Static Electric Polarizability Research Articles

Exact exchange-like electric response from a meta-generalized gradient approximation: A semilocal realization of ultranonlocality

We review the concept of ultranonlocality in density functional theory and the relation between ultranonlocality, the derivative discontinuity of the exchange energy, and the static electric response in extended molecular systems. We present the construction of a new meta-generalized gradient approximation for exchange that captures the ultranonlocal response to a static electric field in very close correspondence to exact exchange, yet at a fraction of its computational cost. This functional, in particular, also captures the dependence of the response on the system size. The static electric polarizabilities of hydrogen chains and oligo-acetylene molecules calculated with this meta-GGA are quantitatively close to the ones obtained with exact exchange. The chances and challenges associated with the construction of meta-GGAs that are intended to combine a substantial derivative discontinuity and ultranonlocality with an accurate description of electronic binding are discussed.

Reconciliation of the Theoretical and Experimental Value of the Static Electric Polarizability of the Aluminum Atom

Reconciliation of the Theoretical and Experimental Value of the Static Electric Polarizability of the Aluminum Atom

Impact of molecular chain length on polarizabilities of model acenes and oligomers

Abstract A systematic quantum chemical study of model linear oligomers and their ring-fused (condensed) analogues based on six-membered and five-membered aromatic units is presented. Static electric polarizabilities were calculated for optimal geometries. The dependence of electronic and vibrational polarizability contributions on the molecular size was discussed and polymer limits were estimated. The presence of a diradical electronic structure in fused six-membered compounds significantly increases the polarizability values.

Minimal nuclear energy density functional

We present a minimal nuclear energy density functional (NEDF) called "SeaLL1" that has the smallest number of possible phenomenological parameters to date. SeaLL1 is defined by 7 significant phenomenological parameters, each related to a specific nuclear property. It describes the nuclear masses of even-even nuclei with a mean energy error of 0.97 MeV and a standard deviation 1.46 MeV, two-neutron and two-proton separation energies with r.m.s. errors of 0.69 MeV and 0.59 MeV respectively, and the charge radii of 345 even-even nuclei with a mean error $\epsilon_r=$0.022 fm and a standard deviation $\sigma_r=$0.025 fm. SeaLL1 incorporates constraints on the EoS of pure neutron matter from quantum Monte Carlo calculations with chiral effective field theory two-body (NN) interactions at N3LO level and three-body (NNN) interactions at the N2LO level. Two of the seven parameters are related to the saturation density and the energy per particle of the homogeneous symmetric nuclear matter, one is related to the nuclear surface tension, two are related to the symmetry energy and its density dependence, one is related to the strength of the spin-orbit interaction, and one is the coupling constant of the pairing interaction. We identify additional phenomenological parameters that have little effect on ground-state properties, but can be used to fine-tune features such as the Thomas-Reiche-Kuhn sum rule, the excitation energy of the giant dipole and Gamow-Teller resonances, the static dipole electric polarizability, and the neutron skin thickness.

Evaluation of the Electric Polarizability for Planar Frequency-Selective Arrays

This paper presents a method to estimate the static electric polarizability of two-dimensional infinitely periodic metal patch arrays with dielectric substrate. The main features of the proposed method is its numerical efficiency and a deep insight into the physics of the fields interacting with the structure. We provide derivation and analysis of the method, and its verification against two another commercial solver-based approaches for various structure geometries. Additionally, we suggest the guidelines for applying the method to bandwidth optimization of frequency selective structures and illustrate this with an example.

In Silico Stark Effect: Determination of Excited-State Polarizabilities of Squaraine Dyes.

The static electric polarizabilities (α) of a quadrupolar squaraine dye are investigated in silico, either as the excess polarizability, i.e., the change from the ground to the lowest excited state, Δα, or as those of the two states separately, depending on the approach. The polarizabilities are worked out by making use of the energy and dipole moment Taylor expansions as a function of the electric field (E), in which α is represented by the quadratic and linear terms, respectively, and also by means of the linear response approach. Dipoles and energies are computed at a few values of the electric field, with different strategies that consider the geometry of the molecule either frozen in the ground state or relaxed at each E value. From a physical standpoint, the most appropriate approach to describing the molecular polarizability depends on the processes in which the molecule is involved: for example, fluorescence methods provide information about relaxed excited states, and absorption methods are used to determine the polarizability changes of excited states frozen in the ground-state conformation. We show that the excited-state polarizability does not strongly differ from the ground-state polarizability when the field is applied along the main axis of the squaraine. In contrast, remarkable differences are found when the field is applied perpendicular to the molecular plane due to a large geometrical distortion of the molecular backbone.

