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Volume 105, Issue 13, 01 October 1996

Resonant two‐photon ionization spectra of the van der Waals complexes: C_{6}H_{5}X⋅⋅⋅N_{2} (X=F, Cl, Br)
View Description Hide DescriptionThe one‐color resonant two‐photon ionization technique is employed to study jet‐cooled van der Waals (vdW) clusters of halobenzene and nitrogen through the S _{0}→S _{1} transition around the 0̄^{0} _{0} band. The spectra obtained exhibit rich information about the clusters’ intermolecular vdW vibrational modes and their solvent internal rotation. We have tentatively assigned all the observed spectral features to a single isomer of C_{6}H_{5}X⋅⋅⋅N_{2} (X=F, Cl, Br). The influence of X on the vdW vibrations and the internal rotation of N_{2} in the complex is investigated. The analysis of the influence of X on the 0̄^{0} _{0} spectral shift suggests that the change in vdW interaction energy upon electronic excitation is mainly due to the dispersion term.

Fourier transform infrared and theoretical isotopic study of the ν_{4}(σ_{ u }) and ν_{5}(σ_{ u }) modes of linear C_{7}
View Description Hide DescriptionA Fourier transform infrared, ^{13}C isotopic study has been made of two previously identified fundamentals, ν_{4}(σ_{ u }) and ν_{5}(σ_{ u }), of the linear C_{7}carbon cluster which, in the present investigation, was formed by trapping the products of the evaporation of graphite in solid Ar at ∼10 K. Measuredisotopic shifts were compared with theoretical predictions in order to confirm the assignments as well as to investigate the general quality of such predictions. The shifts for the ν_{4}(σ_{ u }) mode were found to be highly sensitive to the level of calculation, whereas consistently good agreement between theory and experiment was found for the ν_{5}(σ_{ u }) mode. This difference in behavior between the two modes is predicted by the isotopic sensitivity index which is shown to be a useful guide for future identifications of vibrational modes based on comparisons between measured and theoretically calculated isotopic shifts.

Ab initio model potential calculations on the electronic spectrum of Ni^{2+}‐doped MgO including correlation, spin–orbit and embedding effects
View Description Hide DescriptionAn ab initiotheoretical study of the optical absorptionspectrum of Ni^{2+}‐doped MgO has been conducted by means of calculations in a MgO‐embedded (NiO_{6})^{10−}cluster. The calculations include long‐ and short‐range embedding effects of electrostatic and quantum nature brought about by the MgO crystalline lattice, as well as electron correlation and spin–orbit effects within the (NiO_{6})^{10−} cluster. The spin–orbit calculations have been performed using the spin–orbit‐CI WB‐AIMP method [Chem. Phys. Lett. 147, 597 (1988); J. Chem. Phys. 102, 8078 (1995)] which has been recently proposed and is applied here for the first time to the field of impurities in crystals. The WB‐AIMP method is extended in order to handle correlationeffects which, being necessary to produce accurate energy differences between spin–free states, are not needed for the proper calculation of spin–orbit couplings. The extension of the WB‐AIMP method, which is also aimed at keeping the size of the spin–orbit‐CI within reasonable limits, is based on the use of spin‐free‐state shifting operators. It is shown that the unreasonable spin–orbit splittings obtained for MgO:Ni^{2+} in spin–orbit‐CI calculations correlating only 8 electrons become correct when the proposed extension is applied, so that the same CI space is used but energy corrections due to correlating up to 26 electrons are included. The results of the ligand field spectrum of MgO:Ni^{2+} show good overall agreement with the experimental measurements and a reassignment of the observed E _{ g }(b ^{3} T _{1g }) excited state is proposed and discussed.

