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.     

Discrete and continuum contributions to multipole polarizabilities and shielding factors of hydrogen

Discrete and continuum contributions to the multipole polarizabilities and shielding factors of atomic hydrogen are computed. The discrete series show logarithmic convergence which can be accelerated by the u-transform. The continuum contributions increase with increasing multipole order and are already dominant in the quadrupole polarizability and shielding factor. The shielding factors have greater continuum contributions than the polarizabilities.     

Polarizabilities of heteroaromatic molecules: Azines revisited

Ab initio electron-correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities are reported for benzene and 12 heteroaromatic six-membered rings obtained from it by aza-substitution. Our geometries and dipole moments agree well with available experimental microwave determinations. The polarizabilities are in reasonable agreement with the fragmentary experimental data available. Uncoupled Hartree-Fock calculations indicate that as much as half the polarizability comes from the σ-electrons. Simple empirical formulas based on atom- and bond-additive models correlate the calculated polarizabilities of 33 five- and six-membered heteroaromatic rings (10 azoles, 10 oxazoles, 13 azines) quite well. The correlation improves significantly if systematic data of uniform quality are used. © 1996 John Wiley & Sons, Inc.     

Electric field effects on the shielding constants of noble gases: a four-component relativistic Hartree-Fock study

Second derivatives of nuclear shielding constants with respect to an electric field, i.e., shielding polarizabilities, have been calculated for the noble gas atoms from helium to xenon. The calculations have been carried out using the four-component relativistic Hartree-Fock method. In order to assess the importance of the individual relativistic corrections, the shielding polarizabilities have also been calculated at the nonrelativistic Hartree-Fock level, with spin-orbit and scalar (Darwin and mass-velocity) effects having been established by perturbative methods. Electron correlation effects have been estimated using the second-order polarization propagator approach. The relativistic effects on the tensor components of the shielding polarizabilities are found to be larger and changing less regularly with the atomic number than for the shielding constant itself. However, there is a partial cancellation of the contributions to the parallel and perpendicular components of the shielding polarizability and as a consequence the mean shielding polarizability is far less affected than the individual components.     

A density functional theory-based chemical potential equalisation approach to molecular polarizability

The electron density changes in molecular systems in the presence of external electric fields are modeled for simplicity in terms of the induced charges and dipole moments at the individual atomic sites. A chemical potential equalisation scheme is proposed for the calculation of these quantities and hence the dipole polarizability within the framework of density functional theory based linear response theory. The resulting polarizability is expressed in terms of the contributions from individual atoms in the molecule. A few illustrative numerical calculations are shown to predict the molecular polarizabilities in good agreement with available results. The usefulness of the approach to the calculation of intermolecular interaction needed for computer simulation is highlighted.     

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.     

Evaluation of the dipole moments of organic ions in the gas phase

The dipole moments of a series of substituted benzene radical cations were evaluated on the basis of mass displacements from the expected instrumental value by ion trap experiments. Mass displacements represent a direct measure of the total polarizability, giving access to both the electronic and dipolar polarizabilities, depending on the characteristics of the analyte under investigation. A linear relationship was found between the dipolar polarizabilities and the dipole moments of the corresponding neutrals.     

Dynamic dipole polarizabilities of the ground and excited states of confined hydrogen atom computed by means of a mapped Fourier grid method

Accurate theoretical estimates of static and dynamic dipole polarizabilities are reported for the ground and excited states of hydrogen atom confined at the center of a spherical “box” with impenetrable walls using a novel theoretical algorithm that combines the variational–perturbation approach with an appropriately adapted mapped Fourier grid method and uniformly maintains the numerical accuracy. A variation of computed polarizabilities is observed as a function of the number of grid points. However, rapid convergence to their correct values, even far into the anomalous dispersion region, is achieved by an extrapolation procedure to the limit of an infinitely large number of grid points using a small number of the lowest‐order Padé approximants. It is shown that dipole polarizabilities strongly depend upon the electronic state and the radius of confinement. In particular, the static polarizability of 2s state changes sign under strong confinement. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Electronic and vibrational contributions to first hyperpolarizability of donor-acceptor-substituted azobenzene

In this study we report on the electronic and vibrational (hyper)polarizabilities of donor-acceptor-substituted azobenzene. It is observed that both electronic and vibrational contributions to the electric dipole first hyperpolarizability of investigated photoactive molecule substantially depend on the conformation. The contributions to the nuclear relaxation first hyperpolarizability are found to be quite important in the case of two considered isomers (cis and trans). Although the double-harmonic term is found to be the largest in terms of magnitude, it is shown that the total value of the nuclear relaxation contribution to vibrational first hyperpolarizability is a result of subtle interplay of higher-order contributions. As a part of the study, we also assess the performance of long-range-corrected density functional theory in determining vibrational contributions to electric dipole (hyper)polarizabilities. In most cases, the applied long-range-corrected exchange-correlation potentials amend the drawbacks of their conventional counterparts.     

