Multi-photon ionization in the mass spectrometry of polyatomic molecules: Cross sections

Multi-photon ionization (MPI) with tunable visible/UV laser light is shown to be a sensitive tool for analysis of traces in gas mixtures when combined with a mass spectrometer. Mass spectra of six different organic molecules, obtained with low intensity laser light, are presented and demonstrate the facility of ionization without fragmentation (soft ionization) under proper experimental conditions. Quantitative values for the cross sections for both two photon steps are obtained from the measured intensity dependence and the absolute ion numbers. Such quantitative data help in the evaluation and definition of this new ionization technique in mass spectrometry. Efficiencies of ionization for some molecules are as high as 25% leading to 10⁶ ions in a single pulse from the dye laser (1 kW). Detectability as low as 2 parts in 10⁹ is thus predicted.     

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.     

Semiclassical Low Energy Scattering for One-Dimensional Schr?dinger Operators with Exponentially Decaying Potentials

We consider semiclassical Schr?dinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{{\rm d}^2}{{\rm d}x^2}+V(\cdot;\hbar)$$ with ${\hbar >0 }$ small. The potential V is assumed to be smooth, positive and exponentially decaying towards infinity. We establish semiclassical global representations of Jost solutions ${f_\pm(\cdot,E;\hbar)}$ with error terms that are uniformly controlled for small E and ${\hbar}$ , and construct the scattering matrix as well as the semiclassical spectral measure associated with ${H(\hbar)}$ . This is crucial in order to obtain decay bounds for the corresponding wave and Schr?dinger flows. As an application we consider the wave equation on a Schwarzschild background for large angular momenta ? where the role of the small parameter ${\hbar}$ is played by ? ^?1. It follows from the results in this paper and Donninger et al. (Commun Math Phys 2009, arXiv:0911.3179), that the decay bounds obtained in Donninger et al. (Adv Math 226(1):484–540, 2011) and Donninger and Wilhelm (Int Math Res Not IMRN 22:4276–4300, 2010) for individual angular momenta ? can be summed to yield the sharp t ^?3 decay for data without symmetry assumptions.     

Global dynamics above the ground state energy for the one-dimensional NLKG equation

In this paper we obtain a global characterization of the dynamics of even solutions to the one-dimensional nonlinear Klein–Gordon (NLKG) equation on the line with focusing nonlinearity ${|u|^{p-1}u, p >5 }$ , provided their energy exceeds that of the ground state only sightly. The method is the same as in the three-dimensional case (Nakanishi and Schlag in Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation, preprint, 2010), the major difference being in the construction of the center-stable manifold. The difficulty there lies with the weak dispersive decay of 1-dimensional NLKG. In order to address this specific issue, we establish local dispersive estimates for the perturbed linear Klein–Gordon equation, similar to those of Mizumachi (J Math Kyoto Univ 48(3):471–497, 2008). The essential ingredient for the latter class of estimates is the absence of a threshold resonance of the linearized operator.     

Deuterium isotope effect of single vibronic levels in naphthalene

The isotope effect on the vibronic spectrum of naphthalene has been investigated under conditions of high resolution, enabling the resolution of individual vibronic states. Comparing the isotope effect for fixed vibronic states leads to an unexpected smoothing which is taken as evidence for a triplet communicating system, even though the singlet state is clearly not communicating.     

Hyphenation of gas chromatography and resonance-enhanced laser mass spectrometry (REMPI-TOFMS): A multidimensional analytical technique

