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Volume 83, Issue 2, 15 July 1985

Fluorescence and stimulated emission S _{1} → S _{0} spectra of acetylene: Regular and ergodic regions
View Description Hide DescriptionThe S _{1} → S _{0} transition of acetylene has been studied by spontaneous and stimulated emission. In the spontaneous emission studies, we report new data on low‐resolution dispersed fluorescence from an unrelaxed single rotational level of S _{1}. Transitions into S _{0} levels from the zero‐point level up to ∼28 000 cm^{−} ^{1} of vibrational energy are reported. Earlier investigations of the emission from relaxed acetylene in a neon matrix and of partially relaxed fluorescence from a radio frequency discharge in acetylene have been reexamined and reinterpreted in the light of the present work. The stimulated emission study employed stimulated emission pumping (SEP) for high‐resolution investigations of two regions of S _{0} energies, one near 9550 cm^{−} ^{1} and another near 27 900 cm^{−} ^{1}. Definite vibrational assignments were possible for most of the features observed in the lower energy region. This allowed the determination of two new vibrational constants, y _{2} _{2} _{4} and y _{2} _{4} _{4}. The region near 27 900 cm^{−} ^{1} reveals a hitherto unobserved kind of vibrational behavior. A series of broad features (∼1.5 cm^{−} ^{1} wide) appear at intervals of ∼10 cm^{−} ^{1} in broadband SEP scans. At higher resolution, each of these is found to consist of many individual lines with DUMP‐laser limited linewidths. This structure is discussed in terms of the Franck–Condon principle for the S _{1} → S _{0} transition and the possible relevance of the observed behavior to theories of ergodicity in quantum systems. A detailed treatment of the data, using various measures of quantum ergodicity, appears in the following paper.

Evidence of quantum ergodicity in stimulated emission pumping spectra of acetylene
View Description Hide DescriptionWe investigate the stimulated emission pumping (SEP) spectra of the acetylene X̃ ^{1}∑^{+} _{ g } state near 27 900 cm^{−} ^{1} of vibrational excitation for evidence of quantum ergodicity. The spectra consists of clumps of narrowly spaced lines which arise from transitions into levels with the same lower state J‘ value. Thus, the structure within each clump is purely vibrational. We apply criteria for spectral ergodicity and examine nearest‐neighbor spacing distributions to test the spectra for signs of ergodic molecular dynamics. The criteria applied suggest that the molecular dynamics is nearly ergodic.

^{5} D _{3}–^{5} D _{4} cross relaxation in Tb^{3} ^{+} pairs in CsCdBr_{3} crystals
View Description Hide DescriptionThe ^{5} D _{3}–^{5} D _{4} cross relaxation process of Tb^{3} ^{+} in CsCdBr_{3} has been evaluated by analysis of the decay curves of the ^{5} D _{3} and ^{5} D _{4} emission. The temperature dependence of the cross relaxation rate can be explained assuming phonon‐assisted processes. The results show that the larger amount of Tb^{3} ^{+} ions is incorporated in pairs into the CsCdBr_{3} lattice.

A Raman spectroscopic study of naphthalene:octafluoronaphthalene at high pressure and low temperature
View Description Hide DescriptionThe crystalline 1:1 complex naphthalene:octafluoronaphthalene has been investigated at high pressure under ambient temperature, and down to 10 K at ambient pressure, by Raman spectroscopy. The complex is stable in the pressure range studied, 1 to 80 kbar. The lattice mode frequencies show a strong positive pressure dependence, while the internal modes are only weakly affected. The temperature and pressure dependencies of the phonon frequencies suggest that the bonding interaction between the molecular partners is of the usual van der Waals type, and the results are in agreement with the ‘‘sublattice’’ model proposed by Chen and Prasad. The mode Grüneisen γ_{ i }’s have been obtained from the pressure data. From the measured (∂ν/∂T)_{ p } and (∂ν/∂P)_{ T }, the ‘‘explicit,’’ ‘‘implicit’’ contributions have been extracted.

Theory of the effect of strong vibronic coupling on circular dichroism spectra
View Description Hide DescriptionCircular dichroismline shape functions are derived for a system consisting of two excited electronic states coupled to a single harmonic vibrational mode. A microscopic quantum field representation is used to develop the time‐dependent one‐exciton Green’s functions for two different models of optical activity: the one‐electron model and the coupled oscillator model. An analytic form of the Green’s functions for these models is derived using an approximate diagonalization in the strong coupling limit of a general two‐level exciton–phonon Hamiltonian [Friesner and Silbey, J. Chem. Phys. 7 5, 5630 (1981); Friesner, i b i d. 7 6, 2129 (1982)]. Simulated spectra are presented which demonstrate differences between the coupled oscillator and one‐electron mechanisms. Possible applications and extensions of this theory are discussed.

