Assessment of Gaussian-weighted angular resolution functions in the comparison of quantum-mechanically calculated electron momentum distributions with experiment

We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck-Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.

Diffusion and Fokker-Planck-Smoluchowski Equations with Generalized Memory Kernel

The most populated conformer of tetrahydrofuran (C(4)H(8)O) has been diagnosed as the Cs conformer in the present study, jointly using experimental electron momentum spectroscopy (EMS) and quantum mechanics. Our B3LYP/6-311++G** model indicates that the C1 conformation, which is one of the three possible conformations of tetrahydrofuran produced by pseudorotation in the gas phase, is a transition state due to its imaginary frequencies, in agreement with the prediction from a recent ab initio MP2/aug-cc-pVTZ study (J. Chem. Phys. 2005, 122, 204303). The study has identified the fingerprint of the highest occupied molecular orbital (HOMO) of the C(s) (12a') conformer as the most populated conformer. The identification of the C(s) structure, therefore, leads to the orbital-based assignment of the ionization binding energy spectra of tetrahydrofuran for the first time, on the basis of the outer valence Green function OVGF/6-31G* model and the density functional theory (DFT) SAOP/ET-PVQZ model. The present study explores an innovative approach to study molecular stabilities. It also indicates that energetic properties are not always the most appropriate means to study conformer-rich biological systems.

New diagnostic of the most populated conformer of tetrahydrofuran in the gas phase.

High-accuracy absolute triple differential cross sections for ionisation of molecular hydrogen by approximately 4 keV electron impact have been measured in a coplanar asymmetric arrangement. Ejected electron energies were Eb=20 and 100 eV, and momentum transfer values ranged from K=0.1 au (dipolar region) up to approximately 4 au (impulsive region). They are compared with calculations performed within the framework of the first Born approximation and the impulse approximation. A perturbation treatment developed up to second order where the distortion of the ejected electron trajectory is taken into account is in reasonable agreement with the experiments only under impulsive conditions (large K and Eb values), due to the slow convergence of the series development. The factorised first Born approximation where the ejected electron is described by an orthogonalised Coulomb wave is in general good agreement with the experiments. For this model, the length form is found to be better than the velocity form.

http://iopscience.iop.org/article/10.1088/0953-4075/22/21/012/pdf

Triple differential cross sections for molecular hydrogen, both under Bethe ridge conditions and in the dipolar regime. Experiments and theory

The scope of the present work is to reconcile electron momentum spectroscopy with elementary thermodynamics, and refute conclusions drawn by Saha et al. in J. Chem. Phys. 123, 124315 (2005) regarding fingerprints of the gauche conformational isomer of 1,3-butadiene in electron momentum distributions that were experimentally inferred from gas phase (e,2e) measurements on this compound [M. J. Brunger et al., J. Chem. Phys. 108, 1859 (1998)]. Our analysis is based on thorough calculations of one-electron and shake-up ionization spectra employing one-particle Green’s function theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. Accurate spherically averaged electron momentum distributions are correspondingly computed from the related Dyson orbitals. The ionization spectra and Dyson orbital momentum distributions that were computed for the trans-conformer of 1,3-butadiene alone are amply sufficient to quantitatively unravel the shape of all available experimental (e,...

Study of the molecular structure, ionization spectrum, and electronic wave function of 1,3-butadiene using electron momentum spectroscopy and benchmark Dyson orbital theories.

J.N. Migdall

Papers

The electron momentum distribution of molecular hydrogen