Theoretical investigation of the (hyper)polarizabilities of pyrrole homologues C4H4XH (X = N, P, As, Sb, Bi). A coupled-cluster and density functional theory study

Geometries, inversion barriers, static and dynamic electronic and vibrational dipole polarizability (alpha), and first (beta) and second (gamma) hyperpolarizability of the pyrrole homologues C(4)H(4)XH (X = N, P, As, Sb, Bi) have been calculated by Hartree-Fock, M?ller-Plesset second-order perturbation theory, coupled-cluster theory accounting for singles, doubles, and noniterative triple excitations methods, as well as density functional theory using B3LYP and PBE1PBE functionals and Sadlej's Pol and 6-311G basis sets. Relativistic effects on the heavier homologues stibole and bismole have been taken into account within effective core potential approximation. The results show that the electronic (hyper)polarizabilities monotonically increase with the atomic number of the heteroatom, consistent with the decrease in the molecular hardness. Ring planarization reduces the carbon-carbon bond length alternation of the cis-butadienic unit, enhancing the electronic polarizability values (alpha(e)) by 4-12% and the (hyper)polarizability values (and gamma(e)) by 30-90%. Pure vibrational and zero-point vibrational average contributions to the (hyper)polarizabilities have been determined within the clamped nucleus approach. In the static limit, the pure vibrational hyperpolarizabilities have a major contribution. Anharmonic corrections dominate the pure vibrational hyperpolarizabilities of pyrrole, while they are less important for the heavier homologues. Static and dynamic electronic response properties of the pyrrole homologues are comparable to or larger than the corresponding properties of the furan and cyclopentadiene homologue series.     

Investigation of the structures and absorption spectra for some hemicyanine dyes with pyridine nucleus by TD-DFT/PCM approach

Density-functional theory calculations of the Rayleigh optical activities of small isolated polyglycine molecules are reported. Fully extended β-sheet-like conformations of polypeptides of glycine, (Gly)_n (with n=1–5) are considered. After geometry optimizations, dipole moments and dipole polarizabilities (both the mean and the anisotropic components) are calculated using the B3LYP and B3P86 functionals in three basis sets. The polarizabilities are used to analyze the Rayleigh scattering activities and depolarization ratios. The convergence of the average dipole polarizability per monomer is analyzed. The differences in activity and depolarization for Rayleigh scattered radiation between the extended β-sheet-like and the folded -helix-like forms of tetraglycine are analyzed and found to be relevant, suggesting its possible use in experimental characterization.     

The calculation of molar polarizabilities by the CNDO/2 method: Correlation with the hydrophobic parameter,log P

Results of molecular orbital (MO) calculations by the complete neglect of differential overlap (CNDO /2) method on 50 small molecules are reported. The summation of calculated atomic polarizabilities are equated with molecular polarizabilities, and these are compared with experimentally determined values. It is found that there is very good agreement between calculated and experimental molecular polarizability. This provides a reliable method for the determination of molecular polarizabilities for compounds for which experimental values are not known. The relationship between log P and polarizability is discussed and analyzed in terms of contributions from electronic components to the partitioning energy.     

Vibrational and thermal effects on the dipole polarizability of methane and carbon tetrachloride from vibrational structure calculations

We present a theoretical study of vibrational and thermal effects on the dipole polarizability of methane and carbon tetrachloride. Using a fourth order Taylor expansion in rectilinear normal coordinates of the potential and property surfaces we solve the vibrational problem using vibrational structure theory, e.g., through vibrational self-consistent-field or vibrational configuration-interaction theory. For each vibrational state we calculate in addition the vibrational state average polarizability. Constructing the vibrational partition function by "brute force" allows for prediction of thermal effects on the dipole polarizability. The method is not restricted in any way to polarizabilities nor to the specific representation of the potential and property surfaces employed in this work. Any molecular property with a suitable normal coordinate representation may be considered. We discuss the performance of vibrational self-consistent field as compared to vibrational configuration interaction and study in detail the convergence of the former method with respect to the number of vibrational states included in the thermal averaging. Based on calculations including up to 170,000 vibrational self-consistent-field states we present thermal effects on the dipole polarizability of methane and carbon tetrachloride in the temperature ranges 0-1100 and 0-500 K, respectively. The predicted thermal effect on the dipole polarizability of methane is found to be approximately 0.8% which compare well with previous experimental measurements.     

