Extrapolating DFT Towards the Complete Basis Set Limit: Lessons from the PBE Family of Functionals

<div>In this work, I derive a set of formulas for calculating extrapolation parameters based on the percentage of HF exchange and PT correlation within the functional recipe. I use a set of CBS energies from finite element calculations, calculated with PBE and related functionals, to do so.<br></div><div>The obtained extrapolation parameters perform better than previous, empirically-derived values. They are shown to be transferrable to non-PBE functionals, and the [2,3]-zeta extrapolations work well in cases with non-covalent character.<br></div>

Extrapolating DFT Towards the Complete Basis Set Limit: Lessons from the PBE Family of Functionals

<div>In this work, I derive a set of formulas for calculating extrapolation parameters based on the percentage of HF exchange and PT correlation within the functional recipe. I use a set of CBS energies from finite element calculations, calculated with PBE and related functionals, to do so.<br></div><div>The obtained extrapolation parameters perform better than previous, empirically-derived values. They are shown to be transferrable to non-PBE functionals, and the [2,3]-zeta extrapolations work well in cases with non-covalent character.<br></div>

Extrapolating DFT Towards the Complete Basis Set Limit: Lessons from the PBE Family of Functionals

<div>In this work, I derive a set of formulas for calculating extrapolation parameters based on the percentage of HF exchange and PT correlation within the functional recipe. I use a set of CBS energies from finite element calculations, calculated with PBE and related functionals, to do so.<br></div><div>The obtained extrapolation parameters perform better than previous, empirically-derived values. They are shown to be transferrable to non-PBE functionals, and the [2,3]-zeta extrapolations work well in cases with non-covalent character.<br></div>

The Fundamentality of Fundamental Powers

Dispositional essentialism is the view that all or many fundamental properties are essentially dispositional, or powers. The literature on the dispositional essence of powers is abundant. In contrast, the question of how to understand the fundamentality of fundamental powers has received scarce interest. Therefore, the fundamentality of powers stands in need of clarification. There are four main conceptions of the fundamental, namely as that which is (i) metaphysically independent; or (ii) belonging to a minimally complete basis; or (iii) perfectly natural; or (iv) metaphysically primitive. Here, I present and discuss each of these approaches from the viewpoint of dispositional essentialism. I show that (i) is incompatible with the metaphysics of powers and (ii)–(iv) have more drawbacks than merits. Therefore, my conclusion is that the dispositional essentialist should seek an alternative. Although I offer no positive account, I pave the way to more fruitful views by identifying the shortcoming of these unpromising options.

Discrete Normal Mode Decompositions in Quasigeostrophic Theory

&lt;p&gt;The baroclinic modes of quasigeostrophic theory are incomplete and the incompleteness manifests as a loss of information in the projection process. The incompleteness of the baroclinic modes is related to the presence of two previously unnoticed stationary step-wave solutions of the Rossby wave problem with flat boundaries. These step-waves are the limit of surface quasigeostrophic waves as boundary buoyancy gradients vanish. A complete normal mode basis for quasigeostrophic theory is obtained by considering the traditional Rossby wave problem with prescribed buoyancy gradients at the lower and upper boundaries. The presence of these boundary buoyancy gradients activates the previously inert boundary degrees of freedom. These Rossby waves have several novel properties such as the presence of multiple equivalent barotropic modes, a finite number of modes with negative norms, and their vertical structures form a basis capable of representing any quasigeostrophic state. Using this complete basis, we are able to obtain a series expansion to the potential vorticity of Bretherton (with Dirac delta contributions). We compare the convergence and differentiability properties of these complete modes with various other modes in the literature. We also examine the quasigeostrophic vertical velocity modes and derive a complete basis for such modes as well. In the process, we introduce the concept of the quasigeostrophic phase space which we define to be the space of all possible quasigeostrophic states. A natural application of these modes is the development of a weakly non-linear wave-interaction theory of geostrophic turbulence that takes prescribed boundary buoyancy gradients into account.&lt;/p&gt;

Dataset of Noncovalent Intermolecular Interaction Energy Curves for 24 Small High-Spin Open-Shell Dimers

<div>We introduce a dataset of 24 interaction energy curves of open-shell noncovalent dimers, referred to as the O24x5 dataset. The dataset consists of high-spin dimers up to eleven atoms selected to assure diversity with respect to interactions types: dispersion, electrostatics and induction. The benchmark interaction energies are obtained at the restricted open-shell CCSD(T) level of theory with complete basis set extrapolation aug-cc-pVQZ--> aug-cc-pV5Z.</div>