Edward R. Grant

Topological phase in molecular bound states: Application to the E⊗e system

We extend recent works of Berry, Simon, and others on the evolution of adiabatic wave functions in parameter spaces with nontrivial global geometry, to show the interesting ways in which wave functions can acquire nonintegrable phase (commonly termed Berry’s phase, geometric phase, or topological phase) upon transport along paths in the parameter space. We emphasize the case of arbitrary paths on the Born–Oppenheimer potential energy surfaces (the parameter space of the electronic states in an isolated molecule) of the linear plus quadratic E⊗e Jahn–Teller system. It is found that these surfaces are degenerate not only at the origin but also at three other, equivalent points, which lie on a radius ρ=2k/g. Here k and g are the linear and quadratic vibronic coupling constants, respectively. This radius is then shown to mark a sharp transition between Jahn–Teller behavior, characterized by half‐odd‐integral vibronic angular momentum, and Renner–Teller behavior, which has integral angular momentum. Finally, w...

Rotationally resolved photoionization of H2O

A rotationally resolved one‐photon threshold photoionization spectrum of jet‐cooled water (H2O and D2O) has been obtained by pulsed field ionization of extremely high‐n Rydberg states. Observed spectral intensities for both vibrationless (0,0,0) and vibrationally excited (1,0,0) water cation show a strong propensity for ΔN=0, ±1 transitions. In contrast to earlier work on O2 and HCl, the lack of large ΔN transitions suggests that ionization occurs with only small angular momentum transfers between the core and photoelectron. The presence of both type A and type C ‘‘symmetric top’’ transitions varies from the conclusions of a recent MQDT analysis of H2O photoionization, which predicts only type C transitions. Rotational analysis of the spectra yields improved ionization potentials for both H2O and D2O. The ionization potential of the (1,0,0) vibrational level provides a direct measurement of the symmetric stretch fundamental in H2O+ which is in excellent agreement with an earlier indirect determination. Ro...

On the shape of C6H6

The benzene molecule serves as a benchmark among the aromatic hydrocarbons and has been the subject of numerous experimental and theoretical studies. Despite such intensive investigations, the precise structure of the benzene cation (C6H6+) is not known. Now, experiments measuring high-resolution state-to-state threshold photoionization spectra of benzene concretely establish the terms of vibronic levels in the distorted cation that are split by higher order Jahn-Teller coupling between its 2E1g electronic ground state and ν6 e2g in-plane ring-bending vibrational mode. This assignment, in turn, sets the absolute energy phase of the vibronic pseudorotation in this coordinate and thereby offers a definitive experimental determination of the shape of the benzene cation.

“I believe I will go out of this class actually knowing something”: Cooperative learning activities in physical chemistry

The purposes of this study were to describe the structure of events during cooperative learning activities—Friday discussion sessions—in a graduate-level thermodynamics course and to understand what these activities meant to the students. First, we describe the structure of Friday discussion sessions in our classroom, which were used to focus student attention on conceptual issues rather than algorithmic problem solving. Second, we delineate findings which emerge from the perspective of the students. We found that cooperative learning activities move students away from rote learning strategies and toward more meaningful strategies which allowed them to integrate concepts over the entire semester. In addition, we discovered that the sharing of insights and ideas between students leads to the development of interpersonal skills and communication skills which the students perceive as an important component of the Friday discussion sessions. Implications for further classroom use, low-status versus high-status students, and assessment are discussed. J Res Sci Teach 34: 819–835, 1997.

High-resolution threshold photoionization of N2O

Pulsed field ionization (PFI) has been used in conjunction with a coherent vuv source to obtain high‐resolution threshold photoelectron spectra for the (000), (010), (020), and (100) vibrational states of the N2O+ cation. Simulations for the rotational profiles of each vibronic level were obtained by fitting the Buckingham–Orr–Sichel equations [A. D. Buckingham, B. J. Orr, and J. M. Sichel, Philos. Trans. R. Soc. London, Ser. A 268, 147 (1970)] using accurate spectroscopic constants for the ground states of the neutral and the ion. The relative branch intensities are interpreted in terms of the partial waves of the outgoing photoelectron to which the ionic core is coupled and in terms of the angular momentum transferred to the core. The PFI technique also allows us to report an improved value for the ionization potential of N2O of 103 963±5 cm−1.

