Related papers: Numerical search of discontinuities in self-consis…
Background: The generation of potential energy surfaces is a critical step in theoretical models aiming to understand and predict nuclear fission. Discontinuities frequently arise in these surfaces in unconstrained collective coordinates,…
A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has…
Monitoring ozone concentrations in the Earth's atmosphere using spectroscopic methods is a major activity which undertaken both from the ground and from space. However there are long-running issues of consistency between measurements made…
The difficulty in exploring potential energy surfaces, which are nonconvex, stems from the presence of many local minima, typically separated by high barriers and often disconnected in configurational space. We obtain the global minimum on…
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…
An efficient and trajectory-free active learning method is proposed to automatically sample data points for constructing globally accurate reactive potential energy surfaces (PESs) using neural networks (NNs). Although NNs do not provide…
Non-adiabatic effects play an important role in many chemical processes. In order to study the underlying non-adiabatic potential-energy surfaces (PESs), we present a locally-constrained density-functional theory approach, which enables us…
In order to predict the potential energy surface (PES) from measured structure in equilibrium state, one should typically perform trial-and-error statistical thermodynamic simulation with assumed multibody interactions. Very recently, we…
In this work we show the advantages of using the Coulomb-hole plus screened-exchange (COHSEX) approach in the calculation of potential energy surfaces. In particular, we demonstrate that, unlike perturbative $GW$ and partial self-consistent…
The potential energy surface (PES) of dissociative adsorption of H_2 on Pd(100) is investigated using density functional theory and the full-potential linear augmented plane wave (FP-LAPW) method. Several dissociation pathways are…
The role of numerical accuracy in training and evaluating neural network-based potential energy surfaces is examined for different experimental observables. For observables that require third- and fourth-order derivatives of the total…
Pseudospectral schemes are a class of numerical methods capable of solving smooth problems with high accuracy thanks to their exponential convergence to the true solution. When applied to discontinuous problems, such as fluid shocks and…
A new nine-dimensional potential energy surface (PES) for methane has been generated using state-of-the-art \textit{ab initio} theory. The PES is based on explicitly correlated coupled cluster calculations with extrapolation to the complete…
Potential Energy Surfaces (PESs) are an indispensable tool to investigate, characterise and understand chemical and biological systems in the gas and condensed phases. Advances in Machine Learning (ML) methodologies have led to the…
A new nine-dimensional potential energy surface (PES) and dipole moment surface (DMS) for silane have been generated using high-level \textit{ab initio} theory. The PES, CBS-F12$^{\,\mathrm{HL}}$, reproduces all four fundamental term values…
Finding index-1 saddle points is crucial for understanding phase transitions. In this work, we propose a simple yet efficient approach, the spring pair method (SPM), to accurately locate saddle points. Without requiring Hessian information,…
An analytical discontinuity is reported in what was thought to be the discontinuity-free exact nonparaxial vortex beam phasor obtained within the complex source/sink model. This discontinuity appears for all odd values of the orbital…
Smoothing splines are twice differentiable by construction, so they cannot capture potential discontinuities in the underlying signal. In this work, we consider a special case of the weak rod model of Blake and Zisserman (1987) that allows…
The idea of a Potential Energy Surface (PES) forms the basis of almost all accounts of the mechanisms of chemical reactions, and much of theoretical molecular spectroscopy. It is assumed that, in principle, the PES can be calculated by…
This paper provides a mathematical approach to study metasurfaces in non flat geometries. Analytical conditions between the curvature of the surface and the set of refracted directions are introduced to guarantee the existence of phase…