Angle resolved photoelectron study of resonances near the Si 2p edge of the Si(CH_{3})_{4} molecule
View Description Hide DescriptionPhotoelectron spectra of tetramethylsilane, were measured at selected photon energies in the vicinity of the Si 2p edge, using synchrotron radiation. In addition to known valence and core Si 2p bands, three L V V Auger lines (69, 76, and 80 eV electron energy) were observed for the first time. Partial and differential cross sections for the Si 2p band and two of the Auger lines have been measured at several photon energies from the Si 2p onset up to 135 eV. An intense resonance is evident in the Si 2p continuum as well as in the L V V Auger decay channels. Its position, right above threshold, accounts for only a part of the absorption feature. Another maximum, already seen in absorption around 124 eV, may be a shape resonance associated with the Si 2p continuum.

Fast orientational‐motional correlation time measurements from ESR hyperfine spectra of perdeuterated nitroxides with ^{1} ^{5}N (I=1/2)
View Description Hide DescriptionA simple, direct approach is presented for determining fast orientational‐motional correlation times τ associated with motionally narrowed electron‐spin‐resonance (ESR) hyperfine spectra of perdeuterated nitroxide radicals enriched with ^{1} ^{5}N (I=1/2). This approach is based on (1) the experimental determination of net dynamic line broadening by taking the difference in linewidth between the M=+1/2 and M=−1/2 nitroxide hyperfine components, (2) the Kivelson expression for fast tumbling motional ESR hyperfine linewidth, (3) a simple, effective method of treating the problem of experimental nitroxide ESR hyperfine line shapes consisting of Gaussian and Lorentzian components, and (4) the spin‐Hamiltonian constants adjusted for fast tumbling nitroxide radicals at high temperature from their rigid limit values at low temperatures. It is shown that the present method yields more reliable and accurate experimental τ values than those determined by conventional methods for fast tumbling nitroxide radicals. Detailed experimental procedures are described for the case of poly(ethylene oxide) polymer containing perdeuterated and ^{1} ^{5}N‐enriched TANOL (TANOLD‐15) spin probes.

The electronic absorption spectra of ClCN^{+}, BrCN^{+}, and ICN^{+} in neon matrices
View Description Hide DescriptionThe optical absorptionspectra of the B̃ ^{2}Π_{3/2} ← X̃ ^{2}Π_{3/2} transitions of chloro‐, bromo‐, and iodocyanide cations in neon matrices at 4.5 K have been obtained and vibrationally analyzed. The origin band of the Ã ^{2}Σ^{+} ← X̃ ^{2}Π_{3/2} transition of ICN^{+} is also observed as well as the absorption bands of the CN radical in the spectra of ClCN^{+} and BrCN^{+}. These features and the vibrational frequency data are discussed.

The exact eigenfunctions and eigenvalues of a two‐dimensional rigid rotor obtained using Gaussian wave packet dynamics
View Description Hide DescriptionExact eigenfunctions for a two‐dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eignestates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a p o s t e r i o r i justification of the De Leon–Heller spectral quantization method.

The exact thermal rotational spectrum of a two‐dimensional rigid rotor obtained using Gaussian wave packet dynamics
View Description Hide DescriptionThe exact thermal rotational spectrum of a two‐dimensional rigid rotor is obtained using Gaussian wave packet dynamics. The spectrum is obtained by propagating, without approximation, infinite sets of Gaussian wave packets. These sets are constructed so that collectively they have the correct periodicity, and indeed, are coherent states appropriate to this problem. Also, simple, almost classical, approximations to full wave packet dynamics are shown to give results which are either exact or very nearly exact. Advantages of the use of Gaussian wave packet dynamics over conventional linear response theory are discussed.

Structure and predissociation dynamics of electronically excited nitrogen dioxide: A resonance Raman study
View Description Hide DescriptionResonance Raman spectra of NO_{2} have been recorded as a function of excitation frequency in the range 0–8000 cm^{−} ^{1} above the predissociation threshold. These spectra are interpreted using the time‐dependent formulation of resonant Raman scattering, to elucidate the shape of the excited electronic statepotential energy surface, and the dynamics which occur on it immediately following photoexcitation. Our results show that the dominant optical transition in this spectral range is ^{2} B _{2}–^{2} A _{1}. Our Raman spectra reveal a marked decrease in the dynamical time scale of the predissociation of the ^{2} B _{2} state as excitation frequency increases. At excitation frequencies approximately 4850 cm^{−} ^{1} above the dissociation threshold, the ^{2} B _{2} predissociative lifetime becomes comparable to a vibrational period. We have analyzed the resonance Raman spectra, along with the absorptionspectrum, to determine the magnitudes of the slopes of the potential surface along the symmetric stretch and bending normal coordinates for the ^{2} B _{2}excited state in the Frank–Condon region.