Electron‐spin resonance studies of the titanium cation (Ti^{+},3d ^{3},^{4} F) in rare gas matrices at 4 K: A crystal field interpretation
View Description Hide DescriptionElectron‐spin resonance studies of laser‐ablated titanium metal isolated in neon and argon display an intense feature which exhibits a symmetric, narrow line and a large matrix‐dependent g shift. On the basis of a number of experiments, this is assigned to a matrix isolated 3d ^{3},^{4} F Ti^{+} ion in an octahedral matrix environment. Although the ground state of the gas‐phase Ti^{+} ion is 3d ^{2}4s ^{1},^{4} F, the assignment to the 3d ^{3},^{4} F state is supported by the small hyperfine structure which is observed. The neon magnetic parameters are: g=1.934(1) and A(^{47}Ti)=64(1) MHz; for argon, g=1.972(1) and A=56(1) MHz. This unusual stabilization of an excited atomic state by a rare gas matrix is consistent with ab initio studies, and has been previously found for atomic nickel. A crystal‐field study of the expected behavior of a d ^{3},^{4} F ion isolated in a tetrahedral, octahedral, or cuboctahedral environment supports the assignment to an octahedral Ti^{+}(Rg)_{6} species, and using the atomic spin–orbit parameter, ζ permits accurate values of Dq to be derived from the measured g values. Finally, it is also noted that for small values of Dq/(Dq+ζ), or for a d ^{3},^{4} F ion in a tetrahedral environment, an as yet unobserved, unequal Zeeman splitting of the fourfold degeneracy occurs, causing a departure of the Zeeman energies from the standard formula of E ^{Zeeman}=β_{ eH } _{0} gM, with M=±3/2, ±1/2. For these situations it becomes necessary to define two values of g, corresponding to the more strongly (g _{3/2}) and less strongly (g _{1/2}) affected Zeeman levels, respectively.

On the scattering phenomena for various kinds of polarized light in a nonpolar fluid composed of chiral molecules
View Description Hide DescriptionThe explicit result of the coefficients of the Mueller matrices, which express the Stokes parameters of single and double scattered lights in term of the parameters of the corresponding incident light, are obtained for a nonpolar fluid composed of chiral molecules with the aid of the Ornstein–Zernike form for the correlation function of density fluctuations. The explicit results show that any higher order multiple scattering satisfies the principle of symmetry and law of reciprocity. From the matrices some scattering phenomena for six kinds of completely polarized light in a nonpolar achiral fluid are discussed in the cases of far from and near the critical point. While the degrees of circularity (DCs) give identical information with the circular intensity differences (CIDs) in the region far from the critical point, the critical DCs for circularly polarized lights is quite different from the critical CIDs. The theoretical result of DCs for the circularly polarized lights indicates that the DCs can be other effective experimental tools to measure the critical scattering of a fluid.

Nuclear quadrupole coupling operator for a molecule with an internal rotor
View Description Hide DescriptionThe sequential contact transformation technique is applied to the nuclear quadrupole coupling operator for a molecule containing a threefold symmetric internal rotor in order to be consistent with the transformed vibration–torsion–rotation Hamiltonian to be used in the analysis of the spectra of the molecule. Various higher‐order effects on the nuclear quadrupole coupling energies, such as the centrifugal distortion, the anharmonic corrections and so on, are formulated for a molecule containing one quadrupolar nucleus. The detailed discussion is presented of vibrational–torsional–rotational dependence of these higher corrections to the quadrupole hyperfine energies.

Spectroscopy of mass‐selected niobium trimers in argon matrices
View Description Hide DescriptionThe absorption(scattering depletion) spectrum and Raman spectra for Nb_{3} in an argon matrix prepared by the mass selected ion deposition technique have been obtained. The absorptionspectrum in the visible region shows three overlapping transitions, centered at 20 300 cm^{−1} (A), 18 800 cm^{−1} (B), and 17 000 cm^{−1} (C), respectively. Resonance Raman spectra obtained with excitation into these bands display two distinct fundamental frequencies at 227.4±2.9(e′) and 334.9±2.8(a _{1} ^{′}) cm^{−1} which indicate that the ground state of the Nb_{3} molecule has a nearly equilateral triangular geometry (D _{3h }). The f _{ r } (bond stretch) and f _{ rr } (stretch–stretch interaction) force constants for Nb_{3} are determined to be 1.95 and 0.05 mdyn/Å, respectively. The Raman excitation profiles bear a strong resemblance to the triniobium absorptionspectrum, but the peaks seem more closely spaced than the absorptionspectrum. Both a _{1} ^{′} and e′ vibration are observed with the same intensity near the peak A, while the a _{1} ^{′} vibration dominates the profile at the peak B. Neither displays much intensity near the peak C.