Determination of Sudan I in paprika powder by molecularly imprinted polymers–thin layer chromatography–surface enhanced Raman spectroscopic biosensor

Sudan I is a carcinogenic and mutagenic azo-compound that has been utilized as a common adulterant in spice and spice blends to impart a desirable red color to foods. A novel biosensor combining molecularly imprinted polymers (MIPs), thin layer chromatography (TLC) and surface enhanced Raman spectroscopy (SERS) could determine Sudan I levels in paprika powder to 1 ppm (or 2 ng/spot). Sudan I spiked paprika extracts (spiking levels: 0, 1, 5, 10, 40, 70 and 100 ppm) were prepared. Sudan I imprinted polymers were synthesized by employing the interaction between Sudan I (template) and methacrylic acid (functional monomer), followed by washing to remove Sudan I leaving the Sudan I-binding sites exposed. MIPs were used as a stationary phase for TLC and could selectively retain Sudan I at the original spot with little interference. A gold colloid SERS substrate could enhance Raman intensity for Sudan I in this MIP-TLC system. Principal component analysis plot and partial least squares regression (R(2)=0.978) models were constructed and a linear regression model (R(2)=0.983) correlated spiking levels (5, 10, 40, 70 and 100 ppm) with the peak intensities (721 cm(-1)) of Sudan I SERS spectra. Both separation (30-40s) and detection (1s or 0.1s) were extremely fast by using both commercial bench-top and custom made portable Raman spectrometers. This biosensor can be applied as a rapid, low-cost and reliable tool for screening Sudan I adulteration in foods.

Evolution from a molecular Rydberg gas to an ultracold plasma in a seeded supersonic expansion of NO.

We report the spontaneous formation of a plasma from a gas of cold Rydberg molecules. Double-resonant laser excitation promotes nitric oxide, cooled to 1 K in a seeded supersonic molecular beam, to single Rydberg states extending as deep as 80 cm;{-1} below the lowest ionization threshold. The density of excited molecules in the illuminated volume approaches 1x10;{13} cm;{-3}. This population evolves to produce free electrons and a durable cold plasma of electrons and intact NO+ ions.

Photoelectron spectroscopy and electronic structure of clusters of the group V elements. II. Tetramers: Strong Jahn–Teller coupling in the tetrahedral 2E ground states of P+4, As+4, and Sb+4

High resolution HeI (584 A) photoelectron spectra have been obtained for the tetrameric clusters of the group V elements: P4, As4, and Sb4. The spectra establish that the ground 2E states of tetrahedral P+4, As+4, and Sb+4 are unstable with respect to distortion in the ν2(e) vibrational coordinate. The E⊗e Jahn–Teller problem has been treated in detail, yielding simulated spectra to compare with experimental ones. Vibronic calculations, extended to second order (quadratic coupling) for P+4, account for vibrational structure which is partially resolved in its photoelectron spectrum. A Jahn–Teller stabilization energy of 0.65 eV is derived for P+4, which can be characterized in its ground vibronic state as being highly distorted, and highly fluxional. Linear‐only Jahn–Teller coupling calculations performed for As+4 and Sb+4, show good qualitative agreement with experimental spectra, yielding stabilization energies of 0.84 and 1.4 eV, respectively.

Rovibrational structure of NO+2 and state‐to‐state dynamics in the high‐resolution threshold photoionization of NO2

Triple‐resonant zero‐kinetic‐energy (ZEKE) photoelectron spectroscopy is employed to characterize the rovibrational structure of NO+2. Relative threshold positions determine vibrational frequencies and rotational constants; while anomalous, and in some cases forbidden, intensities of transitions provide information on rotational and vibrational coupling between the NO+2 core and electronic degrees of freedom associated with Rydberg orbitals of very high principal quantum number. Trends in the strengths of anomalous threshold photoionization features establish that mode selectivity, which has a pronounced effect on the vibrational autoionization dynamics of NO2, also operates to determine the envelope of rotational‐line intensities in threshold photoionization. Competition between rotationally and vibrationally mediated coupling leads to a dependence of the rotational profile on the mode of vibrational motion of the core.

Triple‐resonance spectroscopy of the higher excited states of NO2 : Rovibronic interactions, autoionization, and l‐uncoupling in the (100) manifold

Ionization‐detected absorption spectra of the (100) vibrationally autoionizing states of NO2 have been recorded from double‐resonantly prepared N’=1 and N’=7 rotational levels of the 3pσ 2Σ+u (100) Rydberg intermediate state. Photoselection associated with three‐color triple‐resonant absorption spectroscopy resolves single rotational lines in discrete electronic states that lie above the adiabatic ionization threshold at total energies as high as 78 800 cm−1. Most features observed can be assigned to sσ, dσ, and dπ series converging to the (100) vertical threshold. Identified transitions extend over an interval of principal quantum numbers ranging from 9 to more than 40. A fourth short progression of sharp transitions is assigned as a segment of a g series. The complete spectrum of (100) transitions is modulated in intensity by a sequence of dips that form a series of states, recognized as pσ and pπ, converging to the (110) threshold. Evidence is cited for a mirror‐image effect in autoionizing rates, wher...