Index of content:
Volume 69, Issue 11, 01 December 1978

Analysis of torsional spectra of molecules with two internal C _{3v } rotors. X.^{a)} Low frequency vibrational spectra, methyl torsional potential functions, and internal rotation of ethylmethylether (‐d _{0} and ‐d _{3})
View Description Hide DescriptionThe vibrational spectra of gaseous ethylmethylether C_{2}H_{5}OCH_{3} and C_{2}H_{5}OCD_{3} have been investigated at high resolution below 500 cm^{−1}. Considerable torsional data are reported and assigned on the basis of an equilibrium between the s‐t r a n s and the high energy g a u c h e conformers. Asymmetric potential functions for the CH_{2}–O torsions have been calculated from observed transitions, leading to values for the enthalpy difference between the g a u c h e and s‐t r a n s conformers of 1.36 and 1.28 kcal/mole, respectively, for the ‐d _{0} and ‐d _{3} compounds. Analysis of the transitions above 130 cm^{−1} indicates that the two methyl rotors have strongly coupled torsional vibrations in both compounds, and that previous assignments are insufficient for explaining the data. Transitions due to the methyl torsions of the molecules in the first excited states of the asymmetric CH_{2}–O torsions are reported; also, some weak bands have been assigned tentatively as methyl torsions of g a u c h e‐ethylmethylether. Torsional potential functions and barrier heights to internal rotation of the methyl tops have been calculated for both compounds; for the ground state of ethylmethylether the C–CH_{3} and O–CH_{3} barriers are calculated to be 3.08 and 2.61 kcal/mole, respectively.

Collisionless decay, vibrational relaxation, and intermediate case quenching of S _{1} formaldehyde
View Description Hide DescriptionThe decay of fluorescence from the 4^{0} and 4^{1} levels of the S _{1}(Ã ^{1} A _{2}) state of H_{2}CO and D_{2}CO has been monitored as a function of pressure after selective, pulsed laser excitation. For D_{2}CO, single exponential decays modified by 4^{0}↔4^{1}energy transfer were observed over the entire pressure range 4×10^{−5}–4 Torr. The zero pressure lifetimes τ_{0}(4^{0}) =7.8±0.7 μs and τ_{0}(4^{1}) =6.0±0.4 μs are probably the radiative lifetimes. The rate of 4^{1}→4^{0}energy transfer in D_{2}CO was found to be (9.6±0.4) ×10^{−10} cm^{3} molecule^{−1} s^{−1}, about three times the gas kinetic rate. For H_{2}CO at pressures above 0.1 Torr, fluorescence decays were also single exponentials modified by 4^{0} ↔4^{1}energy transfer. However, in the range 2×10^{−4}–0.1 Torr, the decays of the individual 4^{0} and 4^{1} vibronic levels were typically biexponential. The zero pressure decay occurs on a timescale at least 20 times faster than the radiative lifetime of ∼5 μs. The Stern‐Volmer plots of τ^{−1} vs pressure give quenching rates between 2.2×10^{−9} and 6.5×10^{−9} cm^{3} molecule^{−1} s^{−1} for both fast and slow components below ∼20 mTorr. The relative amplitude of the fast component decreases rapidly with pressure and approaches zero at 0.1 Torr. The slow component plots are dramatically curved and give quenching rates of only about 2.2×10^{−11} cm^{3} molecule^{−1} s^{−1} above 1 Torr. The low pressure quenching rates and zero pressure lifetimes for H_{2}CO depend significantly on the K′ rotational quantum number within 4^{0}. The biexponential decays for H_{2}CO may result from variations in lifetime among the J′ states excited by the laser. The large quenching rate constants and the curvature of the Stern–Volmer plots can be qualitatively understood in terms of recent mixed‐state models of collision‐induced radiationless decay.

