Perturbation formulas are derived for calculating the vibrational dynamic polarizability (αv) and hyperpolarizabilities (βv and γv ) of polyatomic molecules. These formulas, based on an initial harmonic oscillator approximation, include corrections for mechanical anharmonicity (cubic) terms in the vibrational potential and electrical anharmonicity (quadratic) terms in the dependence of the electrical field polarization potential on nuclear coordinates. Results are presented for FH and CO2. In the former case, comparison is made to ‘‘exact’’ numerical values. Fully documented computer programs for the perturbation treatment are available.

A perturbation method for calculating vibrational dynamic dipole polarizabilities and hyperpolarizabilities

The dipole (α), quadrupole (C), and dipole–octopole (E) polarizabilities, the dipole–dipole–quadrupole (B) and second dipole (γ) hyperpolarizabilities, and the quadrupole (θ) and hexadecapole (Φ) moments are calculated for the ground state of CO2 at its equilibrium geometry. The values are obtained from fourth‐order many‐body perturbation theory energies of CO2 in the presence of various configurations of point charges. Electron correlation affects the longitudinal components more than the transverse ones; hence, electron correlation effects are greater for the anisotropies than for the isotropic averages of these properties. Our best vibrationless estimates for the isotropic values are ᾱ≂17.63 e2a20E−1h, C≂77.8 e2a40E−1h, B≂−2.1×102 e3a40E−2h, γ≂1.20×103 e4a40E−3h, and θzz≂−3.24 ea20. The quadrupole moment, mean dipole polarizability and hyperpolarizability are in satisfactory agreement with experiment. On the other hand, the polarizability anisotropy Δα≂14.3 e2a20E−1h agrees with experimental estimat...

Polarizabilities and hyperpolarizabilities of carbon dioxide

The performance of a recently proposed two‐body potential model for SiO2 [van Beest et al., Phys. Rev. Lett. 64, 1995 (1990)] was critically evaluated through the calculation of the static and dynamical properties of several polymorphs of SiO2 using molecular dynamics methods. It was found that the calculated static structures are in excellent agreement with experiments. In particular, the pressure–volume equations of state for α‐quartz, cristobalite, and stishovite, the pressure‐induced amorphization transformation in α‐quartz and thermally induced the α→β transformation in cristobalite are well reproduced by this model. The calculated vibrational spectra are in fair agreement with experiments. The strengths and the weaknesses of the potential will be presented and discussed.

The structure and dynamics of silica polymorphs using a two-body effective potential model

Chapter 2. Low-frequency spetroscopic studies of interactions in liquids

The ability of available theoretical models in describing broadening mechanisms is tested for the CO2–O2, CO2–CO2, and CO2–N2 systems. It is shown that the Anderson–Tsao–Curnutte theory is inaccurate since short‐range forces can contribute significantly to broadening. We use the approach of Robert and Bonamy, but the usual expansion of the atom–atom potential to the fourth order around the intermolecular distance appears insufficient at short distances for these particular systems. We propose a better representation of the radial dependence of the atom–atom potential, while keeping the previous analytical expression of the cross section. Satisfactory results are obtained for both the rotational quantum number dependence of room‐temperature CO2–O2, CO2–CO2, and CO2–N2 half‐widths and the evolution of CO2–N2 broadening with temperature. It is shown that the isotropic part of the potential involved in the trajectory calculation must be coherently deduced from the atom–atom interaction potential.

Collisional broadening of CO2 IR lines. II. Calculations

Ab initio calculations have been performed on carbon dioxide to obtain the first derivatives of the dipole-quadrupole polarizability A and of the first hyperpolarizability β in the bending and asymmetric stretching modes. These derivatives are used to assess the relative contributions of A and β to the collision-induced Raman spectrum. It is concluded that most of the intensity arises from the mechanism involving the A tensor. Reasonable agreement is obtained with measured depolarization ratios and relative intensities for the v 2 and v 3 modes in compressed gaseous CO2.

A.D. Buckingham

Papers

Theoretical studies of the collision-induced Raman spectrum of carbon dioxide