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Volume 84, Issue 11, 01 June 1986

Rotational spectrum and structure of CF_{3}H–NH_{3}
View Description Hide DescriptionThe rotational spectrum of CF_{3}H–NH_{3} has been obtained using a pulsed nozzle Fourier transformmicrowave spectrometer. A symmetric top spectrum is observed that is consistent with free internal rotation of the NH_{3} subunit against the CF_{3}H subunit. Rotational transitions have been measured for both the ground and first excited internal rotor state of the complex. The spectroscopic constants which have been obtained include: B _{0}=1996.903(2) MHz, D _{ J } =3.46(12) kHz, and e Q q ^{N} =−3.186(8) MHz. From the quadrupole coupling constant of the nitrogen nucleus, e Q q ^{N}, the bending amplitude of the NH_{3} unit is determined to be 22.57(10)°. The hydrogen bond length is 2.314(5) Å and the weak bond stretching force constant is 0.066(2) mdyn/Å. The bond length and stretching force constant for CF_{3}H–NH_{3} are similar in value to those determined for HCCH–NH_{3} (2.33 Å and 0.070 mdyn/Å, respectively).

Transient electric birefringence of dilute rigid‐body suspensions at low field strengths
View Description Hide DescriptionTransient electric birefringence expressions are derived in the Kerr limit of low field strengths for a dilute monodisperse suspension of arbitrarily shaped rigid bodies. A body is characterized by its diffusiontensors, its optical anisotropytensor, its permanent and instantaneously induced electric dipoles, and its electric charge; no special relation is assumed to hold between these quantities. We specifically allow for charged macromolecules with screw‐like shapes which will rotate as well as translate under the exertion of an electric field force. We consider the rise of the birefringence as the field is turned on, its decay following field turn off, and its behavior following reversal of field direction. The birefringence expressions generally involve eight relaxation times during rise and reversal, with only five of these present during decay. The expressions for reversal and decay do not assume prior steady‐state alignment; the preexponential amplitudes involved explicitly depend on the duration of the preceding buildup. By varying this duration, different birefringence modes involved in reversal and decay can be selectively weighted according to their relaxation times. Certain cases of symmetry are considered which reduce the number of distinct contributing terms. As an example, we examine the behavior of a long bent rod.

Sinusoidal electric birefringence of dilute rigid‐body suspensions at low field strengths
View Description Hide DescriptionKerr‐limit birefringence expressions are presented for a dilute suspension of arbitrarily shaped rigid bodies in the presence of a sinusoidally oscillating electric field. A body is characterized by its diffusiontensors, its optical anisotropytensor, its permanent and instantaneously induced electric dipoles, and its electric charge; no algebraic relation is assumed to hold between these quantities. We specifically allow for charged macromolecules with screw‐like shapes which will rotate as well as translate under the exertion of an electric force. The birefringence exhibits components oscillating at twice the applied frequency as well as nonoscillatory components. The frequency dependence of these components is determined by the j=1 and j=2 eigenvalues of the rotational diffusion operator. Low and high frequency limits are considered, as are special cases which may reduce the number of distinct contributing terms. As an example, we examine the behavior of a long bent rod.

Resonance rotational Raman scattering of symmetric tops: A probe of molecular photodissociation
View Description Hide DescriptionExpressions are derived using irreducible tensor notation describing resonance rotational Raman scattering intensities for symmetric top molecules. Isotropic, antisymmetric, and anisotropicscattering contributions to the resonance O, P, Q, R, and S rotational Raman transitions are considered. Excited state lifetimes in the range of ∼0.02 to 1 ps or ∼1 to 100 vibrational periods can be determined by fitting the pattern of observed relative ΔJ=0 and ΔJ≠0 rotational or rovibrational scattering intensities. UVRaman scatteringspectra resonant with photodissociative levels of the X̃→Ã Rydberg transition of NH_{3} and ND_{3} are used to illustrate this technique. Rates of ammonia photodissociation are found to have a strong dependence on the excited bending level quantum number.

Infrared–microwave double resonance spectroscopy of the ν_{3} band of BF_{3} using a tunable diode laser
View Description Hide DescriptionPure rotational transitions allowed by vibrationally induced dipole moment are observed in the ν_{3} state (E’) of ^{1} ^{0}BF_{3} by infrared–microwave double resonance using a tunable diode laser. The observed rotational transitions are analyzed simultaneously with the infrared vibration–rotation transitions and pure rotational transitions in the ground state to obtain the molecular constants for the ground and ν_{3} states. The C _{0} and D _{ K } constants are determined to be 0.172 165 83(8) and 0.3526(14)×10^{−} ^{6} cm^{−} ^{1}, respectively. Rotational transitions in the ν_{3} state of ^{1} ^{1}BF_{3} reported previously are also analyzed with infrared vibration–rotation transitions including the Fermi resonance with 3ν_{4}.

