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Volume 85, Issue 11, 01 December 1986

Ammonia dimer studied by photoelectron spectroscopy
View Description Hide DescriptionThe He iphotoelectron spectrum of (NH_{3})_{2} is shown to have only a single broad unstructured ionization band near 10 eV. This demonstrates the equivalence or near‐equivalence of the nitrogen lone‐pair orbitals of each NH_{3} unit in the dimer structure. While theory has generally predicted that (NH_{3})_{2} has a classical structure with a near‐linear N‐‐H–N linkage, such a structure would be expected to show two ionization bands separated by about 1.5 eV. However analysis of the observed low ionization energy band suggests that a maximum possible band separation would be only 0.5 eV for ionization from the nitrogen lone‐pair orbitals. While this result concurs with the nonclassical structure for (NH_{3})_{2} proposed by Klemperer and co‐workers, it does not exclude the symmetric C _{2h } structure as a likely equilibrium geometry for the dimer. On the contrary, it is argued that the photoelectron spectrum is supportive of the latter structure. Split‐valence basis Hartree–Fock calculations on (NH_{3})_{2} at various nonclassical geometries indicate that the dimer could have the symmetric C _{2h } geometry but that a relatively shallow potential energy surface for asymmetric van der Waals vibrations would be responsible for the nonzero dipole moment observed by rotational spectroscopy. This conclusion corroborates the finding of the most recent a b i n i t i o calculations on (NH_{3})_{2} by Latajka and Scheiner.

Extraction of alignment parameters from circular dichroic photoelectron angular distribution (CDAD) measurements
View Description Hide DescriptionIn a previous paper, we showed that circular dichroism in photoelectron angular distributions (CDAD) can be used to probe alignment in gas phase atoms and linear molecules. Often this alignment is parametrized through the m o m e n t s of alignment A ^{(} ^{2} ^{)}, A ^{(} ^{4} ^{)}, etc., which are commonly extracted from fluorescencepolarization measurements. In this paper we show how these can be simply extracted from CDAD spectra. This technique can be used in principle to extract the moments to a n y order.

A diabatic model for photoionization. Application to the inner valence x‐ray photoelectron spectrum of acetylene
View Description Hide DescriptionA two‐state diabatic model for high‐energy photoionization is proposed and applied to the inner valence x‐ray photoelectron spectrum of acetylene. The diabatic electronic representation is accomplished by calculating the first order nonadiabatic coupling over the vibrational normal modes. The photoionization overlap amplitudes are expressed in terms of this new basis which is related to the adiabatic representation via an orthogonal transformation. The nonadiabatic (vibronic) coupling leads to a significant redistribution of photoelectron intensity for the totally symmetric states in the inner valence region. This finding resolves previous ambiguities in the analysis of the spectrum.

Determination of the Born–Oppenheimer potential function of CCl^{+} by velocity modulation diode laser spectroscopy
View Description Hide DescriptionOver 70 transitions among the lowest six vibrational states of C^{3} ^{5}Cl^{+} and C^{3} ^{7}Cl^{+} have been measured between 1070–1210 cm^{−} ^{1}. The spectrum has been fitted to a sixth order Dunham expansion to yield an accurate mapping of the Born–Oppenheimer potential function of CCl^{+}. The spectroscopic constants obtained are ω_{ e } =1177.7196(8) cm^{−} ^{1}, ω_{ e } x _{ e } =6.6475(3) cm^{−} ^{1}, and B _{ e } =0.797 940(3) cm^{−} ^{1}. The rotational constants for both CCl^{+}isotopes reported here show the results of the previous electronic emission studies to be incorrect. A fit of the data to a Morse function yields a dissociation energyD of 52 828(50) cm^{−} ^{1}. The rotational temperature has been determined as 540 K±30%. The increase in the effective vibrational temperature with vibrational excitation indicates that CCl^{+} is formed with high internal energy.

Multiple‐quantum NMR spectroscopy of S=3/2 spins in isotropic phase: A new probe for multiexponential relaxation
View Description Hide DescriptionIn nuclear magnetic resonance of quadrupolar spins with S≥3/2, it is shown that excitation and observation of multiple‐quantum coherence is possible in the absence of scalar, dipolar, or quadrupolar splittings, in contrast to the widely accepted view that nonvanishing couplings are a prerequisite for the creation of multiple‐quantum coherence. In the absence of splittings, multiple‐quantum coherence can be excited because the longitudinal (‘‘T _{1}’’) or transverse (‘‘T _{2}’’) relaxation is multiexponential, which occurs if the motional correlation times τ_{ c } are comparable to or larger than the inverse of the Larmor frequency (violation of the extreme narrowing approximation). Two experiments are described, which combine multiple‐quantum filtration with conventional spin‐echo and inversion‐recovery sequences. For isotropic motion each experiment allows one to determine the motional correlation time without knowledge of the magnitude of the quadrupolar coupling constant.