Symmetrized shape oscillation in the structure of ^{6}Li_{7} clusters observed by molecular beam electron‐spin resonance
View Description Hide DescriptionThe electron‐spin‐resonance spectra were measured for free ^{6}Li_{7}clusters by using techniques of molecular beammagnetic resonance. The spectra show a large hyperfine constant a _{1} from two equivalent nuclei and a much smaller hyperfine constant a _{2} from an additional five equivalent nuclei. The cluster geometry consistent with the spectra is a regular pentagonal bipyramid. It has been found that the septemer has two isomers which give the same value for a _{1} to a high accuracy and slightly different values a _{2a } and a _{2b } for a _{2}. There is a relationship between a _{1} and ā _{2}=(a _{2a }+a _{2b })/2 of the form a _{1}/5ā _{2}=1.03≂1. The a _{1} and a _{2} indicate that the septemer is fluctuating in structure between two geometries, the regular pentagonal bipyramid and a deformed one of it. The former corresponds to an oblate ellipsoid of revolution in the ellipsoidal shell model, while the latter means a superposition of five equivalent deformations from the oblate ellipsoid to prolate ellipsoids. The deformation must be symmetrized by the superposition, because the ground electronic state of Li_{7} has no orbital degeneracy in spite of the fivefold axial symmetry of the structure. The symmetrized shape oscillation keeps the vibrational motions of the septemer constant, because the five equivalent deformations mutually cancel all restoring forces. The two ellipsoidal configurations, oblate and prolate, are brought into resonance by a Jahn–Teller effect which takes place on the prolate side. The presence of the two like isomers provides evidence of the Jahn–Teller effect, because there are two mutually independent modes of the Jahn–Teller distortion which divide the septemers into two symmetry types. The simple relation a _{1}≂5ā _{2} further confirms that the electronic states in the two ellipsoidal configurations are in resonance.

Photoelectron spectroscopy of silicon–fluorine binary cluster anions (Si_{ n }F^{−} _{ m })
View Description Hide DescriptionElectronic properties of silicon–fluorine cluster anions (Si_{ n }F^{−} _{ m }; n=1–11, m=1–3) were investigated by photoelectron spectroscopy using a magnetic‐bottle type electron spectrometer. The binary cluster anions were generated by a laser vaporization of a silicon rod in an He carrier gas mixed with a small amount of SiF_{4} or F_{2} gas. The highly abundant clusters are SiF^{−} _{ m } (m=3 and 5) and Si_{ n }F^{−} (n=6, 7, and 10) in their mass spectra. In the photoelectron spectra of SiF^{−} _{ m } (m=1–5), the clusters having odd m have higher electron affinity (EA) than those having even m, indicating that the even/odd alternation in EA is attributed to their electronic structures of a closed/open valence shell. Comparison between photoelectron spectra of Si_{ n }F^{−} and Si^{−} _{ n } (n=4–11) gives the insight that the doped F atom can remove one electron from the corresponding Si^{−} _{ n } cluster without any serious rearrangement of Si_{ n } framework, because only the first peak of Si^{−} _{ n }, corresponding singly occupied molecular orbital (SOMO), disappears and other successive spectral features are unchanged with the F atom doping. In some clusters, furthermore, the vibrational structures could be resolved to determine a vibrational frequency and to presume the geometry with ab initio molecular orbital calculations.

