Volume 75, Issue 2, 15 July 1981
Index of content:

Hyperfine and spin–rotational structure of CaBr X ^{2}Σ (v = 0) by molecular‐beam laser‐rf double resonance
View Description Hide DescriptionThe molecular‐beam, laser–rf, double‐resonance technique has been used to make high‐precision measurements of the spin–rotation and hyperfineinteractions in the X ^{2}Σ (v = 0) electronic ground state of Ca^{79}Br and Ca^{81}Br. The spin–rotation interaction is found to have a strong N dependence. The Frosch–Foley magnetic hyperfine parameters b and c and the electric–quadrupole hfs parameter e q Q are determined for both molecules.

Light scattering spectrum of a suspension of interacting Brownian macromolecules
View Description Hide DescriptionThe joint effect of direct and hydrodynamicinteractions on the dynamic structure S (k,t) of a solution of rigid macromolecules is examined. The initial slope dS/dt and initial curvature d^{2} S/dt^{2} of S(k,t) are obtained. The reference frame correction of Kirkwood e t a l. [J. Chem. Phys. 33, 1505 (1960)] is shown to be wave‐vector dependent. Contrary to some previous results, we argue that the initial slope of S(k,t) is partly due to direct interparticle interactions rather than being due entirely to free‐particle Brownian motion.

Molecular dynamics and spectra. II. Diatomic Raman
View Description Hide DescriptionThis paper and paper I in this series [P.H. Berens and K.R. Wilison, J. Chem. Phys. 74, 4872 (1981)] indicate that infrared and Raman rotational and fundamental vibrational–rotational spectra of dense systems (high pressure gases, liquids, and solids) are essentially classical, in that they can be computed and understood from a basically classical mechanical viewpoint, with some caveats for features in which anharmonicity is important, such as the detailed shape of Q branches. It is demonstrated here, using the diatomic case as an example, that ordinary, i.e., nonresonant, Raman band contours can be computed from classical mechanics plus simple quantum corrections. Classical versions of molecular dynamics, linear response theory, and ensemble averaging, followed by straightforward quantum corrections, are used to compute the pure rotational and fundamental vibration–rotational Raman band contours of N_{2} for the gas phase and for solutions of N_{2} in different densities of gas phase Ar and in liquid Ar. The evolution is seen from multiple peaked line shapes characteristic of free rotation in the gas phase to single peaks characteristic of hindered rotation in the liquid phase. Comparison is made with quantum and correspondence principle classical gas phase spectral calculations and with experimental measurements for pure N_{2} and N_{2} in liquid Ar. Three advantages are pointed out for a classical approach to infrared and Raman spectra. First, a classical approach can be used to compute the spectra of complex molecular systems, e.g., of large molecules, clusters, liquids,solutions, and solids. Second, this classical approach can be extended to compute the spectra of nonequilibrium and time‐dependent systems, e.g., infrared and Raman spectra during the course of chemical reactions. Third, a classical viewpoint allows experimental infrared and Raman spectra to be understood and interpreted in terms of atomic motions with the considerable aid of classical models and of our well‐developed classical intuition.

Polarization studies in multiphoton absorption spectroscopy
View Description Hide DescriptionUsing the principles of quantum electrodynamics, the theory of two‐, three‐, and four‐photon absorption in polyatomic gases and liquids is developed. Expressions are derived for the rates of single‐frequency absorption from plane polarized, circularly polarized, and unpolarized light. It is shown that for n‐photon absorption with n?3, the rate for unpolarized radiation is in each case expressible as a linear combination of the rates for plane polarized and circularly polarized light; no such relationship exists for four‐photon absorption. For each multiphoton process, it is demonstrated how the fullest information about the symmetry properties of excited states can be derived by a simple linear processing of the results from experiments with different polarizations. A detailed examination of the selection rules is made, based on a reduction of the molecular transition tensor into irreducible components, and a new classification scheme is introduced to assist with the interpretation of experimental results. Finally, it is shown that the theory may also be applied to resonance‐enhanced multiphoton ionizationspectroscopy.

