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Volume 78, Issue 7, 01 April 1983

Resonant multiphoton ionization of H_{2} via the B ^{1}Σ^{+} _{ u }, v=7, J=2 and 4 levels with photoelectron energy analysis
View Description Hide DescriptionWe report measurements of photoelectron spectra of an electronically excited state of H_{2} (B ^{1}Σ^{+} _{ u }) in selected vibrational and rotational levels. The excited state was prepared by resonant three photon excitation of H_{2} X ^{1}Σ^{+} _{ g }, v=0, J=3 and subsequently was ionized by a single additional photon. Partially resolved rotational structure is observed in the photoelectron spectra and is discussed in terms of the selection rules for direct photoionization and the partial wave composition of the ejected photoelectrons. An additional peak is observed in the spectra, which is tentatively interpreted as arising from photoionization of H*(n=2) formed by photodissociation of H_{2} in the B ^{1}Σ^{+} _{ u } state.

Auger spectra of tetrahedral halides and hydrides^{a)}
View Description Hide DescriptionAuger electron spectra are presented for the gas‐phase molecular species CF_{4}, SiF_{4}, CCl_{4}, and SiCl_{4} and discussed in terms of the effect of the interaction of the two final‐state holes on the spectralline shapes. The highly polar character of the bonding for this series leads to systematic behavior with respect to this hole–hole interaction, showing rare gas‐like localized halide spectra for SiF_{4} and a delocalized component of increasing intensity as we proceed through the series to SiCl_{4}, CF_{4}, and CCl_{4}. The central atom spectra show a composite line shape resulting from the sum of two versions of the same one‐electron final states but with different values of U (the hole–hole interaction energy). The Auger process occurs as a result of the electron density available at the central atom site but, since the one‐electron orbitals are highly polarized towards the halide, the two holes principally appear around the halide sites. With both holes on the same halide site a rather large U results, but with the two holes on separate halide sites one obtains a reduced value of U. The relative intensity of the smaller U component appears to increase as we proceed through the series SiF_{4}, SiCl_{4}, CF_{4}, and CCl_{4}. This tendency in both the halide spectra and in the central atom spectra depends on the strength of the intersite interaction. The molecular parameter which seems most reasonable to predict this division between localized and delocalized behavior is the ratio of the halide–halide distance to the halide radius. In addition, we demonstrate that for a rather extended series of molecular species the trends in the value of U can be predicted surprisingly well on the basis of an experimental value of U for Ne and the known atomic and molecular dimensions. The implications of this simple predictive capability to other molecular systems is discussed.

Anomalous temperature‐dependent phosphorescence of Cu porphin in anthracene^{a)}
View Description Hide DescriptionThe temperature dependence of the phosphorescence spectrum of copper porphin in anthracene has been studied from room temperature down to 8 K and the 4.2 K spectrum has been obtained. A 23.4 cm^{−} ^{1}crystal field splitting of the orbital components of the T _{ Q } state was observed. The 0–0 transition appears abruptly at approximately 25 K and increases rapidly in intensity as the temperature is lowered. A model involving energy transfer from the copper porphin to the triplet exciton band of anthracene gives a satisfactory explanation for the anomalous temperature dependence of the copper porphin phosphorescence intensity.

Nuclear magnetic relaxation study of fully deuterated sulfolan
View Description Hide DescriptionMolecular motions of the fully deuterated sulfolan molecule (C_{4}D_{8}O_{2}S) have been studied in the solid state by NMR measurements of the deuteron spin‐lattice relaxation times in the laboratory (T _{1}) and rotating (T _{1ρ}) frame. In the crystalline phase, it has been found that the relaxation is determined by the ring puckering motion of the molecule. The plastic crystal phase is found to exhibit effects from both isotropic reorientation and translational diffusion. The modified nature of this phase and the plastic–crystalline transition of the deuterated as compared to the undeuterated solid is discussed in terms of the C–H—O hydrogen bonding between molecules.

Two‐dimensional deuterium NMR of lipid membranes
View Description Hide DescriptionThe intrinsic linewidths of deuterium resonance in randomly oriented solids or liquid crystals can be extracted from two‐dimensional NMRspectra in which spectral dispersion due to the quadrupolar Hamiltonian is removed in the indirectly detected frequency domain ω_{1}. Such spectra can be obtained with a modified quadrupolar echo sequence in which the interval between the excitation and echo radio frequency pulse is rendered the second time variable. With this method, deuterium NMRlinewidths have been measured in two model bilayer membranes as a function of temperature: 1‐myristoyl‐2‐myristoyl‐d _{27}‐phosphatidylcholine and a 3:2 1‐palmitoyl‐2‐palmitoyl‐(16,16,16)‐d _{3}‐phosphatidylcholine:cholesterol mixture.

