonon heat capacity) as the function of the temperature is also calculated to judge our results for future experiment.     

线电荷与介质圆柱所形成的电场

在线电荷电场的电势调和展开式的基础上,得出线电荷电场内存在介质圆柱时电势的级数解.并以此来分析长直线电荷与介质圆柱所形成的电场的电像,从而给出电势与电像有关的解析表达式,进一步得出等势线(面)与电场线方程,并利用软件MATLAB绘制出电场线和等势线图予以验证.     

Dielectric constant of solvents at nano to bulk regimes: linear response theory and statistical mechanics-based approaches

Statistical mechanics and generalised linear response theory based approaches are employed to derive the analytical expressions for size-dependent dielectric constant and normalised orientation polarisation of solvents. As an illustrative example, water is considered and the dielectric constants for the same are calculated over the entire range of water clusters. Our results reveal that the dielectric constant and normalised orientation polarisation are monotonically increasing with the increase in the number of solvent molecules and converge to the respective bulk values in the thermodynamic limit. More importantly, the dielectric constant of water is found to be independent of the nature, geometry and microscopic charges of the non-spherical ions. This finding offers a new platform for calculating the hydration energy and orientation polarisation based on linear response theory for different kinds of ions in the solvent medium.     

An alternative definition of the electron propagator in the superoperator form and its relation to linear response theory in a coupled-cluster framework

In this paper it is shown that (i) there exists an alternative definition of the superoperator resolvent for calculation of difference energy satisfying linked cluster theorem for a coupled-cluster choice of the ground-state function which may even be approximate; (ii) the pole-structure of this propagator-like function in superoperator form is shown to contain information similar to that contained in the conventional propagator. (iii) It is demonstrated that suitable “Killer conditions” and completeness of the “operator manifold”—essential for understanding the pole-structure of the propagator—can be established both for an exact and an approximate ground state function in a coupled-cluster form. (iv) It is also demonstrated that difference energies calculated with these propagator-like functions are identical to those obtained from a linear response theory in a coupled-cluster form put forward recently by Mukherjeeet al and Monkhorst.     

The electrodynamics and statistical mechanics of linear plasma response functions

The purpose of this paper is to review and to extend, wherever possible, the Kramers-Kronig relations, sum rules, and symmetry properties for the electrodynamic transport tensors of a linear plasma medium. For complete generality, we consider both nonrelativistic and relativistic plasmas with and without external magnetic fields. Our study is carried out first within the framework of classical electrodynamics. We then exploit the statistical-mechanical fluctuation-dissipation theorem to further obtain the Onsager symmetry relations and Kubo sum-rule frequency moments. Of special significance is the emergence of a variety of new Kramers-Kronig formulae andf-sum rules for the inverse dispersion tensor.Nomenclature E(k,) electric field intensity - Ê(k,) electric field in absence of plasma particles, - (k,) electric field due to the plasma particles (=E-Ê) - B(k,) magnetic induction - D(k,) electric induction - H(k,) magnetic field strength - B ₀ constant external magnetic field - A ₀ vector potential corresponding toB ₀ - (k,),j(k, co) charge and current densities due to the plasma particles - (k,),J(k,) charge and current densities of the external agency - (k,,B ₀) dielectric tensor of the plasma medium in the presence of B₀ - (k,,B ₀) diamagnetic tensor - (k, co,B ₀) (k,,B ₀) – 1, electric polarizability tensor - (k,,B ₀) magnetic polarizability tensor - (k,,B ₀) ordinary conductivity tensor - (k,,B ₀) external conductivity tensor - D(k,,B ₀) n²T–(k,,B ₀), dispersion tensor, where T=1-kk is the transverse projection tensor (k being the unit vector in the direction ofk) andn = kc/ the index of refraction - n²T – 1, = vacuum wave operator (value of D in vacuum) - 1/2( + ), Hermitian part of - ^{^} 1/2( – ), Anti-Hermitian part of a - , real and imaginary parts of a - R(r,t) dissipated power per unit volume of plasma - U total energy absorbed by the plasma - R(k,) E^*(k,) · (k,,b ₀) ·E(k,) corresponding spectral energy density - W(r,t) 1/2₀E²(r, 0 + (l/2₀) B²(r,t), field energy density - W(k,) 1/2₀E^*k,) ·E(k,) + (l/2₀)B ^*(k,) · B(k,), energy content in a certain domain of (k,)-space for a single mode - x _i,p _i,v _i coordinate, momentum, and velocity of ith electron - _i [1–(_i ²/c²)]^–1/2 - X _j,P _j,V _j coordinate, momentum, and velocity of jth ion - {A _q}, {E_q} field coordinates and momenta - j_k(t),J _k(t) perturbations in the microscopic electron and ion current densities due to the presence of the small external vector potential agencyâ(r,t) = (1/L³) â_k(t) expi k ·r - Liouville distribution function = ⁰ + - ⁰ macrocanonical distribution function characterizing the equilibrium state of the system in the infinite past - small perturbation due toA - H⁰ Hamiltonian of equilibrium system which includes interaction - H Hamiltonian for the interaction between the system and the small external perturbing agencyA - ⁰ = d^R()⁰ expectation value of any quantity over the equilibrium ensemble (d^R is an element of hypervolume in -phase space) - G(12) two-particle distribution function - F(1) one-particle distribution function - g(¦x₂ – x₁ ¦) [G(12)/F(1)F(2)] – 1, pair correlation function - N total number of electron in volume L³ - n ₀ equilibrium density (of electrons) - ^–1 temperature (in energy units) - ₀ (n₀e²/m₀)^1/2, equilibrium electron plasma frequency - _c ¦e ¦–B ₀/m, electron frequency - ^–1 ( ₀/n₀e²)^1/2, Debye length - ₀ (n₀Ze²/M₀)^1/2, equilibrium ion plasma frequency - _c ZeB₀/M, ion cyclotron frequency     