EPR and electronic absorption studies of vanadyl ions in the Cd(NH_{4})_{2}(SO_{4})_{2}⋅6H_{2}O single crystals
View Description Hide DescriptionEPR studies of vanadyl (VO^{2+}) impurity ions in the Cd(NH_{4})_{2}(SO_{4})_{2}⋅6H_{2}O) (CdASH) crystals are reported at 9.4 GHz. The VO^{2+} ions are found to substitute the divalent cadmium site and have fixed orientations along Cd–O_{ w } bond directions. The angular variation of the EPR spectra in the a ^{*} b, b c, and c a ^{*} planes are used to determine the principal g and A values and their direction cosines for the V=O orientations with different populations. A correlation between the two V=O orientations and the metal–water bond directions is observed. The observed superhyperfine structure with the intensity ratio 1:4:6:4:1 is attributed to the interaction of a single unpaired electron with the two pairs of equivalent protons through the oxygen ligands and it indicated the amount of delocalization of unpaired spin density from the vanadium nucleus. The electronic absorptionspectrum of VO^{2+} ions in the CdASH lattice was studied at 80 and 300 K. The characteristicspectrum of the VO^{2+} ion had four absorption bands at 12 158, 13 888, 18 640, and 28 409 cm^{−} ^{1}. From the analysis of the spectrum, the first three bands were attributed to d–d transitions and the last band to characteristiccharge transfer for the VO^{2} ^{+} ion. The results indicate a tetragonal site symmetry for VO^{2+} ions in this lattice. The band positions were calculated using the energy expressions and compared with the observed band positions to confirm the above transitions. The best fit values of the crystal field (D q) and tetragonal (D s and D t) parameters were evaluated from the observed band positions.

Microwave optical double resonance of HNO: Dipole moment of HNO in Ã ^{1} A‘(100)
View Description Hide DescriptionThe MODR technique has been used to observe the Stark splittings of some rotational lines for HNO in the Ã ^{1} A‘(100) state. The components of the dipole moment of HNO inÃ ^{1} A‘(100) have been determined as μ_{ a } =1.057(6) D and 1.089(6) D for K _{ a }=2 and K _{ a }=3, respectively and μ_{ b }=1.311 (8) D.

Electron spin resonance line shapes of randomly oriented molecules in septet and nonet states by a perturbation approach
View Description Hide DescriptionThe electron spin resonanceline shapes of randomly oriented molecules in septet and nonet states are analyzed in terms of the formulas derived from a perturbation treatment to third‐order in the fine‐structure energy. The method is applied to a ground‐state septet hydrocarbon, 3, 3’‐diphenylmethylenebis (phenylmethylene), and a ground‐state nonet hydrocarbon, m‐phenylenebis[(diphenylmethylen‐3‐yl)methylene], randomly oriented in mixed polycrystallinepowders of benzophenone. It is shown that the g factor and the fine‐structure parameters are determined from the line shapes of a K‐band spectrum with nearly the same accuracy as in a single‐crystal experiment. Extra lines have been observed in addition to the canonical lines corresponding to the external magnetic field along the principal axes of the fine‐structure tensor. The appearance of extra lines in the spectra of septet and nonet molecules is discussed relative to the third‐order perturbation theory.

Isotope shifts and spin–spin coupling constants in the ^{1} ^{3}C and ^{1} ^{7}O NMR spectra of carbon monoxide and carbon dioxide
View Description Hide DescriptionOxygen isotope shifts on the ^{1} ^{3}C chemical shifts and carbonisotope shifts on the ^{1} ^{7}O chemical shifts in carbon monoxide and carbon dioxide are reported. Using models developed by Jameson, shielding derivatives with respect to bond lengths can be calculated using the measured isotope shifts. For carbon monoxide, the derivatives were calculated to be [∂σ (^{1} ^{3}C)/∂r]_{ e } =−456±15 ppm/Å and [∂σ (^{1} ^{7}O)/∂r]_{ e } =−1150±130 ppm/Å. Although earlier coupled Hartree–Fock calculations give a much lower value for [∂σ (^{1} ^{7}O)/∂r]_{ e }, recent a b i n i t i o calculations for carbon monoxide agree very well with our experimental results. Furthermore, the observed ^{1} ^{8}O/^{1} ^{6}O iostope shift is similar to values measured previously for a series of metal carbonyls. For carbon dioxide the iostope shift gives [∂σ (^{1} ^{3}C)/∂r]_{ e } =−214±17 ppm/Å which is in excellent agreement with the value obtained from a recent variable temperature gas phase NMR study. In addition, scalar spin–spin coupling constants, ^{1} J(^{1} ^{3}C,^{1} ^{7}O) were measured to be 16.4±0.1 Hz in carbon monoxide and 16.1±0.1 Hz in carbon dioxide. To our knowledge, these are the first directly measured carbon–oxygen coupling constants to be reported in the literature. From general trends in the periodic table, it seems likely that the sign of these coupling constants is positive.