Optical absorption and emission spectra of Cs_{2}NaHoCl_{6}
View Description Hide DescriptionOptical absorption and emission spectra are reported for the cubic Cs_{2}NaHoCl_{6} elpasolite system. Detailed energy and intensity analyses of the high‐resolution, variable‐temperature spectra allow characterization of the crystal field energy level structure associated with eleven of the Ho^{3+} term levels. The term levels included in these analyses are ^{5} I _{8}, ^{5} I _{7}, ^{5} F _{5}, ^{5} F _{4}, ^{5} S _{2}, ^{5} F _{3}, ^{5} F _{2}, ^{3} K _{8}, ^{5} G _{6}, ^{5} G _{5}, and ^{3} K _{7}. Intensity calculations are reported for both the pure magnetic dipole transitions and the vibronically induced electric dipole transitions associated with the ν_{3}(t _{1u }), ν_{4}(t _{1u }), and ν_{6}(t _{2u }) vibrational modes of the octahedral (O _{ h }) HoCl_{6} ^{3−} chromophoric moiety of the Cs_{2}NaHoCl_{6} system. The electric dipole intensity model used in these calculations includes contributions from both the s t a t i c‐c o u p l i n g and d y n a m i c‐c o u p l i n g Ho^{3+}‐ligand interaction mechanisms. Excellent agreement between observed and calculated intensities is found, and the theoretically calculated intensity results proved crucial to our detailed analysis and assignment of the observed spectra.

Luminescence and energy transfer in EuAl_{3}B_{4}O_{12}
View Description Hide DescriptionThe emission and excitation spectra of the Eu^{3+}luminescence and the energy transfer phenomena in single crystals of Gd_{1−x }Eu_{ x }Al_{3}B_{4}O_{12} (0<x?1) have been investigated using time‐resolved site‐selection techniques. In addition, the luminescence properties of single crystals and powders have been compared. The results show that in these compounds there are three major types of Eu^{3+} sites. Most Eu^{3+} ions are on the regular crystallographic sites, but a relatively high percentage of these ions are at nonregular (Al^{3+} and interstitial) sites. The crystals of EuAl_{3}B_{4}O_{12} show quenching at lower temperatures than do the powder samples. This behavior can be explained with the help of a model which takes into account diffusion‐limited migration within the regular Eu^{3+} system and quenching by transfer to Mo^{3+} impurities. These impurities are incorporated into the crystals unintentionally during their growth. The concentration quenching in the single crystals is quite strong and can be explained by means of the percolation concept. In the powder samples, however, the concentration and temperature quenching had less influence due to the relatively low concentration of the quenching centers in these samples. In all samples there was evidence of direct transfer from ’’nonregular’’ Eu^{3+} ions to ’’regular’’ ions. The critical transfer distance was derived.

The luminescence characteristics of 3‐hydroxyflavone as a function of pressure and viscosity
View Description Hide DescriptionThe effect of pressure on the emission of 3‐hydroxyflavone has been studied in isobutanol, glycerol, and two mixtures of these solvents. Below a viscosity of ∼50 P there is an increase in the fraction of emission from the tautomeric state with pressure. At higher viscosities the fraction of tautomeric emission decreased. At viscosities less than ∼50 P the lifetimes obtained from the two emission peaks were the same, indicating that the two excited states were in equilibrium. At higher viscosities, the lifetimes differed, indicating that the distribution was kinetically controlled. In hexamethylnonane (HMN) only tautomer emission was observed even at very high viscosities; also, only tautomer emission occurs in a rigid polyisobutylene film. A few measurements on 7‐hydroxyflavone are briefly discussed.

Magnetic relaxation study of solid ammonia–boron trifluoride complex
View Description Hide DescriptionProton and fluorine magnetic resonance absorption, and spin–lattice relaxation timemeasurements, have been carried out on crystalline ammonia–boron trifluoride complex in the temperature ranges from 4.2 to 300 K in the continuous wave method, and from 89 to 373 K using the pulse technique. The second moment results indicated that the BF_{3} motion is hindered at ∼200 K, as previously reported, while the NH_{3} group is considerably mobile at 77 K but an additional motion occurs at 4.2 K. The magnetization decay of ^{1}H and ^{19}F after a 180 ° pulse showed intrinsically nonexponential behavior. The T _{1} data, taken as the initial decay time constant, are compared with approximate theoretical estimates including three dissimilar spins. For the ^{19}F relaxation at high temperature, a set of three differential rate equations was reduced to a pair of two differential equations in which the effect of the third atom is taken into account in the diagonal coefficients. The temperature dependence was almost completely predicted by this treatment. Three dipolar contributions ^{19}F–^{19}F, ^{19}F–^{11}B, and ^{19}F–^{1}H were found to be 1.244, 2.420, and 0.222×10^{9} s^{−2} for the relaxation constants, respectively. A discrepancy between theory and experiment was observed in the ^{1}H relaxation data at high temperature and for ^{19}F at low temperature, both of which can not be explained by assuming a two‐dissimilar‐spins system and require the consideration of magnetic polarization in the third atom.