The polarisability of atoms and molecules: a comparison between a conceptual density functional theory approach and time-dependent density functional theory

We investigate the local polarisability or polarisability density using both a conceptual density functional theory approach based on the linear response function and time-dependent density functional theory. Using a zero frequency in the latter, we can immediately compare both approaches. Using an analytical expression for the linear response kernel, we are able to systematically analyse α(r) throughout the periodic table. An extension to molecules is also made with a study of the CO molecule retrieving the connection between local softness and local polarisability.     

New ternary superconducting compound La Ru_2As_2:Physical properties from density functional theory calculations

In this paper, we perform the density functional theory(DFT)-based calculations by the first-principles pseudopotential method to investigate the physical properties of the newly discovered superconductor LaRu_2As_2 for the first time.The optimized structural parameters are in good agreement with the experimental results. The calculated independent elastic constants ensure the mechanical stability of the compound. The calculated Cauchy pressure, Pugh's ratio as well as Poisson's ratio indicate that LaRu_2As_2 should behave as a ductile material. Due to low Debye temperature, LaRu_2As_2 may be used as a thermal barrier coating(TBC) material. The new compound should exhibit metallic nature as its valence bands overlap considerably with the conduction bands. LaRu_2As_2 is expected to be a soft material and easily machinable because of its low hardness value of 6.8 GPa. The multi-band nature is observed in the calculated Fermi surface. A highly anisotropic combination of ionic, covalent and metallic interactions is expected to be in accordance with charge density calculation.     

Lattice dynamics of Al‐containing MAX‐phase carbides: a first‐principle study

A systematic study on lattice dynamics of M_{n + 1}AlC_n (n = 1–3) phases using first‐principle calculations is reported, where the Raman‐active and infrared‐active (IR) modes are emphasized. The highest phonon wavenumber is related to the vibration of C atoms. The ‘imaginary wavenumber’ in the phonon spectrum of Nb₃AlC₂ contributes to the composition gap in Nb‐Al‐C system (Nb₂AlC and Nb₄AlC₃ do appear in experiments, but there are no experimental reports on Nb₃AlC₂). The full set of Raman‐active and IR‐active modes in the 211, 312, and 413 M_{n + 1}AX_n phases is identified, with the corresponding Raman and IR wavenumbers. The 211, 312, and 413 M_{n + 1}AX_n phases have 4, 6, and 8 IR‐active modes, respectively. There is no distinct difference among the wavenumber ranges of IR‐active modes for 211, 312, and 413 phases, with the highest wavenumber of 780 cm⁻¹ in Ta₄AlC₃. The Raman wavenumbers of M₂AlC phases all decrease with increasing the d‐electron shell number of transition metal M. However, this case is valid only for the Raman‐active modes with low wavenumbers of M₃AlC₂ and M₄AlC₃. Copyright © 2015 John Wiley & Sons, Ltd.     

Density-functional theory study of structures,stabilities, and electronic properties of the Cu2-doped silicon clusters: Comparison with pure silicon clusters

Equilibrium geometric structures, stabilities, and electronic properties of Si_nCu₂ (n=1–8) clusters and pure silicon Si_n (n=3–10) clusters are investigated systematically by exchange-correlation density functional (B3LYP). The optimized geometries show that the most stable isomers have 3D structure for n=2, 4–8, and Cu-substituted Si_n+2 clusters is dominating growth pattern for the Si_nCu₂ clusters. The calculated averaged binding energies, fragmentation energies, second-order difference of energies, and the HOMO–LUMO gaps show that Si₂Cu₂ and Si₅Cu₂ clusters have enhanced relative stabilities and chemical stability than their neighboring clusters. Electronic properties of Si_nCu₂ (n=1–8) clusters are studied by calculating the natural population analysis and electrostatic potential, where the results show that the two copper atoms always possess positive charge and positive potential surround them. In addition, the VIP, VEA and the chemical hardness (η) are also analyzed and compared.     

