Probability in theoretical chemistry.

Emanuele Curotto

The mathematical structure of gauge theory is a union of many modern algebraic concepts. The book provides the background to understand gauge theory and use it in computational chemistry. It introduces two powerful methods used in modern computational chemistry: The Diffusion Monte Carlo algorithm and Ring Polymer Molecular Dynamics. Gauge theory is used to derive a convergent version of the ground state probability amplitude approach for the simulation of excited states. Contains some recent advances in theoretical and computational chemistry. Clear, coherently written explanation of the various background mathematical concepts. Accessible to undergraduate students with many exercises for readers to achieve mastery of the subjects.

Jan C. A. Boeyens

Hinne Hettema

Jennifer I. L. Chen, Georg von Freymann, Sung Yeun Choi +2 more

A driving force in the rapidly developing field of photonic crystals has been the photonic bandgap, a range of energies where the propagation of light is completely forbidden. The photonic bandgap allows the design of photonic lattices that localize, guide and bend light at sub-micron length scales, providing opportunities for the creation of miniature optical devices and integrated optical circuits to help drive the revolution in photonics. A less well known attribute of photonic crystals is their theoretical ability to slow light to a velocity of zero. This phenomenon can be achieved at the high and low energy edges of photonic stopgaps where the photonic bands are flat and light exists as a standing wave commensurate with the photonic lattice and travels at a group velocity of zero, referred to as “slow photons” herein. It has been shown theoretically that the probability of harvesting slow photons scales inversely with their group velocity. This means that a number of well known photon driven processes and devices in chemistry and physics can be enhanced by capturing this unique property of slow photons. In this paper we will look at slow photons mainly through the eye of chemistry and highlight some recent developments in this exciting and emerging field that demonstrate the potential of slow photons in materials chemistry and nanochemistry.

Guillaume Acke, Daria Van Hende, Ruben Van der Stichelen +1 more

Many quantum chemical similarity measures have been derived and substantiated by applying concepts and quantities from information theory to the electron density. To justify the use of information theory, the electron density is usually equated to a probability distribution, despite the fact that such an assumption can give rise to inconsistencies such as negative Kullback-Leibler divergences. In this work we show, using quantum information theory, that both interpreting electron densities as probability distributions as well as any pragmatic normalization thereof gives rise to far-reaching information theoretical inconsistencies. By applying the theory of open quantum subsystems to quantum chemical partitions, we show using thought experiments that many statements concerning the information content of atoms in molecules need to be reconsidered. This study represents a step towards generalizing and reformulating the information theoretical approach to conceptual quantum chemistry beyond its classical perspective.