Mechanism of thermal electron attachment in N_{2}O–CO_{2} mixtures in the gas phase
View Description Hide DescriptionThe attachment of thermal electrons to nitrous oxide in N_{2}O–CO_{2} mixtures has been studied at room temperature in the pressure range 5–120 torr. Ionization was by pulse radiolysis and the electron concentration was measured as a function of time by microwaveconductivity. Addition of even less than 0.1% CO_{2} to N_{2}O causes a marked increase in attachment rate. However, this enhancement soon saturates in that further additions of CO_{2} have less and less effect. Experiments with ternary mixtures including C_{2}H_{6} showed a further enhancement which was much larger than the additive effects of CO_{2} and C_{2}H_{6} alone. These observations can be explained by a two step three‐body process producing vibrationally excited N_{2}O^{−}* if the rate constant for stabilization of N_{2}O^{−}* by CO_{2} is 4×10^{−30} cm^{6}/molecule^{2}⋅sec. The decrease in effectiveness with increased CO_{2} pressure is interpreted as the collisional ionization of a complex ion, [N_{2}O⋅CO_{2}]^{−}*. The nonadditive effect of hydrocarbon results from the rapid reactive destruction of such complexes by collision with the hydrocarbon. A detailed quantitative treatment of the proposed mechanism was successful in explaining most features of the data. In a limited set of experiments, allene —N_{2}O mixtures were found to behave much like CO_{2}–N_{2}O.

Transmission function vs energy splitting in tunneling calculations
View Description Hide DescriptionTwo methods have been widely employed for computing tunneling rates in a double‐well potential, one based on a transmission function, the second on energy splitting. Semiclassical calculations (Brickmann and Zimmermann) show that the transmission method leads to lower rates than the splitting method. It is shown here without employing the semiclassical approximation that a more accurate relation between the energy splitting and the transmittion function may be obtained by using a decomposition of the stationary states into scattering states. This relation is then used to provide an analytical basis for the usual heuristic picture in which the particle oscillates with classical frequency in one well and has a probability of tunneling to the other well equal to the transmission function in each classical period of oscillation. It is concluded that the transmission method should give more meaningful results, particularly in situations where interactions of the system with a heat bath have significant effects in the tunneling times predicted by the splitting method. This is in accord with previous work in which both methods were used in an attempt to fit experimental data for hydrogen diffusion in niobium.

Melting in a two‐dimensional Lennard‐Jones system
View Description Hide DescriptionFrom molecular dynamics calculations on a two‐dimensional Lennard‐Jones system we find a first order solid–fluid transition with an estimated triple point temperature in good agreement with the triple point temperature of adsorbed monolayers of xenon. The melting obeys Ross’s melting criteria.

Absorption bands in a CsHe system associated with forbidden Cs atomic transitions
View Description Hide DescriptionWe have made direct absorption measurements of the Cs(7S)He←Cs(6S)He absorption band (5250–5700 Å) and the prominent part of the Cs(5D _{5/2})He←Cs(6S)He absorption band (5800–6850 Å). The spectrum of the reduced absorption coefficients we obtained is in reasonable agreement in shape with that recently reported by Sayer e t a l, who used a laser induced fluorescence technique, but our absolute magnitudes are bigger than those of Sayer e t a l by approximately a constant factor of 5.

ir photolysis of SeF_{6}: Isotope separation and dissociation enhancement using NH_{3} and CO_{2} lasers
View Description Hide DescriptionThe isotopically selective ir photodissociation of SeF_{6} using two lasers is reported. The output from an NH_{3} laser (780.5 cm^{−1}, 0.75 J, 0.5 μsec FWHM) and a line tunable CO_{2} TEA laser (2.5 J, 150 nsec FWHM) are combined in order to enhance the photodissociation rate. Although the CO_{2} laser output by itself is ineffective in dissociating SeF_{6}, the CO_{2} laser output can enhance the NH_{3} laser photolysis of SeF_{6} by as much as a factor of 50. We find that the isotopic selectivity is independent of the CO_{2} laser energy, and the rate of dissociation is unaffected by changing the CO_{2} laser frequency.