Analysis of environmental samples usually requires time consuming sample preparation and clean-up procedures prior to instrumental detection. Faster analysis requires an enhanced instrumental selectivity in order to reduce the necessary clean-up effort. In this context we present a novel concept for coupling gas chromartography/mass spectrometry (GC-MS) with high resolution UV spectoscopy to increase selectivity. We use UV-laser induced, resonance-enhanced multi-photon ionization (REMPI)as a compound specifie ion source for time-of-flight mass spectrometry (TOFMS). The REMPI ionization involves the UV absorption spectroscopy into the ionization process as an aditional analytical dimension. The heart of the GC-REMPI-TOFMS coupling is a specially designed valve, which repetitively (20 Hz) expands the chromatographic eluent as short supersonic jet gas pulses (≈ 150 μs duration) into the vacuum of the mass specrtrometer. The sample molecules are cooled down to temperatures of 10-40 K within the jet expansion. Under these conditions, UV absorption spectriscopy (i.e. REMPi spectroscopy) becomes highly compound selective, even able to distinguish isomeric compounds. The ions formed by REMPI ionization are mass analyzed in the TOFMS. Thus the GC-REMPI-TOFMS coupling presented here is actually a three-dimensional analytical instrument, providing gas chromatographic (retention time) as well as mass spectrometric (molecular mass) and UV -spectroscopic (excitation laser wavelength) selectivity. In combination with gas phase sampling and concentration techniques for semi-volatile organic air pollutants based, e.g., on silicone rubber traps the GC-LAMS technique can be a powerful tool for fast environmental target analysis, e.g. for industrial emission control purposes.     

Benzene clusters in a supersonic beam

A supersonic beam is employed to produce benzene clusters (C₆H₆) _n up ton=40. Mass analysis is achieved after two-photon ionization in a reflectron mass spectrometer. Photon energy is chosen so that the internal energy of the cluster ions is less than 700 meV and a slow decay on the µs time scale is observed. By an energy analysis with the reflecting field it is found that the elimination of one neutral benzene monomer is the favoured dissociation process of the cluster ions. Information about the dissociation pathways of the cluster ions is essential if one is to obtain neutral cluster abundances from the ion mass spectrum. Furthermore an experimental method is presented to obtain pure intermediate state (S ₁←S₀) spectra of selected clusters without interferences from the other clusters present in the molecular beam. This method is based on the observation of the metastable decay of the corresponding cluster ion. When the metastable signal is recorded as a function of photon energy it reflects theS ₁←S ₀ intermediate state spectrum. Spectra are presented for the benzene dimer, trimer, tetramer and pentamer.     

Ultrafast dynamics in thiophene investigated by femtosecond pump probe photoelectron spectroscopy and theory

A hybrid of a time-of-flight mass spectrometer and a time-of-flight "magnetic-bottle type" photoelectron (PE) spectrometer is used for fs pump-probe investigations of the excited state dynamics of thiophene. A resonant two-photon ionization spectrum of the onset of the excited states has been recorded with a tunable UV laser of 190 fs pulse width. With the pump laser set to the first intense transition we find by UV probe ionization first a small time shift of the maxima in the PE spectrum and then a fast decay to a low constant intensity level. The fitted time constants are 80+/-10 fs, and 25+/-10 fs, respectively. Theoretical calculations show that upon geometry relaxation the electronic state order changes and conical intersections between excited states exist. We use the vertical state order S1, S2, S3 to define the terms S1, S2, and S3 for the characterization of the electron configuration of these states. On the basis of our theoretical result we discuss the electronic state order in the UV spectra and identify in the photoelectron spectrum the origin of the first cation excited state D1. The fast excited state dynamics agrees best with a vibrational dynamics in the photo-excited S1 (80+/-10 fs) and an ultrafast decay via a conical intersection, presumably a ring opening to the S3 state (25+/-10 fs). The subsequently observed weak constant signal is taken as an indication, that in the gas phase the ring-closure to S0 is slower than 50 ps. An ultrafast equilibrium between S1 and S2 before ring opening is not supported by our data.     

Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow-up solutions for the wave map problem from ℝ²⁺¹→S ² of the form where u is the polar angle on the sphere, is the ground state harmonic map, λ(t)=t ^-1-ν, and is a radiative error with local energy going to zero as t→0. The number can be prescribed arbitrarily. This is accomplished by first “renormalizing” the blow-up profile, followed by a perturbative analysis. Mathematics Subject Classification (1991) 35L05, 35Q75, 35P25