Volume 69, Issue 10, 15 November 1978
Index of content:

The energy levels of the CH_{3} asymmetric bending vibrations of toluene
View Description Hide DescriptionThe energy levels of the CH_{3} asymmetric bending vibrations of toluene were calculated by the use of a finite element method for the two dimensional vibrational Schrödinger equation on the basis of a C _{2v } symmetry of the molecule. The totally symmetric CH_{3} torsion was only considered and some boundary conditions were used for the CH_{3} asymmetric bending vibrations. The splittings of the energy levels were examined in relation to the interaction potential V _{2} or V _{6}′ with the CH_{3} asymmetric bending and the CH_{3} torsional coordinates. The ir spectrum was observed in the region of those vibrations at room temperature and the Raman experiments at about −140 °C. The observed bands were assigned by comparing them with the calculated levels.

Structural phase transformations and temperature dependent Raman spectra of Cs_{2}LiFe(CN)_{6}
View Description Hide DescriptionStructural phase transformations have been observed for Cs_{2}LiFe(CN)_{6} at ∼221 and 170 °K. Aspects of the phase II (221°⩾T⩾170 °K) structure have been probed using Raman scattering, x‐ray diffraction, and optical methods. The distortion of the cubic (F m3m) to the tetragonal (I4/m or P4/m n c) cell proceeds along the F _{1g } symmetry rotary mode. The second phase change at 170 °K involves Cs^{+} translation. Striking differences have been observed in the Raman spectra of the iron and related Cs_{2}LiM(CN)_{6} (M=Cr^{+3}, CO^{+3}, and Ir^{+3}) salts. These differences are discussed in terms of the dynamic Jahn–Teller distortion in the iron salt which is not present in the related Cr^{+3}, Co^{+3}, and Ir^{+3} salts.

Characterization of the unimolecular behavior of recoil hot reaction products in inert bath gases. Application to c‐C_{4}H_{7}T
View Description Hide DescriptionA model for the kinetically controlled, nuclear recoil, chemical activation process is further developed to characterize the generation of excited cyclobutane and its subsequent unimolecular behavior. This approach specifically accounts for the overall effect of mixed bath gases in order to utilize previously reported pressure dependent data for cyclobutane in He, Ne, Xe, N_{2}, and CF_{4}. By incorporating appropriate relative energy transfer efficiencies from the activated molecule to the bath gases, a consistent interpretation for all of the experimental data is obtained. This model also provides information on the primary chemical activation process. The results indicate that ∼46% of the recoiling tritiumenergy is deposited into internal energy of the excited product cyclobutane‐t during the T for H replacement reaction and that the energy distribution of activated molecules is relatively independent of the bath gas present in these mixed bath gas systems.

Multiphoton ionization spectroscopy: A theoretical analysis of the NO spectrum
View Description Hide DescriptionThe multiphoton ionizationspectrum of the NO molecule is described theoretically by calculations of absorption and ionization cross‐sections. Both perturbation theoretic (short‐time) and rate equation (long‐time) descriptions of the stepwise excitation and ionization process are considered. Under the present experimental conditions the two approaches are shown to give qualitatively similar results. Two cases of four‐photon absorption are treated: in the first, called a 2+2 process, resonance occurs on absorption of the second photon; and in the second, 3+1 process, resonance occurs at the third photon level. For the wavelength range considered, there is one state, the A ^{2}Σ^{+}, in the former category and six possible choices for the latter. The 2+2 process is shown to have the higher intensity. For most of the resonant states, relative calculated ionization cross sections are in accord with experiment.

Inverse Raman scattering: Continuous generation in optical fibers
View Description Hide DescriptionContinuous inverse Raman scattering has been observed in several liquids. The scattering cell is in the form of a hollow silica fiber several meters in length with a 4 μm diameter core. The excitation source is a krypton laser providing about 20 mW of power in the fiber core, giving an excitation power density of about 10^{5} W/cm^{2}, and the continuum source is a high‐pressure xenon arc lamp.

