Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

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

Molecular Reaction Dynamics: Frontmatter

Angle-resolved photoelectron spectroscopy has been performed for more than 70 years in various guises, but recently its potential to help solve in detail problems in the photoionization dynamics and intramolecular dynamics of gas-phase molecules has been recognized. One key development has been the design of experiments in appropriate geometries to extract information that pertains to the molecular frame, another has been the development of imaging spectrometers, and a third is the use of ultrafast lasers to cause photoionization. In this review, which is aimed at experimentalists, simple expressions for photoelectron angular distributions (PADs) in various experimental geometries are given and their applications explained.

Photoelectron angular distributions.

The last decade has seen photoelectron angular distributions from isolated molecules used for an increasing variety of purposes, including examining details of electron correlation, demonstrating electron diffraction as a structural probe of single molecules, and probing photochemical processes. In this article these developments are reviewed and it is shown that the stage is set for another decade of innovation in which we can expect to see exciting results from pump–probe experiments using the emerging XUV and X-ray free-electron laser sources.

Photoelectron angular distributions: developments in applications to isolated molecular systems

Time‐of‐flight photoelectron spectroscopy has been used to record energy‐resolved photoelectron angular distributions (PADs) following (1+1’) resonance‐enhanced multiphoton ionization (REMPI) of NO via the vi=1,Ni=22 rovibrational level of the A 2∑+ state. The PADs corresponding to single rotational states of the resulting molecular ion show a strong dependence on the change in ion core rotation ΔN(≡N+−Ni) and also on the angle between the linear polarization vectors of the two light beams. Broken reflection symmetry [I(θ,φ)≠I(−θ,φ)] is observed when the polarization vectors of the two light beams form an angle of 54.7°. A fit to the PADs provides a complete description of this molecular photoionization, namely, the magnitudes and phases of the radial dipole matrix elements that connect the intermediate state to the ‖lλ〉 photoelectron partial waves (Refs. 1 and 2). This information is then used to predict unobserved quantities, such as ion angular momentum alignment and the full three‐dimensional form of ...

Complete description of two‐photon (1+1’) ionization of NO deduced from rotationally resolved photoelectron angular distributions

The photoionization process NO ${\mathit{A}}^{2}$${\mathrm{\ensuremath{\Sigma}}}^{+}$(v=0, N=22)\ensuremath{\rightarrow}${\mathrm{NO}}^{+}$ ${\mathrm{X}}^{1}$${\mathrm{\ensuremath{\Sigma}}}^{+}$(${\mathit{v}}^{+}$=0, ${\mathit{N}}^{+}$)+${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ is studied with sufficient energy resolution that the photoelectron angular distributions associated with individual rotational levels ${\mathit{N}}^{+}$ of the ion are determined. By ionizing with left and right circularly polarized light and observing the change in the rotationally resolved photoelectron angular distributions, we can deduce all dynamical information, including the signs of the relative phase shifts of the photoelectron partial waves. This information constitutes the first complete description of the photoionization of a molecule.

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Complete description of molecular photoionization from circular dichroism of rotationally resolved photoelectron angular distributions.

A formalism is presented in which the laboratory frame photoelectron angular distribution (PAD) is expressed as a convolution of the molecular frame PAD with the laboratory frame molecular axis distribution. Molecular and laboratory frame PADs are discussed in the context of probing intramolecular dynamics in the time domain. Model calculations for a C3v molecule are presented as an illustration of the differences between measurements in these two reference frames, and the effect of the degree of molecular alignment upon the laboratory frame measurements. Different symmetries of the orbital undergoing ionization are also considered in order to illustrate the sensitivity of PADs to nonadiabatic processes.

Katharine L. Reid

Papers

Photoelectron angular distributions.

Photoelectron angular distributions: developments in applications to isolated molecular systems

Complete description of two‐photon (1+1’) ionization of NO deduced from rotationally resolved photoelectron angular distributions

Complete description of molecular photoionization from circular dichroism of rotationally resolved photoelectron angular distributions.

Time-resolved photoelectron angular distributions as a probe of intramolecular dynamics: Connecting the molecular frame and the laboratory frame