Modeling of Ferroelectric Oxide Perovskites: From First to Second Principles

Taking a historical perspective, we provide a brief overview of the first-principles modeling of ferroelectric perovskite oxides over the past 30 years. We emphasize how the work done by a relatively small community on the fundamental understanding of ferroelectricity and related phenomena has been at the origin of consecutive theoretical breakthroughs, with an impact going often well beyond the limit of the ferroelectric community. In this context, we first review key theoretical advances such as the modern theory of polarization, the computation of functional properties as energy derivatives, the explicit treatment of finite fields, or the advent of second-principles methods to extend the length and timescale of the simulations. We then discuss how these have revolutionized our understanding of ferroelectricity and related phenomena in this technologically important class of compounds. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 13 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Pricing of Commodity and Energy Derivatives for Polynomial Processes

Operating in energy and commodity markets require a management of risk using derivative products such as forward and futures, as well as options on these. Many of the popular stochastic models for spot dynamics and weather variables developed from empirical studies in commodity and energy markets belong to the class of polynomial jump diffusion processes. We derive a tailor-made framework for efficient polynomial approximation of the main derivatives encountered in commodity and energy markets, encompassing a wide range of arithmetic and geometric models. Our analysis accounts for seasonality effects, delivery periods of forwards and exotic temperature forwards where the underlying “spot” is a nonlinear function of the temperature. We also include in our derivations risk management products such as spread, Asian and quanto options.

Orbital Energies and Nuclear Forces in DFT: Interpretation and Validation

The bonding and antibonding character of individual Molecular Orbitals has been previously shown to be related to their orbital energy derivatives with respect to nuclear coordinates, known as Dynamical Orbital Forces. Albeit usually derived from Koopmans' theorem, in this work we show a more general derivation from conceptual DFT, which justifies application in a broader context. The consistency of the approach is validated numerically for valence orbitals in Kohn-Sham DFT. Then, we illustrate its usefulness by showcasing applications in aromatic and antiaromatic systems and in excited state chemistry. Overall, Dynamical Orbital Forces can be used to interpret the results of routine ab initio calculations, be it wavefunction or density based, in terms of forces and occupations.

Orbital Energies and Nuclear Forces in DFT: Interpretation and Validation

The bonding and antibonding character of individual Molecular Orbitals has been previously shown to be related to their orbital energy derivatives with respect to nuclear coordinates, known as Dynamical Orbital Forces. Albeit usually derived from Koopmans' theorem, in this work we show a more general derivation from conceptual DFT, which justifies application in a broader context. The consistency of the approach is validated numerically for valence orbitals in Kohn-Sham DFT. Then, we illustrate its usefulness by showcasing applications in aromatic and antiaromatic systems and in excited state chemistry. Overall, Dynamical Orbital Forces can be used to interpret the results of routine ab initio calculations, be it wavefunction or density based, in terms of forces and occupations.

A Proposal to Fix the Number of Factors on Modeling the Dynamics of Futures Contracts on Commodity Prices

In the literature on modeling commodity futures prices, we find that the stochastic behavior of the spot price is a response to between one and four factors, including both short- and long-term components. The more factors considered in modeling a spot price process, the better the fit to observed futures prices—but the more complex the procedure can be. With a view to contributing to the knowledge of how many factors should be considered, this study presents a new way of computing the best number of factors to be accounted for when modeling risk-management of energy derivatives. The new method identifies the number of factors one should consider in the model and the type of stochastic process to be followed. This study aims to add value to previous studies which consider principal components by assuming that the spot price can be modeled as a sum of several factors. When applied to four different commodities (weekly observations corresponding to futures prices traded at the NYMEX for WTI light sweet crude oil, heating oil, unleaded gasoline and Henry Hub natural gas) we find that, while crude oil and heating oil are satisfactorily well-modeled with two factors, unleaded gasoline and natural gas need a third factor to capture seasonality.