Rate constants and quenching mechanisms for the metastable states of argon, krypton, and xenon
View Description Hide DescriptionRate constants have been measured by the flowing afterglow technique at 300 °K for the quenching of Ar(^{3} P _{2}), Ar(^{3} P _{0}), Kr(^{3} P _{2}), and Xe(^{3} P _{2}) by a large number of small molecules. For the same reagent, the magnitudes of the cross‐sections usually increase in the series Ar(^{3} P _{2}), Ar(^{3} P _{0}), Kr(^{3} P _{2}), and Xe(^{3} P _{2}). The Ar(^{3} P _{2}) and Ar(^{3} P _{0}) data are compared to results in the literature for these states and to data for Ar(^{3} P _{1}) and Ar(^{1} P _{1}). The set of thermal quenching cross sections are used to test the correlations between the magnitudes of the cross sections and properties of the reagents as predicted by the orbiting, absorbing‐sphere, golden rule, and curve‐crossing mechanisms for quenching. The best correlation is between the cross sections and the C _{6} coefficient. The analysis supports the proposition that the orbiting‐controlled, curve‐crossing model is the general mechanism governing the magnitude of the thermal cross sections for quenching of the metastable states. This model explains the very large quenching cross sections of F_{2} and OF_{2} (relative to other molecules composed of first row elements) because covalent–ionic curve crossing occurs outside the conventional orbiting radius. The validity of the simple van der Waals dispersion forces as being the dominant entrance channel interaction between the excited state rare gas atoms and the reagents is discussed.

Radiation damage studies by x‐ray photoelectron spectroscopy. II. Electron irradiated Li_{2}CrO_{4} and Li_{2}WO_{4}
View Description Hide DescriptionSingle crystals of Li_{2}CrO_{4} and Li_{2}WO_{4} were irradiatedi n s i t u with 0.3–1.6 keV electrons in an UHV x‐ray photoelectron spectrometer.Chemical shifts of core‐level peaks in XPS spectra indicate formation of Cr(III) on the irradiated Li_{2}CrO_{4}surface and of W (IV) and W (V) on the irradiated Li_{2}WO_{4}surface. Accompanying formation of the reduced species, new peaks attributable to photoelectrons from non‐bonding orbitals appear at binding energies just below the respective Fermi levels. A lower limit of the G value for Cr(III) formation is estimated to be about 1.3×10^{−2} from the differential energy loss of the incident electrons. Comparison of this G value with previous data determined by ESR suggests that solid surfaces are far more sensitive to radiation damage than the bulk. The irradiation of Li_{2}WO_{4} causes a shift in the entire XPS spectrum to lower binding energy, initially ∼2 eV, which decreases over a 20 h period until the original peak positions are recovered. This is interpreted in terms of surface charging caused by electron irradiation.

HCO production, vibrational relaxation, chemical kinetics, and spectroscopy following laser photolysis of formaldehyde
View Description Hide DescriptionFormaldehyde vapor was photolyzed with a tunable pulsed uv laser. Flash kinetic absorption spectra of the HCO produced were recorded by intracavity dye laserspectroscopy with a time resolution of 1 μs. The energy threshold for radical production was confirmed to be at 86±1 kcal/mole. Photolysis at 294.1 nm produced HCO in its ground vibronic state (∼2/3) and with one quantum of vibrational excitation in either the bending (∼1/3) or CO stretching (10^{−1}–10^{−2}) vibrations. Observation of the CO stretching hot band absorptions allowed that frequency to be determined as 1868.4±1 cm^{−1}. Quantitative, state‐resolved measurements of concentration vs time were made in pure H_{2}CO and in mixtures with O_{2}, NO, or Ar. The vibrational relaxation rate for the bending vibration of HCO in collisions with H_{2}CO was (4.3±1) ×10^{−12} cm^{3} molecule^{−1} s^{−1}. Reaction rates for HCO+NO→HNO+CO and HCO+O_{2}→HO_{2}+CO were measured as (1.4±0.2) ×10^{−11} and (4.0±0.8) ×10^{−12} cm^{3} molecule^{−1} s^{−1}, respectively. Approximate rates were determined for the radical–radical reactions H+HCO→H_{2}+CO and 2HCO→H_{2}CO+CO as 10^{−9.26±0.3} and 10^{−10.2±0.5}, respectively.