Vibronic intensities and rotational line strength factors for the three‐photon absorption spectrum of ammonia
View Description Hide DescriptionA perturbation theory approach is used to analyze the rovibronic structure of the three‐photon resonant absorption of ammonia. The vibronic selection rules are presented in a convenient pyramid mnemonic in terms of irreducible representations of the rotation group and of the D _{3h } point group. The analysis is presented for each possible situation, namely, all three photons are different, two photons are identical and one different, and all three photons are identical. The experimentally important case of three identical photons implies only two polarizations and two vibronic tensor elements for each symmetry type. With both the B̃ and C̃′ systems of ammonia one expects a ratio of 5 to 2 in the absorbance for circularly versus linearly polarized light for the N, O, S, and T branches. For the P, Q, and R branches one expects a 21 to 4 ratio of the weight‐1 versus weight‐3 tensor contributions to the C̃′ system in linearly polarized light (21 to 6 for B̃). Weight‐1 terms are absent with circularly polarized light. These predictions are confirmed experimentally. The complete set of rotational line strength factors for three‐photon absorption are given in algebraic form for the first time. The combination of vibronic factors, rotational line strengths, and statistical weights allows one to predict the three‐photon absorptionspectrum. Such calculated spectra are presented for ammonia at 45 K and they compare very favorably with the experimental spectra for both the B̃ system (a perpendicular band) and for the C̃′ system (a parallel band) in both linearly and circularly polarized light.

Avoided‐crossing molecular‐beam experiments on fluoroform (CF_{3}H) and fluoroform‐d (CF_{3}D)
View Description Hide DescriptionThe avoided‐crossing molecular‐beam method for studying normally forbidden (ΔK≠O) transitions in symmetric tops has been applied to fluoroform (CF_{3}H) and fluoroform‐d (CF_{3}D), thus marking the extension of the method to systems which are n o t near spherical rotors. In order to reach the high electric fields required while still retaining the necessarily narrow linewidth, the electric resonance spectrometer has been equipped with a new pair of Stark plates capable of providing electric fields up to about 20 kV/cm with a homogeneity of 1 part in 10^{5} over a length of 3 cm. The anticrossing (J,K) = (1,0)↔(1,±1) has been studied for both CF_{3}H and CF_{3}D. In each case, the rotational constantC _{0} along the symmetry axis has been obtained to 0.002%. From anticrossing spectra observed in combined electric and magnetic fields, the signs of the rotational g factors g_{∥} and g _{⊥} have been shown to be negative. From a conventional molecular beam study for each isotopic species, a value of the permanent electric dipole moment accurate to 60 ppm was determined and improved values of g _{∥} and g _{⊥} were obtained. The direction of the electric dipole moment is shown by two methods to be +HCF_{3}−. A brief discussion of the difficulties in these methods is given.

HF rotational laser emission through photoelimination from vinyl fluoride and 1,1‐difluoroethene
View Description Hide DescriptionRotational laser emission by HF has been observed at 33 frequencies between 325 and 1250 cm^{−1} from the flash photolysis (1.2 μsec FWHM) of vinyl fluoride and of 1,1‐difluorethylene. The transitions lie within the v = 0 to v = 5 manifolds and range from J ^{″}→J ^{′} = 8→7 to 31→30. Increasing the atomic weight or the partial pressure of the inert buffer gas (He, Ne, or Ar) raises the gain of nearly all transitions, showing that collisional relaxation processes are active in pumping the laser emission. The high gains displayed by both precursors in the J = 14→13 transitions for the v = 0,1,2, and 3 manifolds indicate that V→Renergy transfer is pumping molecules into the v ^{′}, J = 14 state from the near‐resonant v ^{′}+1, J = 2, 3, and 4 states. In a similar way, the highest J transitions J = 31→30 to 28→27 with v = 0 and/or 1, are best explained by V→Renergy transfer from near‐resonant low‐J states from much higher vibrational manifoldsv ^{′} = 4, 5, and 6. This would imply collision‐induced multiquantum energy transfer with large Δv (up to Δv = 5) and large ΔJ (up to ΔJ = 26) or a rapid succession of steps with smaller Δv and ΔJ. In contrast, the high gains displayed by the J = 10→9 transitions in the v = 0, 1, and 2 manifolds are best explained in terms of R→T relaxation from a uniform nascent population. While there are indications that the nascent rotational distributions provided by these photoeliminations probably furnish population to high J states, the gain patterns indicate that the V→R and R→T energy relaxation processes are strongly influential, the former surely involving multiquantum steps with large ΔJ and probably with Δv>1 as well.

