Index of content:
Volume 64, Issue 8, 15 April 1976

Resonance fluorescence study of the gas phase reaction rate of nitric oxide with molecular fluorine
View Description Hide DescriptionResonant fluorescent scattering of uv light absorbed by the 0,0 transition of the nitric oxide γ band at 226 nm was used to detect the decrease in NO concentration due to reaction with F_{2} in a standard flow tube geometry. Rate measurements were performed under pseudo‐first‐order conditions with F_{2} in excess at temperatures between 168 and 359 °K. These measurements yielded a temperature dependent bimolecular rate constant for the reaction of NO with F_{2} of 7.0×10^{−13} exp(−1150/T) with an estimated accuracy of ±30%.

Interaction potentials for He–HF and Ar–HF using the Gordon–Kim method
View Description Hide DescriptionInteraction potentials computed by the method of Gordon and Kim are presented for the He–HF and Ar–HF systems. Results are given at five angles and five HF distances for 12 He–HF separations and 14 Ar–HF separations, spanning both the shallow attractive well and part of the repulsive core in each case. Agreement with variationally determined results for He–HF reported previously is very good and similar accuracy is expected for the Ar–HF results. These potentials should therefore be suitable for scattering calculations.

Gas‐phase electron paramagnetic resonance absorption in nitric oxide. II. The effects of nitrogen‐15 and oxygen‐17 and 18 substitution
View Description Hide DescriptionThe X‐band EPR investigation of the six isotopically related molecules of nitric oxide synthesized from ^{14}N, ^{15}N, ^{16}O, ^{17}O, and ^{18}O has been completed. Perturbation theory applied to Hund’s case (a) representation for nitric oxide yielded excellent agreement with experiment. Linear relationships were found between the g values and the reduced mass, and between the field uncoupling splittings and the reciprocal of the reduced mass, which is indicative of the relationship of these values to the rotational constant,B _{0}. The value of the spin orbit coupling constant was determined to be 123.27 cm^{−1} in agreement with the value of James and Thibault (Ref. 7), 123.16±0.020 cm^{−1}. The nitrogen‐15 hyperfine splitting constant was found to be 38.41±0.19 G. The oxygen‐17 hyperfine lines revealed a measurable quadrupoleeffect and the oxygen‐17 hyperfine splitting constant was determined to be 57.6±0.4 G.

Heat‐pipe‐oven reactor (HPOR): I. A new device for flame studies; photon yields in the reaction of Na with CCl_{4} and N_{2}O
View Description Hide DescriptionA new device based on the heat‐pipe oven has been demonstrated to have a unique capability for studying reactions of metal atoms with oxidizers. This device allows spherical diffusionflame studies under known, uniform, and easily adjustable, metal atom concentration. low gas pumping rate, clean window operation, and minimized problems of reactive solid disposal. The reactor was used for the study of chemiluminescence of the reactions of sodium vapors with CCl_{4}, with N_{2}O, and with both CCl_{4} and N_{2}O. The emission from these reactions in the range 2000–9000 Å was identified to be from various excited atomic levels of sodium and from excited C_{2}, mostly in the Swan bands. Even though the emission was very intense, especially in the case of Na+N_{2}O+CCl_{4}(photon yields of about 10%), it was found that the Na excited‐state populations had a Boltzmann distribution corresponding to an electron temperature of 2260 °K. This suggests that the emission of sodium radiation from both the Na+CCl_{4} and Na+CCl_{4}+N_{2}O flames results from V→E transfer from vibrational reservoir states. In the former case, the excitation mechanism must involve energy pooling of C_{2} ^{‡} with either C(^{1} D) or Na(3p) atoms, while in the latter case, CO^{‡} contributes as well. Sodium resonance radiation from the Na+N_{2}O flame is believed to result from secondary reactions of oxygen atoms.