Time resolved emission from OH(C ^{2}Σ^{+}) produced by the pulse radiolysis of water vapor
View Description Hide DescriptionPulse radiolysis was used to study lifetimes and rate constants for quenching by H_{2}O of water vapor fragments emitting in the range 210–360 nm. The radiative lifetimes of OH(C ^{2}Σ^{+}, v=0,1), measured at the bandheads of the (1–8), (1–9), and (0–9) bands of the C ^{2}Σ^{+}→A ^{2}Σ^{+} transition and analyzed by a deconvolution method were 3.8±0.5, 3.6±0.3, and 3.9±0.5 ns, respectively. Quenching rate constants at 292 K were (1.7±0.3) ×10^{−9}, (1.6±0.2) ×10^{−9}, and (2.2±0.3) ×10^{−9} cm^{3}s^{−1} molecule^{−1} for these bands, (0.53±0.02) × 10^{−9} cm^{3}s^{−1} molecule^{−1} for the OH A ^{2}Σ^{+} →X ^{2}Π, (0–0) band and (12.8±1.1) × 10^{−9} cm^{3}s^{−1} molecule^{−1} for an unidentified band at 253–254 nm. The two long lived emissions reported by Remy [Spectrosc. Lett. 4, 319 (1971)] at the head of the (0–9) band of the OH C ^{2}Σ^{+} →A ^{2}Σ^{+} transition were not present.

Infrared intensities: Polar tensors and charge flux parameters
View Description Hide DescriptionAn attempt has been made to streamline the procedure for analysis of infrared intensities of fundamental bands through polar tensor calculations. Different methods used in the literature to calculate the rotational contributions have been compared and a correlation has been pointed out. Using the atomic charge model, a generally applicable expression relating an atomic polar tensor to the equilibrium atomic charges and their flux terms has been derived. The bond moment model has also been used to obtain an analogous expression relating the atomic polar tensor to the bond moments and their derivatives. However, the final equations of these two models indicate that, irrespective of the model chosen for the interpretation of infrared intensities, one would obtain identical information.

Mössbauer, magnetic susceptibility, and EPR studies of intermediate spin iron (III) dithiooxalato halides
View Description Hide DescriptionMössbauer, magnetic susceptibility, and EPRmeasurements have been performed in the series of intermediate spin [Fe(S_{2}C_{2}O_{2})_{2}X]^{2−}, (X=Cl, Br, I) complex anions. All members of the series are paramagnetic down to 1.4 °K. Mössbauer and EPR results establish the axial character of the electronic spin Hamiltonian for the iodide derivative and increasing rhombicity for Br and Cl. Axial zero field splitting parameters D are positive and near 5 °K. The quadrupole splittings are large in the range 3.4–3.6 mm/sec and typical for the S=3/2 state of Fe(III). Isomer shifts are near 0.30 mm/sec indicating substantial d electron delocalization in the π system of the ligand. The magnetic hyperfine constant decreases from the Cl to the I derivative indicating increasing covalency of the metal–halide bond. Pronounced relaxation effects are present in the Mössbauer spectra varying with the halogen ligand. Spectra in applied fields up to 60 kG have seen fitted with a relaxation theory based on a stochastic model.

