There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

Mise au point. Theorie des effets de couplage vibronique multimodes. Probleme a 2 etats. Couplage vibronique mettant en jeu des modes et des etats degeneres. Effets du couplage vibronique multimodes en spectroscopie. Comportement statistique des niveaux d'energie vibroniques. Intersections coniques et evolution temporelle de la fluorescence

Multimode molecular dynamics beyond the Born-Oppenheimer approximation

Recoil-ion and electron momentum spectroscopy is a rapidly developing technique that allows one to measure the vector momenta of several ions and electrons resulting from atomic or molecular fragmentation. In a unique combination, large solid angles close to 4π and superior momentum resolutions around a few per cent of an atomic unit (a.u.) are typically reached in state-of-the art machines, so-called reaction-microscopes. Evolving from recoil-ion and cold target recoil-ion momentum spectroscopy (COLTRIMS), reaction-microscopes—the `bubble chambers of atomic physics'—mark the decisive step forward to investigate many-particle quantum-dynamics occurring when atomic and molecular systems or even surfaces and solids are exposed to time-dependent external electromagnetic fields. This paper concentrates on just these latest technical developments and on at least four new classes of fragmentation experiments that have emerged within about the last five years. First, multi-dimensional images in momentum space brought unprecedented information on the dynamics of single-photon induced fragmentation of fixed-in-space molecules and on their structure. Second, a break-through in the investigation of high-intensity short-pulse laser induced fragmentation of atoms and molecules has been achieved by using reaction-microscopes. Third, for electron and ion-impact, the investigation of two-electron reactions has matured to a state such that the first fully differential cross sections (FDCSs) are reported. Fourth, comprehensive sets of FDCSs for single ionization of atoms by ion-impact, the most basic atomic fragmentation reaction, brought new insight, a couple of surprises and unexpected challenges to theory at keV to GeV collision energies. In addition, a brief summary on the kinematics is provided at the beginning. Finally, the rich future potential of the method is briefly envisaged.

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Recoil-ion and electron momentum spectroscopy: reaction-microscopes

The development of femtosecond time-resolved methods for the study of gas-phase molecular dynamics is founded upon the seminal studies of Zewail and co-workers, as recognized in 1999 by the Nobel Prize in Chemistry.1 This methodology has been applied to chemical reactions ranging in complexity from bond-breaking in diatomic molecules to dynamics in larger organic and biological molecules, and has led to breakthroughs in our understanding of fundamental chemical processes. Photoexcited polyatomic molecules and anions often exhibit quite complex dynamics involving the redistribution of both charge and energy.2-6 These processes are the primary steps in the photochemistry of many polyatomic systems,7 are important in photobiological processes such as vision and photosynthesis,8 and underlie many concepts in molecular electronics.9 Femtosecond time-resolved methods involve a pump-probe configuration in which an ultrafast pump pulse initiates a reaction or, more generally, creates a nonstationary state or wave packet, the evolution of which is monitored as a function of time by means of a suitable probe pulse. Time-resolved or wave packet methods offer a view complementary to the usual spectroscopic approach and often yield a physically intuitive picture. Wave packets can behave as zeroth-order or even classical-like states and are therefore very helpful in discerning underlying dynamics. The information obtained from these experiments is very much dependent on the nature of the final state chosen in a given probe scheme. Transient absorption and nonlinear wave mixing are often the methods of choice in condensed-phase experiments because of their generality. In studies of molecules and clusters in the gas phase, the most popular methods, laser-induced fluorescence and resonant multiphoton ionization, usually require the probe laser to be resonant with an electronic transition in the species being monitored. However, as a chemical reaction initiated by the pump pulse evolves toward products, one expects that both the electronic and vibrational structures of the species under observation will change. Hence, these probe methods can be * To whom corresondence should be addressed. A.S.: telephone (613) 993-7388, fax (613) 991-3437, E-mail albert.stolow@nrc.ca. D.M.N.: telephone (510) 642-3505, fax (510) 642-3635, E-mail dan@radon.cchem.berkeley.edu. 1719 Chem. Rev. 2004, 104, 1719−1757

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Femtosecond time-resolved photoelectron spectroscopy.