Vibrational dynamics of glassy and molten ZnCl_{2}
View Description Hide DescriptionPolarized Raman spectra of ZnCl_{2} were obtained in the liquid phase near the melting point (T = 598 K), and in the glassy phase (T = 293 K). Measurements were performed down to a very low frequency shift (2 cm^{−1}) from the exciting line. Our analysis of the Raman data provides an interpretation of the collision‐like contribution in terms of a structural relaxation time in the picosecond range, while the phonon‐like contribution gives an effective Raman density of states. These results are also discussed in terms of existing structureal models.

Shape resonance effects in the photoabsorption spectra of BF_{3}
View Description Hide DescriptionMultiple‐scattering model calculations of cross sections for dipole transitions from all occupied orbitals of BF_{3} to excited bound states and continuum states of electron kinetic energy <30 eV are presented. The photoelectron angular distribution asymmetry parameters β are also given for all occupied orbitals. The boron and fluorine K‐shell calculations are in qualitative agreement with, and provide a clear interpretation of, the measured spectra. Two shape resonances are found in the low energy continuum: one of a ^{′} _{1} symmetry, the other of e′ symmetry. The resonances are found to be due to trapping of p waves on the fluorine atoms. This atomic localization as well as the dominance of low‐l partial waves outside the molecule put these shape resonances in a class distinct from those observed in diatomic molecules.

The rotational spectrum and molecular structure of the acetylene–HCl dimer
View Description Hide DescriptionThree isotopic species of a weakly bound T‐shaped π complex formed between acetylene and HCl have been observed through the assignment of their rotational spectra by the use of a pulsed, Fourier‐transform spectrometer with a high pressure gas being pulsed into an evacuated Fabry–Perot cavity. The spectra clearly show the complex to be a nearly prolate asymmetric top (κ = −0.9898) with the HCl on the a‐inertial axis and perpendicular to acetylene and with the hydrogen atom pointing towards the middle of the acetylene triple bond. The chlorine is situated, on average, 3.699 Å from the edge of the acetylene molecule. The following molecular constants have been obtained for the C_{2}H_{2}, H^{35}Cl isotopic species: The rotational constants are A = 36 084(838), B = 2481.065(6), and C = 2308.602(6) MHz; the nuclear quadrupole coupling constants are χ_{ a a } = −54.342(4), χ_{ b b } = 26.862(5), and χ_{ c c } = 27.480(9) MHz, and the rotational centrifugal distortion constants are D _{ J } = 7.9(4) and D _{ J K } = 497(8) kHz.

Rotational spectrum, structure, and intramolecular force field of the ArClCN van der Waals complex
View Description Hide DescriptionThe rotational spectrum of the ArClCN van der Waals complex has been assigned using pulsed Fourier transformmicrowave spectroscopy in a Fabry‐Perot cavity with a pulsed supersonic nozzle as the molecular source. ArClCN is T‐shaped and the data were fit to the Watson rotational parameters and an exact expression for the Cl and N nuclear quadrupole coupling. The spectroscopic constants for Ar^{35}ClCN are A′′ = 6152.5411(21) MHz, B′′ = 1577.0362(8) MHz, C′′ = 1246.7514(6) MHz, τ_{1} = −576.0(2) kHz, τ_{2} = −97.28(8) kHz, τ_{ a a a a } = −234.8(17) kHz, τ_{ b b b b } = −55.97(10) kHz, τ_{ c c c c } = −21.60(7) kHz, χ^{Cl} _{ a a } = 37.9468(23) MHz, χ^{Cl} _{ b b } = −79.5239(20) MHz, χ^{N} _{ a a } = 1.6403(22) MHz, and χ^{N} _{ b b } = −3.4571(20) MHz. The centrifugal distortion constants are used to derive the intramolecular force field and a normal coordinate analysis is performed. The Cl nuclear quadrupole coupling tensor indicates that the field gradients in ClCN are slightly perturbed upon complex formation but not enough to proscribe their use in structural determinations of weakly bound complexes.