On magnetic transitions and the interpretation of the partial wave parameter in the CS and IOS approximations in molecular scattering theory
View Description Hide DescriptionThe recent discovery by Khare that choosing the CS partial wave parameter ? to be the initial orbital angular momentum,l _{ i }, leads to a simple differential scattering amplitude for definite polarization transitions is examined in detail. It is found that the resulting scattering amplitude formula, which is a rotation of the usual McGuire–Kouri formula, predicts nonzero magnetic transitions in all frames except that whose Z axis always points in the final observation direction ?. A detailed comparison of l _{ i } and l _{ f } labeling is made and it is shown that both lead to nondiagonal approximations to the p‐helicity amplitude, T ^{ J }(jλ‖j _{0} m _{0}), and to differential scattering amplitudes which have the proper limiting behavior at small and large scattering angles. In addition it is shown that both l _{ i } and l _{ f } labeling yield identical results for all degeneracy averaged cross sections, including the general relaxation cross sections. Further, we show rigorously that if the quantization axis is along a direction perpendicular to the plane of the incident and final momenta, then the l _{ i } and l _{ f } labeled cross sections are identical. It is argued on the basis of available numerical results and on physical grounds that the l _{ i }‐labeled CS is preferred over the l _{ f } CS for calculating magnetic transitions quantized along the incident momentum. We further expect the l _{ f } CS to be preferred for calculating magnetic transitions quantized along the final momentum. However, other ? choices may be better yet for magnetic transitions in general.

Elementary properties of an energy functional of the first‐order reduced density matrix
View Description Hide DescriptionThe Hohenberg–Kohn theorem implies the existence of an energy functional based solely on the first‐order reduced density matrix of the ground state of an atomic or molecular system. Application of the variational principle for the functional E _{ v } ^{ M }[γ] generates a set of coupled Euler equations for the representation coefficients and spin orbitals of a rank‐M approximation to the exact ground‐state density matrix. Defining the (assumed Hermitian) kernel F ^{ M }[γ;x′,x]≡δE _{ v } ^{ M }/δγ (x,x′), the equations in an arbitrary representation for the approximate density matrix, γ (x,x′) =Σ_{ i j } ^{ M }ψ_{1}(x) γ_{ i j }ψ_{ j }* (x′) are the following: FdξF ^{ M }[γ;x′,ξ]ψ_{ i }(ξ) =μψ_{ i }(x′); i=1, 2,...,M; FdξF ^{ M }[γ;x′,ξ] Σ^{ M } _{ i }ψ_{ i }(ξ) γ _{ i j }=Σ^{ M } _{ i }ψ_{ i }(x′) λ_{ i j }; j=1, 2, ...,M. The quantity μ is the chemical potential of the system of interest and the λ_{ i j } are a set of M ^{2} Lagrange multipliers constraining the orthonormality of the spin orbital basis {ψ}. The coefficients γ_{ i j } must be chosen such that F ^{ M } has the degenerate eigenvalue spectrum, F _{ i i } ^{ M }=μ, i=1, 2,...,M, for all partially occupied orbitals. The spin orbitals, for a fixed set of coefficients, must be simultaneously determined so that λ is Hermitian. Provided all occupation numbers lie on the open interval (0,1), the stationary density matrix itself obeys the eigenvalueequationFdξF ^{ M }[γ;x,ξ]γ (ξ,x′) =μγ (x,x′), and for any stationary density matrix the following commutation rules are valid: [F^{ M }[γ], γ]=0; [λ, γ]=0. The matrices γ and λ consequently can be brought simultaneously to diagonal form, and the canonical representation of the energy functional provides an eigenvalueequation determining the natural spin orbitals. The value of the chemical potential is μ=ε_{ i }/n _{ i }, i=1, 2, ...,M; ε=diag (λ); from which follows the distribution function governing the occupation numbers of a stationary density matrix. Two limiting forms of the variational principle are examined, the exact and Hartree–Fock functionals, and related previous work by Gilbert is discussed. The physical content of the equations is illuminated by identification of the chemical potential as the negative of the electronegativity; Sanderson’s Principle of Electronegativity Equalization follows.

