A simple classical prediction of quantal resonances in collinear reactive scattering

Quantal collinear reactive scattering computations have shown that in the vicinity of thresholds of reactant or product vibrational states, one finds resonances in the state to state reaction probability. We find that these resonances can be explained classically in terms of energy transfer between adiabatic reactant and product channels. This transfer is attributable to resonant periodic orbits, resonating between reactants and products. The classical condition for a quantal resonance is that the action of the orbit over one period be an integer (in units of h) and that the energy at which this occurs be lower than the adiabatic barrier heights of the resonating states. These conditions suffice for a prediction of the location of the quantal resonance within a 1% accuracy!     

On the photoexcitation of the 2s→2p transition in light muonic atoms

It is known that the energy of the 2s→2p transition of light μ-atoms can be precisely measured by laser spectroscopy. Such measurements provide a good test of quantum electrodynamics predictions. Here we consider how the hyperfine muon-nucleus interaction effects on the photoexcitation of this transition and on the subsequent X-rays emission. Besides the obvious change of the transition energy the hyperfine interaction mixes the 2p 1/2 and 2p 3/2 orbits. This mixing is rather effective in μ-atoms of¹H,⁷Li,⁹Be,¹⁰B and¹¹B. Its taking into account changes the photoexcitation cross-section of electric dipole transitions between the hyperfine components of the 2s and 2p orbits and an angular X-rays distribution as well. These changes prove to be considerable for some transitions. For example, in μ²H and μ⁷Li the cross-section is decreased by factors of two and four respectively. In μ⁹Be it is increased by a factor of two. Moreover, in μ¹H the angular X-rays distribution becomes more anisotropic. Besides the above subject one more question is discussed here. The fact is that the laser experiments can give an information on the residual muon spin polarization at the 2s orbit and on the degree of alignment of the angular μ-atom momentum in this state. The polarization can be determined by measuring an angular correlation between the X-rays emission direction and the momentum of a hard μ-decay electron. The alignment degree can be found by measuring an anisotropy of the angular X-rays distribution.     

Semiclassical description of large multipole-deformed metal clusters

We use the semiclassical periodic orbit theory to describe large metal clusters with axial quadrupole, octupole, or hexadecapole deformations. The clusters are regarded as cavities with ideally reflecting walls. We start from the case of spherical symmetry and then apply a perturbative approach for calculating the oscillating part of the level density in the deformed case. The advantage of this approach is that one only has to know the periodic orbits of the spherical cavity, which makes the calculation very simple. This perturbative method is a priori restricted to small deformations. However, the results agree quite well with those of quantum-mechanical calculations for deformations that are not too large, such as typically occur for the ground states of metal clusters. We also calculate shell-correction energies. With this, it becomes possible to predict at least qualitatively the deformation energy of metal clusters.     

The phase space geometry underlying roaming reaction dynamics

Recent studies have found an unusual way of dissociation in formaldehyde. It can be characterized by a hydrogen atom that separates from the molecule, but instead of dissociating immediately it roams around the molecule for a considerable amount of time and extracts another hydrogen atom from the molecule prior to dissociation. This phenomenon has been coined roaming and has since been reported in the dissociation of a number of other molecules. In this paper we investigate roaming in Chesnavich’s \(\hbox {CH}_4^+\) model. During dissociation the free hydrogen must pass through three phase space bottleneck for the classical motion, that can be shown to exist due to unstable periodic orbits. None of these orbits is associated with saddle points of the potential energy surface and hence related to transition states in the usual sense. We explain how the intricate phase space geometry influences the shape and intersections of invariant manifolds that form separatrices, and establish the impact of these phase space structures on residence times and rotation numbers. Ultimately we use this knowledge to attribute the roaming phenomenon to particular heteroclinic intersections.     

Optical spectra of sodium microclusters

Photoabsorption spectra have been measured for free neutral sodium clusters containing fromN=3 to 40 atoms. In the size range ofN≈3 to 5, a transition occurs from molecule-like absorption to collective excitations of the valence electrons. ForN≈6 to 12, the data are well described by an ellipsoidal shell model. In open-shell clusters, the multiple surface plasma resonances expected for spheroidal or ellipsoidal shapes are observed. The experimental resonance positions provide a sensitive measurement of the cluster distortions. ForN?13, the per atom strength of these collective resonances is reduced; this may be due to peak fragmentation caused by interaction between the surface plasmon and nearby single-electron resonances. In three distinct wavelength regions, one of which corresponds to the position of the Na atom “D-lines”, additional absorption is seen in the spectra of all investigated clusters.     