The ultrafast intramolecular dynamics of phthalocyanine and porphyrin derivatives
View Description Hide DescriptionThe internal conversion and intramolecular vibrational relaxation processes of nitro‐tri‐tert‐butylphthalocyanine, tetra‐phenylporphyrin (TPP), and tetra‐tert‐butylphthalocyanine (BuPc) in chloroform solution were investigated with an ultrafast time‐resolved fluorescence depletion method. A regular fluorescence depletion was observed, indicating that the vibrational relaxation in the S _{1} state takes a few hundred femtoseconds to several picoseconds. For TPP and BuPc, an additional sharp dip superposes on the regular depletion. It is explained by an ultrafast internal conversion process from the S _{2} state to the S _{1} state with a time of a few tens of femtoseconds.

Classical and quantal calculations for the Penning ionization system N_{2}+He*(2^{3} S)→N^{+} _{2}+He+e ^{−}
View Description Hide DescriptionQuasiclassical trajectory and quantal calculations are carried out for the Penning ionization system N_{2}+He*(2^{3} S)→N^{+} _{2}(^{2}Σ_{ g },^{2}Π_{ u },^{2}Σ_{ u })+He+e ^{−} based on an ab initio resonance potential and energy widths which were obtained in previous work. Total and partial ionization cross sections are evaluated for the collision energy range of 0.1–1.0 eV. For the trajectory calculation, the collisional energy dependence of the cross section is in better agreement with a recent experiment on state resolved Penning ionization than calculations using the classical sudden approximation. The result in the high frequency rotation limit is significantly different from that for the sudden approximation, which is in contrast to the H_{2}–He* system. The results for quantal calculations using the sudden and spherical‐potential approximations confirm the reliability of classical treatments. The results obtained suggest that analyses with the widely used atomic‐target models lose their validity for significantly anisotropic systems in which targets have large moments of inertia.

Theoretical calculation of photodetachment intensities for H_{3}O^{−}
View Description Hide DescriptionWe have calculated total and arrangement‐selected photodetachment intensities for the H_{3}O^{−} anion (and its deuterated form, D_{3}O^{−}) using a Green’s function in a discrete variable representation with absorbing boundary conditions. A multiply‐shifted quasiminimal residual method is used to obtain the Green’s function for many energies at once. We present spectra obtained by explicitly treating two and four degrees of freedom. Comparison with experiment indicates that the bending angles in the anion and neutral are more similar than in the current potential energy surfaces. The calculated spectra are also consistent with the suggestion that the barrier should be ‘‘earlier.’’

State‐to‐state differential cross sections for rotationally inelastic collisions of NO(^{2}Π_{1/2},j=0.5) with Ar at kinetic energies between 117 cm^{−1} and 1694 cm^{−1}
View Description Hide DescriptionState‐to‐state differential cross sections have been measured for scattering of NO(^{2}Π_{1/2},j=0.5) by Ar at kinetic energies of 117, 149, 442, and 1694 cm^{−1}. The differential cross sections at each collision energy are presented as a function of final state (Ω′,j′) at constant center‐of‐mass scattering angle. Center‐of‐mass angular distributions are also given for final rotational states (^{2}Π_{1/2}, j′=1.5, 2.5, 8.5, 12.5, and 14.5) at a kinetic energy of 442 cm^{−1}, and for j′=18.5 at a kinetic energy of 1694 cm^{−1}. Rotational rainbow structure is seen in both types of data. The results are generally in good agreement with quantum scattering calculations carried out by Alexander [J. Chem. Phys. 99, 7725 (1993)] using newly calculated ab initiopotential energy surfaces, and thus may serve as a new benchmark for the microscopic dynamics of molecular energy transfer in open‐shell molecules.

Cluster size determination from diffractive He atom scattering
View Description Hide DescriptionIn a crossed molecular beam arrangement helium atoms are scattered from argon clusters which are produced in an averaged size range of n̄=6 to n̄=90 by adiabatic expansion through sonic and conical nozzles. The diffraction oscillations in the total differential cross section are used to derive information on the size distribution of the clusters by comparison with quantum mechanical calculations based on a model potential. In the size range covered by the measurements, the average cluster size is given by n̄=38.4(Γ^{*}/1000)^{1.64}, where Γ^{*} is the scaling parameter of the source conditions introduced by Hagena [Z. Phys. D 4, 291 (1987)]. The results are in agreement with recent measurements of corrected mass spectra but disagree with the results obtained from electron diffraction. General relations are recommended which connect the scaling parameter with the averaged size.