Theoretical determination of molecular structure and conformation. I. The role of basis set and correlation effects in calculations on hydrogen peroxide
View Description Hide DescriptionEquilibrium structure and barriers to internal rotation of hydrogen peroxide have been accurately determined with the Hartree–Fock method and Rayleigh–Schrödinger perturbation theory using a (9s5p1d/4s1p) [4s3p1d/2s1p] contracted and (11s6p2d/6s2p) uncontracted basis set. Extensive rescaling of the contracted basis accompanied by complete geometry optimization leads to barrier values of 0.7 (t r a n s) and 8 (c i s) kcal/mole. Results obtained with the uncontracted basis indicate an improvement of the barriers to 1.1 and 7.4 kcal/mole comparable to the refined experimental values of Ewig and Harris. Inclusion of correlation does not change the barriers significantly. The latter, however, is necessary to obtain correct equilibrium parameters. The computed bond lengths [R (OO) =1.451 Å, R (OH) =0.967 Å] and angles [α (OOH) =99.3° and ϑ (HOOH) =119.3°] are in good agreement with experiment while near HF values lead to a false structure [R (OO) =1.390 Å, R (OH) =0.943 Å, α (OOH) =102.9°, ϑ (HOOH) =111.2°]. The importance of optimum scaled polarization functions in the perturbation approach is demonstrated.

Theoretical determination of molecular structure and conformation. II. Hydrogen trioxide—a model compound for studying the conformational modes of geminal double rotors and five membered rings
View Description Hide DescriptionThe internal rotational surface of hydrogen trioxide has been calculated with the Hartree–Fock method using basis sets with and without polarization functions and optimizing all structural parameters. These calculations have been repeated at the level of Rayleigh–Schrödinger–Mo/ller–Plesset (RS–MP) perturbation theory in order to study the role of correlation effects on barrier values and structures. The relative energies as well as the computed geometrical parameters underline the importance of polarization functions. Although the intrapair correlation contributions significantly stabilize the planar conformations of H_{2}O_{3}, the net effect of correlation effects on the conformational potential is moderate because of well‐balanced interpair contributions of opposite sign. As in the case of H_{2}O_{2}, the correlation effect on the relative energies further decreases if the basis set is improved. On the other hand, reliable structural parameters can only be achieved at the RS–MP level by employing a large augmented basis. The calculated equilibrium RS–MP structural parameters of H_{2}O_{3} are: R (OO) =143.9 pm, R (OH) =97.2 pm, α (OOO) =106.3°, β (OOH) =100.2°, ϑ=78.1°. Bond angles and OO bond lengths are strongly coupled to the rotational angles. A simultaneous rotation of both OH bonds is hindered by large barriers of 22.5 and 11.5 kcal/mole. These potential maxima can be surrounded in a stepwise flip‐flop rotation of the OH groups. The barriers of this rotational process turn out to be the saddlepoint energies (6.5 and 5.4 kcal/mole) of the internal rotational surface. It is shown that a close relationship exists between the flip‐flop rotation of the geminal double rotor and the pseudorotation of five membered rings. Using the calculated conformational potential V (ϑ_{1},ϑ_{2}), the prediction is made that the envelope form of 1,2,3‐trioxolane is more stable than the corresponding twist form.

Theory of Raman scattering by molecules adsorbed on electrode surfaces
View Description Hide DescriptionIn this work, we provide a simple classical model to explain the enormous intensity enhancement observed for Raman scattering from molecules adsorbed on electrode surfaces. It is proposed that the origin of the intensity enhancement arises from very large changes in the polarizability derivative with respect to a normal coordinate, by virtue of the image field at the admolecule. A qualitative discussion of the role of adsorbed counter ions is presented. We tentatively propose that the dependence of the intensity enhancement on counter ion concentration may be understood in terms of nearest neighbor dipole–dipole stabilization of surface clusters of counter ions with the adsorbate molecule. We also discuss some limitations of the classical model, and propose some further experiments that may lead to clarification of the ideas presented in this work.

