Size- and shape-dependent polarizabilities of sandwich and rice-ball Co(n)Bz(m) clusters from density functional theory

The dipole polarizabilities of Co(n)Bz(m), (n, m = 1-4, m = n, n + 1) clusters are studied by means of an all-electron gradient-corrected density functional theory and finite field method. The dipole moments are relatively large for most of the clusters, implying their asymmetric structures. The total polarizability increases rapidly as cluster size, whereas the average polarizability shows "odd-even" oscillation with relatively large values at (n, n + 1). The polarizabilities exhibit clear shape-dependent variation, and the sandwich structures have systematically larger polarizability and anisotropy than the rice-ball isomers. The dipole polarizabilities are further analyzed in terms of the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, ionization potential, and electron delocalization volume. We conclude that the polarizability variations are determined by the interplay between the geometrical and electronic properties of the clusters.     

Gaussian induced dipole polarization model

A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole-induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability.     

Spectroscopic and theoretical optical properties of indoleninyl-substituted dibenzotetraaza[14]annulenes

Two new macrocyclic dibenzotetraaza[14]annulene (DBTAA) compounds with indolenine ( 5 ) and pyridoindolenine ( 6 ) moieties were synthesized and characterized by spectroscopy. Both DBTAAs exhibit strong UV-Vis absorption properties in the Soret band region. The theoretical second-order nonlinear optical property, electric dipole moment (μ), dispersion-free dipole polarizability (α) and first hyper-polarizability values were calculated by density functional theory and time dependent density functional theory. The ab-initio quantum mechanical calculation by time-dependent Hartree-Fock method was utilized to investigate the dynamic dipole polarizabilities, dynamic second-order, static, and dynamic third-order (γ) hyper-polarizabilities of the DBTAAs. The configuration interaction technique of all doubly occupied molecular orbitals possesses theoretically defined single-photon absorption (OPA) specifications for the examined structures. The computed maximum OPA wavelengths on both macrocyclic compounds coincide with the preceding measurement outcomes.     

Dynamic polarizability of many-electron systems within a time-dependent density-functional theory

Using the time-dependent extension, proposed by us recently, of the Hohenberg—Kohn—Sham density-functional theory, in the presence of an oscillating electric field, we suggest a Karplus—Kolker-type variation—perturbation method for the calculation of dynamic 2^L-pole polarizability of many-electron systems. As an illustration of the present density-functional formalism, the frequency-dependent dipole polarizability of He atom has been calculated in the frequency range 0 ? ω ? 0.65 au, using local density forms of the exchange and correlation potentials. For ω = 0, the results are numerically better than recent density-functional calculations of the static dipole polarizability of He. The corresponding hydrodynamical formulation, which employs the single-particle density as a basic variable, is also presented.     

Complex polarization propagator calculations of magnetic circular dichroism spectra

It is demonstrated that the employment of the nonlinear complex polarization propagator enables the calculation of the complete magnetic circular dichroism spectra of closed-shell molecules, including at the same time both the so-called Faraday A and B terms. In this approach, the differential absorption of right and left circularly polarized light in the presence of a static magnetic field is determined from the real part of the magnetic field-perturbed electric dipole polarizability. The introduction of the finite lifetimes of the electronically excited states into the theory results in response functions that are well behaved in the entire spectral region, i.e., the divergencies that are found in conventional response theory approaches at the transition energies of the system are not present. The applicability of the approach is demonstrated by calculations of the ultraviolet magnetic circular dichroism spectra of para-benzoquinone, tetrachloro-para-benzoquinone, and cyclopropane. The present results are obtained with the complex polarization propagator approach in conjunction with Kohn-Sham density functional theory and the standard adiabatic density functionals B3LYP, CAM-B3LYP, and BHLYP.     

Lagrangian approach to molecular vibrational Raman intensities using time-dependent hybrid density functional theory

The authors propose a new route to vibrational Raman intensities based on analytical derivatives of a fully variational polarizability Lagrangian. The Lagrangian is constructed to recover the negative frequency-dependent polarizability of time-dependent Hartree-Fock or adiabatic (hybrid) density functional theory at its stationary point. By virtue of the variational principle, first-order polarizability derivatives can be computed without using derivative molecular orbital coefficients. As a result, the intensities of all Raman-active modes within the double harmonic approximation are obtained at approximately the same cost as the frequency-dependent polarizability itself. This corresponds to a reduction of the scaling of computational expense by one power of the system size compared to a force constant calculation and to previous implementations. Since the Raman intensity calculation is independent of the harmonic force constant calculation more, computationally demanding density functionals or basis sets may be used to compute the polarizability gradient without much affecting the total time required to compute a Raman spectrum. As illustrated for fullerene C60, the present approach considerably extends the domain of molecular vibrational Raman calculations at the (hybrid) density functional level. The accuracy of absolute and relative Raman intensities of benzene obtained using the PBE0 hybrid functional is assessed by comparison with experiment.     

