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Volume 70, Issue 5, 01 March 1979

Analytic potential functions for weakly bound molecules: The X and A states of NaAr and the A state of NaNe
View Description Hide DescriptionThe interatomic potential functions for the ground and first excited electronic states of the weakly bound molecule NaAr and the first excited state of NaNe are derived by inverting spectral data to analytic potential functions. Using the Thakkar potential expansion, it is shown how one may deduce vibrational assignments, compute accurate dissociation energies, and combine two potentials with an atomic transition to advantage. The resulting potential functions are in excellent agreement not only with spectroscopic data, but also with potentials derived from scattering and atomic resonance line broadening experiments.

Estimation of the dissociation energy of weakly‐bound molecules from spectroscopic data
View Description Hide DescriptionExpressions for the dissociation energy of the Morse potential and the Lennard‐Jones (2n,n) potential are derived in terms of low‐order mechanical constants of diatomic molecules. These expressions are related to a more general series expansion of the potential, and a new expression for the dissociation energy of a weakly bound diatomic is derived. This expression contains B _{ e’}α_{ e’} and the power of R ^{−1} which leads a long‐range expansion of the potential. The expression is accurate to a few percent when compared to reliable experimental values and should be of value when only a limited number of spectral constants can be obtained from experiment.

ν_{3} mode absorption behavior of CO_{2} laser excited SF_{6}
View Description Hide DescriptionInfrared–infrared double resonance measurements of the SF_{6} ν_{3} mode spectral region for excitation levels of up to 1.2 J/cm^{2} are reported. Immediately following the pump laser excitation, the induced absorptionspectrum of the ν_{3} mode shows a pronounced red shift. The spectrum then shifts to shorter wavelengths on a time scale of several microseconds, showing a cooling of the ν_{3} mode. At an excitation level of 3 photons/molecule the measuredspectra approach the thermal spectrum expected for complete vibrational energy thermalization among all of the vibrational degrees of freedom on a time scale of 3±2 μsec. At higher excitation levels (∼10 photons/molecule) the induced spectrum still shifts on a comparable time scale but is broader than a thermal spectrum. At the lower fluence levels (∼3 photons/molecule), a ν_{3} mode temperature can be assigned to the spectra. The time evolution of this temperature exhibits only a weak pressure dependence. A much broader induced absorption band, approximately a factor of 100 weaker than this ’’hot’’ ν_{3} mode absorption, has been observed extending more than 100 cm^{−1} to the high frequency side of the ν_{3} mode absorption band. The spectral dependence of this absorption band is in qualitative agreement with the multiphoton excitationspectrum found in two‐frequency dissociation experiments.

A high‐pressure conductivity and laser Raman spectroscopic study of aqueous orthophosphate solutions at 25 °C
View Description Hide DescriptionConductivities of aqueous solutions of H_{3}PO_{4}, KH_{2}PO_{4}, and Na_{3}PO_{4} (0.001–1 M), and Raman spectra of 0.1, 0.5, 10, and 15.5 M H_{3}PO_{4}, 1 M KH_{2}PO_{4}, and 0.1M Na_{3}PO_{4}, have been obtained at 25 °C, and pressures up to 200 MPa. Pressure enhanced the first dissociation of H_{3}PO_{4} (κp/κ_{⊥}, measured by conductivity vs [H_{3}PO_{4}] goes through a maximum), and reduced the extent of hydrolysis of Na_{3}PO_{4}. Volume changes for the first and third dissociations of H_{3}PO_{4} were ΔV _{1}=21±4 cm^{3} mol^{−1} (conductivity), −18±3 (Raman, 0.1 M H_{3}PO_{4}), −8±2 (Raman, 0.5 M H_{3}PO_{4}), and ΔV _{3}=−36±3 (Raman, 0.1 M Na_{3}PO_{4}). Both Raman and conductivity studies of H_{2}PO_{4} ^{−} were consistent with the presence of hydrogen‐bonded phosphate dimers, H_{4}P_{2}O_{8} ^{2−}, with a formation constant of 2–3 l mol^{−1} (conductivity), and ΔV?0 cm^{3} mol^{−1} (conductivity). This ΔV value agreed with the Raman study which indicated only a very small decrease in dimerization with increasing pressure.

