Numerically Exact Study of Polarizabilities and Hyperpolarizabilities of Correlated Conjugated Organic Models

Polarizabilities and Hyperpolarizabilities of conjugated organic chains are calculated using correlated model Hamiltonians. While correlations reduce the Polarizabilities and extend the range of linear response, the Hyperpolarizabilities essentially are unaffected by the same. This explains the apparently large Hyperpolarizabilities of conjugated electronic systems.

Exact static polarizabilities of correlated finite model systems

A finite-field method for calculating exact polarizabilities of correlated conjugated model systems within the valence bond (VB) framework is presented. The correlations reduce the polarizabilities from their noninteracting values and extend the range of linearity to higher external fields. The large nonlinear polarizabilities observed in strongly correlated conjugated organic molecules cannot be directly attributed to electron correlations. The method described can be employed to calculate static polarizabilities for any desired state of a correlated system.

Electric and magnetic polarizabilities of hexagonal Ln(2)CuTiO(6)(Ln = Y, Dy, Ho, Er, and Yb)

We investigated the rare-earth transition-metal oxide series, Ln(2)CuTiO(6) (Ln = Y, Dy, Ho, Er, and Yb), crystallizing in the hexagonal structure with noncentrosymmetric P6(3)cm space group for possible occurrences of multiferroic properties. Our results show that while these compounds, except Ln = Y, exhibit a low-temperature antiferromagnetic transition due to the ordering of the rare-earth moments, the expected ferroelectric transition is frustrated by the large size difference between Cu and Ti at the B site. Interestingly, this leads these compounds to attain a rare and unique combination of desirable paraelectric properties with high dielectric constants, low losses, and weak temperature and frequency dependencies. First-principles calculations establish these exceptional properties result from a combination of two effects. A significant difference in the MO5 polyhedral sizes for M = Cu and M = Ti suppress the expected cooperative tilt pattern of these polyhedra, required for the ferroelectric transition, leading to relatively large values of the dielectric constant for every compound investigated in this series. Additionally, it is shown that the majority contribution to the dielectric constant arises from intermediate-frequency polar vibrational modes, making it relatively stable against any temperature variation. Changes in the temperature stability of the dielectric constant among different members of this series are shown to arise from changes in relative contributions from soft polar modes.

Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

Gluon-field contribution in QCD sum rules for the magnetic moments of the nucleons

The Wilson coefficient corresponding to the gluon-field strength GμνGμν is evaluated for the nucleon current correlation function in the presence of a static external electromagnetic field, using a regulator mass Λ to separate the high-momentum part of the Feynman diagrams. The magnetic-moment sum rules are analyzed by two different methods and the sensitivity of the results to variations in Λ are discussed.

Intensity of a Raman Overtone Band

Placzek [1] was the first to derive general expressions for the intensities of overtones in case of Raman scattering. He assumed electrical anharmonicity. However, he left the expressions for the derivations of the polarizability tensor undetermined. In 1941, a classical and semiempirical theory was developed by Wolkenstein [2]. He assumed the validity of the additivity of bond polarizabilities. However, the expressions derived by him for the intensities of overtones remain yet to be verified. It is the purpose of this paper to derive a formula for Raman polarizability tensor for overtones of (intramolecular) vibrational spectra along the lines of Kondilenko et al. [3,4].

Quenching of gA in the nuclear medium

The numerical values of gA are evaluated using quantum-chromodynamic sum rules. The nuclear medium effects are taken into account by modifying the chiral symmetry breaking correlation, . Our results indicate a quenching of gA in a nuclear medium. The physical reasons for this fundamental quenching are noted to be the same for the effective mass of the nucleon bound in a nucleus being less than its free space value.

QCD with dynamical Wilson fermions. II

We present results for the QCD spectrum and the matrix elements of scalar and axial-vector densities at β=6/g2=5.4, 5.5, 5.6. The lattice update was done using the hybrid Monte Carlo algorithm to include two flavors of dynamical Wilson fermions. We have explored quark masses in the range ms≤mq≤3ms. The results for the spectrum are similar to quenched simulations and mass ratios are consistent with phenomenological heavy-quark models. The results for matrix elements of the scalar density show that the contribution of sea quarks is comparable to that of the valence quarks. This has important implications for the pion-nucleon σ term.

Linear and nonlinear optical properties of cumulenes and polyenynes: a model exact study

Model exact static and frequency-dependent polarizabilities, static second hyperpolarizabilities and THG coefficents of cumulenes and polyenynes, calculated within the correlated Pariser-Parr-Pople (PPP) model defined over the pi-framework are reported and compared with the results for the polyenes. It is found that for the same chain length, the polarizabilities and THG coefficients of the cumulenes are largest and those of the polyenynes smallest with the polyenes having an intermediate value. The optical gap of the infinite cumulene is lowest (0.75 eV) and is associated with a low transition dipole moment for an excitation involving transfer of an electron between the two orthogonal conjugated pi-systems. The polyenynes have the largest optical gap (4.37 eV), with the magnitude being nearly independent of the chain length. This excitation involves charge transfer between the conjugated bonds in the terminal triple bond. Chain length and frequency dependence of alpha(ij) and gamma(ijkl) of these systems are also reported. The effect of a heteroatom on the polarizability and THG coefficients of acetylenic systems is also reported. It has been found that the presence of the heteroatom reduces the polarizability and THG coefficients of these systems, an effect opposite to that found in the polyenes and cyanine dyes. This result has been associated with the different nature of the charge transfer in the acetylenic systems.

First-order hyperpolarizabilities of octupolar aromatic molecules: symmetrically substituted triazines

The first hyperpolarizabilities of some symmetrically substituted triazines have been measured and compared with those of the corresponding symmetrically substituted benzenes. The octupolar triazines have higher quadratic polarizabilities than the corresponding octupolar benzenes. The triazine ring seems to be a better central acceptor than the benzene ring, but if it acts as a donor as in sym-triphenyl triazine, the nonlinearity improves further.