Electric Polarizability Tensor Research Articles

Non-resonant optical rectification in optically active liquids

It is shown that optical rectification can be produced by linearly polarized light via the fourth-order susceptibility in optically active liquids and solutions. In order to induce a static polarization, two beams of different frequency are necessary, however. The mechanisms responsible for the effect are described in terms of both linear and nonlinear electric dipole polarizability tensors, and the magnitude of the effect is estimated.

Polarizabilities of fullerenes C20 through C240 from atom monopole-dipole interaction theory

The linear uniform field electric dipole polarizability tensors of 46 fullerenes in the range C[sub 20] through C[sub 240] are calculated by the Olson-Sundberg atom monopole-dipole interaction (AMDI) theory, using the monopole and dipole polarizabilities of the carbon atom found previously to fit polarizability tensors of aromatic hydrocarbons. The structures are taken to be those predicted by Zhang and co-workers by molecular dynamics energy optimization. The isotropic mean polarizabilities calculated for C[sub 60] and C[sub 70] are comparable to experimental data from solid film studies and to quantum mechanical calculations. Polarizability tensors are also calculated for conducting ellipsoidal shells which have the same moment of inertia tensor as the corresponding fullerenes. These are substantially smaller than the AMDI polarizabilities for the smaller fullerenes, but the two calculations tend to converge for the larger molecules. 26 refs., 1 fig., 2 tabs.

Determination of higher electric polarizability tensors from unrelaxed coupled cluster density matrix calculations of electric multipole moments

The CCSDT-1 method is used to calculate electric dipole, quadrupole, and octopole moments for the HF and H2O molecule and the F− anion, together with the associated higher-order polarizabilities. All multipole moments are computed as expectation values. Externally perturbed moments are used to determine the components of the electric tensors of second and higher order. It is shown that the correlated electric moments are in good agreement with experiment and that they may be used to obtain the electric polarizability and hyperpolarizability tensors in an effective way. © 1994 John Wiley & Sons, Inc.

Electric properties of chlorine

We have calculated near-Hartree-Fock values for the independent components of all electric multipole moment and polarizability tensors, up to the fourth rank, of ground state chlorine, Cl 2(X 1Σ g +). Using a large carefully optimized basis set consisting of [8s6p5d2l or 152 contracted gaussian-type functions, we obtained Θ zz = 2.2696 e a 0 2 and Φ zzz = 80.25 e a 0 4 for the quadrupole and hexadecapole moments respectively. For the isotropic and anisotropic components of the dipole polarizability our values are α = 29.94 and Δα = 18.16 e 2 a 0 2 E h −1. For the isotropic components of the quadrupole polarizability, the second dipole hyperpolarizability and the dipole-dipole-quadrupole hyperpolarizability we report C = 162.56 e 2 a 0 4 E h −1, γ = 3472 e 4 a 0 4 E h −3 and B = −569 e 3 a 0 3 E h −2. Finally, for the longitudinal and transverse components of the dipole-octopole polarizability we report E z, zzz = 327.8 and E x, xxx = −138.1 e 2 a 0 4 E h −1. All values pertain to the experimental equilibrium bond length of 1.988 Å.

Symmetry of the polarizability tensors for molecules with D 5h and I h symmetry

We present the spatial symmetry relations between the components of the linear and nonlinear electric dipolar polarizability tensors for the symmetry groups of C 60 and C 70 molecules viz., I h and D 5h. We show that the first hyperpolarizability β of C 7 0 vanishes although the molecule is not inversion symmetric. The second hyperpolarizability γ for C 60 has the same structure as that for an isotropic system. Based on these results, optical harmonic generation measurements to study the inter-molecular bonding in C 60 and C 70 crystals are suggested.

A complete description of the electric dipole moment, polarizability, and hyperpolarizability tensors of hydrogen peroxide

We report a complete description of the electric dipole moment tensor (μα), dipole polarizability (ααβ), first (βαβγ), and second (γαβγδ) dipole hyperpolarizability tensors of hydrogen peroxide. All the independent components of the four tensors are extracted from self-consistent field (SCF) and Mo/ller–Plesset perturbation theory (MP) calculations of the energy of the molecule perturbed by a static homogeneous electric field. Electron correlation decreases the dipole moment and increases the dipole polarizability of the molecule, has a strong effect on the first dipole hyperpolarizability and an even stronger effect on the second dipole hyperpolarizability. The best values of the permanent dipole moment and the mean polarizabilities ᾱ, β̄, and γ̄ obtained in this work are 0.6165 ea0, 14.95 e2a20E−1h, −8.56 e3a30E−2h, and 1601 e4a40E−3h, respectively.