Investigation of autoionizing CuI-states in the region of the second ionization limit CuII 3d 94s

The combination of collisional and laser excitation was used for the investigation of autoionizing CuI states in the region of the second ionization limit CuII 3d ⁹ 4s at 85000–95000 cm^?1. The analysis of the complicated signal structure was concentrated on the first measurement of CuI 3d ⁹ 4p ² levels. The experimental results are compared with Hartree-Fock calculations of the energy values and level widths of the autoionization resonances.     

Stereoisograms for reorganizing the theoretical foundations of stereochemistry and stereoisomerism. Part 3: rational avoidance of misleading standpoints for pro-R/pro-S-descriptors

The stereoisogram approach is introduced to settle the misleading terminology due to ‘prochirality’ in modern stereochemistry. After the term prochirality is redefined as having a purely geometric meaning, a method based on probe stereoisograms and another method based on equivalence classes (orbits) are introduced to determine prochirality and/or pro-RS-stereogenicity. Enantiotopic and RS-diastereotopic relationships appearing in probe stereoisograms are respectively used to determine prochirality and pro-RS-stereogenicity, where ‘stereoheterotopic’ relationships used in modern stereochemistry are abandoned. Alternatively, an enantiospheric orbit for specifying prochirality and an RS-enantiotropic orbit for specifying pro-RS-stereogenicity are emphasized by using coset representations and Young tableaux. The pro-R/pro-S-system is clarified to be based on pro-RS-stereogenicity and not on prochirality.     

Photoionization of highly excited atomic sodium involving core-excited resonances

Resonant photoionization in thenl outer-shell of 2p ⁶ nl excited sodium is studied between 32.50 and 33.50 eV. Resonances are of the type 2p ⁶ nl → 2p ⁵ 3snl → 2p ⁶ ελ, i.e. corresponding to the excitation of a 2p core-electron to a 3s orbital. Experimental technique combines laser and synchrotron radiation for exciting sequentially sodium atoms. The main features of the resonances — energies and total oscillator strengths — are measured or estimated. From the results, one concludes that the valence electron is almost decoupled from the core, with respect to the core excitation.     

Exohedral interaction in cationic lithium metallofullerenes

We present a density functional theory study on the exohedral interaction between a singly positively charged lithium atom and fullerenes: Li⁺?C _n , n = 70, 60 and 50. We have found that the interaction is of electrostatic nature: the cation polarizes the π electronic cloud of the fullerene in an ion-induced dipole attraction. We show that these systems present a shallow potential energy surface where the local minima correspond to the interaction of the cation on top of one pentagonal or one hexagonal face of the fullerene and transition states connect them through a movement of the cation over a C?C bond. The type of interaction and the shape of the potential energy surface give rise to the so-called planetary systems, where the alkali cation is revolving around the carbon cage in orbits. The studied systems present several pathways that are more likely than others to behave as potentially favorable orbits.     

Orbiting trajectories and the adiabatic approximation to the capture cross section

For the potentialV(R)=CR ^?4(1+ε(cos²??1/2)) and a planar geometry we compute classical trajectories, which are a good approximation to those trapped orbits which separate collisions with “capture” from those without. Two possible types of such trajectories (rotating or librating in the rotating reference frame) and the transition between both types are discussed. From the limiting impact parameters accurate capture cross sections may be calculated. They can be compared with the popular approximation known as ADO — (average dipole orientation) — theory, but an analysis of the latter shows that it is theoretically not justified. Instead, the adiabatic approximation for planar collisions is developed with and without angular momentum conservation. It fits numerical calculations very well as long as the transition from rotation to libration lies inside the centrifugal wall, i.e. the separating orbit is a rotation. In the opposite case only qualitative agreement is obtained. Finally, a simple approximation to get 3D capture cross sections from planar calculations is discussed.     

Photoabsorption of Fe,Co, and Ni atoms embedded in Al-clusters near 3p-ionization threshold of impurity

Photoionization cross sections of Fe, Co, and Ni atoms inside Al jellium-clusters (containing up to 90 atoms) in the energy range near the 3p ionization threshold of the impurity atom are calculated using the time-dependent local spin-density approximation. The spectra are dominated by resonances and depend markedly on the cluster size. It is obtained that the resonances have an autoionization character and are caused by the interference between discrete electronic transitions from the 3p shell of the impurity atom to unfilled d shells of the jellium-cluster and ionization excitations ofd electrons. For comparison, within the same approach, photoionization cross sections of atomic Fe, Co, and Ni are computed.     

Autocollimation spectroscopy for fast hydrogenic ions

We propose a new experimental method (Autocollimation Spectroscopy), which provides a strong suppression of systematic error contributions in the laser resonance spectroscopy of broad resonances. Using a bidirectional laser beam with a fixed wavelength in connection with high current pulsed ion beams an accuracy ofΔE _Exp/Γ≈5·10^?5 (Γ: resonance width) for the resonance energy seems to be achievable. Applying this technique to 2S-Lamb shift (LS) measurements on medium heavy ions would yield a precision ofΔE _Exp/E _LS≈1·10^?5, i.e. an improvement by a factor up to 100 as compared to present experiments.     

