Showing papers on "Hyperpolarizability published in 1968"
TL;DR: In this article, the zeroth, first and second order perturbed Schrodinger equations for the helium atom in an external electric field have been solved to high accuracy through the variation principle.
Abstract: The zeroth, first and second order perturbed Schrodinger equations for the helium atom in an external electric field have been solved to high accuracy through the variation principle. A ground-state energy, differing by only about 1 part in 109 from Pekeris's extrapolated figure, was obtained with a wave function ϕ0 containing 181 adjustable parameters (compared to Pekeris's 1078). The first-order wave function ϕ1, and hence the second-order energy and polarizability of the atom, was obtained with up to 84 adjustable parameters in ϕ1. The polarizability α is 1.38319 a.u. = 0.204956 × 10–24 cm3= 0.228044 × 10–40 C2m2 J–1. The dipole shielding factor differs from its exact value of unity by a few parts in 105. The second-order wave function ϕ2, and hence the fourth-order energy and hyperpolarizability γ, were obtained for various wave functions ϕ0 and ϕ1, and with up to 106 adjustable parameters in ϕ2. Smooth convergence was obtained, yielding γ= 43.10 a.u. = 2.171 × 10–38 e.s.u. = 2.688 × 10–63 C4m4J–3. However, an extension to ϕ1 may be needed before an accurate value of γ can be computed. Accurate values have also been obtained for the δ-values of the unperturbed atom and for the quadrupole and octopole polarizabilities.
59 citations
TL;DR: The theory of the electric birefringence of a dilute gas of diatomic molecules is developed, account being taken of the quantization of rotational energy as mentioned in this paper, leading to corrections to the classical formula for the molar Kerr constant which involve the ratio of the rotational constant hcB 0 to the thermal energy kT.
Abstract: The theory of the Kerr effect (electric birefringence) of a dilute gas of diatomic molecules is developed, account being taken of the quantization of rotational energy. The theory leads to corrections to the classical formula for the molar Kerr constant which involve the ratio of the rotational constant hcB 0 to the thermal energy kT . These corrections are appreciable at normal temperatures for only a few hydrides; they are particularly important for molecular hydrogen. The Kerr effect has been observed in gaseous H 2 from -30 to +60°C and from 25 to 85 atm, a 6328 A laser light source and phase-sensitive detector being used. The temperature dependence of the Kerr constant is in good agreement with the quantum theory. Analysis of the results yields a value for the hyperpolarizability γ of H 2 of (0∙28 ± 0∙03) x 10 -36 e. s. u. The Kerr constant of D 2 is also reported. The observed pressure dependence of the molar Kerr constant of H 2 is compared with theoretical results based on a calculation of the polarizability anisotropy of a pair of molecules.
40 citations
TL;DR: In this paper, the authors calculated mean second molecular hyperpolarizabilities for six non-polar organic liquids by subtracting the Gans' theory value from the experimental value.
Abstract: Hyperpolarizability contributions to the electro-optic Kerr effect are calculated for six non-polar organic liquids by subtracting the Gans' theory value from the experimental value. Mean second molecular hyperpolarizabilities calculated in this way agree with other estimates. The bond-additivity approximation for mean second hyperpolarizabilities is approximately verified for molecules in the n-alkane series, and the bond values are estimated.
13 citations
TL;DR: In this article, the hyperpolarizability of benzene was calculated using a free-electron model for the π -electron system and the results showed that only the components γ zzzz, γ xxxx, γ yyyy and γ nzzz are non-zero.
Abstract: The hyperpolarizabilities of benzene have been calculated using a free-electron model for the π-electron system. The first hyperpolarizability is identically zero. For the second hyperpolarizability only the components γ zzzz ; γ xxxx ; γ yyyy ; γ zzxx ; γ zzyy ; γ xxyy are non-zero. Some of these γ quantities show dispersion near the characteristic absorption band of the benzene molecule. The polarizability α of the π-electron system also shows similer dispersion.
2 citations