Search

Development and applications of neural network (NN)-based approaches for representing potential energy surfaces (PES) of bound and reactive molecular systems are reviewed. Specifically, it is shown that when the density of ab initio points is low, NNs-based potentials with multibody or multimode structure are advantageous for representing high-dimensional PESs. Importantly, with an appropriate choice of the neuron activation function, PESs in the sum-of-products form are naturally obtained, thus addressing a bottleneck problem in quantum dynamics. The use of NN committees is also analyzed and it is shown that while they are able to reduce the fitting error, the reduction is limited by the nonrandom nature of the fitting error. The approaches described here are expected to be directly applicable in other areas of science and engineering where a functional form needs to be constructed in an unbiased way from sparse data. © 2014 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The XPS of many oxides are quite complex and there may be several peaks of significant intensity for each subshell. These peaks arise from many-electron effects, which normally are treated with configuration interaction (CI) wavefunctions where static correlation effects are taken into account. It is common to use semiempirical methods to determine the matrix elements of the CI Hamiltonian and there are few rigorous CI calculations where parameters are not adjusted to fit experiment. In contrast, we present, in the present work, theoretical XPS spectra obtained with rigorous CI wavefunctions for CeO2 where the XPS are especially complex; several different core levels are studied. This study uses an embedded CeO8 cluster model to represent bulk CeO2 and the relativistic CI wavefunctions are determined using four-component spinors from Dirac-Fock calculations. In particular, we examine the importance of interatomic many-body effects where there is a transfer of electrons from occupied oxygen 2p orbitals into empty cation orbitals as it is common to ascribe the complex XPS to this effect. We also contrast the importance of many-body charge-transfer effects for the isoelectronic cations of Ce4+ and La3+. The long-range goal of this work is to relate the XPS features to the nature of the chemical bonding in CeO2 and we describe our progress toward this goal. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [ABSTRACT FROM AUTHOR]

We informally discuss a number of puzzling fundamental issues that illustrate one might view the laws of physics as a loosely connected patchwork of different theories, rather than a grand unified scheme, even within the realm of chemistry. One long-lasting difficulty is the merging of special relativity and quantum mechanics: the many-body Dirac equation, which is the most satisfactory description of the effects of relativity in chemistry, is not Lorentz invariant. In this article, we address the formulation of a manifestly Lorentz invariant classical mechanics in which each particle is described by individual space and time coordinates, while the system as a whole evolves according to a Hamiltonian dynamics based upon a universal evolution parameter. The physical interpretation of the theoretical framework, or its agreement with experiment, in particular when the transition would be made to a quantum theory in four dimensions, is not clear at present. Our search for an understanding of the physical concepts underlying the covariant mechanics has led to a broader view on the use of mathematical and theoretical physics: it could possibly be at the basis for a “computable physics” in which the laws of physics are redesigned such that they are optimally suited for computer simulations, rather than aim for the accurate description of physical reality. In the final section of the article, it is argued that this may be a fertile way to address some of the natural resource problems the world is likely to face in the future. This article essentially covers much of the material presented by one of the authors (MN) at the Odyssey meeting in Edmonton, June 2008, and we hope reflects some of the stimulating discourse that can ensue when people from different disciplines are brought together to share their thoughts. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [ABSTRACT FROM AUTHOR]