Piezo‐ and elasto‐optic properties of liquids under high pressure. I. Refractive index vs pressure and strain
View Description Hide DescriptionThe variation of the refractive index of liquid with pressure to 14 kbar has been determined by an optical interferometric method. The liquids studied are carbon tetrachloride, n‐pentane, n‐hexane, n‐heptane, n‐octane, n‐nonane, n‐decane, benzene, chlorobenzene, methyl alcohol, and water at room temperature. Since most of these liquids freeze at room temperature even before 14 kbar is reached, the measurements were carried out up to the freezing point or 14 kbar, whichever pressure is lower. In every case the refractive index increases with pressure with pronounced nonlinearity, particularly at high pressure. This nonlinearity is reduced considerably when the same data on Δn are considered as a function of the volume strain indicating that the nonlinear piezo‐optic behavior of liquids is just a manifestation of nonlinear P–V relationship. Further, it is found that the slight nonlinearity noticed in the Δn−ΔV/V _{ o } relationship could be still further reduced when the variation in refractive index is treated as functions of the Lagrangian and Eulerian strains. In particular, the Eulerian strain ε is found to yield a much larger range of strain over which a simple linear relationship between Δn and ε is obtained irrespective of the nature of the liquid or the equation of state used to compute the strain.

Piezo‐ and elasto‐optic properties of liquids under high pressure. II. Refractive index vs density
View Description Hide DescriptionIn Paper I of this series it was shown that high pressure interferometric measurements on a number of liquids reveal that the refractive index of liquids increases linearly with Eulerian strain even though the volume strain involved is as high as 33%. Further, it was also found that this linearity criterion can be used to discriminate between the various equations of state for liquids and that Keane’s equation appears to be universally valid for all liquids. Having thus established the P–V relationship of liquids, the next problem of the refractive index–density relationship of liquids is considered in this article. The various equations prevalent in the literature—namely, Lorentz–Lorenz, Drude, Eykman, Onsager–Bottcher, Kirkwood–Brown, and Omini equations— are analyzed. The last two equations have been derived using a detailed statistical mechanical approach. It is found that none of these equations can predict the elasto‐optic behavior of liquids at high pressure quantitatively even though the latter two equations appear to yield values in reasonably good agreement with experimentally observed values.

Generation of O_{2}(c ^{1}Σ_{ u } ^{−}, C ^{3}Δ_{ u }, A ^{3}Σ_{ u } ^{+}) from oxygen atom recombination
View Description Hide DescriptionThe spectrum produced in the afterglow of an O_{2}–He discharge has been studied between 4000 and 8000 Å. Until recently, only the O_{2}(A ^{3}Σ_{ u } ^{+}→X ^{3}Σ_{ g } ^{−}) emission bands had been observed in this region. The work of Lawrence e t a l. established that, under the appropriate conditions, the O_{2}(c ^{1}Σ_{ u } ^{−} →X ^{3}Σ_{ g } ^{−}) system could also be observed. We were able to duplicate their results, and in addition we have discovered three O_{2} band systems not previously seen in gas phase laboratory spectra. These systems are C ^{3}Δ_{ u }→a ^{1}Δ_{ g }, C ^{3}Δ_{ u } →X ^{3}Σ_{ g } ^{−}, and c ^{1}Σ_{ u } ^{−}→a ^{1}Δ_{ g } and were positively identified by isotopic substitution experiments. The 0–v ^{″} progression in the C–a system is the first gas phase spectrum involving a large range of the higher vibrational levels in the a ^{1}Δ_{ g } state. Analysis of the system establishes a new set of a ^{1}Δ_{ g } vibrational constants : ω_{ e }=1510.23 ±0.34 cm^{−1}, and ω_{ e } x _{ e }=13.368±0.12 cm^{−1}. The C–a system involves only the Ω=1 spin component of the C ^{3}Δ_{ u } state. The C ^{3}Δ_{ u }→X ^{3}Σ_{ g } ^{−} system, on the other hand, radiates mainly through the Ω=2 component. By combining the present data on the C ^{3}Δ_{ u }(v=0) level, the absorption measurements of Herzberg on the v=5 and v=6 levels, the known dissociation energy, and the high‐pressure bands measured by Herman and by Finkelnburg and Steiner, we have established vibrational constants for the C ^{3}Δ_{ u } state. These are ω_{ e }=803.5±1.0 cm^{−1}, ω_{ e } x _{ e }=8.18±0.13 cm^{−1}, and ω_{ e } y _{ e } =−0.872±0.006 cm^{−1}. From data existing in the literature, combined where necessary with the present measurements, we have estimated radiative lifetimes for the three O_{2} metastable states that we observed. From the band strength data of Hasson e t a l., one may calculate τ=250–160 msec for A ^{3}Σ_{ u } ^{+}(v=0–6), and deduce an estimate of τ=25–50 sec for c ^{1}Σ_{ u } ^{−}(v= 0–10). For C ^{3}Δ_{ u }(Ω=1, v=0–6), the estimated lifetime is 5–50 sec, and for C ^{3}Δ_{ u }(Ω=2, v=6), the estimated lifetime is 10–100 sec. The O_{2}spectra have been produced not only in O_{2}‐He afterglows, but also in NO‐titrated N_{2}–He afterglows (i.e., in an O_{2}‐free environment), proving that the source of excited O_{2} molecules is oxygen atom recombination. The results are pertinent to O_{2} emissions in the terrestrial and Venusian air glows, and to combustion processes.