Third‐order nonlinear mixing in polydiacetylene solutions
View Description Hide DescriptionThird‐order mixing has been measured in solutions of the polydiacetylenes. The Raman molecular vibration contribution to the third‐order susceptibility χ_{ T } ^{(3)} (−ω_{3}, ω_{1}, ω_{1}, −ω_{2}) has been characterized completely. A surprisingly strong polymer two‐photon absorption contribution to χ_{ T } ^{(3)} was found. The cross section for two‐photon absorption at 2ω_{1}=32 000 cm^{−1} is 6×10^{−47} cm^{4} sec photon^{−1}(polymer repeat unit)^{−1}. The polymer nonresonant susceptibility could not be determined because of the strong two‐photon contribution to χ_{ T } ^{(3)}.

Dissociation of CO and NO by fast H^{+}, He^{+}, and O^{+} projectiles
View Description Hide DescriptionIn this work we report on studies of the dissociativeionization of CO and NO induced by 1‐MeV H^{+}, He^{+}, and O^{+} projectiles. The time‐energy spectroscopy (TES) technique is used to identify the dissociation fragments according to their mass‐to‐charge (m/q) ratios, and to record kinetic energy spectra for each fragment species. The spectra fragments with 1^{+}, 2^{+}, and 3^{+} charges show overlapping peaks for which energy assignments are made. In most case, the He^{+} and O^{+} projectiles appear to form dissociative states of CO^{2+} and NO^{2+} which decay into singly charged fragments. The H^{+} projectile appears to form CO^{+} and NO^{+} which subsequently dissociate into charged and neutral fragments. The dissociative states excited in this experiment are different from those reported in K‐shell ionization studies.

Semiclassical approximations for low‐energy inelastic scattering
View Description Hide DescriptionSeveral semiclassical methods are developed to treat low‐energy vibrationally and rotationally inelastic scattering. The quantal close coupling (CC) equations are approximated by treating the orbital angular momentum in a classical limit. This removes l from the coupled equations and introduces a dependence in the potential on the classical orbital angle. Unlike the coupled states (CS) approximation, l is not frozen. Next, the rotational motion is treated in the sudden approximation. For vibrationally inelastic scattering, this yields an approximation which involves the solution of N coupled differential equations for Nvibrational states. For the pure rotational case, the theory reduces to a sudden approximation superior to the current alternatives. Unlike the traditional approach, it is not a perturbation theory based on an elastic trajectory. Unlike the infinite order sudden approximation (IOS), it converges properly at large impact parameters. Indeed, the IOS is obtained as a special case by freezing the orbital motion. A fast numerical procedure is derived for evaluating the matrices occurring in the sudden approximation.

Calculations of deuterium quadrupole coupling constants employing semiempirical molecular orbital theory
View Description Hide DescriptionDeuterium quadrupole coupling constants (DQCC) for deuterium nuclei in a variety of bonding situations have been obtained by means of semiempirical molecular orbital wavefunctions in the INDO approximation. All integrals of the operator entering the electronic contributions have been included with no approximations in their evaluation. Analytical expressions are tabulated for the relevant two‐center integrals; three‐center integrals were obtained by numerical integration techniques. The factors responsible for the very strong dependence of deuterium QCC on internuclear distance, and the relative constancy of the parameters for a given bonding situation are discussed with regard to the types of terms which enter the integral expressions and the molecular electronic distributions. Some interesting and possibly useful predictions are also included in the tabulated results; the DQCC for the bridging deuterium in diborane is predicted to have a value of −110 kHz, which may be the first negative value for a DQCC; the effects of hydrogen bonding can be significant, the result of lengthening of the D–X bond on hydrogen bondformation.