Laser induced fluorescence excitation spectrum of jet‐cooled benzoic acid dimers
View Description Hide DescriptionIntermolecular hydrogen bonding in gas phase dimers of benzoic acid is investigated following preparation in a pulsed free‐jet expansion. Laser induced fluorescence excitation spectra are analyzed to provide information regarding the vibrational assignments of the ^{1} L _{ b }excited state. In agreement with studies in low temperature mixed crystals, the electronic excitation is essentially localized on one monomer unit in the dimer. A 58 cm^{−} ^{1} band is associated with the ν_{3}hydrogen bonding stretch+bend mode and is prominent in combination bands involving internal motion in the carboxyl groups. The free jet technique has been shown to be particularly advantageous in studies of intermolecular hydrogen bonding.

Systematics in two‐photon rovibrational contours of 14^{1} _{0} (^{1} B _{2u }←^{1} A _{1g }) in benzene derivatives
View Description Hide DescriptionTwo‐photon rotational contours of the principal vibronic band (14^{1} _{0}) in the ^{1} B _{2u }←^{1} A _{1g } transition in benzene and its s‐C_{6}H_{2}D_{4}, o‐C_{6}H_{4}D_{2}, C_{6}H_{5}F, p‐C_{6}H_{4}F_{2}, o‐C_{6}H_{4}F_{2} derivatives have been recorded by multiphoton ionization at room temperature with a laser excitation bandwidth of 0.1 cm^{−1}. The main peaks in the rotational contour are shown to result from multiple coincidences of rovibronic transitions due to ‘‘oblate rotorlike’’ and ‘‘prolate rotorlike’’ behavior of the asymmetric rotor molecules. The observed separations between these features agree very well with the predicted ones obtained from simple formulas. These systematics in the two‐photon rotational contours are found to hold over a range of the asymmetry parameter from the least κ=1 to κ=−0.9. The theory is used to obtain the rotationless origin for each of the molecules studied.

Rayleigh–Brillouin scattering of transverse and longitudinal acoustic waves in a supercooled viscoelastic liquid
View Description Hide DescriptionRayleigh–Brillouin spectra of 3‐phenyl propanol are studied over the temperature range from −119.5° to 98.1 °C. The orientation relaxation time is obtained as a function of temperature. The depolarized spectra exhibit clear shear wave sidebands at temperatures below −29.5 °C. The polarized spectra give peaks due to the longitudinal acoustic wave whose frequency displays kinks at the glass transition temperature and at 37 °C (T _{ k }). T _{ k } is 55 °C above the melting temperature (−18 °C). The shear wave frequency decreases linearly with increasing temperature. The experimental results on the V Hscattering spectra are analyzed according to viscoelastictheories based upon the Voigt and Maxwell models. Comparison of the theory with observed spectra shows that the Voigt model gives a better fit to the experimental data. Microscopic theory has also been developed to derive the Voigt and Maxwell models. Angular dependent studies are proposed to differentiate the various theories which give different predictions about the physical nature of the parameters.

Site‐selection spectroscopy of Eu^{3} ^{+}‐doped germinate glass
View Description Hide DescriptionA tunable dye laser was used to selectively excite Eu^{3} ^{+} ions in nonequivalent types of crystal field sites in a germinate glass host. The results demonstrate the existence of three major types of sites in this host. In addition, time‐resolved spectroscopy results show the presence of energy transfer between ions in these different types of sites.

Difference frequency laser spectroscopy of the ν_{1} band of the HO_{2} radical
View Description Hide DescriptionThe ν_{1} (O–H stretching) band of the HO_{2} radical was observed in absorption by using a difference frequency output obtained from an Ar ion laser and a cw dye laser as a source, combined with a multiple‐reflection discharge cell. Zeeman modulation was employed to improve the sensitivity. The HO_{2} radical was generated directly in the cell by a dc discharge in a mixture of allyl alcohol and oxygen. About 280 lines were observed and analyzed to precisely determine the rotational constants, centrifugal distortion constants, and spin‐rotation interaction constants in the ν_{1}=1 state. The band origin was determined to be 3436.1951(4) cm^{−} ^{1}, which is 22 cm^{−} ^{1} higher than the value previously obtained by a matrix isolation study.