A study of 3d→4s transitions by modulation spectroscopy
View Description Hide DescriptionIn order to gain further information on the 3d→4s transitions of transition metal ions (V^{++}, Mn^{++}, and Co^{++}) in host crystals both the magnetic circular dichroism (in KMgF_{3}) and the linear dichroism (in MgF_{2}) were studied. A quantitative interpretation of the results shows the following: the transitions are promoted by t _{ i u }‐type modes and the intensity comes from the nearby 3d→4p transitions; the zeroth moment of linear dichroism is heavily dependent upon the modification by the crystal of the vibronic matrix elements connecting the 4p and 4s states. The orthorhombic perturbation parameters of the 3d ^{ n−1}4s states in MgF_{2} host are not the same as those of the 3d ^{ n } states. The symmetry assignments of the 3d ^{ n−1}4s states are confirmed.

Evidence for a very slow transformation in ice VI at low temperatures
View Description Hide DescriptionThe high‐frequency permittivity of ice VI decreases steadily at 123.1 K and increases again when warmed to 127.8 K. There is therefore a new transformation occurring slowly in this region. The transformation of samples of H_{2}O, D_{2}O, and 1% D_{2}O in H_{2}O was followed for 252 days, and it was not yet completed. The experimental conditions were within the region of stability of ice VI, so the transformation is not to a known phase of ice. It was too slow to be an ordering transformation determined by the dielectric relaxation time, and it is likely that a wholly new phase was being produced.

Longitudinal nuclear relaxation of an ABX spin system application to a ^{13}C–^{13}C–^{1}H fragment with and without proton irradiation
View Description Hide DescriptionThe longitudinal relaxation and the nuclear Overhauser enhancement, relative to the A and B transitions of an ABX spin system, are studied theoretically. A complete treatment based on density tion of X transitions. Assuming a doubly enriched fragment of the type O=^{13}C_{ A }–^{13}C_{ B }–^{1}H_{χ}, numerical simulations have been performed with the aim to study the effects of cross‐correlation spectral densities and motional anistropy. For the example considered, the initial slopes of carbonyl lines recovery curves yield a wealth of information. This interesting behavior arises from mixing effects produced by the observing pulse. The other data (recovery curves and NOE factors) can be, to a good approximation, interpreted in terms of generalized Solomon equations. These latter conclusions are however valid regarding the geometry of the considered fragment and, in the general case, cross‐correlation terms must be taken into account.

Threshold photoelectron spectra of atmospheric molecules. I. Description of method and application to H_{2}, D_{2}, and N_{2}
View Description Hide DescriptionThreshold photoelectron spectra (TPES) are presented for H_{2}, D_{2}, and N_{2} with a resolution of 28 meV full width at half maximum. The results are compared with Franck–Condon transition probabilities, previous TPES and electron attachment threshold photoelectron spectra. Peaks in the TPES not predicted by Franck–Condon calculations are explained by autoionization processes. These processes in N_{2} make possible the observation of vibrational levels of the ions not visible spectroscopically or in photoelectron spectra. A shift of the TPES peaks in N_{2} toward lower energy is explained by conversion of rotational energy in the ionization transition. Peaks between the v=O and v=1 vibrational levels of the X ^{2}Σ_{ g } ^{+} state of N_{2} ^{+} consist of near monoenergetic electrons implying little or no change in the rotational quantum number in the autoionization process.

Power law scaling for rotational energy transfer
View Description Hide DescriptionWe have applied a new scaling law to several sets of rotational energy transfer cross sections. The new law asserts that the square of the T‐matrix depends on the amount of energy transferred as a power law. Two different kinds of angular momentum statistics are assumed, one corresponding to m _{ j } being conserved and the other corresponding to m _{ j } being completely randomized. Numerical fits are presented which demonstrate that the data follow the power law better than the widely used exponential gap law.

The solvent effect on di‐t e r t‐butyl nitroxide. A dipole–dipole model for polar solutes in polar solvents
View Description Hide DescriptionNew measurements of the solvent effect on the nitrogen hyperfine coupling constant of di‐t e r t‐butyl nitroxide are reported. These, together with literature data, are used to test various models for the solvent effect. At the Hückel level of approximation, a_{N} is a linear function of the applied electric field. Thus various reaction field theories may be considered. The widely used Onsager reaction field does not account for the effects of the more polar solvents or for the differences between polar and nonpolar solvents. The Wertheim and Block–Walker reaction fields are better, especially for very polar solvents. However none of these continuum reaction fields is entirely satisfactory theoretically or experimentally. We propose a dipole–dipole model for polar solvents which is superior to the continuum models. From the dipole–dipole model, we suggest that the quantity μρ/M is a convenient linear parameter for polar solvent effects, the factors being solventdipole moment, density, and molecular weight. The dipole–dipole model should apply to a wide range of polar solutes. Some special situations are not explained by the model, including hydrogen‐bonding solvents, halogenated aromatics, and solvents with more than one conformation. The temperature dependence of the solvent effect is also considered.

