Charge-transfer in time-dependent density-functional theory via spin-symmetry-breaking

Long-range charge-transfer excitations pose a major challenge for time-dependent density functional approximations. We show that spin-symmetry-breaking offers a simple solution for molecules composed of open-shell fragments, yielding accurate excitations at large separations when the acceptor effectively contains one active electron. Unrestricted exact-exchange and self-interaction-corrected functionals are performed on one-dimensional models and the real LiH molecule within the pseudopotential approximation to demonstrate our results.Comment: 5 pages, 4 figure

Density functional theory in one-dimension for contact-interacting fermions

A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for short-ranged interactions. The exact-exchange contribution to the total energy is a local functional of the density. A local density approximation for correlation is obtained using perturbation theory and Bethe-Ansatz results for the one-dimensional contact-interacting uniform Fermi gas. The ground-state energies are calculated for two finite systems, the analogs of Helium and of Hooke's atom. The local approximation is shown to be excellent, as expected.Comment: 10 pages, 7 Figure

Use of isotopes for studying reaction mechanisms. 4. Distinguishing between single minima and rapidly equilibrating structures

The method of isotopic perturbation of equilibrium is described. In conjunction with nuclear magnetic resonance spectroscopy, the procedure can be used to distinguish between double well and single minimum potential energy surfaces. Some representative studies on classical and non-classical carbocations are discussed

Organic reaction mechanisms

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Use of isotopes for studying reaction mechanisms: 3. Secondary kinetic isotope effect

The effects of isotopic substitution on equilibrium constants and reaction rates in processes which do not directly involve the isotopic atom are described. In particular, the mechanistic details which can be obtained by quantifying the secondary kinetic isotope effect and steric isotope effect are illustrated

Adaptive Seeding for Gaussian Mixture Models

We present new initialization methods for the expectation-maximization algorithm for multivariate Gaussian mixture models. Our methods are adaptions of the well-known $K$-means++ initialization and the Gonzalez algorithm. Thereby we aim to close the gap between simple random, e.g. uniform, and complex methods, that crucially depend on the right choice of hyperparameters. Our extensive experiments indicate the usefulness of our methods compared to common techniques and methods, which e.g. apply the original $K$-means++ and Gonzalez directly, with respect to artificial as well as real-world data sets.Comment: This is a preprint of a paper that has been accepted for publication in the Proceedings of the 20th Pacific Asia Conference on Knowledge Discovery and Data Mining (PAKDD) 2016. The final publication is available at link.springer.com (http://link.springer.com/chapter/10.1007/978-3-319-31750-2 24

Synthetic Magnetic Resonance Imaging Revisited

Synthetic magnetic resonance (MR) imaging is an approach suggested in the literature to predict MR images at different design parameter settings from at least three observed MR scans. However, performance is poor when no regularization is used in the estimation and otherwise computationally impractical to implement for three-dimensional imaging methods. We propose a method which accounts for spatial context in MR images by the imposition of a Gaussian Markov Random Field (MRF) structure on a transformation of the spin-lattice relaxation time, the spin-spin relaxation time and the proton density at each voxel. The MRF structure is specified through a Matrix Normal distribution. We also model the observed magnitude images using the more accurate but computationally challenging Rice distribution. A One-Step-Late Expectation-Maximization approach is adopted to make our approach computationally practical. We evaluate predictive performance in generating synthetic MR images in a clinical setting: our results indicate that our suggested approach is not only computationally feasible to implement but also shows excellent performance