Analysis of the spin‐Hamiltonian parameters for Mn^{2+} in axial sites of the alkali chlorides and fluorides
View Description Hide DescriptionThe applicability of the superposition model to the quadrupole spin‐Hamiltonian parameters of Mn^{2+} in axial symmetry sites of the alkali chlorides and fluorides is analyzed. In addition, taking advantage of the EPR spectra of Mn^{2+} in tetragonal sites of RbCl, the fourth‐order parameters b ^{0} _{4} and b ^{4} _{4} have been determined in order to test the applicability of the superposition model not only for the n=2, but also for the n=4 spin‐Hamiltonian parameters. It was found that the sign and value obtained in this work, for the intrinsic parameter ?_{2} of Mn^{2+} with Cl^{−} ligands, are in good agreement with those estimated by Newman and Siegel from the ?_{2} value of Eu^{2+} ions, if the power law exponent of ?_{2} is taken to be equal to seven.

The hot‐atom collisional energy density function
View Description Hide DescriptionUsing stochastic methods we have computed the hot‐atom collisional energy density functional,n (E) d E, the number of collisions suffered by a translationally hot atom between E and E + d E. We examine the dependence of n (E) on several variables such as the mass and energy of the hot atom and the parameters of the intermolecular potential.

Rayleigh–Brillouin scattering from acetic acid
View Description Hide DescriptionRayleigh–Brillouin scattering is studied in acetic acid as a function of temperature over the normal liquid range. The Brillouinlinewidth displays a maximum at 30°C. The spectra are analyzed in terms of the general viscoelastictheory of light scattering developed by Rytov. Relaxation times for reorientation and structural relaxation are derived from the data.

Raman depolarization ratios and order parameters of a nematic liquid crystal
View Description Hide DescriptionThe depolarization ratios of the Raman vibrational bands from the terminal C≡N and the central C–C biphenyl link of an oriented nematic liquid crystal [p‐n‐pentyl‐p′‐cyanobiphenyl (5CB)] have been measured. The orientational order parameters 〈P _{2}〉 and 〈P _{4}〉 were calculated. The parameter 〈P _{4}〉 remained far less than the mean‐field theory prediction although a systematic discrepancy between the order parameters obtained from the two bands was noted. The Raman tensor of C≡N band was found n o t to be uniaxial, contrary to the previous assumption, and a strong association of molecules is suggested. Problems associated with this technique are discussed.

Extended basis set calculations of nonlinear susceptibilities of conjugated hydrocarbons
View Description Hide DescriptionWe reconsidered perturbation treatments of molecular eigenstates by expanding in terms of other molecular eigenstates. This constitutes an improvement over a previously reported treatment where we considered molecular orbitals which were expanded in terms of other molecular orbitals. In the present paper, we take the ground state molecular wavefunction as a single determinant SCF function. Fourth order energy perturbations are then obtained as a sum of contributions from singly and doubly excited molecular configurations. We evaluated the various fourth‐order energy perburbations and corresponding third‐order electric susceptibilities for a group of about 30 aromatic hydrocarbons and for a group of linear conjugated hydrocarbons. Our results are roughly consistent with the limited experimental information that is available for these molecules.