The multipole Hamiltonian and magnetic circular dichroism
View Description Hide DescriptionThe Power–Zienau–Woolley transformation in molecular quantum electrodynamics is carried out for a molecule in an external static magnetic field. From the gauge‐independent multipole Hamiltonian thus obtained the Einstein B coefficients for the absorption of left and right circularly polarized photons by an oriented molecule in a uniform magnetic field are evaluated. The B coefficients are related to the macroscopic absorption coefficients by treating the line shapes phenomenologically and by introducing a Boltzmann factor. A familiar expression for magnetic circular dichroism in a dilute medium is thereby recovered; the calculation is extended beyond the electric dipole approximation so as to include the leading contribution of natural circular dichroism. A simple use of the appropriate Kramers–Kronig dispersion relation leads to the deduction of the optical rotatory dispersion, both natural and magnetic, in spectral regions far removed from absorption bands.

On the relation between collinear and three dimensional collision rates with applications to vibrational energy transfer
View Description Hide DescriptionA simplistic procedure for the generation of three dimensional rate constants is introduced and applied to vibrational energy transfer. The method is based on correcting for the different volumes in phase space available to the products of a collinear and a 3‐D collision. Explicit expressions are derived for the 3‐D distribution of final vibrational states and the effect of reagent vibrational excitation on the rate for collisions where the initial translational (and rotational) energy is thermally distributed. The procedure is applied to an exactly soluble collinear model of vibrational excitation. The resulting 3‐D detailed rate constants are shown to correspond to an exponential decay of the bulk mean vibrational energy. The temperature dependence of the rates is compared to experimental results for the He–CO, Ar–HCl, He–HCl, and He–H_{2} systems. A surprisal analysis of the rates conforms to an ’’exponential gap’’ representation.

Nonadiabatic transitions induced by a time‐dependent Hamiltonian in the semiclassical/adiabatic limit: The two‐state case
View Description Hide DescriptionWe show rigorously, within the two‐state approximation, that in the semiclassical limit h/→0 a nonadiabatic transition induced by an analytic time‐dependent Hamiltonian is localized to the vicinity of a complex crossing of the two adiabatic potential curves, with transition amplitude independent of the nonadiabatic coupling and given by a simple formula of A. M.Dykhne.

Mass‐spectral study of CF_{3}I and C_{3}F_{7}I photolysis
View Description Hide DescriptionA mass‐spectrometric method for study of the photodissociation of alkyl iodides is developed. It permits the observation of iodine atom concentrations both in the ground and in electronically‐excited states. The rate constant of iodine quenching in molecular oxygen is obtained. The relative yields of 5 ^{2} P _{1/2} iodine in the photolysis of CF_{3}I and n‐C_{3}F_{7}I are compared.

Oscillator strengths for transitions involving excited states not lowest of their symmetry: NitrogenI and nitrogenII transitions
View Description Hide DescriptionTheoretical f values are reported and compared to experiment for the 1134 and 1200 Å transitions of NI and the 660, 746, 747, and 858 Å transitions of NII. These involve states which are not the lowest of their symmetry. These results are obtained with the nonclosed shell many electron theory of Sinano?lu and the proper application of the Hylleraas–Undheim–MacDonald theorem. The results of this work are in much better agreement with experiment than Hartree–Fock calculations and other results found in previous literature.

Vibrational progressions in vibronically induced transitions
View Description Hide DescriptionIt is shown that progressions of totally symmetric vibrations in vibronically induced spectra do not show the same intensity distribution as comparable progressions in allowed spectra. This is due to cross terms, involving both totally symmetric and inducing mode coordinates, in the Herzberg–Teller expansion. These cross terms express the modulation of the vibronic coupling resulting from differences in interatomic distances between the borrowing and lending states. The effect is universal, as opposed to effects based on normal‐coordinate rotation or totally symmetric inducing modes, and enters even in the absence of anharmonic coupling. It leads to anomalous intensity distributions which, moreover, are different for emission and absorption spectra. Quantitative estimates are presented which indicate that it should be readily observable in many molecules.

