J. C. Decius

Theory of Hyper‐Raman Effects (Nonlinear Inelastic Light Scattering): Selection Rules and Depolarization Ratios for the Second‐Order Polarizability

The symmetry properties of the third‐rank tensor β which comprises the set of coefficients of quadratic terms in the expansion of the induced‐dipole moment in the electric field are investigated, and the various linear combinations belonging to the irreducible representations are tabulated for the important molecular symmetry groups. Depolarization ratios are calculated for a sample composed of randomly oriented molecules (liquid phase). Examples of the selection rules in both liquid and crystalline phases are discussed, and these selection rules are contrasted with the ones appropriate for infrared absorption and the ordinary Raman effect.Molecular modes allowed in the infrared are always allowed in the hyper‐Raman effect and have a depolarization ratio (for linearly polarized incident radiation) ≤⅔, while allowed hyper‐Raman transitions forbidden in the infrared have a depolarization ratio of ⅔.

Compliance Matrix and Molecular Vibrations

It is shown that treatment of the molecular vibration problem in the form | F—1G—1—λ—1E | =0 has certain advantages when the data from vibrational spectroscopy are to be combined with information from mean amplitudes of vibration or centrifugal distortion toward the end of determining a complete quadratic potential function. The matrix F—1=C is a compliance matrix; its elements presumably have as much physical significance as those of F. Some new isotopic sum rules are formulated, appropriate to the compliance scheme, but they are not nearly so general as those involving the λs. Linear molecules are discussed, and some numerical examples are given for nonlinear XY2 and XY4.

Coupling of the Out‐of‐Plane Bending Mode in Nitrates and Carbonates of the Aragonite Structure

The infrared absorption of polycrystalline samples of KNO3 and BaCO3 in the form of Nujol mulls has been observed between 11.3 and 12.5 microns under conditions such that the rotational lines of the NH3 spectrum separated by 1.5 cm—1 could be clearly resolved. When the N15 or C13 content is increased to the order of 50 percent, fine structure is observed which is not present e.g., in NaNO3, which possesses a crystal structure similar to calcite. The fine structure is interpreted by postulating a force constant which couples the out‐of‐plane vibrations of nearest neighbors in the aragonite‐type lattice.Very satisfactory agreement between the calculated and observed spectra is then found; in the case of BaCO3, the vibrations of CO3 ions which occur in isotopic isolation, as pairs, triplets, and quadruplets are resolved. The significance of the coupling constant is discussed; in principle, it may be used to evaluate the dipole derivative for the mode under consideration.

Dipolar Coupling and Molecular Vibration in Crystals. I. General Theory

Coupling of the transition dipoles associated with infrared‐active vibrations produces one source of frequency shift and splitting of transverse and lingitudinal modes in solids. The intrinsic part of the dipole is distinguished from the induced part, the latter being related to the electronic polarizabilities of the molecular or atomic units in the structure. Although approximate treatments neglecting the induced part of the dipole have been given previously and, also, certain estimates of the effective field (related to the induced dipole) have appeared earlier in the literature, we here take both effects fully into account for a number of noncubic crystal structures.

Vibrational Spectrum of Cyanate Ion in Various Alkali Halide Lattices

The infrared absorption spectra of dilute solid solutions of cyanate ion in KI, KBr, KCl, and NaCl single crystals have been examined between 600 and 5000 cm—1 at temperatures ranging from 150 to 480°K. Over fifty distinct maxima have been observed and assigned (including numerous isotopic, combination, and hot bands) in the most concentrated sample, for which KBr was the solvent. A strong Fermi resonance between 2ω2 and ω1 occurs. The vibrational energy has been expressed in terms of the eleven fundamental frequency and anharmonicity constants appropriate to a linear, unsymmetric triatomic molecule. Force constants in the KI solvent lattice are fNC=15.51, fCO=11.03, f′=1.35, and (fα/l1l2)=0.506 mdyne/A, a result which shows very clearly that the NC bond is of higher order than the CO bond in the cyanate ion, and that the latter bond is notably weaker in cyanate ion than in CO2, where its force constant is 16.0.In general, the fundamental frequencies increase as the lattice constant decreases. Fairly deta...