Imogolite类纳米管直径单分散性密度泛函理论研究

采用密度泛函理论方法研究了三种imogolite类(未取代、NH₂取代和F取代)纳米管的直径单分散性及表面电荷的分布情况, 并从键长方面定性地解释了直径单分散性的原因. 我们给出了IMO, IMO_NH₂和IMO_F的应变能曲线, 结果表明三种纳米管结构的最稳定管径值按照IMO < IMO_NH₂ < IMO_F的顺序递增, 而imogolite类纳米管直径单分散性是由于管径的增大导致内部Si–O, Al–O键与外部Al-OH键键长变化趋势相反造成的, 总之是内部Si–O, Al–O 键和外部Al–OH键相互作用的结果. 此外, 对三种稳定的纳米管结构做了Mulliken布局分析, 并总结了纳米管直径变化对表面电荷的影响. 结果表明正电荷主要积聚在外表面, 而内表面则感应出负电荷, 同时随着纳米管直径的增大表面电荷逐渐增加, 揭示了表面电荷与管径大小的关系. 研究表明, 可以通过改变imogolite内表面不同的官能化取代来控制纳米管直径, 进而调节表面电荷的分布情况, 这在imogolite类材料的分子设计及应用方面有着重要意义.     

Ab initio vibrational and dielectric properties of chalcopyrite CuInS <Emphasis Type="Bold">2</Emphasis>

We have performed a first-principles study of structural, dynamical, and dielectric properties of the chalcopyrite semiconductor CuInS₂. The calculations have been carried out within the local density functional approximation using norm-conserving pseudopotentials and a plane-wave basis. Born effective charge tensors, dielectric permitivity tensors, the phonon frequencies at the Brillouin zone center and mode oscillator strengths are calculated using density functional perturbation theory. The calculated properties agree with infrared and Raman measurements. Received 12 December 2002 / Received in final form 17 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: resul@ibu.edu.tr     

Fabrication of a curved linear grating by using a laser direct writer system

We present the lithography technique to fabricate a curved linear grating by using a Cartesian coordinates laser direct writer (LDW) system. The grating with the period of 15 μm is made on the convex lens surface. This is a new application of the LDW system. After the chromium coating and the photoresist removing procedures, a convex reflecting grating is obtained.     

Ni掺杂MgF2电子结构和光学性质的第一性原理研究

基于密度泛函理论(DFT) 的第一性原理平面波超软赝势方法,计算了过渡金属Ni不同比例（16.67%,12.5%,8.33%,6.25%）掺杂MgF2晶体的几何结构、电子结构和光学性质。通过对比发现,由于Ni原子的掺入, 体系的禁带宽度减小且能带中出现中间杂质带。另外, 介电函数虚部以及吸收光谱图中均出现双峰结构,结合前人的计算给出了详细的物理机制。上述现象,揭示了Ni掺杂MgF2 体系在光学元器件方面的潜在应用。     

Ni掺杂MgF2电子结构和光学性质的第一性原理研究

基于密度泛函理论(DFT) 的第一性原理平面波超软赝势方法,计算了过渡金属Ni不同比例（16.67%,12.5%,8.33%,6.25%）掺杂MgF2晶体的几何结构、电子结构和光学性质。通过对比发现,由于Ni原子的掺入, 体系的禁带宽度减小且能带中出现中间杂质带。另外, 介电函数虚部以及吸收光谱图中均出现双峰结构,结合前人的计算给出了详细的物理机制。上述现象,揭示了Ni掺杂MgF2 体系在光学元器件方面的潜在应用。     

A coupled cluster treatment of intramonomer electron correlation within symmetry-adapted perturbation theory: benchmark calculations and a comparison with a density-functional theory description

Symmetry-adapted perturbation theory (SAPT) with intramonomer electron correlation described by coupled cluster theory limited to single and double excitations was applied to 21 noncovalent complexes in their minimum geometries. The resulting benchmark contributions to the interaction energy were utilized to examine the accuracy of a more approximate variant of the SAPT method, where interacting molecules are described by density functional theory (DFT) with different functionals, like LDA, PBE, B3LYP, PBE0, M05, M05-2X, M06, and M06-2X (in all cases the asymptotic correction for the exchange-correlation functional has been utilized). Average errors for individual energy components of SAPT(DFT) are not larger than 10% for best functionals under study. Among the tested functionals PBE0, M05, and B3LYP should be especially recommended for the SAPT(DFT) approach. The M06 functional gives the largest errors with respect to SAPT(CCSD) and should not be used for describing intramonomer correlation in SAPT.