ESR line shape studies of trapped electrons in γ‐irradiated ^{17}O enriched 10M NaOH alkaline ice glass: Model for the geometrical structure of the trapped electron
View Description Hide DescriptionThe ESR line shape and width of a trapped electron (e _{ t } ^{−}) has been measured in 34% ^{17}O enriched 10M NaOH alkaline ice glass at 77 K. The second moment of e _{ t } ^{−} due to ^{17}O coupling is 134 G^{2}. Analysis of the second moment contributions from ^{17}O coupling together with the constraint from electron spin echo studies that the e _{ t } ^{−}–O distance is greater than 2 Å show that the e _{ t } ^{−}–^{17}O hyperfine coupling is mainly isotropic. Simulation of the e _{ t } ^{−}ESR line under these constraints on ^{17}O coupling and previous ones determined for H or D coupling for various numbers n of equivalent water molecules in the first solvation shell of e _{ t } ^{−} give a best fit to the experimental line shape for n=6. For n?4 definite structure would be expected in the e _{ t } ^{−} line shape which is not seen experimentally. The n=6 result together with previous data allows a rather complete geometrical description of the trapped, hydrated electron to be defined.

Oxygen wagging and ring puckering in ? ^{1} A _{2} cyclobutanone
View Description Hide DescriptionAnalysis of the near ultraviolet spectrum of cyclobutanone shows that in its excited state the oxygen atom is bent out of the C_{2}C_{1}C_{4} plane, producing an inversion doubling of the carbonyl out‐of‐plane mode in the excited state. The out of plane angle is 39° at the potential minimum, from a fit to the eigenvalues for a quadratic Lorentzian‐type potential function. The barrier to inversion of the varbonyl group in the excited state is 1550 cm^{−1}. The interval of 98 cm^{−1} which is observed throughout the spectrum is assigned as a v′=1, v ^{″}=1 sequence transition in the ring puckering mode Q _{20}, from which we have ν′_{20}=134 cm^{−1}, compared to the ground state value of ν^{″} _{20}=36 cm^{−1}. The quartic + quadratic potential for the upper state, which was evaluated from this data, was found to contain only a single minimum, which indicates that the C_{1}C_{2}C_{3}C_{4}carbon atoms are coplanar in this state. CNDO‖2 potential energy curves for the C_{1}C_{3} and C_{2}C_{4}ring puckering coordinates in the two electronic states were found to predict correctly the trends in the spectroscopically derived potentials. The eigenvector coefficients from the CNDO‖2 calculation were subjected to a Mulliken population density analysis. The bond density differences obtained in this calculation attribute the large increase in ring strain energy which occurs on electronic excitation to transannular interaction in the C_{2}C_{4} direction.

Negative ENDOR study of an irradiated single crystal of triglycine sulfate and its ferroelectric phase transition
View Description Hide DescriptionWith the use of the negative ENDOR technique an x‐ray irradiated crystal of triglycine sulfate was studied over the temperature range from 170 to 420 K (T _{ c }=322 K). Within the 11–17 MHz frequency range, signals from more than four different types of protons were detected. Each of these proton signals including the one from H_{7} is a singlet when T≳T _{ c }, while the signal splits into a double when T<T _{ c }. Although the splitting depends on temperature, no evidence for line broadening was detected. This temperature behavior was explained in terms of a simple quantum‐tunneling process, the exchange integral (Γ) of which was estimated to be 10^{2} cm^{−1} in order of magnitude.

Diatomic molecules as perturbed Morse oscillators. I. Energy levels
View Description Hide DescriptionA formula is obtained for the rotational–vibrational energy levels of a diatomic molecule using a perturbed Morse potential V (r) =V _{ e }[(1−e ^{−a q })^{2}+b _{4}(1−e ^{−a q })^{4} +b _{5}(1−e ^{−a q })^{5}+⋅⋅⋅], along with additional perturbations describing rotational energy. Results are equivalent to Dunham’s formulas, but have superior convergence properties for analyzing spectra. How to choose the ’’best’’ unperturbed Morse potential and how to evaluate perturbation parameters are briefly discussed. Formulas are applied to the ground state of CO, and results are compared with those for RKR and other potentials.

