Polarizability Approximation Research Articles

Bilayer terahertz chiral metasurfaces with different dihedral symmetries

In this paper, we discuss the isotropic chiroptical response of two-layered metasurfaces with n -fold dihedral symmetries of resonators ( D n ) in the terahertz (THz) range. The analysis of numerical calculations is based on the homogenization model through effective polarizability approximation. We reveal the impact of resonator symmetry on circular dichroism and polarization anisotropy of the metasurface. In particular, it is shown that an increase in the symmetry order of a metasurface unit cell leads to a proportional resonance red shift in circular dichroism spectra. This research has both fundamental and applied relevance, and may enable the realization of THz devices capable of polarization manipulation or possessing polarization sensitive features.

Luminescence of a Two-Particle Complex from a Spherical Quantum Dot and Plasmon Nanoglobule in an External Magnetic Field

Based on a specially created theoretical model, frequency dependences of the luminescence intensity of the two-component “exciton-activated semiconductor quantum dot (QD)–plasmon nanoparticle (NP)” system in a constant magnetic field are calculated. In contrast to previous models, it goes beyond the scope of the approximation of dipole polarizability of a spherical NP. The induced NP dipole moment was calculated taking into account the inhomogeneous character of the field created by the QD containing an exciton. It is shown that, with a change in induction of the external magnetic field, one can observe transformation of exciton luminescence spectra of such system as a result of the exciton–plasmon interaction between cluster particles and magnetization of the NP electron plasma. The competition of radiative and nonradiative decay channels of the excited state of a two-particle complex is taken into account. It is shown that, in rate spectra of the nonradiative energy transfer from the QD to the NP, as well as of spontaneous emission of the nanocomplex, stripes of higher order multipole transitions are formed in addition to dipole stripes; they are split into doublet components in the magnetic field.

Dependence of the vibrational spectra of amorphous silicon on the defect concentration and ring distribution

The Raman spectra of nine 216-atom models of amorphous silicon (a-Si) are calculated using the bond polarizability approximation of Raman scattering. These a-Si models, generated by the activation relaxation technique, have different concentrations of coordination defects, ring statistics and local strain distributions, which cause changes in the vibrational density of states and the Raman scattering. Analysis of the vibrational modes indicates that an increase in the number of coordination defects leads to an increase in the high-frequency localization and to mixing of the TA modes with other high-frequency modes. Calculation of partial Raman spectra indicates that five-coordinated Si atoms enhance the high-frequency part of the LO Raman peak at about 400 cm-1 and lead to characteristic band at about 600 cm-1 on the high-frequency side of the TO Raman peak. For their part, the three-coordinated Si atoms contribute to the low-frequency part of the LO peak. A weak correlation between the number of four-membered rings and the intensity of the LO Raman peak is also established although there is no correlation between the number of three- and four-membered rings and the total strain energy.

Lateral localization of optical phonons in GaAs quantum islands

Lateral localization of phonons in GaAs islands formed on the (100) surface under conditions of (2 × 4) structural reconstruction is detected by means of Raman scattering. The triplet structure of the peak corresponding to laterally localized phonons is detected in the Raman scattering spectra of a GaAs0.6/AlAs5 sublattice grown by molecular-beam epitaxy. The distribution of islands over different configurations is determined by comparing the theoretical Raman scattering spectra, calculated in the Vol’kenshte\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \)n bond polarizability approximation, with the experimental spectra. The atomic configuration of the islands is identical to the results obtained previously by scanning tunneling microscopy. According to the calculation, 70% of the islands contain fewer than 18 Ga atoms, and lateral localization occurs with AlAs barrier thickness of 2 or more monolayers.

Computer simulation study of the Rayleigh light scattering in the isotropic phase of PCH5

Configurations of 200 p-n-pentyl-(p-cyanophenyl)-cyclohexane (PCH5) molecules from molecular dynamics simulations were used to calculate the Rayleigh light scattering spectra of the isotropic phase. The interaction induced contribution is calculated to the first order dipole–induced dipole terms in the point molecular polarizability approximation. The effect of the size of the simulated system is checked from different points of view. Molecular flexibility is explicitly taken into account and comparisons in terms of time correlation functions are performed. In contrast to systems of small-sized molecules no cancellation effect is observed for the interaction induced contribution to the scattered light intensities of this mesogen. Studies of the different contributions induced by the isotropic and the anisotropic part of the molecular polarizability, evidenced the negligibility of the second one and showed the importance of orientational-translational intermolecular correlations for spectra formation in mesogen systems. The problem of comparing anisotropic and isotropic components of Rayleigh spectra is outlined.