Direct observation of the fine structure transitions in the Ne^{+} and Ar^{+} ions with diode lasers
View Description Hide DescriptionThe ^{2} P _{1/2}–^{2} P _{3/2} fine structure transitions in the ground (n p ^{5}) state of the neon (n=2) and argon (n=3) atomic ions have been observed in absorption in the positive column of a liquid–nitrogen cooled discharge cell, by employing tunable infrared diode lasers as sources. The transition frequencies were measured to be 780.4240±0.0011 and 1431.5831±0.0007 cm^{−} ^{1} for Ne^{+} and Ar^{+}, respectively. A few transitions have also been observed for the neutral Ne and Ar atoms.

Inelastic collisions of CaCl(X ^{2}Σ^{+}) with Ar: A collaborative theoretical and experimental study
View Description Hide DescriptionWe investigate rotationally inelastic cross sections of CaCl(X ^{2}Σ^{+}) with Ar at a collision energy of 0.24 eV. Theoretical cross sections, determined by coupled states calculations based on an electron‐gas description of the potential surface, are compared with experimental cross sections, determined in a molecular beam apparatus involving initial state selection by an electric quadrupole field and final state detection by laser‐induced fluorescence. The agreement between theoretical and experimental cross sections is excellent, except for the e → e transitions with ΔN=even, which suggests a residual inaccuracy in the theoretical description of the second Legendre moment of the anisotropy in the potential. Both the theoretical and experimental cross sections clearly confirm a propensity toward conservation of the spectroscopic e/ f label. The sets of experimental and theoretical cross sections can be well fit by the sudden scaling relation, although the entire set of base cross sections can not be well represented by a simple power law.

Quenching of the 1.0 and 2.3 μm excited electronic states of PuF_{6} at room temperature by selected rare gases and small polyatomic molecules
View Description Hide DescriptionThe quenching rate constants k _{ q } for the following rare gases and small molecules (He, Ar, Xe, H_{2}, D_{2}, N_{2}, O_{2}, F_{2}, Cl_{2}, HF, CO, CO_{2}, CH_{4}, CHF_{3}, CF_{4}, NO_{2}F, SOF_{4}, SF_{6}, and UF_{6}) are reported in units of cm^{3} molecule^{−} ^{1} s^{−} ^{1} for both the 1.0 and 2.3 μm excited electronic states of PuF_{6} (see Table I). The self‐quenching rate constants for PuF_{6} at room temperture are k _{ q }(1.0 μm) =1.12±0.01×10^{−} ^{1} ^{2} and k _{ q }(2.3 μm)=5.01±0.11×10^{−} ^{1} ^{5} cm^{3} molecule^{−} ^{1} s^{−} ^{1}. The magnitude of the quenching rate constants for most all of the gases considered above suggest that the dominant process in the collisional deexcitation of excited state PuF^{*} _{6} (1.0 or 2.3 μm) molecules at room temperature is physical quenching (i.e., E‐T or electronic‐to‐translational collisional energy transfer). Our data also indicate that E‐V (electronic‐to‐vibrational) energy transfer is responsible for the efficient quenching of electronically excited PuF_{6} by H_{2}, HF, CH_{4}, and CHF_{3}. There is also evidence from our data that the efficient quenching of the excited states of PuF_{6} by ground state PuF_{6} molecules proceeds via resonant energy transfer.

On the effect of slightly endothermic reactivity on ion–molecule association rates
View Description Hide DescriptionIt has been proposed recently that the existence of a slightly endothermic mode may facilitate ion–molecule association by providing a pass leading to the most stable configuration of the ion formed and also by lengthening the lifetime of the activated complex. Accepting the first of these effects the second is investigated and shown to be generally inappreciable.

Quantum mechanical reactive scattering via exchange kernels: Infinite order exchange on a grid
View Description Hide DescriptionA general methodology is described for carrying out quantum mechanical reactive scattering calculations. The approach is based on Miller’s [J. Chem. Phys. 5 0, 407 (1969)] formulation of quantum reactive scattering in which rearrangement processes (i.e., chemical reactions) are characterized by nonlocal exchange interactions that couple different arrangements. The specific approach described here requires that nonreactive coupled channel calculations first be carried out separately in the various arrangements—this is a relatively standard inelastic scattering problem—and the non‐local exchange interactions are then discretized on a grid in (translational) coordinate space; straightforward linear algebra calculations then lead to the scattering matrix. (Discretizing the exchange kernels on a grid is suggested because exchange is very short range.) The attractiveness of the overall method is its straightforwardness, generality, and special suitability for the vector‐processing character of modern supercomputers. Application to a standard test problem (the collinear H+H_{2}reaction) shows that it is numerically stable over a wide range of collision energies.