Fluctuations of cross sections in chemical processes: Infrared photoquenching of fluorescent states in thiophosgene
View Description Hide DescriptionPronounced fluctuations have been observed in the cross section for the quenching of the fluorescence of the different members of the vibrational manifold belonging to the Ã ^{1} A _{2} state of thiophosgene. This phenomenon is reminiscent of fluctuations that occur for nuclear reactions in regions of high level density, and that can be interpreted in terms of reduced transition amplitudes that are approximately normally distributed. The analysis of the fluctuations gives an effective number of independent reaction channels; in general, the greater the number of channels, the narrower is the range of the fluctuations. A knowledge of the number of independently contributing channels can be useful in the interpretation of experimental results, and sometimes lends important insight into reaction processes. The quenching cross sections for thiophosgene were therefore examined to see whether an analysis of their fluctuations would be useful. It was found necessary to develop a form of analysis that circumvents a serious obstacle in the chemical data, namely, the existence of significant correlations among the cross sections. The resulting formalism is quite simple to apply however, and, after suitable generalization, should be widely applicable to chemical experiments in which resolved cross sections that exhibit fluctuations are measured. Application of this formalism to the thiophosgene quenching cross sections shows that two hypotheses of the quenching mechanism must be rejected, but provides no reason to reject a third, that quenching is via absorption by states in a ‘‘bottleneck’’ region that is reached by rapid photon transitions from the fluorescent target states, which transitions cannot be statistically distributed. The analysis also reveals the existence of an important, experimentally determined constraint that must still be accounted for by any successful hypothesis, viz. the number of channels increases approximately as the square root of the peak power of the quenching infrared radiation.

Variational transition state theory and tunneling for a heavy–light–heavy reaction using an ab initio potential energy surface. ^{37}Cl+H(D) ^{35}Cl→H(D) ^{37}Cl+^{35}Cl
View Description Hide DescriptionAb initio POL–CI calculations, augmented by a dispersion term, are used to predict the potential energy surface for the reaction Cl+HCl. The saddle point is found to be nonlinear. The surface is represented by a rotated‐Morse‐oscillator spline fit for collinear geometries plus an analytic bend potential. Variational transition state theory calculations, based on a linear reference path, are carried out, and they yield much smaller rate constants than conventional transition state theory, confirming that earlier similar results for this heavy–light–heavy mass combination were consequences of the small skew angle and were not artifacts of the more approximate potential energy surfaces used in those studies. Transmission coefficients are calculated using approximations valid for large‐reaction‐path curvature and the potential along the reference path is scaled so that the calculated rate constant agrees with experiment. The resulting surface is used to compute the H/D kinetic isotope effect which is in qualitative agreement with experiment.

A quasiclassical trajectory study of the F+HH⇄FH+H reaction
View Description Hide DescriptionA detailed forward and reverse quasiclassical trajectory computation for the FHH reaction is presented. An adiabatic analysis of the results shows that to a large extent the differences between HF(v=3) and HF(v=2) product distributions are due to the existence of an exit channel adiabatic barrier for the v=3 state. A sideways peak in the angular distribution for HF(v=2, j) is found in the reverse quasiclassical computation. Total cross sections computed from reverse quasiclassical trajectories are in good agreement with the quantal l _{ i } _{ n } reactive infinite order sudden approximation. We conclude that many of the discrepancies between forward quasiclassical results and quantal computations are not due to quantal resonances but rather to the large boxing of vibrational states.

Scavenging probability of a geminate pair in the presence of an external electric field. Application of the method of matched perturbation solutions
View Description Hide DescriptionAn analytical expression for the scavenging probability of a geminate pair interacting with a general potential in the presence of an external electric field is derived for both small scavenger concentrations and small field strengths. The derivation is based on the method of matched perturbation solutions of the differential equation satisfied by the recombination probability. The expression includes as an integral part the rate constant observed for reaction of the geminate partners in the bulk. Agreement of the expression with the exact ones is found when it is applied to ion recombination and recombination of the electron photodetached from an anion.

State resolved rotational excitation in HD+D_{2} collisions. II. Angular dependence of 0→2 transitions
View Description Hide DescriptionTime‐of‐flight spectra for the scattering of HD molecules from D_{2} molecules have been measured at a collision energy of E=70.3 meV over a range of center‐of‐mass scattering angles from 45° to 158°. The spectra reveal clearly resolved transitions at the energy loss ΔE=33 meV which corresponds to 0→2 transitions of HD and the double transition 0→1 of HD and 0→2 of D_{2}. The differential cross sections derived from these spectra increase with increasing scattering angle from 1.7% to 34.7% of the elastic cross section. The pure 0→2 transition of D_{2} which only needs 22 meV to be induced could not be detected within our experimental sensitivity of 0.02 Å^{2}/sr. Closed coupled calculations based on the ab initiopotential surface of Meyer and Schaefer show that this result can be explained by the different coupling terms which are responsible for these transitions. In contrast to the 0→1 transition the 0→2 transition of HD proved to be sensitive to the anisotropic part of the interaction potential for the homonuclear system. The comparison of experimental and calculated cross sections for the ab initio potential of Meyer and Schaefer reveals discrepancies for the 0→1 transition of HD, but shows agreement for the 0→2 transition of HD at intermediate angles.