Normal mode theory of two step relaxation in liquids: Polarizability dynamics in CS2

An instantaneous normal mode (INM) theory is given for relaxation in liquids by a fast β process followed by a slow α process. The β process is harmonic dynamics in the wells of the N-body potential, while the α process is structural relaxation coincident with barrier crossing to a neighbor well. The theory introduces a new parameter, the ‘‘harmonic fraction’’ denoted FH, which is the fraction of the mean-square fluctuations of a dynamical variable capable of being relaxed by the harmonic β process. Theory and computer simulation are compared for the polarizability correlation function, PC(t), and the polarizability time derivative correlation function, DPC(t), in a model of CS2 including internal degrees of freedom. Agreement is good, with the INM theory clearly showing the ‘‘signature’’ time dependence of a correlation function undergoing αβ relaxation in a low temperature liquid; there are no adjustable parameters in the theory. The polarizability is calculated in the ‘‘point atomic polarizability approximation’’ (PAPA) which is sensitive to molecular vibrations, so a preliminary classical INM treatment of Raman scattering is obtained. The PAPA overestimates the derivative of the polarizability with respect to the internal coordinates, and in reality the vibrations behave quantum mechanically, so the Raman intensities are inaccurate, but otherwise a plausible description is obtained for several features of the spectrum. It is explained how an improved PAPA will be combined with a quantum INM theory in future Raman calculations.

Wave-vector dependence of Raman scattering intensity in folded modes of long-period alpha -SiC.

It is found that the relative Raman intensity of several folded transverse-acoustic modes in silicon carbide polytypes varies markedly with the scattering wave vector q of the phonons under off-resonance conditions. A simple expression for the q-dependent intensity of Raman scattering is derived, based on the bond-polarizability concept. Using atomic displacements obtained from a linear-chain model, the variation of the intensity with q is calculated. The results agree well with the experimental results for 6H, 8H, 15R, and 21R polytypes. This agreement indicates that the bond polarizability approximation is valid for \ensuremath{\alpha}-SiC.

Hyperpolarizability dependent dispersion forces and absorption spectra in simple liquids

A general quantum statistical perturbation expansion for molecular fluids, with term ordering in increasing order of molecular susceptibilities, reproduces results of recent theories on absorption spectra in liquids when taken to lowest order, i.e. including only linear polarizability terms. Inclusion of higher order, cubic polarizability terms produces solvent effects on impurity electronic absorption spectra. The impurity line shift obtained is a functional of the dipole pair correlations of the pure solvent and of the two-frequency dependent cubic polarizability tensor γ(ω, ξ, -ξ) of the impurity molecule. A simple form of γ based on a 3-level isotropic molecular model, together with a linear polarizability approximation for the solvent dipole correlations leads to a blue shift of the impurity lowest excitation frequency. The magnitude of the shift depends of the position of the impurity line relative to the excitonic band spectrum of the pure solvent and on molecular parameters of the impurity obtaina...

Random-phase calculation of the low-energy circular dichroism in glucans.

AbstractThe CD of the long‐wavelength electronic transition in the α‐(1 → 4)‐linked glucan dimer (maltose) and polymer (amylose), and in the β‐(1 → 6)‐linked dimer (gentiobiose) and polymer (pustulan), are calculated in the random‐phase approximation using time‐dependent Hartree theory. This long‐wavelength transition (180–190 nm) is assumed to be localized on the linkage oxygen atom and to be of a σ*/3 s ← n character. The zerothorder σ*/3s ← n magnetic‐dipole transition moment is coupled to the CC, CO, and CH bond density of states via a polarizability approximation. We assume this coupling is dominated energetically by the electric‐dipole, electric‐dipole interaction terms in the context of Schellman's μe‐μm coupling mechanism of rotatory power. The CD is calculated as a function of rotation about the two single bonds of the linkage oxygen atom and also as a function of rotation about the C(5)‐C(6) bond. For maltose, four rotational isomers are considered, resulting from combinations of the gg and gt C(6)H2OH group rotational isomers. The calculated CD values were then Boltzmann‐averaged over an empirical potential, and the resulting CD was found to compare satisfactorily with experiment. In the case of the polymers, only structures having periodicity (helicity) were examined.

The anisotropic ligand polarization intensity mechanism in dihedral lanthanide(III) complexes

The f-f electronic spectra of a D 4 coordination compound [Eu(III)(2,2′-bipyridine-N,N′-dioxide)4]3+ and of D 3 analogues indicate, on comparison, that only the ΔMJ = ±1 component of the quadrupolar Eu(III) 7 F 0 → 5 D 2 transition is active in the D 4 case. The intensity of a quadrupolar metal-ion transition in a D 4 complex is governed uniquely by a single rank-2 environmental ligand tensor, within the restriction to one-electron operators, and it generates a first order electric dipole moment solely for the ΔMJ = ± 1 transition component. A rank-2 ligand tensor cannot arise from a configurational interaction mechanism based upon a static point-charge or dipolar crystal field, nor from the dynamic ligand-polarization mechanism in the mean polarizability approximation. The extension of the latter mechanism to include the polarizability anisotropy of the ligand bonds gives a rank-2 ligand polarization field tensor F (2) 0 which accounts for the 7 F 0 → 5 D 2 dipole strength of the D 4 complex investigated.