Polarization justified Fukui functions: the theory and applications for molecules

The Fukui functions based on the computable local polarizability vector have been presented for a group of simple molecules. The necessary approximation for the density functional theory softness kernel has been supported by a theoretical analysis unifying and generalizing early concepts produced by the several authors. The exact relation between local polarizability vector and the derivative of the nonlocal part of the electronic potential over the electric field has been demonstrated. The resulting Fukui functions are unique and represent a reasonable refinement when compared to the classical ones that are calculated as the finite difference of the density in molecular ions. The new Fukui functions are strongly validated by their direct link to electron dipole polarizabilities that are reported experimentally and by other computational methods.     

B2-PPW91: a promising double-hybrid density functional for the electric response properties

A new double-hybrid density functional, termed B2-PPW91, is presented which includes the Becke88 (B88) exchange in conjunction with Perdew-Wang91 (PW91) gradient-corrected correlation functional. The fitting parameters are obtained by minimization of mean absolute error of the static dipole polarizability of 4d transition metal monohalides against the CCSD(T)∕aug-cc-pVTZ∕SDD results. The performance of proposed functional has been assessed for estimation of other response properties, such as dipole moment and excitation energy, for the same species. We then proceed to explore the validity of B2-PPW91 method for calculation of the dipole polarizability of some 5d transition metal monofluorides. In all cases, the improvement compared to common density functional methods and even previously reported double-hybrid functionals such as B2-PLYP and mPW2-PLYP has been observed. This indicates that the utility of double-hybrid density functional methods can be further extended to study linear and non-linear optical properties of transition metal containing molecules.     

The frequency-dependent dipole polarizability of the mercury dimer from four-component relativistic density-functional theory

The frequency-dependent dipole polarizability of Hg(2) is calculated using response theory within four-component relativistic density-functional theory [using the local-density approximation (LDA) and the hybrid functional B3LYP] including corrections for the basis-set superposition error. The anisotropic component of the polarizability tensor agrees well with the values obtained from collision-induced Raman spectroscopy carried out at a wavelength of 488 nm. The values obtained from the two density functionals agree closely with the experimentally derived anisotropy component of the dipole polarizability, despite their rather large differences in the dimer potential-energy curves (LDA is strongly overbinding while B3LYP is purely repulsive). The first two refractivity virial coefficients for the generalized Clausius-Mossotti function are derived.     

Molecular geometry and polarizability of small cadmium selenide clusters from all-electron ab initio and Density Functional Theory calculations

We have calculated molecular geometries and electric polarizabilities for small cadmium selenide clusters. Our calculations were performed with conventional ab initio and density functional theory methods and Gaussian-type basis sets especially designed for (CdSe)(n). We find that the dipole polarizability per atom converges rapidly to the bulk value.     

Geometrical derivatives of dipole moments and polarizabilities

Molecular dipole moments and polarizabilities, as well as their geometrical derivatives, are given analytical expressions for multiconfiguration self-consistent-field and configuration interaction wavefunctions. By considering the response of the electronic wavefunction induced by electric field and geometrical displacement terms in the Hamiltonian, the response of the total electronic energy to these terms is analyzed. The dipole moment and polarizability are then identified through the factors in the energy which are linear and quadratic in the electric field, respectively. Derivatives with respect to molecular deformation are obtained by identifying factors in these moments which are linear, quadratic, etc., in the distortion parameter. The analytical derivative expressions obtained here are compared to those which arise through finite-difference calculations, and it is shown how previous configuration-interaction-based finite difference dipole moment and polarizability derivatives are wrong. The proper means of treating such derivatives are detailed.     

Nonstationary perturbation theory for open-shell molecules

Nonstationary perturbation theory equations have been obtained for open-shell molecules. The equations were formulated in terms of a density matrix in the MO-LCAO method. The first variant is coupled perturbation theory in the framework of the restricted Hartree-Fock method for open shells, and the second variant is variational perturbation theory for ground and excited electronic states of molecules, in which the perturbed wave function of the system is constructed in the form of a superposition of the ground and singly excited configurations composed of the Hartree-Fock orbitals of the open shell. A calculation of the Cauchy moments of the dynamic dipole polarizability of several molecules of conjugated open-shell hydrocarbons, viz., doublet states of odd alternant hydrocarbons, as well as triplet excited states and doublet states of radical ions of even alternant hydrocarbons, has been carried out in the framework of both methods.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 1, pp. 18–27, January–February, 1985.     