Fluorescence from extreme ultraviolet photoexcitation of CF_{4}
View Description Hide DescriptionPhotoabsorption and fluorescence cross sections of CF_{4} were measured in the 50–130 nm region using synchrotron radiation as a light source. Oscillator strengths for Rydberg states were determined from the absorption cross sections measured. The fluorescence spectra were dispersed to identify the emission species. Fluorescences appear in the excitation wavelength regions of 50–57.4, 75–80, and 85–95 nm, in which the emitters are attributed to CF^{+} _{4}, CF_{2}, and CF_{3}, respectively. The fluorescence quantum yield has been determined from the absorption and fluorescence cross sections measured simultaneously. The yield has a maximum of 26% at 55 nm.

Time‐resolved fluorescence polarization and four‐wave mixing from an ensemble of free symmetric rotors
View Description Hide DescriptionA theoretical treatment of time‐resolved fluorescencepolarization and two time‐resolved four‐wave mixing processes(polarizationspectroscopy and transient gratings) from a thermal ensemble of free symmetric top rotors is presented. Time‐dependent signals are calculated for both parallel and perpendicular transitions at low and high temperatures. At high J, both the fluorescence anisotropies and the nonlinear signals exhibit transients near time zero which level out to essentially constant values within several average rotational periods. These transients, which represent rigid‐body rotational motion in a classical picture, arise in a quantum mechanical treatment from interferences between different intermediate rotational states that are coupled to the same pair of initial and final states. The nonlinear signals are sensitive not only to rotational dynamics but also to the total dephasing rates between the final pairs of coupled levels and to effects of selective phase matching. The relevance of these short‐time effects for designing and interpreting experiments to probe rotational dynamics of large molecules is discussed.

An unsuspected Fermi perturbation in the acetylene Ã ^{1} A _{ u } 3ν_{3} level
View Description Hide DescriptionA previously undetected perturbation in the HCCH Ã ^{1} A _{ u } 3ν_{3} (t r a n s‐bend) level has been found and analyzed. The perturbing level is identified as the Ã ^{1} A _{ u } ν_{2}+2ν_{4} level. Locally deperturbed molecular constants for the 3ν_{3} and perturbing level are obtained, along with the perturbation matrix element and the J‐dependent mixing coefficients. The Ã‐state torsional fundamental, ν_{4}≈850 cm^{−} ^{1}, is estimated from the energy of perturbing level. The presence of the perturbation explains large differences between the rotational line intensity patterns observed in the absorption and fluorescence excitation spectra. The perturbed 3ν_{3} and extra lines are especially prominent in a fluorescence excitation spectrum of the Ã ^{1} A _{ u }–X̃ ^{1}Σ^{+} _{ g } 3^{3} _{0} K ^{1} _{0} subband of acetylene rotationally cooled in a supersonic jet.

The structure of several electronic states of the Hg–Ar complex as determined by laser double resonance in a supersonic jet
View Description Hide DescriptionThe electronic states of the Hg–Ar complex have been studied in a supersonic free jet expansion using a laser double resonance technique. Detailed observations were made of the states correlating with the mercury 6 ^{3} P levels ^{3} P _{0}, ^{3} P _{1}, and ^{3} P _{2}. The states correlating with the ^{3} P _{0} and ^{3} P _{2} metastable states had not been studied previously since they are optically inaccessible from the ground state. A model was developed which accounts for the structures of the various states. The binding energies can be related simply to the average orientation of the 6pmercury orbital with respect to the internuclear axis. In addition, the Hg(7 ^{3} S _{1})–Ar Rydberg state was reinvestigated and shown conclusively to exhibit a double minimum potential, with a deep well similar to the Hg–Ar^{+} ion and a shallow van der Waals minimum at larger internuclear distances.

Measurement of hyperfine polarization quantum beats in a polyatomic molecule
View Description Hide DescriptionPolarizationquantum beats between hyperfine components of perturbed rotational states in the S _{1}→S _{0}fluorescence of propynal (HC≡CCHO) have been measured. The quantum beats are explained by a periodic transfer of molecular alignment to nuclear spinpolarization.