Anisotropic ligand polarization contributions to the Laporte-forbidden transition probabilities of open-shell metal complexes

The inclusion of ligand polarizability components making up the symmetric anisotropy tensor α(2) in the ligand polarization analysis of the d-d or f-f transition probabilities of open-shell metal coordination compounds is found to account for the known cases where the corresponding mean polarizability approximation fails. For a given point group symmetry of the metal complex, the addition of the ligand polarizability anisotropy to the dynamic coupling treatment generates the number of intensity parameters required group theoretically for a given multipole transition of the metal ion.

Raman studies of argon dimers in a supersonic expansion. I. Spectroscopy

Detection of argon dimers by means of Raman scattering is reported. This first observation of dimers by Raman scattering in a supersonic expansion provides a new technique for the study of the low-lying excitations of dimers and perhaps larger clusters, useful in determining interatomic potentials, etc. Spectra were recorded at low temperature and density in a supersonic expansion of pure argon. Both the pure rotational and the much weaker vibrational Raman transitions were observed for the lowest two vibrational states of the dimer. Raman transition frequencies were determined from the spectra. Theoretical spectra were generated with the use of the polarizability approximation. By using a classical point-dipole-induced dipole model in the calculation of the matrix elements and assuming a thermal distribution over the dimer levels, we could reproduce the rotational spectra to within experimental uncertainty.

Structure and equilibrium optical properties of liquid CS2

Equilibrium optical properties of liquid carbon disulphide (CS2), i.e. its refractive index, Kerr constant and depolarized light scattering intensity are calculated using two models of optical response of the fluid. The first one, the point polarizability approximation (PPA) assumes that a point dipole, proportional to the total polarizability, is induced in each molecule. The second one, the point atomic polarizability approximation (PAPA) assumes that point dipoles are induced in individual atomic sites. The symmetry components of the intermolecular pair distribution function needed to calculate optical properties of the fluid are obtained by Monte Carlo computer simulation on a hard triatomic model of CS2 as well as by two approximate approaches using this same model. The approximations are both based on the use of the site superposition approximation (SSA) for the intermolecular pair distribution function. In the first approach, the SSA pair distribution is obtained using the Monte Carlo site-site fun...

Random-phase circular dichroism calculations of the σ/3s←n transition in chiral alcohols

The circular dichroism of the long wavelength electronic transition in 10 chiral alcohols is calculated in the random-phase approximation using time-dependent Hartree theory. This long wavelength transition (1850–2000 Å) which is associated with the hydroxyl group is assumed to be largely localized on the oxygen atom and to originate in nonbonding density of the ground state, namely in an oxygen 2p orbital. The upper state is mixed, having both intravalence σ and Rydberg 3s character. The σ*/3s←n electric-dipole transition moment (μe) is perpendicularly polarized with respect to the COH plane, while the associated magnetic-dipole transition moment (μm) is polarized in plane. The circular dichroism is calculated as a function of hydroxyl rotation about the CO bond by coupling the zeroth-order σ*/3s←n transition moments to the backbone CC and CH bond density of states via a polarizability approximation. These values are then Boltzmann averaged over an empirical rotational potential, and the resulting circular dichroism is satisfactorilly compared with experiment. The empirical potential functions for hydroxyl rotation were found to be in as good or better agreement with experiment as ab initio potentials in the case of simple alcohols. The 10 alcohols c chiroptically studied belong to three different structural classes, borneols, decalols, and sterols, all of which have well defined, rigid, cyclic carbon backbone structures. The extent of hydroxyl rotational freedom among these alcohols varies from the highly restricted case of a single potential well to the more conventional case of a trimodal staggered potential with barriers less than 1.5 kcal mol−1. This potenital function variability, in addition to the calculated sensitivity of the alcohol classes to the direction of polarization of the σ*/3s←n μm, forms a basis for the following conclusion. The low order σ*/3s←n transition mechanism invoked is sufficient to give qualitative agreement with previously reported circular dichroism values. The sensitivity of the sterols and the insensitivity of the borneols to the in-plane μm polarization suggests that the σ* component of the upper state has greater antibonding character along the CO bond than along the OH bond. The coupling of the σ*/3s←n transition to the backbone density of states is dominated energetically by electric–dipole, electric–dipole interaction terms in the context of Schellman’s μeμm-coupling mechanism of rotatory power and the σ*/3s←n electric–dipole moment provides a basis for explaining the sector rule proposed by Kirk, Mose, and Scopes for saturated chiral alcohols.