Electron beam fluorescence spectrometry of internal state populations in nozzle beams of nitrogen and nitrogen/rare gas mixtures
View Description Hide DescriptionRotational level populations of N_{2} were measured downstream from the skimmer in beams of pure N_{2} and in mixtures of N_{2} with He, Ne, and Ar expanded from room temperature nozzles. The range of p _{0} D was from 5 to 50 Torr cm. The formation of dimers and higher condensates of beam species was monitored during the runs. The effect of condensationenergy release on rotational populations and parallel temperatures was readily observed. Two different methods for evaluating the rotational population distributions were compared. One method is based on a dipole‐excitation model and the other on an excitation matrix obtained empirically. Neither method proved clearly superior. Both methods indicated nonequilibrium rotational populations for all of our room temperature nozzle expansion conditions. Much of the nonequilibrium character appears to be due to the behavior of the K = 2 and K = 4 levels, which may be accounted for in terms of the rotational energy level spacing. In particular, the overpopulation of the K = 4 level is explained by a near‐resonant transfer of rotational energy between molecules in the K = 6 and K = 0 states, to give two molecules in the K = 4 state. Rotational and vibrational temperatures were determined for pure N_{2}beams from nozzles heated up to 1700 °K. The heated nozzle experiments indicated a 40% increase in the rotational collision number between 300 and 1700 °K.

Analysis of the Auger spectra of CO and CO_{2}
View Description Hide DescriptionThe electron‐excited gas phase carbon and oxygen Auger spectra of CO and CO_{2} are compared to the spectra calculated by a one‐electron theory. Calculated Auger transition intensities and energies are generally in good agreement with experiment. The disagreement between certain calculated intensities and experiment, however, illustrates those cases where configuration interaction can be expected to provide significant corrections to the one‐electron theoretical results. In addition, a comparison of calculated to experimental final state binding energies reveals the existence, in covalent molecules, of localized two‐hole final states in which two holes are always on the same site. A simple two‐electron theory predicts where such states will occur in the Auger spectra of homonuclear diatomic molecules.

Measuring differential cross sections using the Doppler shift
View Description Hide DescriptionWe discuss two methods, one of them new, for recovering level‐specific differential cross sections in crossed molecular beams experiments from the Doppler profiles of line shapes observed by laser induced fluorescence. The angular resolutions of the two methods are compared and shown to be complementary. An experiment using both methods can have moderately good angular resolution at all scattering angles. In the first method, which has previously been demonstrated experimentally, the Dopper profile is taken with the laser beam parallel to the relative velocity of the collision system. Good angular resolution is obtained between π/4 and 3π/4. In the second method, which is proposed here, the Doppler profile is taken with the laser beam perpendicular to this relative velocity, and the best angular resolution is obtained in the regions 0 to π/4 and 3π/4 to π. This method requires an integral transform to recover the cross section from the Doppler profile. A practical implementation of this transform is presented along with a numerical example showing its relative insensitivity to noise in the profile.

Reactions of Si^{+} with H_{2}O and O_{2} and SiO^{+} with H_{2} and D_{2}
View Description Hide DescriptionThe reaction of Si^{+} with H_{2}O to form SiOH^{+} has a measured rate constant of 2.3(−10) cm^{3} s^{−1} at 300 K. This is the major loss of Si^{+} ions in the Earth’s atmosphere above ∼90 km. The three‐body reaction of Si^{+} with O_{2} (in He) produces stable SiO_{2} ^{+} ions with a rate constant of 1(−29) cm^{6} s^{−1} at 300 K. The endothermic binary reaction of Si^{+} with O_{2} to produce SiO^{+} has been measured from threshold to ∼2 eV. The association of Si^{+} with O_{2} is the dominant loss process for Si^{+} ions below ∼90 km in the Earth’s atmosphere and leads to siliconoxidation to SiO_{2} since a large fraction of the SiO_{2} ^{+} ions are produced in excited states which charge transfer with O_{2} before relaxation. The reaction of SiO^{+} ions with H_{2} (and D_{2}) is found to have a thermal energy rate constant of 3.2(−10) cm^{3} s^{−1} [and 2.0(−10) cm^{−3} s^{−1}] to produce SiOH^{+} (and SiOD^{+}). This process has been suggested as a step in SiO production in the interstellar medium. The proton affinity of SiO is found to be 8.1±0.7 eV and the dissociation energy of SiO^{+} to be 4.8 eV and definitely less than 4.9 eV.

Laser‐collision induced chemical reactions: A comparison of quantum mechanical and classical model results
View Description Hide DescriptionWe compare the results of a classical model for the laser enhancement of the H+LiF→Li+HF reaction to accurate quantum mechanical results. Structure in the reaction probability as a function of collision energy below the fieldfree threshold predicted classically by Orel and Miller is found to be less pronounced in the quantum results. A much better understanding of the various causes of the observed maxima and also of the reliability of this classical model are obtained as a result of these calculations. A fundamental inconsistency in the classical model introduced when the Langer modification is made which can lead to unphysical results is discussed and a procedure for correcting this inconsistency is presented. Improved results are obtained.