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.

We present an inversion method called pBasex aimed at reconstructing the original Newton sphere of expanding charged particles from its two-dimensional projection by fitting a set of basis functions with a known inverse Abel integral. The basis functions have been adapted to the polar symmetry of the photoionization process to optimize the energy and angular resolution while minimizing the CPU time and the response to the cartesian noise that could be given by the detection system. The method presented here only applies to systems with a unique axis of symmetry although it can be adapted to overcome this restriction. It has been tested on both simulated and experimental noisy images and compared to the Fourier-Hankel algorithm and the original Cartesian basis set used by [Dribinski et al.Rev. Sci. Instrum. 73, 2634 (2002)], and appears to give a better performance where odd Legendre polynomials are involved, while in the images where only even terms are present the method has been shown to be faster and simpler without compromising its accuracy.

Two-dimensional charged particle image inversion using a polar basis function expansion

In this Perspective we discuss photoelectron circular dichroism (PECD), a relatively novel technique that can detect chiral molecules with high sensitivity. PECD has an enantiomeric sensitivity of typically 1–10%, which is two to three orders of magnitude larger than that of the widely employed technique of circular dichroism (CD). In PECD a chiral molecule is photoionized with circular polarized light, and the photoelectron angular scattering distribution is detected using particle imaging techniques. We present the general physical principles of photoelectron circular dichroism and we address both single- and multiphoton excitation. PECD has been measured with synchrotron radiation in single-photon ionization as well as, very recently, with femtosecond laser radiation in multiphoton ionization. We discuss the experimental implementation of PECD, focusing on velocity map coincidence imaging where the momentum distribution of both the electron and the coincident ion is measured. The coincident detection of the mass and momentum of the ion adds very powerful mass-correlated information to the PECD measurement of the chiral molecule. We illustrate the capabilities and the potential of PECD with various experimental examples and introduce computational methods that are able to model quantitatively experimental PECD results. We conclude with an outlook on novel developments and (analytical) implementations of PECD that may further broaden the application of PECD for the sensitive detection of chirality in molecules.

Detecting chirality in molecules by imaging photoelectron circular dichroism

Here, we provide a detailed account of novel experiments employing electron-ion coincidence imaging to discriminate chiral molecules. The full three-dimensional angular scattering distribution of electrons is measured after photoexcitation with either left or right circular polarized light. The experiment is performed using a simplified photoelectron-photoion coincidence imaging setup employing only a single particle imaging detector. Results are reported applying this technique to enantiomers of the chiral molecule camphor after three-photon ionization by circularly polarized femtosecond laser pulses at 400 nm and 380 nm. The electron-ion coincidence imaging provides the photoelectron spectrum of mass-selected ions that are observed in the time-of-flight mass spectra. The coincident photoelectron spectra of the parent camphor ion and the various fragment ions are the same, so it can be concluded that fragmentation of camphor happens after ionization. We discuss the forward-backward asymmetry in the photoelectron angular distribution which is expressed in Legendre polynomials with moments up to order six. Furthermore, we present a method, similar to one-photon electron circular dichroism, to quantify the strength of the chiral electron asymmetry in a single parameter. The circular dichroism in the photoelectron angular distribution of camphor is measured to be 8% at 400 nm. The electron circular dichroism using femtosecond multiphoton excitation is of opposite sign and about 60% larger than the electron dichroism observed before in near-threshold one-photon ionization with synchrotron excitation. We interpret our multiphoton ionization as being resonant at the two-photon level with the 3s and 3p Rydberg states of camphor. Theoretical calculations are presented that model the photoelectron angular distribution from a prealigned camphor molecule using density functional theory and continuum multiple scattering X alpha photoelectron scattering calculations. Qualitative agreement is observed between the experimental results and the theoretical calculations of the Legendre moments representing the angular distribution for the two enantiomers. The electron-ion coincidence technique using multiphoton ionization opens new directions in table-top analytical mass-spectrometric applications of mixtures of chiral molecules.

Imaging photoelectron circular dichroism of chiral molecules by femtosecond multiphoton coincidence detection

The differing interaction of left and right circularly polarized light with chiral molecules is shown to lead to different angular distributions of the photoelectrons created by photoionization of a given enantiomer, even when the target molecules are randomly oriented Numerical calculations are presented to demonstrate the magnitude of this effect for the C3H6O3 structural isomers lactic acid and glyceraldehyde, including two different conformations of the latter Circular dichroism in the angular distributions (CDAD) of the valence electrons of these biomolecules is most pronounced close to threshold, but tends to vanish as the electron kinetic energy approaches 20 eV and above CDAD signals are predicted to range, typically, from 10% to 40% and sometimes to more than 60% of the differential cross section

Photoelectron circular dichroism of the randomly oriented chiral molecules glyceraldehyde and lactic acid

Partial table of contents: An Historical Introduction to Threshold Photoionization (T. Baer & P.-M. Guyon). High Resolution Spectroscopy with Photoelectrons: ZEKE Spectroscopy of Molecular Systems (K. Muller-Dethlefs). State-Resolved Photoionization Dynamics of Small Molecules Using Coherent VUV Radiation (R. Wiedman & M. White). VUV-ZEKE Photoelectron Spectroscopy: Final-State Interactions in Small Molecular Systems (F. Merkt & T. Softley). Rotationally Resolved Autoionization of Molecular Rydberg States (H. Lefebvre-Brion). Exploiting Polarization in the Study of Molecular Photoionization Dynamics (K. Reid & D. Leahy). ZEKE Studies with Picosecond Lasers (J. Knee). Physics of Near-Threshold States in Molecular Hydrogen (E. Eyler). Indexes.

Ivan Powis

Papers

Two-dimensional charged particle image inversion using a polar basis function expansion

Detecting chirality in molecules by imaging photoelectron circular dichroism

Imaging photoelectron circular dichroism of chiral molecules by femtosecond multiphoton coincidence detection

Photoelectron circular dichroism of the randomly oriented chiral molecules glyceraldehyde and lactic acid

High resolution laser photoionization and photoelectron studies