ESR and ENDOR study of x‐irradiated single crystals of β‐alanine at room temperature
View Description Hide DescriptionThree radicals have been identified in the room temperature ESR spectra of x‐irradiated single crystals of β‐alanine (N^{+}H_{3}CH_{2}CH_{2}CO^{−} _{2}). ENDOR spectra from one radical exhibit hyperfine coupling to 1 α‐proton (A _{ x x }=−33.12, A _{ y y }=—20.68, A _{ z z }=−10.50 G) and 2 β‐protons [A _{iso}(H_{β1}) =13.24 G, A _{iso}(H _{β2}) =4.89 G]. From the anisotropic nature of the α‐proton coupling it has been determined that these splittings arise from a N^{+}H_{3}CH_{2}ĊHCO^{−} _{2} radical. It has been shown that this radical is the decay product of the unstable low temperature oxidation product. A second room temperature radical, N^{+}H_{3}CH_{2}CH_{2}Ċ=0, has been shown to be a decay product of the primary reduction product. A minor room temperature product has been tentatively identified as a ĊH_{2}–CH_{2}–R radical.

Photoionization of ethylene clusters
View Description Hide DescriptionThe energetics of the ethylene ion–molecule reactions has been investigated in more detail than previously possible in two body collision experiments by photoionization of the neutral van der Waals ethylene dimer. The stability of the ion–molecule collision complex (18.2±0.5 kcal) as well as the highest potential barrier along the reaction coordinate for decomposition have been determined for this exothermic reaction. In a similar manner, the energetics of the solvated ethylene ion has been investigated by photoionization of the ethylene trimer.

A study of the thermal polymerization of styrene by depolarized Rayleigh light scattering spectroscopy
View Description Hide DescriptionThe technique of depolarized Rayleigh light scattering spectroscopy has been applied to follow the kinetics of the thermal polymerization of styrene. By measuring the spectrum of the depolarized scattered light we are able to separate the intensity of light scattered by the polymer being formed from the intensity of light scattered by the monomer. The spectrum consists of a wide Lorentzian due to the monomer and a central spike with instrumental width due to the polymer. This separation occurs because the polymerrelaxation time which is determined by the longest Rouse–Zimm mode or by overall rotation is four orders of magnitude longer than the relaxation time of the monomer which is governed by overall rotation. Using the intensity data, the initial rate of the polymerization reaction is measured and is found to agree with the rate determined in previous experiments using classical techniques. After about one‐third of the reaction is complete, the rate increases by 50%. This increase in rate is interpreted as resulting from the large increase in viscosity preventing the termination of the reaction by coupling of polymer radicals. Also the rotational relaxation time of the monomer is determined for the first 80% of the reaction and is found to increase linearly with time. However the value of the monomer rotational relaxation time at 80% of reaction is only 1.5 times the inital value. This indicates the monomer rotational motion is not determined by the large macroscopic viscosity, but by a local viscosity in the region of the monomer.

Forbidden Raman scattering processes. I. General considerations and E1–M1 scattering
View Description Hide DescriptionThe generalized theory of forbidden Raman scattering processes is developed in terms of the multipole expansion of the electromagnetic interaction Hamiltonian. Using the general expressions, the theory of electric dipole–magnetic dipole (E1–M1) Raman scattering is derived in detail. The ^{1} S _{0}→^{3} P _{1} E1–M1 Raman scattering cross section in atomic magnesium is calculated for two applicable laser wavelengths using published f‐value data. Since resonantly enhanced cross sections larger than 10^{−29} cm^{2}/sr are predicted it should be possible to experimentally observe this scattering phenomenon. In addition, by measuring the frequency dependence of the cross section near resonance, it may be possible to directly determine the relative magnitudes of the A⋅p and A⋅A contributions to the scattering cross section. Finally, possible applications of the effect in atomic and molecular physics are discussed.