Kramers’s theory of chemical kinetics: Eigenvalue and eigenfunction analysis
View Description Hide DescriptionThe Smoluchowski equation for a double‐minimum potential is studied as a means of calculating rate constants for chemical reactions. In the one‐dimensional case, a symmetric fourth‐degree potential is used, and the solution is obtained in terms of eigenvalues and eigenfunctions. Asymptotic expressions for the lower eigenfunctions are found by means of singular perturbation theory, and the corresponding eigenvalues are obtained via a variational principle. A quantum‐mechanical analogy is used to generate the higher eigenvalues and eigenfunctions. The expression for the rate constant is seen to be a generalization of earlier results, and its range of validity is determined by solving the appropriate equations numerically. It is found that the new formula is accurate over a rather wide range of barrier heights. In the three‐dimensional case, the rate constant is again found by means of a variational calculation, using as a trial function the eigenfunction for a separable potential. The result is seen to reduce to the more familiar expression in the appropriate limit, and its range of validity is investigated through direct numerical computations of the eigenvalues.

Application of saturation spectroscopy for measurement of atomic Na and MgO in acetylene flames
View Description Hide DescriptionThe technique of laser induced fluorescencesaturation spectroscopy is evaluated for determination of absolute atomic and molecular concentrations in flame sources. The combustor is an aspirating slot burner using premixed acetylene and air to create a stable homogeneous flame source. Concentration measurements of atomic sodium and MgO (X ^{1}Σ^{+} and A ^{1}Π) are made by saturation spectroscopy and laser induced fluorescence techniques. Independent atomic and molecular absorption measurements are made for Na and MgO (X ^{1}Σ^{+}) which are in agreement with saturation spectroscopy concentration determinations. The effect of using various laser beam profiles (rectangular, Gaussian, and truncated Gaussian) are evaluated. It is found that MgO exists in the flame in a significant inversion in the (A ^{1}π) state and possible production mechanisms for MgO in the flame are considered.

Atomic and molecular model potentials
View Description Hide DescriptionA constructive theory of atomic and molecular model potentials is developed using the work of Bottcher and Dalgarno as a point of departure. In this theory, all of the terms required by successful, empirical, model potential calculations are obtained from a perturbation theory in which exchange is neglected. We find that valence electrons must be allowed to penetrate into the core regions even in systems with well defined cores and distant valence electrons. Within this theory, exact model potentials for hydrogenlike atoms and H_{2}‐like molecules are obtained and specific, short‐ and long‐range forms of the model potentials are proposed for other atoms and molecules.

Penning and associative ionization in the metastable helium–atomic deuterium system
View Description Hide DescriptionMeasurements of Penning and associative ionization cross sections (Q _{PI} and Q _{AI}) and branching ratios (R) for the He*–D system have been repeated in this laboratory. The studies were made using a merging‐beams technique for a relative kinetic energy W of the reactants from nominally 0.01 to 10 eV. This is a wider energy range than covered previously. The He* represents a composite of about 15% He(2 ^{1} S) and 85% He(2 ^{3} S). The new results are more acurate than the old due to improvements in the apparatus. From the new studies, a well depth of approximately 2.1 eV was obtained for the He(2 ^{3} S) –D potential and between 0.25 and 0.4 eV for the He(2 ^{1} S) –D potential. These well depths agree with values obtained by others. Laboratory‐energy distributions of Penning ions indicate differences in the kinetics of reaction for He(2 ^{1} S) and He(2 ^{3} S). The new Q _{AI}, Q _{PI}, and R agree with those of several other experimenters although there are discrepancies in Q _{PI} and R with the calculations of Hickman and Morgner.

Luminescence from Al_{2x }Ga_{2(1−x)}O_{3}:Cr^{3+}
View Description Hide DescriptionDetailed luminescence and lifetime data are presented for the mixed crystal system Al_{2x }Ga_{2(1−x)}O_{3}:Cr^{3+}, where x=0, 0.02, 0.20, 0.35, 0.98, 1.0. The experimental data, obtained under broadband excitation at 77 K and 4 K, indicate that our pressure‐grown microcrystalline samples all have the corundum (α‐Al_{2}O_{3}) structure. The main features of the luminescence are explained in terms of the shifts, due to strain, of the chromium ion energy levels. Some experimental evidence for energy transfer among the optical centers is also presented.