J. Manz

On the concentration and time dependence of the energy transfer to randomly distributed acceptors

In this paper we derive a general exact expression for the ensemble averaged time decay of the excitation of a donor due to the incoherent direct energy transfer to randomly distributed acceptors in a solid. Various acceptor species may be present simultaneously. The formula found is valid for all times and for arbitrary acceptor concentrations. It lends itself readily to numerical evaluation and can, for microscopic interactions of particular interest, be approximated analytically. As special cases we retrieve the Forster–type decay laws for isotropic multipolar interactions in spaces of arbitrary dimensions, and the Golubov–Konobeev exact expression for a single acceptor species. From the numerical results we establish the limits of validity of the Forster‐type equations, and determine the influence of the lattice structure on the excitation decay. In some cases the lattice leads to an additional pattern superimposed on the smooth decay.

Collinear triatomic reactions described by polar Delves coordinates

Delves, i.e., polar coordinates with the three‐atom coincidence as origin, are adapted for computations of collinear collisions, involving vibrationally inelastic, reactive, and dissociative channels and for arbitrary masses. The exact quantum reaction probabilities are obtained by S matrix propagation from the strong interaction region towards the asymptotic reactant, product and dissociation configurations. The new method is approved by excellent agreement with the exact solution of an idealized model reaction with L‐shaped potential and infinite walls.

Theory of optimal laser pulses for selective transitions between molecular eigenstates

Abstract We present a new theoretical approach to optimal laser pulses designed for selective transitions between molecular eigenstates, within the semiclassical dipole approximation. Optimization proceeds iteratively, starting from a rather arbitrary, e.g. continuous wave, reference and yielding efficient modulations of the laser field intensities, frequencies, and phases. The method is verified by successful application to state-selective vibrational excitation of a Morse oscillator representing the OH bond in H 2 O by a subpicosecond laser pulse. The present theory is also compared with complementary approaches to optimal laser pulses inducing selective dissociations or excitations to bond-selective stretches in model polymers.

Dynamics of hyperspherical and local mode resonance decay studied by time dependent wave packet propagation

Time dependent wave packet propagation of resonance states of ABA molecules is used to demonstrate the correlation between the directionality of the lobes of the wave functions and mode selectivity of the unimolecular decay. This correlation was inferred by Hose and Taylor. The molecule is modeled by the Thiele–Wilson coupled Morse oscillators. A near‐degenerate pair of resonances with extreme motions is studied in detail: The local ‘‘bond’’ mode with lobes pointing towards the exit valleys of the potential decays about 30 times faster than the hyperspherical ‘‘restricted precession’’ mode with dominant lobe on the potential ridge. This is in close analogy to mode selectivity in the Henon–Heiles system. The wave function propagation technique also yields detailed insight into the dissociation mechanism. Out of several choices, only a single lobe penetrates into the exit valley. For the local mode resonance vibrational predissociation starts out primarily from extended vibrationally excited diatomic config...

A new possibility of chemical bonding: vibrational stabilization of IHI

Abstract The IHI system has four vibrationally bonded collinear bound states. They are located in the saddle point region of a minimum-free potential energy surface.

Oscillating reactivity of collinear symmetric heavy+light–heavy atom reactions

The oscillatory reaction probability (as a function of energy) of collinear heavy+light–heavy systems (e.g., I+HI→IH+I) that has been seen in earlier quantum mechanical reactive scattering calculations is shown to be described quantitatively by a semiclassical WKB model. Because these reactions are highly vibrationally adiabatic they reduce to a two‐state symmetric resonance system (analogous to symmetric charge transfer, e.g., H++H→H+H+) that involves only the phase shifts of the one‐dimensional g (symmetric) and u (antisymmetric) combinations of the two states. Comparisons of the semiclassical and quantum mechanical reaction probabilities over a wide range of energy for the cases I+MuI→IMu+I and I+HI→IH+I show almost perfect agreement. The vibrationally adiabatic symmetric exchange problem is also solved classically (analytically) and is seen to have an interesting relation to the quantum/semiclassical result. The classical reaction probability is also an oscillatory function of energy, although the str...

The effect of reagent energy on chemical reaction rates: An information theoretic analysis

The effect of changing reagent vibrational and rotational energy on the reaction rate has been analyzed for over 20 chemical reactions. In most cases the selectivity in energy requirements could be characterized by a single (’’consumption potential’’) parameter, even when the reactivity varied by many orders of magnitude. The reactions analyzed covered atom–diatom and diatom–diatom collisions and included both simple rearrangement (’’exchange’’) reactions as well as collision induced dissociation (CID) and quenching of electronically excited states. The results were derived both from experiments and classical trajectory computations and include the variation in reactivity at both a given total collision energy and at a given translational (and rotational) temperature. In all cases the analysis was based on evaluating the surprisal of the energy consumption, i.e., the observed (or computed) reaction rate constant was compared to the rate expected on prior grounds when all states (at a given total energy) r...

Exact quantum transition probabilities by the state path sum method: Collinear F + H2 reaction

Exact quantum mechanical transition probabilities have been calculated for the collinear F + H2 →H + HF reaction by the State Path Sum method. The potential energy surface used is based on the ab initio SCF CI surface of Bender et al. For the energy range considered, four product channels are open. Pronounced level inversion is found. The dominant transition is the 3 ←0 one. It has a resonance-like energy dependence which is similar to that for the 2 ←0 transition. The 1 ←0 and 0 ←0 transition probabilities are negligible. These results are compared with those of Wu et al. and Schatz et al. who use semi-empirical LEPS surfaces.

Selective preparation of enantiomers by laser pulses: quantum model simulation for H2POSH

Abstract This Letter presents the first quantum model simulation of the selective preparation of enantiomers by means of optimal, elliptically polarized, infrared picosecond laser pulses. The laser-driven molecular dynamics is demonstrated by the time evolution of the representative wavepacket, from the initial state which corresponds to a 50:50% racemate of two equivalent enantiomers with opposite chiralities towards the nearly 100:0% preparation of a single enantiomer. The wavepacket dynamics is based on the quantum ab initio potential energy surface and dipole functions for the torsional vibration of the hydrogen atom around the P–S molecular axis of the model system H 2 POSH.

Selective preparation of enantiomers from a racemate by laser pulses: model simulation for oriented atropisomers with coupled rotations and torsions

Abstract We design a laser pulse which drives a racemate of oriented atropisomers at low temperature to a preferential target enantiomer. The overall laser pulse consists of a series of individual circularly polarized laser pulses which induce corresponding selective transitions between coupled rotational and torsional states. The underlying theory is derived in detail for a model system. It consists of two fragments which may carry out torsional and rotational motions around a molecular bond which is oriented along the direction of the laser pulses. Exemplarily, results are demonstrated for the model system H 2 POSH in the electronic ground state, based on a quantum chemical ab initio potential and on the components of the dipole functions describing the laser–dipole interaction. The series of laser pulses for the preparation of the pure enantiomers for this demanding system is based on analogous results for simpler scenarios, originally starting from local control.