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Notes: Explicitly electron-correlated wave functions have been used to calculate the hypermagnetizability anisotropy (Δη) for H2 and D2. This property is the essential feature of the birefringence of a material in the presence of a magnetic field (the Cotton–Mouton effect). The calculations were carried out in the framework of perturbation theory and both dispersion and vibrational effects were fully taken into account. A detailed analysis of our results is made and it is concluded that electron correlation and "pure'' vibrational effects are less important than vibrational averaging and dispersion. The experimental results are only in fair agreement with our theoretical ones.

Notes: Accurate and explicitly electron-correlated wave functions have been used to determine the dynamic hyperpolarizability tensor (γ) and the dynamic field-gradient polarizabilities (B and C) for helium. The γ-tensor is related to nonlinear optical processes such as the Kerr effect, second- and third-harmonic generation and degenerate-four-wave mixing. In the static limit our results agree completely with a previous highly accurate variational-perturbation treatment. For second-harmonic generation at λ=4880 A(ring) the ratio γzzzz/γxxzz is 2.950, which may be compared with the experimental value of 2.949.

Notes: Accurate wave functions of the James–Coolidge type, which account for electron correlation, are used to calculate for H2 and D2 the dynamic second hyperpolarizabilities (γ) which mediate the nonlinear optical processes: dc Kerr, dc electric-field-induced second-harmonic generation and third-harmonic generation. Values are given for a range of frequencies (ω=0 to ω=0.05 a.u.) as well as for some common laser frequencies. The effects of vibration are explicitly considered. As well, values of the dynamic field-gradient polarizabilities B and C are found. The results are more accurate than those previously published.

Notes: The vibrational contributions to the Kerr effect and to electric-field-induced second-harmonic generation (ESHG) are calculated for methane for a number of optical frequencies. The latter results, together with the experimental ESHG values of the total mean second hyperpolarizability, allow for the determination of the ω2L-dispersion curve for the mean electronic hyperpolarizability. Since this curve is identical, to fourth order, for both processes, we are able to combine it with the calculated Kerr vibrational hyperpolarizabilities and predict the total Kerr hyperpolarizabilities for CH4 for several laser frequencies. © 1995 American Institute of Physics.

Notes: Electronic and vibrational contributions to the linear and nonlinear optical properties of the HF dimer have been calculated for the first time. The vibrational components are very significant with mechanical anharmonicity effects, as determined by perturbation-theoretic formulas, playing a major role. We identify the important anharmonic potential constants and analyze the validity, as well as the possible extension, of our theoretical treatment. Parallel computations, for purposes of comparison, have also been performed for the monomer. © 1995 American Institute of Physics.

Notes: Dynamic dipole polarizabilities pertinent to the Raman intensities of the fundamental and first two overtones of H2 and D2 have been calculated. To do this an energy-shifted sum-over-states formula has been used in conjunction with accurate electron-correlated wave functions. The results for the relevant polarizability ratios agree, in the static limit, with a previous calculation. The dynamic values are in fair agreement with the recent experimental ones for H2 but there is a strong disagreement with a previous experimental determination for D2.

Notes: For atoms or molecules of D∞h or higher symmetry, this work gives equations for the long-range, collision-induced changes in the first (Δβ) and second (Δγ) hyperpolarizabilities, complete to order R−7 in the intermolecular separation R for Δβ, and order R−6 for Δγ. The results include nonlinear dipole-induced-dipole (DID) interactions, higher multipole induction, induction due to the nonuniformity of the local fields, back induction, and dispersion. For pairs containing H or He, we have used ab initio values of the static (hyper)polarizabilities to obtain numerical results for the induction terms in Δβ and Δγ. For dispersion effects, we have derived analytic results in the form of integrals of the dynamic (hyper)polarizabilities over imaginary frequencies, and we have evaluated these numerically for the pairs H...H, H...He, and He...He using the values of the fourth dipole hyperpolarizability ε(−iω; iω, 0, 0, 0, 0) obtained in this work, along with other hyperpolarizabilities calculated previously by Bishop and Pipin. For later numerical applications to molecular pairs, we have developed constant ratio approximations (CRA1 and CRA2) to estimate the dispersion effects in terms of static (hyper)polarizabilities and van der Waals energy or polarizability coefficients. Tests of the approximations against accurate results for the pairs H...H, H...He, and He...He show that the root mean square (rms) error in CRA1 is ∼20%–25% for Δβ and Δγ; for CRA2 the error in Δβ is similar, but the rms error in Δγ is less than 4%. At separations ∼1.0 a.u. outside the van der Waals minima of the pair potentials for H...H, H...He, and He...He, the nonlinear DID interactions make the dominant contributions to Δγzzzz (where z is the interatomic axis) and to Δγxxxx, accounting for ∼80%–123% of the total value. Contributions due to higher-multipole induction and the nonuniformity of the local field (Qα terms) may exceed 15%, while dispersion effects contribute ∼4%–9% of the total Δγzzzz and Δγxxxx. For Δγxxzz, the α term is roughly equal to the nonlinear DID term in absolute value, but opposite in sign. Other terms in Δγxxzz are smaller, but they are important in determining its net value because of the near cancellation of the two dominant terms. When Δγ is averaged isotropically over the orientations of the interatomic vector to give Δγ¯, dispersion effects dominate, contributing 76% of the total Δγ¯ (through order R−6) for H...H, 81% for H...He, and 73% for He...He. © 1996 American Institute of Physics.

Notes: Accurate calculations of the polarizability and hyperpolarizability tensors at imaginary frequency, α(−iω;iω) and γ(−iω;iω,0,0), for H, He, and H2 are reported for a range of frequencies (ω) useful for Gauss–Legendre quadrature. They have been used to evaluate the dispersion polarizability coefficients which govern the nonclassical contribution to the change in electronic polarizability due to long-range interactions between the aforementioned species. Previously, these coefficients have only been found by more approximate methods. The basis of the calculations of α(−iω;iω) and γ(−iω;iω,0,0) was the sum-over-states method and, for He and H2, electron correlation was explicitly taken into account. With respect to γ(−iω;iω,0,0), we believe these to be the first calculations of any kind.