Infrared Absorption of Lanthanum, Scandium, and Indium Borate and the Force Constants of Borate Ion

The infrared absorption spectra of LaBO3, InBO3, and ScBO3 have been observed as crystalline powders in the wavelength range from 7 to 20 microns. The borates had a B10/B11 ratio varying from the natural abundance (18/82) up to about 96/4. The four fundamental frequencies for B10 fell within the ranges, ω1 = 939, ω2 = 740–790, ω3 = 1265–1330, ω4 = 606–675, all in cm—1. The totally symmetric frequency, ω1 is observed only in LaBO3, which has less than threefold site symmetry, unlike the other two salts.The GVF force constants have been calculated and are compared with those of BF3. A very strong specific coupling of the out‐of‐plane bending mode (ω2) is observed in LaBO3, but the fine structure is not well resolved, and only a rough estimate of the coupling constant and dipole derivative can be made.

Dipolar Coupling and Molecular Vibrations in Crystals. IV. Frequency Shifts and Dipole Moment Derivatives

The internal vibrational modes of a dipole coupled crystal are discussed in terms of two models, a “back‐ground polarization” model which differs from the transition moment dipole coupled “resonant mode” model in that the additional induced dipolar coupling due to electronic polarization is included. The transverse–longitudinal mode splittings as well as factor group splittings are discussed in terms of these two models. The contribution to the frequency shifts from nonresonant modes is calculated and the effect of dipolar coupling on the overtone frequencies is examined. Dipole moment derivatives and static crystal field frequencies of the ν3 doubly degenerate stretching mode are calculated for a few rhombohedral crystals.

The Infrared Spectrum of Crystalline Nitrogen Pentoxide

The infrared absorptions of thin films of crystalline N214O5 and N215O5 maintained at liquid nitrogen temperature have been investigated between 4 and 20 microns. The spectrum is readily interpreted on the basis of the NO2+NO3— structure previously indicated by Raman and x‐ray data. All the constants of the most general quadratic potential functions for the two ions have been evaluated, and the relatively large errors in these constants and their significance in relation to the electronic structure is discussed.

Dipolar Coupling and Molecular Vibrations in Crystals. III. Polarizabilities of Molecular Anions and the Internal Field in Some Rhombohedral Crystals

Using the formalism and the dipole coupling sums developed in an earlier paper the equations relating the optical refractive indices to ionic polarizabilities are given for certain classes of rhombohedral crystals. Anion polarizabilities are calculated from measured refractive indices and previously calculated cation polarizabilities for several series of crystals. Finally the validity of the widely used Lorentz–Lorenz internal field in these systems is examined.

The Raman spectrum of the ordered phase of NH4Cl and ND4Cl: Dipole and polarizability derivatives

The polarized Raman spectra of NH4Cl and ND4Cl have been observed at temperatures of the order of 25–35 K such that the crystal is in the ordered Td phase. The transverse, longitudinal frequency separations for modes ν3, ν4, ν5 (the lattice translation) and the Fermi resonant combination ν2+ν4 in NH4Cl have been used to deduce the infrared intensity parameters ∂μ/∂Q. Then, using these quantities together with an estimate of the electronic contribution to the nonlinear susceptibility, and measurements of the relative intensities of longitudinal, transverse Raman line pairs, we calculate ∂α/∂Qj for j=3, 4, 5. Since only the mode j=5 is well determined by this procedure, the final values of the polarizability derivatives are based upon mode 5 as an internal standard along with the intensities of the other modes relative to 5. The theory is developed on the assumption of additive molecular polarizabilities, and the ∂α/∂Qj values reported are those for vanishing local field. Both the ∂μ/∂Q and ∂α/∂Qj parameter...