Two-photon absorption of dissociating TLI in strong laser fields

In a strong laser field (I=2 GW/cm²) TlI is dissociated by a two-photon process and the Tl fragment is detected state specifically. The yield of Tl 6p ² P _3/2 (Tl*) is measured as a function of the dissociation wavelength (480 nm–540 nm). If the dissociation wavelength is close to two-photon transitions of the Tl atom from 6p ² P _3/2 to np² P _1/2,3/2 or mf² F _5/2,7/2,n=10 ... 15,m=7 ... 12 dips in the yield are observed. These dips show a significant asymmetric broadening, compared to a free atomic transition and the observation is interpreted as an absorption process of the transient state of dissociating TlI during the laser pulse. By applying the Landau-Zener approximation for the potential crossing of dressed molecular states, we are able to describe the broadening and the power density dependence of the observations. Simulations show that the asymmetry is determined by the difference potential of the electronic states which are coupled by the laser field.     

Non-linear dynamics of the photodissociation of nitrous oxide: equilibrium points, periodic orbits, and transition states

The diffuse vibrational bands, observed in the ultraviolet photodissociation spectrum of nitrous oxide by exciting the molecule in the first (1)A' state, have recently been attributed to resonances localized mainly in the NN stretch and bend degrees of freedom. To further investigate the origin of this localization, fundamental families of periodic orbits emanating from several stationary points of the (1)A' potential energy surface and bifurcations of them are computed. We demonstrate that center-saddle bifurcations of periodic orbits are the main mechanism for creating stable regions in phase space that can support the partial trapping of the wave packet, and thus they explain the observed spectra. A non-linear mechanical methodology, which involves the calculation of equilibria, periodic orbits, and transition states in normal form coordinates, is applied for an in detail exploration of phase space. The fingerprints of the phase space structures in the quantum world are identified by solving the time dependent Schro?dinger equation and calculating autocorrelation functions. This demonstrates that different reaction channels could be controlled if exact knowledge of the phase space structure is available to guide the initial excitation of the molecule.     

57Fe NMR Chemical shifts and 57fe, 13C coupling constants in α-ferrocenyl carbocations. Direct metal participation in the stabilization of metallocenyl carbocations

The ¹³C{⁵⁷Fe} double resonance method has been used to investigate ⁵⁷Fe-enriched samples of ferrocene derivatives, α-ferrocenyl carbocations and carbonyl complexes with various σ- and π-hydrocarbon ligands. In the α-ferrocenyl carbocations the ⁵⁷Fe resonances span a 1200 ppm range, being a sensitive tool of direct iron participation in the stabilization. The ⁵⁷Fe resonances in the carbocations [FcCH₂][HSO₄] (I), [FcCHMe][HSO₄] (II), [FcCHPh][HSO₄] (III), [FcCHC₅H₄ Mn(CO)₃][CF₃CO₂] (IV), [(Fc)₂CH][BF₄] (V), [FcCHC₅H₄RuC₅Hs][BF₄] (VI) and [FcCMe₂][HSO₄] (VII), ?523.6, ?219.3, 221.0, 368.7, 699.0, 405.0 and 288.5 ppm, respectively, relative to ferrocene, are interpreted in terms of rehybridization of the iron non-bonding d orbitals (shielding effect and the electron withdrawing effect of the substituent in the cyclic ligand (deshielding effect). The role of rehybridization of non-bonding iron orbitals in the low-frequency shift of the ⁵⁷Fe resonances, in addition to that in the previously investigated complex [(C₅H₅)₂FeH][BF₃OH] (?1109.3 ppm), has been demonstrated for bridge-substituted [3]ferrocenophanes, whose ring tilting induces a low-frequency shift of up to 340 ppm relative to their unbridged analogues.The ¹³C NMR spectra of carbocations V and VI reveal a temperature dependence due to the rotation around the C(1)C_α exocyclic bonds. In carbocation VI the ruthenium atom effectively competes with the iron atom to bond with C_α whereas in carbocation V two equivalent metal atoms possess the same ability for such bonding; as a result, complex V has a more pronounced “carbenium ion” nature than IV and VI, as indicated by the relative positions of the ¹³C_α resonances in carbocations IV, V and VI: δ 122.4, 147.2 and 116.9 ppm, respectively.The values of ⁵⁷Fe, ¹³C coupling constants for α-ferrocenyl carbocations exclude Fe-C_α σ-bonding and support a structure in which the iron atom is π-bonded with six carbon atoms of a fulvenoid ligand. According to the data on ⁵⁷Fe resonances and ⁵⁷Fe, ¹³C coupling constants in α-ferrocenyl carbocations the strength of FeC_α bonding is markedly influenced by the electronic effect of the substituent at C_α, being even lower in carbocation I than that of Fe-cyclopentadienyl carbon atoms.     

