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.

Molecule-frame photoelectron angular distributions are obtained by the measurement of electron–ion recoil vector correlations in the dissociative 5a1−1 photoionization of CF3I. The laboratory frame orientation of an ionized molecule is inferred from the CF3+ fragment ion recoil direction and the contributions of radiation polarized perpendicular and parallel to the molecular axis can be estimated. This allows the degenerate ka1 and ke continua to be distinguished, each having a distinctive angular distribution. Experimental data are compared with calculated fixed-molecule photoelectron angular distributions.

The 5a1−1 photoionization of oriented CF3I molecules: Angular distributions of the ka1 and ke photoelectron continua

The distributions of internal energy released into translation in the fragmentation of energy-selected acetone ions (as determined by photoelectron-photoion coincidence studies) are shown to obey a scaling law, as do the calculated distributions derived from a statistical-dynamical phase space theory. A single function contains the dynamical history of the reaction system, at least at higher energies, in contrast to the predictions of the rigid rotor harmonic oscillator model. The scaling law provides an analysis of the bimodal form of the translational energy distributions which are found for the dissociation of the enol form of the acetone ion. This is shown to be consistent with the ergodic hypothesis.

Scaling relationships in photoelectron-photoion coincidence studies: The aceton ion dissociation

A photoelectron—photoion coincidence study of acetaldehyde and ethylene oxide molecular ions

K.L.R. acknowledges EPSRC for funding Grant Nos.
GR/M83759 and GR/R72297, including postdoctoral support
for J.A.D. and S.M.B.

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An unusual π* shape resonance in the near-threshold photoionization of S₁ para-difluorobenzene

Multiphoton photoelectron circular dichroism (MP-PECD) has been observed as an asymmetry in the angular distribution of photoelectrons emitted in the ionization of pure enantiomers of the small chiral molecule methyloxirane using a femtosecond laser operated at 420 nm. Energetically, this requires the uptake of four photons. By switching the laser between left- and right-circular polarization, and observing the differences in the full three-dimensional electron momentum distribution recorded in an electron–ion coincidence technique, the chiral (odd) terms in the angular distribution expression can be isolated. Electron events can additionally be filtered by coincident ion mass, providing mass-tagged electron distributions and quantitative measures of the MP-PECD asymmetry that help characterize the different ionization channels. For the production of ground state parent cation, the magnitude of the mean chiral asymmetry is measured to be 4.7%, with a peak magnitude exceeding 10%

Ivan Powis

Papers

The 5a1−1 photoionization of oriented CF3I molecules: Angular distributions of the ka1 and ke photoelectron continua

Scaling relationships in photoelectron-photoion coincidence studies: The aceton ion dissociation

A photoelectron—photoion coincidence study of acetaldehyde and ethylene oxide molecular ions

An unusual π* shape resonance in the near-threshold photoionization of S₁ para-difluorobenzene

Chiral Asymmetry in the Multiphoton Ionization of Methyloxirane Using Femtosecond Electron–Ion Coincidence Imaging