ALBERT

Notes: Using a time-dependent variational method, we study the evolution of nonstationary states in Longuet-Higgin's model of a Jahn–Teller molecule. Conditions are found for the nuclear motion to be adiabatic. The effects of wave-packet spreading are neglected upon specializing to the case of nearly harmonic motion. It is shown explicitly how the effective vector potential introduced by Mead and Truhlar gives rise to an electronic Berry phase. In a semiclassical approximation sufficient to produce the electronic adiabatic phase anticipated from the result for a given sequence of nuclear configurations, it is demonstrated that the effective vector potential has a negligible effect on the nuclear motion; the effective vector potential, the source of an effective field proportional to (h-dash-bar), is seen to affect the nuclear trajectory only in higher order. For the special case of periodic nuclear motion the electronic adiabatic phase is seen as a contribution to the geometric phase attending an arbitrary cyclic evolution. It is demonstrated that a molecular state prepared with identically pseudorotating nuclear wave packets in both electronic levels corresponds, in a weak coupling limit, to a spin 1/2 in a conically varying external field. Geometrical phase differences are shown to make discernible contributions to the frequencies of oscillation of the electronic charge and current densities, which may serve as classical sources for superradiant emission. Our results are shown to be gauge invariant.

Notes: High resolution laser spectroscopy of the NiH molecule in a magnetic field has revealed strong homogeneous and heterogeneous perturbations among all of the low-lying electronic states. Fully resolved Zeeman splitting patterns from transitions between NiH magnetic sublevels were recorded with the technique of Zeeman optical–optical double resonance (ZOODR) spectroscopy. Using only the zero-field rotational energy levels as input to an electronic structure model, we have calculated Zeeman splittings (g values) for 19 rotational levels, and the predicted splittings are in very good agreement with observed Zeeman spectra. A group of 10 NiH molecular electronic states is seen to form a supermultiplet of levels originating from the Ni+ (3d9)2D atomic multiplet. We describe an effective Hamiltonian matrix that contains explicit terms coupling low-lying states through spin–orbit, vibrational, and rotational interactions. Supermultiplet eigenvectors graphically illustrate the profound mixing hidden beneath the apparent regularity of term value plots for the low-lying states of NiH. The success of the supermultiplet model for this simplest case (a single hole in a highly contracted 3d subshell), namely the successful prediction of strongly J dependent g values, makes us confident that this model will be applicable to other transition metal monohydrides.

Notes: A model for the calculation of the electronic spectrum of a triatomic molecule for the case of a forbidden transition that becomes allowed due to vibronic coupling is presented. The model represents the upper electronic state potential in terms of a small number of variables that can be determined from experimental measurements, and takes into account the dependence of the transition moment on the geometry of the molecule. The model is used to analysis the 225 nm system of OCS. In general, there is good agreement between available experimental information on the absorption spectrum and the results obtained from the model. There are however some limitations in the model, particularly in the way in which it treats higher order and coupling terms in the upper state stretching modes of OCS. The model is useful for predicting the effect of vibrational excitation on a molecular electronic spectrum. The model can be used to analyze the spectra of a number of other molecules besides OCS, and provides a starting point for more sophisticated photodissociation models.

Notes: We introduce a novel spectroscopic technique which utilizes a two-pulse sequence of femtosecond duration phase-locked optical laser pulses to resonantly excite vibronic transitions of a molecule. In contrast with other ultrafast pump–probe methods, in this experiment a definite optical phase angle between the pulses is maintained while varying the interpulse delay with interferometric precision. For the cases of in-phase, in-quadrature, and out-of-phase pulse pairs, respectively, the optical delay is controlled to positions that are integer, integer plus one quarter, and integer plus one half multiples of the wavelength of a selected Fourier component. In analogy with a double slit optical interference experiment, the two the two pulse experiments reported herein involve the preparation and quantum interference of two nuclear wave packet amplitudes state of a molecule.These experiments are designed to be sensitive to the total phase evolution of the wave packet prepared by the initial pulse. The direct determination of wave packet phase evolution is possible because phase locking effectively transforms the interferogram to a frame which is referenced to the optical carrier frequency, thereby eliminating the high (optical) frequency modulations. This has the effect of isolating the rovibrational molecular dynamics. The phase locking scheme is demonstrated for molecular iodine. The excited state population following the passage of both pulses is detected as the resultant two-beam dependent fluorescence emission from the B state. The observed signals have periodically recurring features that result from the vibrational dynamics of the molecule on the electronically excited potential energy surface. In addition, coherent interference effects cause the magnitude and sign of the periodic features to be strongly modulated. The two-pulse phase-locked interferograms are interpreted herein by use of a simple analytic model, by first order perturbation theory and by quantum mechanical wave packet calculations. We find the form of the interferogram to be determined by the ground state level from which the amplitude originates, the deviation from impulsive preparation of the wave packet due to nonzero pulse duration, the frequency and anharmonicity of the target vibrational levels in the B state, and the detuning of the phase-locked frequency from resonance. The dependence of the interferogram on the phase-locked frequency and phase angle is investigated in detail.