On the problem of assigning electronic transitions in diketonate complexes. Polarized crystal spectra of tin(IV) and antimony(V) mono(acetylacetonate) and ‐(tropolonate) complexes
View Description Hide DescriptionPolarized crystal spectra of some (mono acetylacetonate) and ‐(tropolonate) complexes were recorded in the visible and ultraviolet region. The intense internal ligand π–π* transitions of the diketonates were measured for the first time on extremely thin single crystals (0.1–1 μm). All crystal spectra exhibit high dichroic ratios due to favorable alignment of the molecules. Since no Davydov splitting is evident, the observed absorption bands in the crystals belong to electronic transitions localized on the individual complexes. For those cases where the complete crystal structures are known, the spectra polarized, to a good approximation, parallel to the molecular axes x,y,z were obtained as well. Several problems concerning the assignment of internal ligand transitions were solved. In (diketonato)tetrachlorostannates the y‐polarized π–π* bands are not superimposed on other transitions of appreciable intensity, therefore their absorption profiles can be measured directly. The lowest, x‐polarized n–π* transition of the acetylacetonates is very weak and is located for Sb(acac)Cl_{4} at an energy lower than that of the π–π* absorption. Some new evidence has been obtained on acetylacetonate‐to‐metal charge‐transfer transitions: two peaks observed in Sb(acac)Cl_{4} are most probably π(acac)‐Sb and O(acac)‐Sb charge‐transfer in origin. These types of transitions should be considered in the interpretation of electronic spectra of acetylacetonate complexes when optical electronegativities of the central ion are larger than 1.6–1.7.

Gerade Rydberg states and n s ^{3}Σ^{+} _{ u }(1_{ u },0^{−} _{ u }) photoionization spectra of the rare gas dimers (n=2–6)
View Description Hide DescriptionTransient absorption spectra of rare gas dimer Rydberg transitions in the ultraviolet, visible, and near infrared (220≤λ≤900 nm) spectral regions have been observed in electron beam excited rare gases. The most prominent molecular bands for He_{2}, Ne_{2}, Ar_{2}, Kr_{2}, and Xe_{2} are assigned to the m p ^{3}Π_{ g }←n s ^{3}Σ^{+} _{ u } (He:n=2, 3≤m≤10; Ne:n=3, 4≤m≤10; Ar:n=4, 5≤m≤15; Kr:n=5, 6≤m≤16; Xe:n=6, 8≤m≤11) Rydberg series of the dimer. Adiabatic ionization potentials, relative to the n s ^{3}Σ^{+} _{ u } state, are determined by extrapolation of the series to their limits (m→∞) to be 34 361.4±30 cm^{−} ^{1} (4.260±0.004 eV) for He_{2}, 34 396.3±25 cm^{−} ^{1} (4.265±0.003 eV) for Ne_{2}, 29 351.9±15 cm^{−} ^{1} (3.639±0.002 eV) for Ar_{2}, 28 428.5±10 cm^{−} ^{1} (3.525±0.001 eV) for Kr_{2}, and 26 664.5±250 cm^{−} ^{1} (3.306±0.031 eV) for Xe_{2}. Absorption bands which are ascribed to m’p ^{3}Σ^{+} _{ g }←ns ^{3}Σ^{+} _{u}Rydberg series of Ne_{2}(m’=4,6,8), Ar_{2}(5≤m’≤10), Kr_{2}(6≤m’≤10), and Xe_{2}(m’=8,9) are also reported, and the n s ^{3}Σ^{+} _{ u }ionization potentials found to be identical to the respective values quoted above. All of the observed molecular Rydberg states have an A ^{2}Σ^{+} _{1/2u } ion core. The lowest vibrational quanta (ΔG _{1} _{/} _{2}) for the n s ^{3}Σ^{+} _{ u } states are determined from vibronic structure in the Rydberg transitions to be 1723 cm^{−} ^{1} for He_{2}, 539 cm^{−} ^{1} for Ne_{2}, 302 cm^{−} ^{1} for Ar_{2}, 172 cm^{−} ^{1} for Kr_{2}, and 135 cm^{−} ^{1} for Xe_{2}, and are consistent with previously reported values. The instability of the n s ^{3}Σ^{+} _{ u } metastable state with respect to the dimer ion core potential [D _{0}(A ^{2}Σ^{+} _{1/2u })−D _{0}(n s
^{3}Σ^{+} _{ u })] is calculated to be 0.508±0.004 eV for He_{2}, 0.681±0.003 eV for Ne_{2}, 0.572±0.002 eV for Ar_{2}, 0.560±0.001 eV for Kr_{2}, and 0.52±0.03 eV for Xe_{2}. Using these values and those reported in the literature for the dissociation energy of the dimer ion A ^{2}Σ^{+} _{1/2u } state, D _{0}(n s ^{3}Σ^{+} _{ u }) is estimated (Ne_{2}: 0.67±0.07 eV; Ar_{2}: 0.76±0.02 eV; Kr_{2}: 0.62±0.02 eV; Xe_{2}: 0.52±0.03 eV). By comparing energy level spacings, quantum defects, and absorption oscillator strengths for transitions between molecular or atomic states, the m p ^{3}Π_{ g }Rydberg levels appear to correlate with the m p[3/2]_{2}+^{1} S _{0} atomic asymptotes. An important aspect of the experimental approach is that the diatomic excited states are studied in the vicinity of R _{ e } rather than at the van der Waals (ground state) minimum. Chemical forces (as opposed to ion‐induced dipole interactions) dominate at small R and the resulting spectra are largely free of congestion arising from the perturbations and avoided curve crossings that are prevalent at large R. Therefore, insight can be obtained into the structure and behavior of molecular Rydberg states in the region near the first ionization limit A ^{2}Σ^{+} _{1/2u }[1(1/2)_{ u }].

