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.     

The influence of excluded volume and excess ion polarisability on the capacitance of the electric double layer

ABSTRACT

We apply a modified Poisson–Boltzmann theory which permits ions of different sizes and excess polarisabilities to the study of these properties’ effects on the differential capacitance of the electric double layer. For a planar electrode, we find an analytical expression for the differential capacitance, which is examined in the limits of low- and high-applied potential. In the low potential limit, a reduction of the solution relative permittivity caused by the ion polarisability causes the differential capacitance to decrease above a certain concentration, relative to the Gouy–Chapman–Stern theory. A similar effect is observed for the excluded volume, but only if the ions are of different sizes. In the high potential limit, the differential capacitance decreases inversely with the square root of the applied voltage. In a mixed electrolyte, asymmetries in both ion size and excess polarisability alter the surface adsorption of species: at high potentials, smaller ions displace larger ions and less polarisable ions displace more polarisable ions. The extent of the displacement agrees favourably with experimental data. A further consequence of this displacement is the appearance of a second peak in the differential capacitance, which is enhanced by excess ion polarisability.     

Effect of donor acceptor substitution position on the electrical responsive properties of azulene system: a computational study

Effect of donor–acceptor substitution position on the electrical responsive properties like polarisability, first hyper polarisability of donor–acceptor substituted azulene derivatives have been investigated using HF and Density functional theory with various hybrid functional and basis. It is observed that among the DFT methods, CAM-B3LYP hybrid functional with correlation consistent polarised triple-zeta, cc-pVTZ basis show less overestimated value of polarisability and first hyperpolarisability compare to other hybrid functional and it is again advantageous than HF with similar basis in term of its price and performance ratio. An apparent violation of minimum polarisability principle among the studied azulene derivatives are observed and it has been explain due to non-constancy of the potential functions upon substitution of donor (NMe₂) and acceptor (NO₂) groups at different position of azulene ring. Computed β_av values are in accordance with the extent of charge transfer character of the azulene with a few exceptions. Position of donor and acceptor group at the five- and seven-member ring also play a big role in determining the electrical responsive parameter has been discussed. It is also observed that 2 and 6 carbon atom of azulene are highly sensitive towards donor acceptor substitution.     

Influence de la temperature sur les intensites des raies Raman de resonance

Using an analytical expression for the resonance Raman scattering tensor, the influence of the temperature on the scattered intensities is studied.The variation of the intensities as a function of the temperature is different from the result given by the polarisability theory. However, it is shown that the usual ratio $\text{I}{}_{\mathrm{<mtext>Stokes</mtext>}}\text{I}{}_{\mathrm{<mtext>antiStokes</mtext>}}$ is still valid with a good approximation.     

Plasmon energy, bulk modulus, electronic polarisability of AIBIIIC2VI and AIIBIVC2V ternary chalcopyrite semiconductors

A simple relation between the bulk modulus, plasmon energy, electronic polarisability are given for ternary chalcopyrite semiconductors. Bulk modulus has been evaluated from plasmon energy by proposing a linear relation between them. From bulk modulus electronic polarisability has been evaluated. The estimated values are in good agreement with the experimental values and earlier researchers.     

The nuclear mass dependence of the Dunham coefficients and the breakdown of the Born-Oppenheimer approximation

The general expression for a Dunham coefficient of a ground ¹Σ state diatomic molecule is discussed after allowing for the breakdown of the Born-Oppenheimer approximation. The expression is cast in a form suitable for use in fitting data on several isotopes, and is compared to a slightly different expression that has been used in the past.     

Stark-shift of impurity fundamental state in a lens shaped quantum dot

We calculate the Stark effect and the polarisability of shallow-donor impurity located in the centre of lens shaped quantum dot by a variational method and in the effective-mass approximation. Our theoretical model assumes an infinite confinement to describe the barriers at the dot boundaries and the electric field is considered to be applied in the z-direction. The systematic theoretical investigation contains results with the quantum dot size and the strength of the external field. Our calculations reveal that the interval wherein the polarisability varies depends strongly on the dot size.     

Applicability of medium-size basis sets in calculations of molecular dynamic polarisabilities

Static and dynamic average polarisabilities and polarisability anisotropies of seven linear non-polar and polar molecules are calculated within the CCS, CC2, and CC3 approximations using a range of medium-sized basis sets: the polarised LPol-n (n = ds, dl, fs, fl), the aug-pc-n (n = 1, 2), the def2-SVPD, and -TZVPD basis sets. Reference values are obtained using a hierarchy of Dunning's (d-)aug-cc-pVXZ (X = D, T, Q, 5) basis sets. The results are discussed together with the available CCSD values in terms of basis set and correlation method errors, and their ratio. Detailed analysis shows that already the def2-SVPD basis set can be used in CCS polarisability calculations. When affordable, the slightly larger aug-pc-1 basis set is recommended, as it leads to significant reduction of basis set error. The def2-TZVPD, LPol-ds, and aug-pc-2 basis sets are optimal choice within the CC2 approximation, with the latter allowing to approach the CC2 basis set limit. The LPol-ds, -dl, and def2-TZVPD sets outperform the aug-cc-pVTZ set in average polarisability CCSD calculations, with the def2-TZVPD being competitive to other reduced-size sets also in determination of polarisability anisotropy. The aug-pc-2 basis is a particularly attractive choice for CCSD, giving the accuracy of aug-cc-pVQZ at a significantly reduced computational cost. The polarisability anisotropy is shown to be more computationally demanding than the average polarisability, in particular with respect to the accuracy of the correlation method and an accurate evaluation of this property requires at least the CCSD model.     

