A master equation approach to the dynamics of zero electron kinetic energy (ZEKE) states and ZEKE spectroscopy.

We have theoretically studied important dynamic processes involved in zero electron kinetic energy (ZEKE) spectroscopy using the density matrix method with the inverse Born-Oppenheimer approximation basis sets. In ZEKE spectroscopy, the ZEKE Rydberg states are populated by laser excitation (either a one- or two-photon process), which is followed by autoionizations and l-mixing due to a stray field. The discrimination field is then applied to ionize loosely bound electrons in the ZEKE states. This is followed by using the extraction field to extract electrons from the ZEKE levels which have a strength comparable to that of the extraction field. These extracted electrons are measured for the relative intensities of the ion states under investigation. The spectral positions are determined by the applied laser wavelength and modified by the extraction electric field. In this paper, all of these processes are conducted within the context of the density matrix method. The density matrix method can provide not only the dynamics of system's population and coherence (or phase) but also the rate constants of the processes involved in the ZEKE spectroscopy. Numerical examples are given to demonstrate the theoretical treatments.

Molecular dynamics of hydrogen bonds in protein-D2O: the solvent isotope effect.

We suggest that the H-bond in proteins not only mirrors the motion of hydrogen in its own atomistic setting but also finds its origin in the collective environment of the hydrogen bond in a global lattice of surrounding H2O molecules. This water lattice is being perturbed in its optimal entropic configuration by the motion of the H-bond. Furthermore, bonding interaction with the lattice drop the H-bond energy from some 5 kcal/mol for the pure protein in the absence of H2O, to some 1.6 kcal/mol in the presence of the H2O medium. This low value here is determined in a computer experiment involving MD calculations and is a value close to the generally accepted value for biological systems. In accordance with these computer experiments under ambient conditions, the H-bond energy is seriously depressed, hence confirming the subtle effect of the H2O medium directly interacting with the H-bond and permitting a strong fluxional behavior. Furthermore, water produces a very large change in the entropy of activation due to the hydrogen bond breakage, which affects the rate by as much as 2 orders of magnitude. We also observe that there is an entire ensemble of H-bond structures, rather than a single transition state, all of which contribute to this H-bond. Here the model is tested by changing to D2O as the surrounding medium resulting in a substantial solvent isotope effect. This demonstrates the important influence of the environment on the individual hydrogen bond.

Dissociation kinetics of peptide ions.

The dissociation of peptide ions has been found to have ultrafast components that in many ways are uniquely different from typical unimolecular kinetics. As such, some peptide reactions provide new channels, which do not conform to statistical models of reaction kinetics. When the dissociation rates are in the 100 fs range, they are in a time scale where statistical methods do not yet apply, although molecules that have not yet dissociated will later in time undergo statistical redistribution of their excess energy, which, however, may not lead to noticeable reactivity within the experimental time frames for large peptides and hence are simply dissipative. This work is meant to reconcile the long time statistical results of Lifshitz et al. (2003) with the work of Schlag et al. (1995/6) that suggests an alternate parallel and much faster time scale for dissociation. It is argued that the two sets of results and interpretations augment one another and in fact open up a most interesting new field of peptide kinetics in addition to the unimolecular behavior, which becomes de facto arrested by the shear size of the molecule being unable to find a transition state on any reasonable time scale.

Energetics of hydrogen bonds in peptides.

Hydrogen bonds and their relative strengths in proteins are of importance for understanding protein structure and protein motions. The correct strength of such hydrogen bonds is experimentally known to vary greatly from approximately 5-6 kcal/mol for the isolated bond to approximately 0.5-1.5 kcal/mol for proteins in solution. To estimate these bond strengths, here we suggest a direct novel kinetic procedure. This analyzes the timing of the trajectories of a properly averaged dynamic ensemble. Here we study the observed rupture of these hydrogen bonds in a molecular dynamics calculation as an alternative to using thermodynamics. This calculation is performed for the isolated system and contrasted with results for water. We find that the activation energy for the rupture of the hydrogen bond in a beta-sheet under isolated conditions is 4.76 kcal/mol, and the activation energy is 1.58 kcal/mol for the same beta-sheet in water. These results are in excellent agreement with observations and suggest that such a direct calculation can be useful for the prediction of hydrogen bond strengths in various environments of interest.

Logic gates using high Rydberg states.

Connected logic gates can be operated on the levels of one molecule by making use of the special properties of high Rydberg states. Explicit experimental results for the NO molecule are provided as an example. A number of other options, including that of several gates concatenated so as to operate as a full adder, are discussed. Specific properties of high Rydberg states that are used are: their autoionization is delayed so that they can be distinguished from direct multiphoton ionization, during their long life such states also can decay by energy transfer to the molecular core in a way that can be controlled by the judicious application of very weak external electrical fields, and the Rydberg states can be detected by the application of an ionizing electrical field. The combination of two (or three) color photons with and without external weak fields allows the construction of quite elaborate logic circuit diagrams and shows that taking advantage of the different intramolecular dynamics of levels that differ by their excitation enables the compounding of logic operations on one molecular frame.

Dynamical principles in biological processes: a model of charge migration in proteins and DNA.

The generalized master equations (GMEs) that contain multiple time scales have been derived quantum mechanically. The GME method has then been applied to a model of charge migration in proteins that invokes the hole hopping between local amino acid sites driven by the torsional motions of the floppy backbones. This model is then applied to analyze the experimental results for sequence-dependent long-range hole transport in DNA reported by Meggers et al. [Meggers, E., Michel-Beyerle, M. E., & Giese, B. (1998) J. Am. Chem. Soc. 120, 12950-12955]. The model has also been applied to analyze the experimental results of femtosecond dynamics of DNA-mediated electron transfer reported by Zewail and co-workers [Wan, C., Fiebig, T., Kelley, S. O., Treadway, C. R., Barton, J. K. & Zewail, A. H. (1999) Proc. Natl. Acad. Sci. USA 96, 6014-6019]. The initial events in the dynamics of protein folding have begun to attract attention. The GME obtained in this paper will be applicable to this problem.

Charge conductivity in peptides: dynamic simulations of a bifunctional model supporting experimental data.

Our previous finding and the given mechanism of charge and electron transfer in polypeptides are here integrated in a bifunctional model involving electronic charge transfer coupled to special internal rotations. Present molecular dynamics simulations that describe these motions in the chain result in the mean first passage times for the hopping process of an individual step. This "rest and fire" mechanism is formulated in detail-i.e., individual amino acids are weakly coupled and must first undergo alignment to reach the special strong coupling. This bifunctional model contains the essential features demanded by our prior experiments. The molecular dynamics results yield a mean first passage time distribution peaked at about 140 fs, in close agreement with our direct femtosecond measurements. In logic gate language this is a strongly conducting ON state resulting from small firing energies, the system otherwise being a quiescent OFF state. The observed time scale of about 200 fs provides confirmation of our simulations of transport, a model of extreme transduction efficiency. It explains the high efficiency of charge transport observed in polypeptides. We contend that the moderate speed of weak coupling is required in our model by the bifunctionality of peptides. This bifunctional mechanism agrees with our data and contains valuable features for a general model of long-range conductivity, final reactivity, and binding at a long distance.