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.

As an intermediate state of matter between the free monomeric gas phase and the solid state, clusters may exhibit a specific electronic structure and photoionization dynamics that can be unraveled by different types of electron spectroscopies. From mass-selected ion yield scans measured for photoionization of (R)-camphor, the ionization potentials (IPs) of the monomer (8.66{+-}0.01 eV), and of the homochiral dimer ({<=}8.37{+-}0.01 eV) and trimer ({<=}8.30{+-}0.01 eV) were obtained. These spectra, combined with threshold photoelectron spectroscopy and velocity map ion imaging, allow us to show that the camphor monomer and dimer photoionization channels are decoupled, i.e., that the highest occupied molecular orbital (HOMO) of the dimer does not undergo a dissociative ionization process that would lead to a spurious contribution to the monomer ion channel. Therefore mass selection, as achieved in our imaging photoelectron-photoion coincidence experiments, leads to size selection of the nascent monomer or dimer species. Since both the monomer and dimer are chiral, their photoelectron angular distribution (PAD) not only involves the usual {beta} anisotropy parameter but also a chiral asymmetry parameter b{sub 1} that can generate a forward-backward asymmetry in the PAD. This has been investigated using circularly polarized light (CPL) to record the photoelectron circular dichroism (PECD)more » in the near-threshold vacuum-ultraviolet (VUV) photoionization region. Analysis of size-selected electron images recorded with left- and right-handed CPL shows that over the first 1.5 eV above the HOMO orbital ionization potentials (IPs), the {beta} parameter is not affected by the dimerization process, while the chiral b{sub 1} parameter shows clear differences between the monomer and the dimer, confirming that PECD is a subtle long-range probe of the molecular potential.« less

Effects of dimerization on the photoelectron angular distribution parameters from chiral camphor enantiomers obtained with circularly polarized vacuum-ultraviolet radiation

In the present work the photoelectron circular dichroism of camphor has been theoretically studied using B-spline and continuum multiple scattering-Xα methods, and comparisons are made with available experimental data. In general, rather large dichroism effects have been found for both valence and core (O 1s, C 1s) photoionizations. The agreement between the two calculations reported here and previous experimental measurements for core C 1s data is essentially quantitative. For valence ionization satisfactory agreement between theory and experiment has been obtained and the discrepancies have been attributed to both exchange-correlation potential limitations and the absence of response effects in the adopted formalism. The calculations predict, moreover, important features in the cross-section profiles, which have been discussed in terms of dipole-prepared continuum orbitals.

Theoretical study on the circular dichroism in core and valence photoelectron angular distributions of camphor enantiomers.

Molecule coordinate frame anisotropy in dissociative photoionization of CF3I

Measurements made with a dilute, non-oriented, gas-phase sample of a selected fenchone enantiomer using circularly polarized synchrotron radiation demonstrate huge chiral asymmetries, approaching 20%, in the angular distribution of photoelectrons ejected from carbonyl C 1s core orbitals. This asymmetry in the forward-backward scattering of electrons along the direction of the incident soft X-ray radiation reverses when either the enantiomer or the left-right handedness of the light polarization is exchanged. Calculations are provided that model and explain the resulting photoelectron circular dichroism with quantitative accuracy up to approximately 7 eV above threshold. A discrepancy at higher energies is discussed in the light of a comparison with the closely related terpene, camphor. The photoelectron dichroism spectrum can be used to identify the absolute chiral configuration, and it is more effective at distinguishing the similar camphor and fenchone molecules than the corresponding core photoelectron spectrum.

Giant chiral asymmetry in the C 1s core level photoemission from randomly oriented fenchone enantiomers.

The ionization energy of CF3+ is investigated by synchrotron radiation photoionization experiments using a skimmed molecular beam of CF3Br. Care is taken to eliminate contributions from higher energy second-order radiation from the monochromator gratings and to characterize the molecular beam. From the corrected 0 K CF3+ appearance energy of 12.07 ± 0.02 eV, we calculate the adiabatic CF3 ionization energy to be 9.04 ± 0.04 eV, a value in excellent agreement with recent calculations and a number of experiments. Apparent discrepancies with other, significantly lower, determinations of the ionization potential are discussed and explained − particularly those arising from a previous CF3Br molecular beam experiment − confirming a recently proclaimed consensus favoring a value as obtained here.

Ivan Powis

Papers

Effects of dimerization on the photoelectron angular distribution parameters from chiral camphor enantiomers obtained with circularly polarized vacuum-ultraviolet radiation

Theoretical study on the circular dichroism in core and valence photoelectron angular distributions of camphor enantiomers.

Molecule coordinate frame anisotropy in dissociative photoionization of CF3I

Giant chiral asymmetry in the C 1s core level photoemission from randomly oriented fenchone enantiomers.

Ionization Energy of CF3 Deduced from Photoionization of Jet-Cooled CF3Br