Vibration–rotation excitation of CO by hot hydrogen atoms: Comparison of two potential energy surfaces
View Description Hide DescriptionCollision cross sections for rotational and vibrational excitation of CO by fast H atoms are calculated for two potential energy surfaces, the older Bowman–Bitman–Harding potential and the recently constructed surface of Werner, Keller, and Schinke. Both quantum mechanical and classical calculations are performed. The results obtained with the new potential energy surface are very similar to those obtained with the older potential; in particular, they do not rectify the discrepancies between the experimental and theoretical cross sections for vibrationally elastic transitions into small rotational states of CO.

The high‐pressure range of the reaction of CH(^{2}Π) with N_{2}
View Description Hide DescriptionThe pressure dependent thermal rate constant of the reaction of CH(^{2}Π) and N_{2} has been studied from 200 to 715 K at total pressures between 1 and 150 bar of helium. The CH radicals have been generated using multiphoton laser flash photolysis of CHClBr_{2} or CHBr_{3} at 248 nm and detected by saturated laser induced fluorescence (SLIF). At 200, 250, 300, 400, and 500 K falloff curves have been constructed and the high pressure limit rate constant has been determined to be k _{1,∞}=(4.1±0.8)10^{−11} (T/300 K)^{−0.15} cm^{3} molecule^{−1} s^{−1}. At higher temperatures thermal decomposition of the CHN_{2} adduct has been observed and the equilibrium constant derived by analyzing the concentration decays. By third law analysis the equilibrium constant has been evaluated with a reactionenthalpy ΔH°_{ R } (0 K)=−(97±10) kJ mol^{−1}. Our results are compared with recent calculations of the potential energy surface (PES) and other experimental data at low pressures as well as shock tube studies. The high‐pressure limiting rate constants are treated in terms of statistical reaction rate theory. A simple kinetic model has been developed to describe the measured rate constants in an extended pressure (10^{−3}–150 bar) and temperature range (200–3500 K).

A microscopic frictional theory for reactions in condensed phases: Influence of nonlinear couplings
View Description Hide DescriptionOn the assumption of external bath equilibrium, a set of simultaneous linear generalized Langevin equations (GLE) for a microscopic Hamiltonian is derived, whose potential function includes cubic (i.e., nonlinear) coupling terms, which are linear in internal coordinates but quadratic in external bath coordinates. Furthermore, on the linear GLE treatment, a closed expression of time‐dependent friction coefficient and a rate constant in the Grote–Hynes theory (GHT) are derived microscopically, reflecting the reactant and solvent structures. By comparing the rate constant of GHT with that of the multidimensional transition‐state theory(TST) for the whole solution system, we conclude that these rate expressions are different from each other and the deviation is due to the dynamiceffect via the nonlinear coupling among the reaction, internal, and external normal coordinates. Moreover, the friction coefficient depends on temperature and the deviation becomes larger with temperature increasing. By the second‐order perturbation theory, we have estimated the deviation which is approximately equal to a transmission coefficient κ, for a real cluster reaction system: the formic acid–water–water system. We have obtained κ of 0.92, which is smaller than unity. A mode analysis shows that two hindered translational motions of the solvent with low frequencies prevent the reaction from proceeding. Besides, we have investigated the isotope effect of a medium water molecule and found that the dynamicisotope effect for the reaction is quite large, i.e., κ for heavy water is much smaller than that for light water. Not the change of the reactive frequency on the free energy surface but that of the frictional effect in the deuterium substitution mainly contributes to the isotope effect. Further, the temperature dependence of κ for the reaction has been estimated and it is found that κ becomes smaller with temperature increasing and the change of the frictional effect in temperature contributes to the temperature dependence of κ more largely than that of the reactive frequency on the free energy surface.

