Janusz Pipin

Improved dynamic hyperpolarizabilities and field‐gradient polarizabilities for helium

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 the ratio γzzzz/γxxzz is 2.950, which may be compared with the experimental value of 2.949.

Effect of vibration on the linear and nonlinear optical properties of HF and (HF)2

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.

Calculation of the polarizability and hyperpolarizability tensors, at imaginary frequency, for H, He, and H2 and the dispersion polarizability coefficients for interactions between them

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.

Long‐range, collision‐induced hyperpolarizabilities of atoms or centrosymmetric linear molecules: Theory and numerical results for pairs containing H or He

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 e(−iω; iω, 0, 0, 0, 0) obtained in this work, along with other hyperpolarizabilities calculated previously by Bish...

Static electric properties of H and He

Abstract Exact values of all static polarizabilities and hyperpolarizabilities of the H atom up to the sixth degree are reported. Corresponding non-analytic but very accurate results are given for the He atom.

HYPERMAGNETIZABILITY ANISOTROPY (COTTON-MOUTON EFFECT) FOR H2 AND D2

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.

Nonlinear optical properties of H2 and D2

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.

Nonlinear optical properties of H sub 2 and D sub 2

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.

Methods for introducing vibrational effects in the calculation of electric dipole polarizabilities and hyperpolarizabilities (with reference to H+ 2)

Three different methods for taking into account nuclear motion while calculating molecular static dipole polarizabilities and hyperpolarizabilities are discussed. Within these methods both the purely variational and the variational-perturbational techniques are used to obtain numerical results for the α zz and γ zzzz polarizability components of the H+ 2 molecular ion in its rovibronic ground state.

THEORETICAL INVESTIGATION OF THE KERR EFFECT FOR CH4

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.