High-precision nonadiabatic calculations of dynamic polarizabilities and hyperpolarizabilities for low-lying vibrational-rotational states of hydrogen molecular ions

The static and dynamic electric multipolar polarizabilities and second hyperpolarizabilities of the ${{\mathrm{H}}_{2}}^{+}$, ${{\mathrm{D}}_{2}}^{+}$, and ${\mathrm{HD}}^{+}$ molecular ions in the ground and first excited states are calculated nonrelativistically using explicitly correlated Hylleraas basis sets. The calculations are fully nonadiabatic; the Born-Oppenheimer approximation is not used. Comparisons are made with published theoretical and experimental results, where available. In our approach, no derivatives of energy functions nor derivatives of response functions are needed. In particular, we make contact with earlier calculations in the Born-Oppenheimer calculation where polarizabilities were decomposed into electronic, vibrational, and rotational contributions and where hyperpolarizabilities were determined from derivatives of energy functions. We find that the static hyperpolarizability for the ground state of ${\mathrm{HD}}^{+}$ is seven orders of magnitude larger than the corresponding dipole polarizability. For the dipole polarizability of ${\mathrm{HD}}^{+}$ in the first excited state the high precision of the present method facilitates treatment of a near cancellation between two terms. For applications to laser spectroscopy of trapped ions we find tune-out and magic wavelengths for the ${\mathrm{HD}}^{+}$ ion in a laser field. In addition, we also calculate the first few leading terms for long-range interactions of a hydrogen molecular ion and a ground state H, He, or Li atom.

Dependence of the Upper Limit of the Electric Polarizability of Mesons on the Mass Ratio of Their Constituent Quarks

The dependence of the upper limit of the static electric polarizability of pions and kaons on the mass ratio of their constituent quarks is investigated.

Active polarized target: Measurement of proton spin polarizabilities

The static (electric and magnetic) polarizabilities of the proton are known from measurements of low-energy Compton scattering of real photons. However, no experimental data are so far available about its spin polarizabilities, which describe the response of the proton spin to a varying electromagnetic field. These fundamental structure constants can be obtained in the most model-independent way from measurements of double-polarized Compton scattering at energies below the pion threshold using a polarized photon beam and a polarized proton target. An active polarized target based on polystyrene doped with a scintillator allows recoil protons to be detected directly in the target material, background from the coherent Compton effect on heavier nuclei (12C etc.) to be eliminated and precise data on spin polarizabilities to be obtained.

Bound-state field-theory approach to proton-structure effects in muonic hydrogen

A bound-state field theory approach to muonic hydrogen is set up using a variant of the Furry representation in which the lowest-order Hamiltonian describes a muon in the presence of a point Coulomb field, but the origin of the binding field is taken to be three charged quarks in the proton which are modeled as Dirac particles that move freely within a spherical well. Bound-state field theory techniques are used to evaluate one- and two-photon effects. Particular attention is paid to two-photon exchange diagrams, which include the effect of proton polarizability. In addition the modification of the electromagnetic self energy of the proton by the electric field of the muon is examined. Finally, the model is used to carry out a calculation of the static electric polarizability of the proton.

New basis sets for the evaluation of interaction-induced electric properties in hydrogen-bonded complexes

Interaction-induced static electric properties, that is, dipole moment, polarizability, and first hyperpolarizability, of the CO-(HF)(n) and N(2)-(HF)(n), n = 1-9 hydrogen-bonded complexes are evaluated within the finite field approach using the Hartree-Fock, density functional theory, Møller-Plesset second-order perturbation theory, and coupled cluster methods, and the LPol-n (n = ds, dl, fs, fl) basis sets. To compare the performance of the different methods with respect to the increase of the complex size, we consider as model systems linear chains of the complexes. We analyze the results in terms of the many-body and cooperative effects.

Long-range interactions between like homonuclear alkali metal diatoms

Long-range electrostatic and van der Waals coefficients up to terms of order R(-8) have been evaluated by the sum over states method using ab initio and time-dependent density functional theory. We employ several widely used density functionals and systematically investigate the convergence of the calculated results with basis set size. Static electric moments and polarizabilities up to octopole order are also calculated. We present values for Li(2) through K(2) which are in good agreement with existing values, in addition to new results for Rb(2) and Cs(2). Interaction potential curves calculated from these results are shown to agree well with high level ab initio theory. Preliminary results are reported that demonstrate the applicability of the method to larger alkali clusters.