Computation of the polarizability of anthracene

The purpose of this study is the calculation of the electric polarizability tensor for anthracene at the SCF level. The finite-field method and Dunning's 9s5p basis set augmented with one set of polarization functions were used. To provide an estimate of the accuracy of the results presented, the polarizability of benzene was evaluated in parallel using the same techniques and basis set. A comparison of these results with previous experimental and theoretical results for both benzene and anthracene is presented. The inclusion of a second polarization function to Dunning's set significantly increases the accuracy of the results. The values obtained are in good agrement with the most recent experimental determinations.

Dialogue and teaching styles. Centre for information technology in education report no. 62

We have calculated near-Hartree-Fock values for the independent components of all electric multipole moment and polarizability tensors, up to the fourth rank, of ground state chlorine, Cl2(X1Σg+). Using a large carefully optimized basis set consisting of [8s6p5d2l or 152 contracted gaussian-type functions, we obtained Θzz = 2.2696 e a02 and Φzzz = 80.25 e a04 for the quadrupole and hexadecapole moments respectively. For the isotropic and anisotropic components of the dipole polarizability our values are α = 29.94 and Δα = 18.16 e2 a02 Eh−1. For the isotropic components of the quadrupole polarizability, the second dipole hyperpolarizability and the dipole-dipole-quadrupole hyperpolarizability we report C = 162.56 e2 a04 Eh−1, γ = 3472 e4 a04 Eh−3 and B = −569 e3 a03 Eh−2. Finally, for the longitudinal and transverse components of the dipole-octopole polarizability we report Ez,zzz = 327.8 and Ex,xxx = −138.1 e2 a04 Eh−1. All values pertain to the experimental equilibrium bond length of 1.988 Å.

Sum rules for Cartesian polarizability derivative tensors

Raman and Raman optical activity intensities are determined from the Cartesian derivatives of electric dipole—electric dipole, electric dipole—magnetic dipole and electric dipole—electric quadrupole polarizability tensors. These tensors obey certain translational and rotational sum rules. In this communication, we present these sum rules and verify them through ab initio calculations.

Relations between electric and magnetic polarizabilities and other related quantities

The magnetic polarizability tensor, the demagnetization tensor, and the depolarization tensor of an ellipsoid are all related to its electric polarizability tensor. The four tensors are completely described by two scalars. The relationship between the electric and magnetic polarizabilities of an ellipsoid can be applied directly to an elliptic aperture. The total cross section of an antenna integrated over wavelength is given by the antenna's polarizabilities.

Electric field N.M.R.

Application of a strong de electric field to solutions of apolar molecules in an apolar solvent leads to partial orientation of the molecules. This orientation could be detected by N.M.R. spectroscopy through the anisotropic spin interactions that show up in the spectra. Subsequent analysis of the spectrum leads to information about the static electric polarizability tensor (a). The electric field N.M.R. (EFNMR) method was applied to measure, from the 2H EFNMR spectrum of naphthalene-d8, the anisotropy of a (i.e. Δα), and asymmetry (δα). The result is: 7·1 ± 0·3 and -(4·4 ± 0·5) × 10-24 cm3 for Δα and δα respectively. For triphenylene-d12 the value of Δα is measured to be -(14·4 ± 1·4) × 10-24 cm3. The results from the EFNMR method and from other methods are compared and discussed

Influence of pure reorientational processes on magneto-chiral birefringence and dichroism of diamagnetic molecules in strong optical fields

The theory of magneto-chiral birefringence and dichroism is extended to systems composed of diamagnetic molecules acted on by an optical field. For molecules with the point group symmetries 3, 4, 6, ∞, 32, 422, and 622 expressions are derived for the magneto-chiral birefringence and dichroism in the presence of weak as well as very strong optical molecular reorientation caused by a linearly polarized, circularly polarized, or unpolarized laser beam. Measurements of magneto-chiral birefringence and dichroism at optical saturation provide direct information on the respective magnetic dipole and electric quadrupole polarizability tensor components.

HF SCF electric polarizabilities and hyperpolarizabilities for the ground state of the hydrogen molecule

Using Hartree-Fock SCF wavefunctions all independent components of all electric polarizability and hyperpolarizability tensors up to the fourth rank have been calculated for the ground state of the hydrogen molecule. Our values for the isotropic components of the α,γ, C and B tensors are 5.13 e 2 a 0 2 E h −1, 683 e 4 a 0 4 E h −3 , 8.03 e 2 a 0 4 E h −1 and −76.4 e 3 a 0 4 E h −2 at the experimental internuclear separation of 1.401146 a 0.