Raman spectrum modification in the presence of solvated electrons. Observation by polarization CARS

The multiple-scattering series for depolarized light scattering from simple liquids is investigated. It is found that the leading term in the series, due to double—double scattering, is probably not large compared to double—triple (DT) scattering contributions. Existing theories, which neglect DT scattering, have concluded that the experimental data cannot be explained using the dipole—induced dipole (DID) model for the pair polarizability. It is suggested that a theory which includes DT scattering will not lead to rejection of the DID model.     

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.     

Excited state dipole moments and polarizabilities of centrosymmetric and dimeric molecules. II. Polyenes, polyynes and cumulenes

Electro-optical absorption spectra are measured for a series of polyenes, polyynes and cumulenes with centrosymmetric π-chromophores in cyclohexane solution at 298 K. For all molecules the long-axis component of the polarizability tensor is considerably larger in the first dipole-allowed singlet state compared to the ground state. The transition moments are found to be parallel to the long molecular axis. All polyenes and one cumulene show a linear Stark component indicating a long-axis excited state dipole moment. Both the dipole moments and the polarizabilities are corrected within the extended Onsager model for solvent cavity and reaction field effects. It is suggested that symmetry lowering solvent perturbations are the reason for the apparent excited state dipole moments.     

Coupled-cluster calculation of dispersion contributions to interaction energies and polarizabilities

 The induced dipole dispersion-type contributions to the two-body and nonadditive three-body energies and electric dipole polarizabilities are studied for long-range interactions involving the He, Ne, Ar and Kr atoms and the H₂ and N₂ molecules. The coupled-cluster singles and doubles model and large basis sets are used. Comparison of the energy contributions with data derived from experiment shows in most cases the deviations to be less than 1%; therefore, it may be expected that the calculated polarizability increments are accurately determined and can be used to estimate the accuracy of approximate methods. Received: 20 March 2001 / Accepted: 5 April 2001 / Published online: 27 June 2001     

Polarizability of negatively charged helium‐like ions interacting with Coulomb and screened Coulomb potentials

The dipole and quadrupole polarizabilities (both static and dynamic) of negatively charged helium‐like ions are investigated. The mass dependence of the polarizability is studied by changing the mass of the positively charged particle from one unit of electron mass to infinitely heavy. The calculations are carried out in the framework of the pseudostate summation method using exponential correlated wave functions having pseudorandomly generated nonlinear variational parameters. The dipole and quadrupole polarizabilities in terms of frequency and nuclear mass are reported for the first time. The effect of screened Coulomb potentials on the polarizabilities of D^–, T^–, ¹H^–,Pi^–, Mu^–, and Ps^– are also presented.     

Hirshfeld‐based intrinsic polarizability density representations as a tool to analyze molecular polarizability

In this work, a general scheme to visualize polarizability density distributions is proposed and implemented in a Hirshfeld‐based partitioning scheme. This allows us to obtain easy‐to‐interpret pictorial representations of both total and intrinsic polarizabilities where each point of the density is formed by the contribution of any atom or group of atoms in the molecule. In addition, the procedure used here permits the possibility of removing the size dependence of the electric‐dipole polarizability. Such a development opens new horizons in exploring new applications for the analysis of the molecular polarizability tensor. For instance, this visualization shows which atoms or regions are more polarizable distinguishing, moreover, the fine structure of atoms affected by the vicinity, and might extend the dipole polarizability as a tool for aromaticity studies in polycyclic aromatic hydrocarbons. Additionally, this approach can serve us to assess the methods performance in describing the interaction of electric fields with a molecule and local electron correlation effects in intrinsic polarizabilities. © 2015 Wiley Periodicals, Inc.     

Calculation of the electric susceptibilities of the helium atom

We calculated the static and the dynamic dipole polarizabilities and the static quadrupole polarizability of the helium atom. The results are α = 0.2070 × 10^?24 cm³ for the static dipole polarizability and γ₄ = 0.1038 × 10^?40 cm⁵ for the static quadrupole polarizability.