Static electric and optical properties of two coupled noble metal nanoparticles

The static electric polarizability and absorption spectrum of the coupled noble metal (Ag, Au, Cu) cluster-pair are investigated within density functional theory (DFT). The results show that the HOMO–LUMO gap gradually widens with increasing cluster distance D, and the static polarizability exhibits a maximal value as D is near the average bond length of cluster. In the absorption spectrum, the spectral strength is related to electric dipole moments which sensitively rely on D. With the increase of D the low-energy peaks (LEPs) obviously blue shift while the high-energy peaks (HEPs) keep their positions unmoved. The LEPs (HEPs) mostly comes from the transitions between near (far) the HOMO and LUMO energy levels. In these transitions, the low-energy excitations are dominantly contributed by d-electrons, indicating the fact that intense coupling effects can weaken the screen of d-electrons on sp-electrons. By means of the competition mechanism between charge transfer and electron cloud distortion, the spacing dependence behaviors of both electric and optical properties are explained self-consistently.

The static electric polarizability of a particle bound by a finite potential well

We derive an expression for the static electric polarizability of a charged particle bound by a finite potential well by employing the elegant Dalgarno-Lewis perturbative technique. The derivation does not make explicit use of the continuum states, is much simpler than the usual perturbation derivation, and allows us to separate the contributions to the polarizability from the classically forbidden and classically allowed regions of the finite potential well.

Casimir potential of a compact object enclosed by a spherical cavity

We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is a universal function of its displacement from the center of the sphere, independent of other details of the object's electromagnetic response. Furthermore, we compute the exact Casimir force between two metallic spheres contained one inside the other at arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the leading order correction to the Proximity Force Approximation for two metallic spheres both outside and within one another.

Lower Bounds on the Q of Electrically Small Dipole Antennas

General expressions are obtained for the lower bounds on the quality factor <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(Q)$</tex></formula> of electrically small electric- and magnetic-dipole antennas confined to an arbitrarily shaped volume <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$V$</tex> </formula> and excited by general sources or by global electric-current sources alone. The lower-bound expressions depend only on the direction of the dipole moment with respect to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$V$</tex> </formula> , the electrical size of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$V$</tex> </formula> , and the static electric and magnetic polarizabilities per unit volume of hypothetical perfectly electrically conducting and perfectly magnetically conducting volumes <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$V$</tex> </formula> . The lower bounds are obtained directly from the electromagnetic field expressions for <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$Q$</tex> </formula> with the help of current equivalence principles and the uncoupling of Maxwell's equations for electrically small volumes into quasi-electrostatic and quasi-magnetostatic fields.

Polarizability and hyperpolarizability of COS and NNO

We have used very large, purpose-oriented Gaussian-type basis sets to calculate static electric (hyper)polarizabilities for COS and NNO. For COS, we have obtained near-Hartree–Fock values with a [9s6p5d2f1g/9s6p5d2f1g/9s8p5d2f1g] basis set. Our best SCF values for the mean first and second hyperpolarizability of COS are β ¯ / e 3 a 0 3 E h - 2 = - 75.7 and γ ¯ / e 4 a 0 4 E h - 3 = 4966 . For NNO a [9s6p5d3f1g/9s6p5d3f1g/9s6p5d3f1g] basis yields SCF values β ¯ / e 3 a 0 3 E h - 2 = 38.0 and γ ¯ / e 4 a 0 4 E h - 3 = 1369 . Electron correlation effects have been calculated at the CCSD(T) level of theory. Our best values for the respective corrections are β ¯ / e 3 a 0 3 E h - 2 = - 22.9 (COS), −2.2 (NNO) and γ ¯ / e 4 a 0 4 E h - 3 = 1383 (COS), 485 (NNO).

Variational principles for the static electric and magnetic polarizabilities of anisotropic media with perfect electric conductor inclusions

We present four variational principles for the electric and magnetic polarizabilities for a structure consisting of anisotropic media with perfect electric conductor (PEC) inclusions. From these principles, we derive monotonicity results and upper and lower bounds on the electric and magnetic polarizabilities. When computing the polarizabilities numerically, the bounds can be used as error bounds. The variational principles demonstrate important differences between electrostatics and magnetostatics when PEC bodies are present.

Electronic structures and nonlinear optical properties of supramolecular associations of benzo-2,1,3-chalcogendiazoles by the elongation method

The investigations of one-dimensional periodic associations of benzo-2,1,3-chalcogendiazoles have been carried out by the elongation method. S, Se and Te chalcogens have been in use. For the polymers, band structures and local densities of states were extracted from ab initio calculations of electronic structure of the 15 units’ oligomers. Static electric (hyper)polarizabilities were studied by the elongation finite-field method.

Collective dipole excitations in sodium clusters

Some properties of small and medium sodium clusters are described within the RPA approach using a projected spherical single particle basis. The oscillator strengths calculated with a Schiff-like dipole transition operator and folded with Lorentzian functions are used to calculate the photoabsorbtion cross section spectra. The results are further employed to establish the dependence of the plasmon frequency on the number of cluster components. Static electric polarizabilities of the clusters excited in a RPA dipole state are also calculated. Comparison of our results with the corresponding experimental data show an overall good agreement.