Spectral line parameters of the ν_{4} s ^{ R } R (8,3) transition of NH_{3} using a CO laser
View Description Hide DescriptionThe close coincidence between the 13–12 P (8) CO laser line and s ^{ R } R (8,3) transition in the ν_{4} band of NH_{3} is used to find the spectral parameters of the absorbing line by fitting the Doppler and Voigt shapes to the appropriate regions of the transmittance curves. The self‐broadening parameter (linewidth) is found to be (8.11±0.43) ×10^{−4} Torr^{−1} cm^{−1}. The foreign gas broadening coefficient with respect to N_{2} is measured to be 5.28±.90. The frequency offset between the laser and the center of the transition is determined to be approximately half the full Doppler width. From the line strength measurement, δμ/δQ is found to be 6.3±1.8 esu, approximately 20% smaller than that derived in an earlier determination based on total band strength, rather than that of a single line as is done here. The difference may be due in part to the unavoidable inclusion in the earlier work of the overlapping 2ν_{2} band.

Entropy of a quantum square‐well potential gas at low temperatures
View Description Hide DescriptionWe calculate the quantum second virial coefficients and their contributions to the canonical entropy for two‐ and three‐dimensional systems interacting with a hard‐core square‐well potential. This provides three examples of quantum mechanical systems in which the canonical entropy becomes greater than the canonical entropy for the corresponding ideal (noninteracting) systems over a finite temperature interval when Boltzmann statistics is assumed, thus contradicting the conjecture of Baierlein. In addition, low temperature expansions of the second virial coefficient and its contributions to the canonical entropy are made for the general three‐dimensional system in powers of the (reduced) temperature.

LEED analysis of acetylene and ethylene chemisorption on the Pt(111) surface: Evidence for ethylidyne formation
View Description Hide DescriptionThe stable surface species formed from the chemisorption of acetylene (C_{2}H_{2}) or ethylene (C_{2}H_{4}) on the Pt(111) surface (T∼300–350 K) has been studied by a low‐energy electron diffraction intensity analysis. High resolution electron energy lossspectra reported by Ibach e t a l. have been interpreted by comparison to infrared data on relevant model compounds. The surface species most consistent with these studies is ethylidyne ( C–CH_{3}). The species is coordinated to a threefold surface site with the C–C axis normal to the surface within an uncertainty of ∼15°. A saturated C–C bond length of 1.50±0.05 Å and three equivalent Pt–C bond lengths of 2.00±0.05 Å are determined by the LEEDanalysis and are consistent with the reported structures of ethylidyne in organometallic clusters. The ethylidyne group forms readily upon exposure of C_{2}H_{4} to the Pt(111) surface at T∼300 K with the loss of one hydrogen atom per ethylene. The complete conversion of C_{2}H_{2} to ethylidyne requires the presence of hydrogen atoms and proceeds rapidly at T∼350 K. By comparison to reported reaction mechanisms on related transition metal clusters it seems likely that vinylidene ( C=CH_{2}) is an intermediate in both reactions.

Electron impact spectra of methane, ethane, and neopentane
View Description Hide DescriptionElectron impact spectra of methane, ethane, and neopentane have been obtained at scattering angles of 0° and 90° and at impact energies from ?30 to 250 eV. The data are consistent with the lowest excitation in all of these systems to involve promotion of an electron to a 3s Rydberg‐like orbital. Differences between 0° and 90° onsets are attributed to large‐angle intensity enhancements of transitions to the 3sRydberg triplets. At 90° all of the spectra exhibit very similar intensity redistributions with strong enhancement of transitions in the 12 and 15 eV region as compared to lower‐lying transitions. Assignments of the spectra and possible origins of the angular dependence are discussed.

Magnetic circular dichroism spectra of decacyclene and hexabenzocoronene
View Description Hide DescriptionThe magnetic circular dichroism(MCD)spectra of decacyclene (I) and hexabenzocoronene (II) have been measured. The absorption spectra of I and II located in the lowest wavenumber region (22–30×10^{3} cm^{−1}) were assigned by using the MCDspectra and the results of the SCF screened potential π‐MO CI calculations. The ^{1} E′ and ^{1} E _{ l u }excited states of I and II are located at 26.5 and 26.1×10^{3} cm^{−1}, respectively. The calculated Faraday A/D values for these excited states agreed well with the experimental values both in signs and in magnitudes. The calculated Faraday B values for these excited states tended to be larger than the experimental values.

A statistical theory of three‐body ion–molecule reactions
View Description Hide DescriptionA theory of three‐body ion–molecule reactions at low pressures which incorporates the principle of detailed balancing is presented. Agreement between theory and recent experiments on a variety of polyatomic reactive systems is assessed and found to be satisfactory.