State resolved rotational excitation in D_{2}+H_{2} collisions
View Description Hide DescriptionIn a crossed molecular beam experiment time‐of‐flight distributions of ortho D_{2} molecules scattered from normal H_{2} (nH_{2}) and para H_{2} (pH_{2}) have been measured in a center‐of‐mass angular range of 75° to 180°. The collision energies were 84.1 and 87.2 meV, respectively. In all spectra the rotational excitation of D_{2} from j=0 to j=2 has been resolved. With pH_{2} as secondary beam the same transition could also be observed for H_{2}. The measurements show that the probability for rotational excitation of D_{2} depends on whether the scattering partner H_{2} is rotating (nH_{2}) or not (pH_{2}). In the first case the cross sections are larger by a factor of approximately 2. The reason for this behavior is the presence of an additional interaction term which is at long range distances, identical to the quadrupole–quadrupole interaction and which is absent if H_{2} is in the j=0 state. The experimentally derived differential cross sections for the rotational excitation of D_{2} and H_{2} are compared with theoretical results obtained by close coupling calculations based on the ab initiopotential surface of Meyer and Schaefer. The comparison shows a remarkable agreement. However, small deviations in the positions of the diffraction oscillations of the elastic differential cross section curve suggest that the isotropic potential term has to be shifted to smaller distances. In order to maintain the relative position of the inelastic differential cross section curves which are well predicted by the ab initio potential the same shift has to be applied to the anisotropic potential terms.

Calculation of higher‐order semiclassical scattering phase shifts: The effect of a barrier maximum
View Description Hide DescriptionEvaluation of high‐order semiclassical scattering phase shifts is extended to situations involving a potential barrier. Calculations by using appropriate semiclassical phase shift formulas yield accurate results for energies above and below as well as in the immediate neighborhood of the barrier maximum.

Imbedded matrix Green’s functions in atomic and molecular scattering theory
View Description Hide DescriptionThis paper presents a general, simple, and unified treatment of Green’s function approaches to the solution of the sets of coupled second order differential equations encountered in the theory of inelastic and reactive scattering. The standard scalar theory of Sturm–Liouville problems is extended to systems of equations without recourse to spectral resolutions of the Green’s operator. A nonstandard approach to invariant imbedding is then developed to yield the most general kind of recursion relation for Wigner R matrices possible; the R‐matrix propagation of Light and Walker and the variable interval‐variable step algorithm of Parker, Schmalz, and Light are shown to be particularly simple examples of this more general scheme. Extensions and simplifications are offered. Also recurrence relations, stabilization of solutions, adiabatic and diabatic representations, and the use of nonorthogonal bases are all treated in a transparent manner.

Semiclassical determination of adiabatic barriers on a three‐dimensional potential energy surface
View Description Hide DescriptionA recently proposed method, based on periodic orbits, for finding vibrationally adiabatic barriers and wells in collinear collisions is generalized to the full three‐dimensional case. The main idea is a consistent use of the adiabatic approximation—one first solves for the fast vibrational motion to obtain an effective Hamiltonian for the slower bend motion which in turn is solved to obtain an effective Hamiltonian for the overall rotation. The method is applied to the hydrogen exchange reaction. We find the bend‐vibration adiabatic barrier levels for the H_{2}(v=1) state. The zero point motion in the bend degree of freedom is found to be substantial (0.1 eV) and is a source for nonnegligible discrepancies between approximate theories such as the infinite order sudden and quasiclassical trajectory approach and exact quantal scattering computations. Having found the barrier levels we are able to evaluate the collision cross section. Our analysis points out that differences between experimental cross sections and theoretical predictions may be due to inaccuracy in the potential energy surfaces. The available surfaces probably overestimate the adiabatic barrier height.

Exact scattering solutions in an energy sudden (ES) representation
View Description Hide DescriptionIn this paper, we lay down the theoretical foundations for computing exact scattering wave functions in a reference frame which moves in unison with the system internal coordinates. In this frame the (internal) coordinates appear to be fixed and its adoption leads very naturally (in zeroth order) to the energy sudden (ES) approximation [and the related infinite order sudden (IOS) method]. For this reason we call the new representation for describing the exact dynamics of a many channel scattering problem, the ES representation. Exact scattering solutions are derived in both time dependent and time independent frameworks for the representation and many interesting results in these frames are established. It is shown, e.g., that in a time dependent frame the usual Schrödinger propagator factorizes into internal Hamiltonian, ES, and energy correcting propagators. We also show that in a time independent frame the full Green’s functions can be similarly factorize. Another important feature of the new representation is that it forms a firm foundation for seeking corrections to the ES approximation. Thus, for example, the singularity which arises in a conventional perturbative expansions of the full Green’s functions (with the ES Green’s function as the zeroth order solution) is avoided in the ES representation. Finally, a number of both time independent and time dependent ES correction schemes are suggested.