Notes: The solvation of the cesium ion by methanol has been investigated by gas-phase vibrational spectroscopy and Monte Carlo simulations of small ion clusters: Cs(CH3OH)+N, N=4–25. The solvated ions, generated by thermionic emission and a molecular-beam source, have considerable amounts of internal energy. After excessive energy is dissipated by evaporation, quasistable cluster ions are mass-selected for vibrational predissociation spectroscopy using a line-tunable cw-CO2 laser. Analysis of the vibrational spectra indicates that the first solvation shell about the cesium ion consists of ten methanol molecules. Larger Cs(CH3OH)+N (N〉18) appear to have small clusters of methanol bound to the surface of a solvated ion. Monte Carlo simulations using pairwise interaction potentials at 200, 250, and 300 K have been performed on Cs(CH3OH)+N, N=6–16 and 25. The results from the simulations are consistent with the observed solvent shell size and suggest a significant role for hydrogen bonding in the larger solvated ions (N≥10). Once the first solvation shell is filled, the size of the solvent shell appears to be independent of the number of additional solvent molecules. Gas-phase solvated ions appear to be extremely useful models for dilute electrolyte solutions.

Notes: We analyze the use of vibrationally abrupt nonresonant laser pulses to prepare coherently pseudorotating states in a model Jahn–Teller molecule. Our derivation of impulsive excitation invokes the dynamical adiabatic phase for the perturbed electronic ground state. Polarization selection between two Raman active distortion coordinates allows creation of an orbit of arbitrary eccentricity. Repetition of the pulse pair at the pseudorotational frequency amplifies the nuclear motion. Timing of a resonant pulse of given polarization, or choice of polarization for a given delay, transfers the moving wave packet to either or both Jahn–Teller branches of an electronic excited state.

Notes: Exact calculations are presented which detail the process of polaron formation in the one-dimensional acoustic chain. Exact solution is possible because the limit considered is the transportless limit in which the Hamiltonian matrix elements responsible for the motion of an excitation among site states have been set to zero. The polaron formation process is found to be decomposable into two subprocesses having distinct time scales. A disparity of time scales is possible in the case of long wavelength excitations. The consistency of our conclusions is demonstrated through the consensus of results obtained for the discrete acoustic chain, the Debye model, and the elastic continuum.

Notes: The ionization potentials (IPs) of several large carbon clusters Cn (n≥48), including the enhanced abundance ("magic number'') clusters C50, C60, and C70, have been determined by Fourier transform ion cyclotron resonance (FTICR) mass spectrometric charge transfer bracketing experiments. The IPs of C50, C60, and C70 were bracketed by the same two charge transfer compounds, leading to a common value of 7.61±0.11 eV. The IPs of even numbered clusters adjacent to these magic number clusters were found to be lower by as much as 0.5 eV and all clusters between C50 and C200 were determined to have IPs greater than 6.20 eV. The reaction rates of C+60 and C+70 with metallocenes were anomalously slow in comparison to the other large carbon cluster ions. IP and reactivity results suggest that C50, C60, and C70 may indeed have different or more stable structures than neighboring clusters, which supports the hypothesis of closed-shell, spherical species. The implications of these results for the mechanism of C+n formation by direct laser vaporization are also discussed.

Notes: We show that the relation between D-branes and noncommutative tachyons leads very naturally to the relation between D-branes and K-theory. We also discuss some relations between D-branes and K-homology, provide a noncommutative generalization of the ABS construction, and give a simple physical interpretation of Bott periodicity. In addition, a framework for constructing Neveu–Schwarz fivebranes as noncommutative solitons is proposed. © 2001 American Institute of Physics.