Solvent dynamics: Modified Rice–Ramsperger–Kassel–Marcus theory. II. Vibrationally assisted case
View Description Hide DescriptionExpressions are given for a solvent dynamics‐modified Rice–Ramsperger–Kassel–Marcus (RRKM) theory for clusters. The role of vibrational assistance across the transition state region is included. The usual differential equation for motion along the slow coordinate X in constant temperature systems is modified so as to apply to microcanonical systems. A negative entropy term, −S _{ v }(X), replaces the (1/T)∂U/∂X or (1/T)∂G/∂X which appears in canonical systems. Expressions are obtained for the RRKM‐type rate constant k(X) and for the S _{ v }(X) which appear in the differential equation. An approximate solution for steady‐state conditions is given for the case that the ‘‘reaction window’’ is narrow. The solution then takes on a simple functional form. The validity of the assumption can be checked a posteriori. Recrossings of the transition state are included and the condition under which the treatment approaches that in Part I is described.

Vibrational enhancement of the charge transfer rate constant of N^{+} _{2}(v=0–4) with Kr at thermal energies
View Description Hide DescriptionThe charge transferreaction of N^{+} _{2}(v=0–4)+Kr→N_{2}+Kr^{+} is studied at thermal energy as a function of vibrational excitation in the reactant ion. The selected‐ion flow tube technique coupled with laser‐induced fluorescence detection is used to measure the vibrationally state specific rate constants. A dramatic vibrational enhancement is observed; measuredrate constants are 1.0 (±0.6)×10^{−12}, 2.8 (±0.3)×10^{−12}, 2.1 (±0.2)×10^{−11}, 5.1 (±0.2)×10^{−11}, and 8.3 (±0.4)×10^{−11} cm^{3} molecule^{−1} s^{−1} for v=0, 1, 2, 3 and 4, respectively. Mass spectrometric kinetics experiments are also performed to confirm that vibrational relaxation, N^{+} _{2}(v)+Kr→N^{+} _{2}(v′<v)+Kr, is a negligible process. The charge transfer for v=0 is extremely slow in spite of the large exothermicity (e.g., 0.915 eV for the production of N_{2}(v′=0)+Kr^{+}(^{2} P _{1/2}) states), yet the reaction is enhanced when the apparent energy mismatch is greater for the vibrationally excited reactant. A simple model is proposed to explain the experimental results at thermal energies (≪1 eV). The model assumes that only the most energy‐resonant exothermic transitions, N^{+} _{2}(v)+Kr→N_{2}(v+3)+Kr^{+}(^{2} P _{1/2}), occur within the duration of the ion–molecule collision complex and that the charge transfer takes place with probabilities governed by the corresponding Franck–Condon factors. However, the Franck–Condon factors are modified by a trial displacement of 0.02 Å to account for the changes in vibrational wave functions of N^{+} _{2} and N_{2} during a close approach of the (N_{2}–Kr)^{+} pair; this method gives an excellent description of the experimental results.

Ab initio calculation of hydrogen abstraction energetics from silicon hydrides
View Description Hide DescriptionIn this article, we present calculated energies for the abstraction of hydrogen from silicon monohydride and silicon dihydride surface bonding units by atomic hydrogen obtained using ab initioconfiguration interactiontheory. Three and four silicon atom clusters are used to model the dihydride and monohydride units, respectively. Heats of reaction and activation energy barriers are calculated, including the vibrational energies of the initial, final, and transition states. Hydrogen abstraction from a Si–H unit (H+Si_{4}H_{10}→Si_{4}H_{9}+H_{2}) is found to be exothermic by 9.4 kcal/mol with a transition state energy barrier of 5.5 kcal/mol when H approaches along the surface normal. The dihydride abstraction reaction, H+Si_{3}H_{8}→Si_{3}H_{7}+H_{2}, is exothermic by 7.7 kcal/mol and has an energy barrier of 7.3 kcal/mol when H is approaching along Si–H axis. The barrier is larger for hydrogen atom approaching along the surface normal. The larger barrier for abstraction from a dihydride unit is consistent with our experimental observation of a preferential reduction in monohydride bond concentrations when hydrogenated silicon films are exposed to atomic hydrogen during plasma deposition.