The structural determination of fluorite‐type oxygen excess uranium oxides using EXAFS spectroscopy
View Description Hide DescriptionExtended x‐ray absorption fine structure (EXAFS)spectroscopy has been carried out at 77 K at the uraniumL _{III} edge for UO_{2}, β‐U_{3}O_{7}, and U_{4}O_{9} with the aim of determining the structure of these highly defective (oxygen excess) uranium oxide phases, which are of industrial importance. Use has been made of a difference Fourier technique for U_{3}O_{7}, in which the EXAFS of a perfect lattice model is subtracted. U–O bond lengths calculated from the remaining EXAFS signal, assumed to result only from interstitial oxygens, have been used to determine the atomic coordinates of these interstitials. The analysis of EXAFS data in terms of coordination number has allowed an insight into the defect aggregate arrangement of oxygens in U_{3}O_{7} and U_{4}O_{9}. Furthermore, EXAFS data indicate that the uranium sublattice is perturbed by the incorporation of additional oxygen atoms.

O^{−} detected by ESR as a primary electron‐excess defect in x‐irradiated K_{2}SO_{4}
View Description Hide DescriptionESRspectra of K_{2}SO_{4} crystals irradiated with x rays at 26 K contain signals from a novel type of defect in three inequivalent configurations. The gtensors,linewidths, and hyperfine splittings from one potassium nucleus all indicate that the defects are structurally analogous to the primary electron‐excess defects [O^{−},ClO^{−} _{3} ] in KClO_{4}. Hence the spectra are assigned to the complex [O^{−},SO^{2−} _{3} ]. The directions in the K_{2}SO_{4} lattice of the unique axes of the three gtensors support this assignment. The occurrence of dissociative electron attachment to SO^{2−} _{4} and ClO^{−} _{4} contrasts the well‐established existence of the radical ions SeO^{3−} _{4} and BrO^{2−} _{4}.

Homodyne photon‐correlation spectroscopy of a supercooled liquid: 1,3,5‐Tri‐α‐naphthyl benzene
View Description Hide DescriptionHomodyne depolarized photon‐correlation functions of 1,3,5‐tri‐α‐naphthyl benzene (TαNB) have been measured at the 90° scattering angle in the temperature range of 75–110 °C. The correlation functions are analyzed in terms of a fractional exponential function and a modified constrained regularization method originally developed by Provencher. The results from both methods of data analysis are in agreement. The temperature dependence of the mean orientational relaxation time when fitted to the Arrhenius equation, gives an apparent activation energyE=85.3 kcal/mol. The Antoine–WLF equation provides a better fit of the mean reorientational relaxation time data. It is also found that orientational time τ̄ is linearly proportional to η/T, indicating that the Debye–Stokes–Einstein equation is applicable to describe molecular reorientation in the supercooled TαNB liquid.