Calculation of one‐ and two‐electron molecular properties by the method of diatomics‐in‐molecules
View Description Hide DescriptionA procedure is proposed for extending the diatomics‐in‐molecules approach to the calculation of one‐ and two‐electron properties of polyatomic molecules. The method requires an input knowledge of appropriate one‐ and two‐electron properties of the isolated atomic and diatomic fragments. Selected one‐electron properties of CH_{2}(^{3} B _{1}) are computed as an illustration. Results are in good agreement with those of an a b i n i t i o study reported by Langhoff and Davidson.

Ultraviolet emission in O^{+}–H_{2} reactive scattering
View Description Hide DescriptionLuminescence resulting from O^{+}–H_{2} collisions at relative energies between 1.5 and 35 eV has been studied in order to identify internal energy states of product species; A→X transitions of OH and OH^{+} are observed. Metastable states of reactant O^{+} are shown to be responsible for the production of these excited species at low relative energies; ground state O^{+} ions may contribute to the OH^{+}(A ^{3}Π) yield when sufficient kinetic energy is available to surmount the energy barrier that probably exists in addition to the thermochemical endoergicity of the process. Ground state O^{+} does not appear to be a major factor in the formation of OH(A ^{2}Σ^{+}). These conclusions are consistent with the nature of the potential energy surfaces of H_{2}O^{+} inferred from an electronic state correlation diagram.

Coherent energy migration in solids: Determination of the average coherence length in one‐dimensional systems using tunable dye lasers
View Description Hide DescriptionThe coherent nature of energy propagation in solids at low temperatures was established from the time resolved response of the crystal to short optical pulses obtained from a dye laser (pumped by a nitrogen gas laser). The trapping and detrapping of the energy by shallow defects (x traps) was evident in the spectra and enabled us to extract the coherence length: l≳700 ?=186 m o l e c u l e s f o r t h e o n e‐d i m e n s i o n a l t r i p l e t e x c i t o n s o f 1,2,4,5‐t e t r a c h l o r o b e n z e n e c r y s t a l s a t T<4.2 °K. This length which clearly exceeds the stochastic random walk limit is related to the thermalization mechanisms in this coupled exciton–trap system, and its magnitude supports the notion that exciton–phonon coupling is responsible for the loss of coherence on very long molecular chains (trap concentration is 1/256 000).

Continuum and bound molecular electronic wavefunctions for generalized multiple‐scattering potentials
View Description Hide DescriptionExisting multiple‐scattering treatments of bound and continuum electronic states of molecules are restricted to monopole potentials in the various spherical regions. We extend the treatment within these regions to a general potential. The corresponding multiple‐scattering equations should facilitate accurate treatment of, e.g., effects of the buildup of charge between atomic centers due to bonding, of the dipole character of polar molecules, and of external fields.

Optical intensities of holmium in tellurite, calibo, and phosphate glasses
View Description Hide DescriptionThe intensities of the electric dipole transitions of Ho^{3+} in three oxide glasses have been obtained from the absorption spectra in the visible and ir for tellurite glasses, and in the uv, visible, and ir parts of the spectrum for calibo and phosphate glasses. From the experimental values of the oscillator strengths and calculated matrix elements, the Judd–Ofelt intensity parameters were obtained by least‐squares analysis. Radiative transition probabilities from the emitting (^{5} S _{2}, ^{5} F _{4}) and ^{5} F _{5} levels to all lower states were calculated using these parameters. Emission and excitation spectra and the decay times of the (^{5} S _{2}, ^{5} F _{4}) fluorescence were measured. It was found that the fluorescence in tellurite glass has intensities two orders of magnitude higher than in the other two oxide glasses. A concentration dependence study of the fluorescence in tellurite glass was performed. A mechanism for the quenching is proposed.

Complex scaling in two‐center wavefunctions
View Description Hide DescriptionIn the solution of the three‐body problem by the Born–Oppenheimer separation it is necessary to scale the electronic wavefunctions in order to produce asymptotically correct internuclear potentials. In general, two different scalings are necessary for any particular three‐particle system, corresponding to the two different atoms into which the system may dissociate. Such dual scaling is mandatory for applications to reactive scattering involving both of the different atoms. In the case of equally charged nuclei of unequal mass, the scale parameters are complex numbers.