Solving the ultranonlocality problem in time-dependent spin-density-functional theory

It has been known for some time that the exchange-correlation potential in time-dependent density-functional theory is an intrinsically nonlocal functional of the density as soon as one goes beyond the adiabatic approximation. In this paper we show that a much more severe nonlocality problem, with a completely different physical origin, plagues the exchange-correlation potentials in time-dependent spin-density functional theory. We show how the use of the spin current density as a basic variable solves this problem, and we provide an explicit local expression for the exchange-correlation fields as functionals of the spin currents.     

Electron-induced scattering dynamics of Boron,Aluminium and Gallium trihalides in the intermediate energy domain

This article is focused on the calculation of electron-induced ionisation and total scattering cross sections by Boron, Aluminium and Gallium trihalide molecules in the intermediate energy domain. The computational formalism, spherical complex optical potential has been employed for the study of these two scattering cross sections. The ionisation cross section has been derived from the inelastic cross section using a semi-empirical method called complex scattering potential-ionisation contribution (CSP-ic) method. We have also calculated the ionisation cross section using the BEB theory with Hartree–Fock and density functional theory (DFT- ωB97XD) orbitals so that a comparison can be made with the cross sections predicted by CSP-ic method. For this theoretical study, we have also calculated polarisability and bond length of some targets which were not found in literature using DFT/B3LYP in Gaussian 09 software.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum, it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantum theory.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton‘s theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein‘s general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.     

Theoretical investigations of the vapour-liquid equilibrium and dielectric properties of dipolar Yukawa fluids in an external field

In a low field approximation, using the dipolar Yukawa fluid model (in mean spherical approximation as a reference system) a consistent field-dependent free energy expression is proposed for the calculation of the vapour-liquid equilibrium of polar fluids in an applied electric field. A perturbation theory high field approximation expression of the free energy is also proposed to study the field-dependent properties of fluids. In the high field approximation, equations for the field-dependent polarization and for the nonlinear dielectric constant (or Piekara constant) are also predicted. It has been discussed that our approximations are appropriate to describe the vapour-liquid-like phase equilibria and the magnetization curves of magnetic fluids.     

二元无规混合系统的有效介质理论

本文从二元无规混合物的两种不同拓扑结构出发,在Maxwell-Garnett理论的基础上,提出一种自洽的方法以改进类平均场的Bruggeman有效介质理论。导出了二元无规混合物有效电导率的普适式,研究了一些实际材料的电导率和热导率问题,理论计算结果与实验数据符合甚好。 关键词：     

Optical rotation of solid solutions of sodium chlorate and sodium bromate

The optical rotary dispersion (ORD) data for a mixed crystal of sodium chlorate and sodium bromate have been analysed. It is found that the ORD exhibited by these solid solutions cannot be explained using Vegard's law of additivity. Based on the model proposed by Wasastjerna, a special form of additivity of polarisability is assumed in which the asymmetric distribution of the anions around the cation is considered. A formula has been proposed for the additivity of optical rotation in solid solutions and this is found to fit the data for optical rotation in mixed crystals of NaClO₃-NaBrO₃ of different compositions.     

Density-functional method for surface properties of two-component plasmas of liquid metals

A general density-functional formalism for an inhomogeneous two-component liquid metal is described. The expression for the free energy is obtained and the gradient approximation is used for its simplification. Both electronic and ionic gradients are present in the theory.     

Molecular dipole static polarisabilities and hyperpolarisabilities of conjugated oligomer chains calculated with the local π-electron coupled cluster theory

A new semi-empirical π-electron local coupled cluster theory has been developed to calculate static dipole polarisabilities and hyperpolarisabilities of extended π-conjugated systems. The key idea of the approach is the use of the ethylene molecular orbitals as the orbital basis set for π-conjugated compounds (the method is termed the Covalent Unbonded Molecules of Ethylene method, cue). Test calculations of some small model organic conjugated compounds demonstrate high accuracy of the version of the cue local coupled cluster theory developed in this work in comparison with the π-electron full configuration interaction (FCI) method. Calculations of different conjugated carbon-based oligomer chains (polyenes, polyynes, polyacenes, polybenzocyclobutadiene, etc.) demonstrate fast convergence (per π-electron) of the polarisability and hyperpolarisability values in the calculations when more classes of orbital excitations are included in the coupled cluster single and double (CCSD) excitation operator. The results show qualitatively correct dependence on the system size.     

The study on the gain expression in the single-particle theory of free electron laser

Nonlinear pendulum equation is the fundamental one of the single particle theory in the free electron lasers (FELS). From its solution the gain expression can be derived. In this paper, an exact solution of it has been obtained for the first time, and similar result is also obtained as in the approximation of weak field by Colson.     

Compton scattering of an X-ray photon by an open-shell atom

A nonrelativistic quantum theory for the nonresonant Compton scattering of an X-ray photon by a free many-electron atom with an open shell in the ground state has been constructed in the single-configuration Hartree-Fock approximation outside the impulse approximation widely used in the literature. The transition to an atom with closed shells reproduces the results obtained previously in [6, 7]. The results of a test calculation for atoms with open (Ti, Fe) and closed (Zn) 3d core shells are presented. The effects of the radial relaxation of one-electron states in the field of core vacancies have been taken into account. The results of the calculation agree well with the experimental results [15, 16]. It has been established that the results of the impulse approximation in the investigated X-ray photon energy ranges disagree with those of our theory not only quantitatively but also qualitatively. In particular, the impulse approximation near the elastic (Thomson and Rayleigh) scattering line leads to a gross overestimation of the contributions from the deep atomic shells involved in the inelastic photon scattering only virtually to the scattering probability. The presented theory is general in character and its applicability to a particular element of the Mendeleev table with an open core shell or to a many-electron atomic ion is limited only by the requirement that the nonrelativistic Hartree-Fock approximation be properly used in describing the scattering-state wave functions.