Hückel method | EPFL Graph Search

The Hückel method or Hückel molecular orbital theory, proposed by Erich Hückel in 1930, is a simple method for calculating molecular orbitals as linear combinations of atomic orbitals. The theory predicts the molecular orbitals for π-electrons in π-delocalized molecules, such as ethylene, benzene, butadiene, and pyridine. It provides the theoretical basis for Hückel's rule that cyclic, planar molecules or ions with 4n+2 π-electrons are aromatic. It was later extended to conjugated molecules such as pyridine, pyrrole and furan that contain atoms other than carbon and hydrogen (heteroatoms). A more dramatic extension of the method to include σ-electrons, known as the extended Hückel method (EHM), was developed by Roald Hoffmann. The extended Hückel method gives some degree of quantitative accuracy for organic molecules in general (not just planar systems) and was used to provide computational justification for the Woodward–Hoffmann rules. To distinguish the original approa

Comparison of computational methods for the electrochemical stability window of solid-state electrolyte materials

Aris Marcolongo, Matthieu Gilles Mottet

Superior stability and safety are key promises attributed to all-solid-state batteries (ASSBs) containing solid-state electrolyte (SSE) compared to their conventional counterparts utilizing liquid electrolyte. To unleash the full potential of ASSBs, SSE materials that are stable when in contact with the low and high potential electrodes are required. The electrochemical stability window is conveniently used to assess the SSE-electrode interface stability. In the present work, we review the most important methods to compute the SSE stability window. Our analysis reveals that the stoichiometry stability method represents a bridge between the HOMO-LUMO method and the phase stability method (grand canonical phase diagram). Moreover, we provide computational implementations of these methods for SSE material screening. We compare their results for the relevant Li- and Na-SSE materials LGPS, LIPON, LLZO, LLTO, LATP, LISICON, and NASICON, and we discuss their relation to published experimental stability windows.

ROYAL SOC CHEMISTRY2020

Modern computational approaches for quantifying inter- and intramolecular interactions

Jérôme Florian Gonthier

This thesis introduces modern computational approaches for quantifying and analyzing both intra- and intermolecular interactions. An original formalism to quantify intramolecular interactions ab initio is first introduced. Inspired from intermolecular Symmetry-Adapted Perturbation Theory (SAPT), we derive a zeroth-order wavefunction, Ψ(0), suitable for development of an intramolecular variant of SAPT. Ψ(0) is constructed based upon the Chemical Hamiltonian concept and uses strictly localized orbitals to suppress the interactions between two intramolecular fragments. As a result, the total zeroth-order energy corresponds to a relaxed wavefunction that excludes interactions between relevant intramolecular fragments. Numerical tests on propane and halogenated derivatives yield both reasonable energy convergence and intuitive chemical trends. Moreover, the proposed scheme provides a promising description of intramolecular hydrogen bonds and energy profiles. Thus, Ψ(0) delivers the relevant information necessary to the prospected derivation of intramolecular SAPT. Besides our quest for a rigorous ab initio intramolecular energy scheme, we also propose a simpler method based on bond separation reactions to assess (de)stabilizing interactions associated with various 1,3-nonbonded substituent patterns within highly branched alkanes. While n- and singly methylated alkanes show positive bond separation energies (BSE) (i.e., stabilization), which increase systematically along the series, permethylated alkanes are characterized by decreasing BSEs (i.e., destabilizing interactions). Our quantitative analysis shows that singly methylated alkanes are more stabilized than linear alkane chains and that the unique destabilizing feature of permethylated alkanes arises from the close proximity of bulky methyl groups causing highly distorted geometries along the carbon backbone. The enhancement of intermolecular interactions constitutes yet another objective of this thesis. We demonstrate that π-depleted polyaromatic molecules present superior π-stacking ability. This somewhat counterintuitive realization is quantified using a novel computational criterion, LOLIPOP, that identifies π-conjugated frameworks presenting the desired electronic features. The screening of molecular targets benefits greatly from such a rational design criteria, which can detect the most promising candidates. The utility of the LOLIPOP criterion is thus demonstrated by identifying chemosensors presenting enhanced π-stacking ability. In particular, we have designed tailored chemosensors, which display remarkable sensitivity and selectivity towards caffeine relying upon the formation of π-π stacked complexes. Finally, the importance of weak intermolecular interactions was also shown to be essential when considering an assembly of four tetrathiafulvalene (TTF) molecules as a potential metal-free molecular catalyst for the four-electron reduction of O2 to H2O. Based on experimental evidence, we demonstrated that vii Acknowledgements the formation of a non-covalently bond helical tetramer [TTF4H2]2+ is able to deliver the needed four electrons and protons to convert O2 into water.

EPFL2013

Regret Minimization in Stochastic Non-Convex Learning via a Proximal-Gradient Approach

Volkan Cevher, Shaul Nadav Hallak

This paper develops a methodology for regret minimization with stochastic first-order oracle feedback in online, constrained, non-smooth, non-convex problems. In this setting, the minimization of external regret is beyond reach for first-order methods, and there are no gradient-based algorithmic frameworks capable of providing a solution. On that account, we focus on a local regret measure defined via a proximal-gradient mapping, that also encompasses the original notion proposed by Hazan et al, (2017). To achieve no local regret in this setting, we develop a proximal-gradient method based on stochastic first-order feedback, and a simpler method for when access to a perfect first-order oracle is possible. Both methods are order-optimal (in the min-max sense), and we also establish a bound on the number of proximal-gradient queries these methods require. As an important application of our results, we also obtain a link between online and offline non-convex stochastic optimization manifested as a new proximal-gradient scheme with complexity guarantees matching those obtained via variance reduction techniques.

JMLR-JOURNAL MACHINE LEARNING RESEARCH2021

Modern computational approaches for quantifying inter- and intramolecular interactions

Jérôme Florian Gonthier

EPFL2013