Time-dependent Hartree-Fock polarizability and random phase approximation sum rules

Abstract The linear response of a nucleus in an external oscillating field has been studied in the framework of TDHF theory. The dynamic polarizability evaluated in TDHF theory has been related to RPA energies and matrix elements and a method to obtain RPA sum rules from the TDHF polarizability has been explicitly developed. This method can be applied to isoscalar as well as to isovector and spin excitations. Finally, a prescription to identify mass and restorting force parameters of various collective models with RPA sum rules is given.

Time-dependent Hartree-Fock polarizability and random phase approximation sum rules

Abstract Different isovector and isoscalar giant resonances (dipole, monopole and quadrupole) have been studied by evaluating energy-weighted and cubic energy-weighted sum rules. Calculations have been performed within the RPA using different variants of the Skyrme interaction. The link between the two RPA rum rules and the parameters of a collective Hamiltonian has been explicitly shown. Excitation energies and strengths are compared with experiments and with the predictions of other approaches.

Random-phase calculation of the circularly dichroic 3000 Å band of (+)−D-camphor

Time-dependent Hartree theory is applied in the random-phase, coupled-oscillator approximation to the calculation of the circular dichroism of the carbonyl π*←n transition in (+)−D-camphor. X-ray evidence indicating a very slight pyramidal distortion of the C(CO)C array in the ground state and the observation of the 000←000 member of a 00vs←000 progression (ν′ s∼1100 cm−1) in both absorption (f∼3×10−5) and circular dichroism lead us to conclude that a principal component of the π*←n transition mechanism is one which is electric-dipole allowed. Each such electric-dipole allowed member is in addition both magnetic-dipole and electric-quadrupole allowed. In coupling the 00vs←000 π*←n transitions to the CC and CH densities of states via a polarizability approximation, it is verified that the circular dichroism arising from the coupling of the electric-dipole transition moment is negligible in comparison with that resulting from the coupling of the magnetic-dipole transition moment with the backbone density of states. Moreover it is shown that the associated electric−quadrupole transition moment dominates the coupling energetics. The observed inhomogeneous dissymmetry, Δε/ε, occurs as a result of additional thermally populated 00vs←0va′0 (ν″ a′∼400 cm−1) and 00vs←va″00 (νa″″∼500 cm−1) progressions which contribute appreciably to the absorption intensity but not to the circular dichroism.

Theory of two-phonon Raman spectrum of diamond

The Raman spectrum of diamond in the high-frequency part of the two-phonon region is investigated. An interpretation of the sharp line at the two-phonon cutoff as a simple overtone is supported in terms of a harmonic model for the potential and a bond polarizability approximation for the scattering Hamiltonian. Polarization features as well as the anomalous position and width of the peak are discussed and interpreted, giving general agreement between theory and experiment. A comparison is made with the Raman spectrum of silicon, and differences in the spectra are accounted for by a different behavior of the dispersion relation along $\ensuremath{\Delta}$ for the two lattices, which has its origin in the greater angle-stiffness forces in diamond, ultimately due to greater covalency in diamond. A new set of critical points for the LO branch of diamond is also proposed.

Raman scattering by normal modes in vitreous silica, germania and beryllium fluoride

Contributions to the Raman scattering intensity, calculated in the bond polarizability approximation, are presented for vitreous SiO2, GeO2 and BeF2. The computed frequency spectrum-scattering intensity relationship for SiO2 shows only partial agreement with that derived from experiment.

The calculated circular dichroism of polyproline II in the polarizability approximation.

AbstractThe circular dichroism (CD) spectrum of polyproline II (PPII) has heretofore been moderately well calculated from exciton theory only at the expense of assuming unreasonable chain conformations and accepting a conservative spectrum in the 180–250‐nm region (which is not observed). We have incorporated far uv transitions in the polarizability approximation and, together with the π2π* transition, have calculated the resulting correction to the exciton model. This has been accompanied by a modified assignment of the ππ* transition in PPII, and a simultaneous calculation of the absorption and CD spectra of the α‐helix, β structure, PPI, and PPII. We obtain good agreement with the observed CD spectrum of PPII in the 180–250‐nm region for acceptable chain conformations. In addition, we predict a negative CD into the far uv, in agreement with recent experimental observations. Our calculations also reproduce features of the far uv CD spectrum of the α‐helix, and are in agreement with the CD spectra of the β chain and PPI. The calculated CD of the unordered polypeptide chain is not significantly influenced by far uv contributions, indicating that our previous calculation is valid for such a system. These results demonstrate the importance of incorporating far uv transitions in order to achieve an adequate theoretical explanation of the CD spectra of polypeptides.