ESR and ENDOR studies of irradiated potassium dihydrogen phosphate
View Description Hide DescriptionIrradiated single crystals of potassium dihydrogen phosphate were studied via ESR and ENDOR techniques in order to define phosphate group structures. A precursor cation species was produced at 4.2 K which converted upon warming to a radical previously reported for 77 K irradiation. The g values and protonENDOR results allowed detailed models for both species to be constructed. Phosphorous ENDOR resonances were also detected and provided complete hyperfine splittingtensors for both species which reflected small internal phosphate group polarization densities.

Multiphoton coherent excitation of molecules
View Description Hide DescriptionTwo different approaches to multiphoton excitation of an anharmonic multilevel system are presented. Both methods result in nearly complete population of the upper state. The first approach involving phase shifting portions of the coherent excitation is treated analytically with square pulses. The second approach uses sequences of several pulses with selected relative phase and delays. Some numerical examples are presented for three‐ and four‐photon excitation of the vibrational level structure of CH_{3}F. This particular molecule is again taken as model to demonstrate four‐photon excitation with a five pulse sequence, taking into account the rotational line structure. The rotational line distribution in the upper state is seen to correspond to a lower temperature than in the ground state.

Electronic structures of H_{2}O⋅BF_{3} and related n–v addition compounds: A combined EELS–UPS study in vapor phase
View Description Hide DescriptionThe detailed electronic structure of the n–v addition compound H_{2}O⋅BF_{3} has been investigated for the first time by a combined use of electron energy loss spectroscopy(EELS) and UVphotoelectron spectroscopy (UPS) augmented by MO calculations. The calculated molecular orbital energies of H_{2}O⋅BF_{3} agree well with the UPS results and have been used to assign the electronic transitions obtained from EELS and to construct an orbital correlation diagram.

Photodissociation of energy selected C_{4}H^{+} _{6} ions: The isomerization barrier between butyne and 1,3 butadiene ion isomers
View Description Hide DescriptionIons are energy selected by photoelectron photoion coincidence (PEPICO) and subsequently photodissociated by a pulsed excimer pumped dye laser. The laser is triggered by the delayed zero energy electron signal so that the laser pulse intercepts the single ion at a fixed point in the ion trajectory. The product ions are separated from the undissociated parent ions by their time of flight. Evidence is presented for both single and multiphoton dissociation of the butadiene ions. The derived kinetic energy release distribution (KERD) of the C_{3}H^{+} _{3} product ions is consistent with the statistically predicted KERD. Finally, the isomerization barrier between 1‐ and 2‐butyne and butadiene ions is measured by probing the ion structure with the laser as a function of the C_{4}H^{+} _{6} internal energy. Because this rearrangement requires only H atom shifts, the measured barrier is associated with the ubiquitous H atom scrambling process commonly observed in unsaturated hydrocarbon ions.

Computational study and complex angular momentum analysis of elastic scattering for complex optical potentials
View Description Hide DescriptionA systematic study of elasticscattering by complex valued optical potentials has been carried out. A Lennard‐Jones (12,6) potential with an imaginary r ^{−s } term has been used in the calculations. The collision parameters are chosen to model the elasticscattering of K by HBr and Li by HBr. First‐order semiclassical single turning point phase shifts are compared with accurate quantum phase shifts and close agreement is found. It is straightforward to calculate semiclassical phase shifts for an optical potential; it is unnecessary to introduce additional approximations (for numerical convenience) as is usually done in the literature. Up to 15 000 terms in the partial wave series are used to calculate elasticangular distributions. It is shown that a rich interference structure and a backward glory can occur in the large angle scattering, provided the transition from absorbency to transparency is sufficiently rapid. Different optical potentials can result in similar angular distributions. A complex angular momentum (Regge pole) analysis of the large angle scattering has been carried out. It is shown that the interference effects have a physical interpretation in terms of surface waves that propagate around the core of the potential and the directly reflected elasticscattering.

Spin‐orbit state‐selected reactions of Kr^{+}(^{2} P _{3} _{/} _{2} and ^{2} P _{1} _{/} _{2}) with H_{2}, D_{2}, and HD from thermal energies to 20 eV c.m.
View Description Hide DescriptionSpin‐orbit state‐selected reactions of Kr^{+}(^{2} P _{ J }), J=3/2 and J=1/2, with isotopic molecular hydrogen (H_{2}, D_{2}, and HD) to form KrH^{+} and KrD^{+} are investigated using guided ion beam techniques. Reaction cross sections for each spin‐orbit state are measured as a function of the relative translational energy of the reactants from near thermal energies up to 20 eV c.m. At low energies, the cross sections for reaction with H_{2} and D_{2} are each about 2.6 times larger for the ^{2} P _{3} _{/} _{2} ground spin‐orbit state of krypton ion than for the ^{2} P _{1} _{/} _{2}excited state. For the HD reaction, the ^{2} P _{3} _{/} _{2} reactivity is enhanced by a factor of about 4.2. A higher‐energy process, which exhibits an apparent activation energy of about 1 eV, is present o n l y for the ^{2} P _{3} _{/} _{2} spin‐orbit state. The Kr^{+}(^{2} P _{3} _{/} _{2}) spin‐orbit state exhibits a strong intermolecular isotope effect, showing the unusual dependence σ(HD)>σ(H_{2})>σ(D_{2}) for the total reaction cross sections at low energies. Cross sections for the Kr^{+}(^{2} P _{1} _{/} _{2}) state show a much smaller dependence on the hydrogen isotope. The intramolecular isotope effect for the individual KrH^{+} and KrD^{+} channels in the reaction with HD shows several reversals over the energy range studied. These results are discussed in terms of the potential energy surfaces of the krypton–hydrogen system.