Electron–nuclei coupling accompanying excitation and relaxation processes is a fascinating phenomenon in molecular dynamics. A striking and unexpected example of such coupling is presented here in the context of photoelectron circular dichroism measurements on randomly oriented, chiral methyloxirane molecules, unaffected by any continuum resonance. Here, we report that the forward-backward asymmetry in the electron angular distribution, with respect to the photon axis, which is associated with photoelectron circular dichroism can surprisingly reverse direction according to the ion vibrational mode excited. This vibrational dependence represents a clear breakdown of the usual Franck–Condon assumption, ascribed to the enhanced sensitivity of photoelectron circular dichroism (compared with other observables like cross-sections or the conventional anisotropy parameter-b) to the scattering phase off the chiral molecular potential, inducing a dependence on the nuclear geometry sampled in the photoionization process. Important consequences for the interpretation of such dichroism measurements within analytical contexts are discussed.

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Vibrationally induced inversion of photoelectron forward-backward asymmetry in chiral molecule photoionization by circularly polarized light

Ion Chemistry in Atmospheric and Astrophysical Plasmas Ion Chemistry in the Spacecraft Environment Ion-Molecule Reaction Dynamics at Very Low Temperatures Radiative Relaxation of Vibrational States in Small Molecular Ions Ion-Molecule Radiative Association Kinetics in a Finite Heat Bath Systematic Studies of the Thermal Reactivities of Metal Ions Photoelectron Spectroscopy of Reactive Intermediates Interaction of Low Energy Molecular Ions with Metal Surfaces.

Unimolecular and bimolecular ion-molecule reaction dynamics

Circular dichroism in the angular distribution of valence photoelectrons emitted from randomly oriented chiral molecules has been observed in experiments that use circularly polarized VUV synchrotron radiation. Photoionization of the outermost carbonyl oxygen lone pair electrons from pure enantiomers of the prototype chiral molecule camphor is shown to have an asymmetry in the forward–backward scattering of photoelectrons (relative to the propagation direction of the light beam) of magnitude approaching 3% at 9.2 eV photon energy. The asymmetry reverses on exchange of either the helicity of the radiation or of the molecular enantiomer, confirming theoretical predictions of an effect that arises in the pure electric-dipole approximation.

Circular dichroism in the photoelectron angular distribution from randomly oriented enantiomers of camphor

An electron imaging technique has been used to study the full angular distribution of valence photoelectrons produced from enantiomerically pure molecular beams of camphor when these are photoionized with circularly polarized light. In addition to the familiar beta parameter, this provides a new chiral term, taking the form of an additional cosine function in the angular distribution which consequently displays a forward-backward electron ejection asymmetry. Several ionization channels have been studied using synchrotron radiation in the 8.85-26 eV photon energy range. With alternating left and right circularly polarized radiations the photoelectron circular dichroism (PECD) in the angular distribution can be measured and shows some strong dynamical variations with the photon energy, depending in sign and intensity on the ionized orbital. For all orbitals the measured PECD has a quite perfect antisymmetry when switching between R and S enantiomers, as expected from theory. In the HOMO(-1) channel the PECD chiral asymmetry curves show a double maxima reaching nearly 10% close to threshold, and peaking again at approximately 20% some 11 eV above threshold. This is attributed to a resonance that is also visible in the beta parameter curve. Newly optimized CMS-Xalpha photoionization dynamics calculations are also presented. They are in reasonably good agreement with the experimental data, including in the very challenging threshold regions. These calculations show that PECD in such randomly oriented samples can be understood in the electric dipole approximation and that, unlike the case pertaining in core-shell ionization-where a highly localized achiral initial orbital means that the dichroism arises purely as a final state scattering effect-in valence shell ionization there is a significant additional influence contributed by the initial orbital density.

Determination of chiral asymmetries in the valence photoionization of camphor enantiomers by photoelectron imaging using tunable circularly polarized light

Ivan Powis

Papers

Vibrationally induced inversion of photoelectron forward-backward asymmetry in chiral molecule photoionization by circularly polarized light

Unimolecular and bimolecular ion-molecule reaction dynamics

Circular dichroism in the photoelectron angular distribution from randomly oriented enantiomers of camphor

Determination of chiral asymmetries in the valence photoionization of camphor enantiomers by photoelectron imaging using tunable circularly polarized light

Valence shell one-photon photoelectron circular dichroism in chiral systems