Anisotropy and asymmetry of the polarizability of anthracene, studied by NMR

NMR of dielectrically aligned apolar molecules in solution is presented as a new technique for the study of their electric polarizability tensor (α). Spectral changes in the 2H NMR spectrum of anthracene-d10 (in dilute benzene solution), subjected to a very strong external dc electric field, were interpreted in terms of Δα and δα, the anisotropy and asymmetry of the polarizability. The results are: Δα=(15.4±0.4)×10−24 cm3 and δα=(−9.6±1.2)×10−24 cm3. The new NMR method is outlined and compared with existing methods for the determination of α.

Electric polarizabilities and hyperpolarizabilities for the ground state of the nitrogen molecule

The static polarizabilities of the ground state of N2 were calculated at three different internuclear separations in the LCAO-SCF-MO approximation. All independent components of electric polarizability tensors up to the fourth rank were included. The isotropy and anisotropy of the γ tensor are γ = 766, Δ1γ = 2264 and Δ2γ = -76e 4 a 4 0 E -3 h respectively (at the experimental internuclear separation of 2·0744 a 0).

On the Hyperpolarizability of the Lithium Dimer

All independent components of all electric polarizability and hyperpolarizability tensors up to the fourth rank have been calculated near the Hartree-Fock limit for Li2(l σg 2 1 σu 2 2 σg 2 X1 Σg +). Many of the molecular properties reported in this paper appear for the first time in the literature. Our values for the isotropic components of the C, B and γ hyperpolarizabilities are 1487 e2 a0 4Eh −1, −490 x 102e3 a0 4Eh −2 and 510.5 x 103 e4 a0 4 Eh −3 respectively.

Magnetic dipole and electric quadrupole polarizabilities from depolarized differential rayleigh light scattering for molecules with non-degenerate electronic states

A general expression is proposed for the depolarized differential Rayleigh light scattering intensity (DDRLS) of circularly polarized light at arbitrary scattering angles θ and arbitrary symmetries of molecules, non-degenerate in their electronic ground state. The molecular symmetries for which DDRLS occurs at θ = π/2 and θ ≠ π/2 are specified. It is shown that for molecules with point group symmetries 3, 4, 6, ∞, 32, 422 and 622 the two mutually independent components of the electro-magnetic polarizability tensor G and that of the electric quadrupole polarizability tensor A can be determined from measurements of DDRLS and optical activity. For molecules with the symmetries 23, 432, Y and K a simple relation is shown to hold, for arbitrary θ, between the DDRLS intensity and the rotation of the light beam in the optical activity effect.

Electric moments and polarizabilities for LiH (X1?+)

Near Hartree-Fock values have been obtained for all independent components of electric multipole moment and polarizability tensors up to the fourth rank for the ground state of LiH. The dependence of the electric properties on internuclear separation is inferred from calculations at three different bond lengths. The calculation of the interaction potential LiH. e− leads to deductions about the relative importance of the polarizability tensors in intermolecular interaction studies. The independent components of the tensors at r e =3.034286 a0 are, in atomic units, α zz =22.0884, α xx =25.2846, β zzz =224.3, β zxx =203.1, γ zzzz =76848, γ xxxx =21472, and γ xxzz =19485.

Information theory and basis set quality. Automatic classification and systematic improvement of approximate wavefunctions IV. A study on BH( X1Σ +), CH( X2Π r) and NH( X3Σ −)

An information theoretical approach to the study of the quality of theoretical molecular descriptions is applied to the molecules BH(1σ 22σ 23σ 2, X 1Σ +), CH(1σ 22σ 23σ 21π 1, X 2Π r) and NH(1σ 22σ 23σ 21π 2, X 3Σ −). The controlability of the LCAO-SCF-MO wavefunction depends strongly on the size of the basis set and the molecular system studied. The dependence of the electric moments on the non-linear parameters of the basis set anticipates a similar behaviour for the electric polarizability tensors. Property-optimal polarization functions are proposed and their utility in calculations concerning intermolecular forces and polarizability tensor components is discussed. Rovibrational corrections to the multipole electric moments become important as the rank of the respective tensor increases but are small compared to the available experimental data.

An ab initio SCF calculation of the polarizability tensor, polarizability derivatives and Raman scattering activities of the water-dimer molecule

The electric polarizability tensor, polarizability derivatives and the resulting Raman scattering activities and depolarization ratios of the water dimer, calculated within the framework of ab initio SCF theory, are reported. While the calculated mean polarizability of the dimer is almost the same as for two isolated monomers, the polarizability anisotropy is considerably larger. The mean polarizability derivatives with respect to normal coordinates are quite small in the case of intermolecular modes and significant deviations from the monomeric values occur only for three intramolecular modes, all stretches. The Raman intensities parallel the behaviour of the mean polarizability derivatives. Consequently the main effect of hydrogen bonding on the Raman intensities of water is a charge in the intensities of the stretching modes. In the case of (H2O)2 the Raman intensity of the intramolecular hydrogen-bond stretch is about twice that of the symmetric stretch of the H2O monomer.