Experimental determination of the moments of the generalized oscillator strength distribution of He
View Description Hide DescriptionWe report here the experimental determination of the moments, S(n,K), of the generalized oscillator strength (GOS) distribution of Helium for n=−5,−4,−3,−2,−1,1,2. Our results for n=1,2 agree with the recent calculation of Sharma and Thakkar. Our results for n=−5, −4, −3, −2, and −1 agree, in the optical limit, to the earlier reported values of the moments of the optical oscillator strength distribution. We also discuss the problems encountered in using the Bethe sum rule for normalizing spectra taken at a fixed angle over a finite energy loss range.

Decoupled isotopomer vibrational frequencies in cubic ice: A simple unified view of the Fermi diads of decoupled H_{2}O, HOD, and D_{2}O
View Description Hide DescriptionThe existing infrared spectroscopic data for the isotopomers of water [H_{2}O, D_{2}O, (HOD)_{2}, and HOD] decoupled in cubic ice at 90 K are reviewed and combined with new results to complete the infrared data for the internal vibrational modes. An assignment of the observed absorption bands, including the perturbed Fermi diads for ν_{ s } in resonance with 2ν_{2}, that largely follows established views is offered. This assignment is shown to be internally self‐consistent by the analysis of the Fermi diads within a single framework based on the simplest representation of the effects of Fermi resonance and using the Burneau–Corset value for the Fermi‐interaction parameter appropriate to cubic ice (60 cm^{−} ^{1} for H_{2}O). It is shown that the inclusion of the decoupled‐HOD diads significantly lowers the estimated value of ν_{ s } for H_{2}O and, consequently, allows the downshift of this mode to the observed frequency value (3225 cm^{−} ^{1}), through resonance with 2ν_{2} (where ν_{2}=1735 cm^{−} ^{1}), to be closely modeled using the relatively small Fermi‐interaction parameter of Burneau and Corset.

Precise measurement of the J=2←1 fine structure interval in N(II) by far‐infrared laser magnetic resonance
View Description Hide DescriptionFar‐infrared laser magnetic resonancespectroscopy has been used to measure the J=2←1 fine structure intervals in the ^{3} Pground states of singly ionized ^{1} ^{4}N and ^{1} ^{5}N atoms. In ^{1} ^{4}N(II) this separation is 2459.3703(14) GHz, and in ^{1} ^{5}N(II) it is 2459.3816(19) GHz. The hyperfine constants and g _{ J } factors have been evaluated for both isotopes. Zero field energies for the hyperfine components of the J=2←1 transition in both isotopes are given in an effort to facilitate their observation in interstellar sources. A complete description of the hyperfine and Zeeman Hamiltonian matrix elements for atomic fine structure transitions is given in an LS coupled basis set.

Excitation spectroscopy of jet‐cooled ozone: The Huggins system
View Description Hide DescriptionExcitation spectra of rotationally cooled ozone have been taken in the Huggins band (λ∼325 nm). The extreme rotational cooling, achieved by supersonic expansion (T _{rot} ∼3 K) has allowed partial resolution of rotational structure in the (501) and (600) band systems. Rotational contour analysis of these bands has led to the conclusion that the excited state responsible for the Huggins system is the ^{1} B _{2} state (the same as for the Hartley system). From the contour analysis we also obtain an upper bound on the lifetime of 3.6 ps for this state and approximate inertial constants of A≊2.1 cm^{−} ^{1}, B̄≊0.45 cm^{−} ^{1}.

Rovibrational analysis of an intermolecular hydrogen‐bonded vibration: The ν^{1} _{6} band of HCN‐‐‐HF
View Description Hide DescriptionThe infrared spectrum of the intermolecular bending vibration, the ν^{1} _{6} band, of the heterodimer HCN‐‐‐HF has been obtained with 0.010 cm^{−} ^{1} resolution, and the rotational structure of this band has been assigned. The spectroscopic constants of the ν^{1} _{6} state in cm^{−} ^{1} are: ν_{0}=550.0285(2); B _{6}=0.117 652 9(10); D ^{6} _{ J } =0.2791(5)×10^{−} ^{6}; q _{6}=0.579(8)×10^{−} ^{4}; α_{6}=−0.002 137(1), where the uncertainties cited are one standard deviation.