Polarization and polarizability in extended one-dimensional organic materials

The modern theory of polarization in extended insulators is applied to one-dimensional models for conjugated polymers and charge transfer salts. Closed expressions for the dependence of the polarization on the site and bond energy alternations are presented for uncorrelated models, and results from exact real-space diagonalization are obtained for correlated models. Changes in polarization induced by lattice phonons or molecular vibrations are directly related to the intensity of infrared bands in the far and mid-IR, respectively. We model intensities by introducing linear electron-vibration coupling and show that coupling to delocalized electrons generates a combination band consisting of a lattice phonon and a molecular vibration. The displaced dipole operator is defined on a real-space basis allowing for the finite field calculation of linear polarizability in finite size systems with periodic boundary conditions. Size-consistency arguments are used to demonstrate that the resulting polarizability becomes exact in the thermodynamic limit, and numerical calculations demonstrate that this approach leads to reliable results that converge rapidly to the thermodynamic limit.     

Ground-state properties and static dipole polarizabilities of the alkali dimers from K2 n to Fr2 n(n=0,+1) from scalar relativistic pseudopotential coupled cluster and density functional studies

The newly adjusted energy-consistent nine-valence-electron pseudopotentials for K to Fr are used to calculate spectroscopic properties for the neutral and positively charged alkali dimers using coupled cluster and density functional theory. For the neutral dimers the static dipole polarizability was calculated. The coupled cluster results are all in excellent agreement with experimental values. The density functionals used can give quite different spectroscopic properties especially for the dipole polarizability, with the Perdew-Wang PW91 functional performing best.     

Effective molecular polarizabilities and crystal refractive indices estimated from x-ray diffraction data

Although it was proposed some time ago that (hyper)polarizabilities might be estimated from the results of x-ray charge density refinements, early results were unconvincing. In this work we show that the one particle density obtained from the usual multipole refinement model does not contain sufficient information to determine these response properties and instead pursue the "constrained wave function" approach of fitting to x-ray structure factors. Simplified sum-over-states expressions are derived for determining the dipole polarizability from these wave functions, and these clearly show that the earlier work ignored important two-electron expectation values for the dipole polarizability, and two- and three-electron terms for Beta, etc. Correction factors for the simplified sum-over-states polarizability tensors from the constrained wave function are obtained by calibration against coupled Hartree-Fock ab initio results to yield in-crystal effective polarizability tensors. Results obtained for benzene, urea, and 2-methyl-4-nitroaniline demonstrate that the effective molecular polarizabilities clearly include the effects of intermolecular interactions and electron correlation, especially for urea where the effects on the polarizability are known to be quite large. We also carefully consider the way in which the linear bulk susceptibility, chi((1)), and refractive indices are determined from the x-ray fitted polarizabilities, employing three models based on a rigorous treatment of the local field. Incorrect results are obtained for the sort of molecules that are of interest in nonlinear optical applications if the molecules are approximated by single point dipoles. In contrast, the use of Lorentz-factor tensors averaged over several sites yields excellent results, with refractive indices obtained using this model in remarkably good agreement with optical measurements extrapolated to zero frequency.     

Synthesis,Mesomorphic and Computational Characterizations of Nematogenic Schiff Base Derivatives in Pure and Mixed State

Homolog series based on three aromatic rings bearing terminal alkoxy chain of various lengths named 4-(4-(alkoxy)phenylimino)methyl)phenyl nicotinate (An) were synthesized. The alkoxy-chain length changed between 6, 8 and 16 carbons. Mesomorphic and optical properties were carried out via differential scanning calorimetry (DSC) and polarized optical microscopy (POM). Elemental analyses, FT-IR and NMR spectroscopy were carried out to elucidate the molecular structures of the prepared derivatives. Mesomorphic results indicated that all the synthesized homologs (An) are monomorphic possessing the nematic (N) phase enantiotropically with wide thermal stability. Computational simulations were measured via density functional theory (DFT) theoretical calculation tool. The estimated thermal and geometrical parameters are in agreement with the experimental data. By discussing the estimated parameters, it was found that the molecular architecture, dipole moment and the polarizability of the investigated compounds are highly affected by the length of the attached terminal flexible chain and the location of the nitrogen atom in the other terminal aromatic ring. Binary phase diagrams of two corresponding homologs with different proportionating terminals were constructed, and their binary phase physical properties were discussed in terms of the temperature range and stability of the N phase.