Line patterning of (Sr,Ba)Nb2O6 crystals in borate glasses by transition metal atom heat processing

Some NiO-doped Bi₂O₃,La₂O₃-SrO-BaO-Nb₂O₅-B₂O₃ glasses giving the formation of strontium barium niobate Sr_0.5Ba_0.5Nb₂O₆ (SBN) crystals with a tetragonal tungsten-bronze structure through conventional crystallization in an electric furnace have been developed, and SBN crystal lines have been patterned on the glass surface by heat-assisted (250-300 °C) laser irradiation and scanning of continuous-wave Nd:YAG laser (wavelength: 1064 nm). The surface morphology and the quality of SBN crystal lines are examined from measurements of confocal scanning laser micrographs and polarized micro-Raman scattering spectra. The surface morphology of SBN crystal lines changes from periodic bump structures to homogeneous structures, depending on laser scanning conditions. It is suggested that the line patterned at the laser irradiation condition of laser power P=1 W and of laser scanning speed S=1 μm/s in 2NiO-4La₂O₃-16SrO-16BaO-32Nb₂O₅-30B₂O₃ glass has a possibility of the orientation of SBN crystals along the laser scanning direction. The present study demonstrates that the transition metal atom heat processing (i.e., a combination of cw Nd:YAG laser and Ni²⁺ ions) is a novel technique for spatially selected crystallization of SBN crystals in glass.     

Lineshape theory for three-level double resonance in the presence of infrared laser radiation

A set of coupled optical Bloch equations has been solved to obtain the absorption lineshape for both copropagating and counterpropagating three-level double resonances in the presence of a strong infrared laser source. The resonance conditions and lineshapes derived for the Lamb dip and three-level double resonances are confirmed by recent experimental findings in ¹⁵NH₃.     

Infrared predissociation spectrum of the CH+ ion

A high-resolution infrared spectrum of the CH⁺ ion has been recorded in the range 875–1095 cm⁻¹ using a laser/ion beam spectrometer. Eighty-seven transitions were detected by monitoring increased production of C⁺ fragment ions at resonance arising from predissociation of the upper states. Frequencies, linewidths, doublet splittings, relative intensities and upper state excess energies are reported for the transitions. A prediction of the spectrum, based on data from previous ab initio calculations and spectroscopic studies, was performed by using rotationally adiabatic potentials. Good qualitative agreement between the reported features of the observed spectrum and the prediction is found; the agreement suggests that the majority of the resonances are vibration-rotation transitions within the a ³Π state involving J = 20 to 40 and v = 7 to 12. The doublet splittings (16–672 MHz) are accounted for in terms of the proton nuclear hyperfine Fermi conctact interaction within this state.     

Line-profile analysis of excitation spectroscopy in the even 4p5(2P1/2)nl′ [K′]J（l′=1,3） autoionizing resonances of Kr

The even-parity autoionizing resonance series 4p5np′[3/2]1,2,[1/2]1,and 4p5nf′[5/2]3of krytpon have been investigated by laser excitation from the two metastable states 4p55s[3/2]2and 4p55s′[1/2]0in the photon energy region of 29000–40000 cm 1at experimental bandwidth of~0.1 cm 1.The excitation spectra of the even-parity autoionizing resonance series,most of which are experimentally studied for the first time in this work,show typical asymmetric line shapes.Complementary information on level energies,quantum defects,line profile indices and resonance widths,resonance lifetimes and reduced widths of the autoionizing resonances are derived by Fano-type line-shape analyses of the experimental results.Results from this work indicate that the line profile index(q)and the resonance width()are approximately proportional to the effective principal quantum number(n*);the line separation of the 4p5np′autoionizing resonances is also in good agreement with theoretical model.     

Two-photon spectra of gases by three-wave mixing

We show that the two-photon resonances in the third-order susceptibility can be exploited to yield two-photon spectra of molecular gases at moderately high spectral resolution. This form of spectroscopy does not depend on the occurrence of processes (such as fluorescence of photoionization) leading to indirect methods of two-photon absorption. The method is direct and leads in principle to values for a two-photon cross section. Comparisons of two-photon and coherent anti-Stokes Raman resonances leads to ratios of Raman and two-proton cross sections independent of the laser powers and spatial characteristics. The technique is documented with rotationally resolved spectra of SO₂ and NO. A value for |α_xxα_yy| of 1.5 × 10^?52 cm⁶ was measured for the O₁₂ (6$\text{built:1}\text{2}$) component of the (A)²Σ ← (X)² Π_{$\text{1}\text{2}$} transition of nitric oxide.