Carbon‐13 NMR of liquid crystal solutions with magic‐angle spinning. Hindered rotation in 6‐(dialkylamino)fulvenes
View Description Hide DescriptionWith magic‐angle spinning, the carbon‐13 NMR spectra of nematic liquid crystals having positive anisotropy of the magnetic susceptibility show sharp peaks. Solutes which have carbon‐13 peaks in the ‘‘window’’ regions of the solvent spectra can be conveniently studied. The hindered rotation of the dialkylamino group in 6‐(dimethylamino)fulvene, 6‐(diethylamino)fulvene, and 6‐(N‐piperidyl)fulvene in a liquid crystalsolvent (E8) has been investigated by carbon‐13 NMR with magic‐angle spinning. The results are compared with those obtained in isotropic solutions of the same compounds in CDCl_{3} and CDCl_{3}+E8. The free energy of activation (ΔG ^{≠}) of each compound in the three solvents is the same within experimental error.

Theory of initial yields of ions generated by electrons in binary mixtures
View Description Hide DescriptionInteractions of charged particles with matter concerns most often mixtures or chemically impure substances. This paper presents the first rigorous treatment of the ionization yields in a binary mixture of gases A and B in the absence of energy transfer between molecules. The Fowler equation was used, and as a first example the system Ar–H_{2} was studied. Results for the number of all ions N and for the number of ions of types A or B are presented for incident electron energies T up to 2000 eV. The calculations cover the complete range of the mixture composition. Comparison with available experimental data shows excellent agreement. The mean numbers of Ar and H_{2} ions present a very interesting dependence on the concentration of the species; their ratio is approximately proportional to the ratio of their partial concentrations.

The a p r i o r i calculation of collisional energy transfer in highly vibrationally excited molecules: The biased random walk model
View Description Hide DescriptionAn a p r i o r i calculation of collisional energy transfer has been carried out, based on an extension of Gilbert’s ‘‘biased random walk’’ model [J. Chem. Phys. 8 0, 5501 (1984)]. The model assumes that energy migration during the collision is random except for certain physical and statistical constraints. It is shown that the probability of energy transfer can be obtained accurately from a relatively small number (10–50) of trajectories using a Smoluchowski equation and generalized Langevin equation approach. Calculations for the azulene/argon system, employing realistic inter‐ and intramolecular potentials, show excellent agreement with the experimental results of Rossi, Pladziewicz, and Barker [J. Chem. Phys. 7 8, 6695 (1983)] and Hippler, Lindemann, and Troe [J. Chem. Phys. 8 3, 3906 (1985)]. This suggests that the extended model may be reliably and economically used to calculate appropriate energy transfer quantities. Moreover, a number of general trends seen in experimental results can be rationalized with the model.

Field‐induced fluctuation correlations and the effects of van der Waals interactions on molecular polarizabilities
View Description Hide DescriptionNew expressions for the van der Waals contribution to the collision‐induced, static polarizability of a molecular pair (Δα_{vdW}) are derived within a reaction‐field theory. For molecules interacting at long range, multipole expansions are used to determine the reaction field; at shorter range, where overlap is small but nonnegligible, the derivation is based on a nonlocal polarizability density model. In both cases, we obtain Δα_{vdW} in terms of integrals over imaginary frequencies, each involving the product of a hyperpolarizability for one molecule and a polarizability or hyperpolarizability for the other molecule. In addition, we show that the polarizability changes induced by van der Waals interactions between two molecules stem from two distinct physical effects. First, in an applied field F, each molecule is polarized nonlinearly by the simultaneous action of the field due to the fluctuating charge distribution of its neighbor and the field F. Second, the applied field F alters the correlations between the spontaneous, quantum mechanical fluctuations in the charge density of each molecule, thus affecting its interaction with the neighboring molecule. Effects of field‐induced fluctuationcorrelations have not been included in earlier models for the van der Waals contributions to pair polarizabilities.

Transient x‐ray scattering calculated from molecular dynamics
View Description Hide DescriptionWith the continued development of pulsed x‐ray sources, it may in time be possible to use transient x‐ray diffraction to follow the molecular dynamics of chemical reactions in the liquid and solid states. To explore this possibility from the theoretical side, we have calculated, using classical molecular dynamics, the picosecond time‐resolved x‐ray scattering of a simplified model for a liquid state chemical reaction of substantial interest: the photodissociation of I_{2} molecules in rare gas and hexane solvents. The time scale of the separation of the I atoms and the effect of the solvent on their motion are observed in the computed transient x‐ray diffraction patterns, and such effects might also be observed in a suitably designed experiment. This illustrates that transient x‐ray diffraction might be an experimental tool for discovering the molecular dynamics of chemical reactions, with the advantage over transient optical spectroscopies such as infrared, electronic, and Raman that the connections between dynamics and diffraction can be precisely computed without uncertainties due to imprecise knowledge of dipole moments, transition dipole moments, and polarizabilities.