Molecular beam scattering measurements of differential cross sections for D+H_{2}(v=0)→HD+H at E _{c.m.}=1.5 eV
View Description Hide DescriptionThe reaction D+H_{2}→HD+H has been studied in a crossed molecular beamscattering experiment at a most probable collision energy of E _{c.m.}=1.5 eV. Angular and time‐of‐flight distributions of the HD product have been measured over a wide range of angles. The experimental data are compared with quasiclassical trajectory(QCT) calculations on the LSTH potential hypersurface. The QCT calculations fit the experimental data quite satisfactorily. The sensitivity of the experiment to the different properties of the cross section has been investigated.

A molecular representation of Al^{3} ^{+}+H charge transfer reactions
View Description Hide DescriptionThe charge transferreaction Al^{3} ^{+}+H→Al^{2} ^{+}+H^{+} has been studied within a molecular representation appropriate for slow to intermediate velocity collisions. A b i n i t i o electronic potential energy curves were computed for the lowest four ^{2}Σ^{+} states of AlH^{3} ^{+}, which dissociate to the limits Al^{3} ^{+}+H and Al^{2} ^{+}(^{2} S,^{2} P ^{0},^{2} D)+H^{+}. The configuration interactionwave functions were constructed to represent the four states in an unbiased fashion yielding asymptotic energy splittings within 1% of experimental values. Radial and dipole coupling matrix elements were obtained as a function of internuclear separation. Two formal criteria are proposed to evaluate the accuracy of the radial coupling elements which, in this case, were obtained through the Hellman–Feynman theorem. The nuclear scattering equations were solved in the semiclassical straight line trajectory approximation for the range of barycentric collision energies 0.01–1.0 keV/amu.

An improved log derivative method for inelastic scattering
View Description Hide DescriptionA new method for solving the close coupled equations of inelastic scattering is presented. The method is based on Johnson’s log derivative algorithm, and uses the same quadrature for the solution of the corresponding integral equations. However it differs from the original method in the use of a piecewise constant diagonal reference potential. This results in a reduction in matrix operations at subsequent energies, and an improved convergence of the solution with respect to the number of grid points. These advantages are clearly demonstrated when our method is applied to an atom–diatom rotational excitation problem.

Complex periodic oscillations and Farey arithmetic in the Belousov–Zhabotinskii reaction
View Description Hide DescriptionOur experiments on the manganese‐catalyzed Belousov–Zhabotinskii reaction in a stirred flow reactor reveal many sequences of distinct multipeaked periodic states. In the parameter ranges studied the waveform for each periodic state consists of an admixture of small and large amplitude oscillations. No chaos is discernible, and in many cases the transitions from one periodic state to another occur without any observable hysteresis. Two types of sequences were studied in detail, one with waveforms consisting of concatenations of two basic patterns and another with waveforms consisting of concatenations of three basic patterns. The sequences of states with two patterns are described well by Farey arithmetic, which provides rational approximations of irrational numbers. These states can be characterized by a firing number, the ratio of the number of small amplitude oscillations to the total number of oscillations per period. For our data this ratio is a monotone stepwise‐increasing function of flow rate, and the steps have a fractal dimension. The relationship between the observed sequence and the Farey arithmetic and the observation of a fractal dimension for the steps in the firing number suggest that the states formed by concatenating two patterns can be interpreted in terms of frequency locking on a 2 torus in phase space. The sequences of states with three basic patterns are described by a generalized Farey arithmetic that provides rational approximations for pairs of irrational numbers that are mutually irrational; this suggests that these states can be interpreted in terms of frequency locking on a 3 torus. A piecewise‐linear two‐dimensional map is shown to yield a phase diagram in qualitative accord with the measured phase diagram for these sequences.