In this work, we dissect the performance of  two modern Perdew-Burke-Ernzerhof (PBE)-based double-hybrid (DH) density functionals to predict the isotropic and anisotropic polarizabilities of water nanoclusters (H2O)n [n = 2-6]. The considered models include the cubic integrand (CI) and quadratic integrand (QI) functions as well as the spin-opposite-scaled...

In this paper the study of a nonlocal second order Cahn–Hilliard-type singularly perturbed family of functions is undertaken. The kernels considered include those leading to Gagliardo fractional seminorms for gradients. Using Γ convergence the integral representation of the limit energy is characterized leading to an anisotropic surface energy on interfaces separating different phases.

We study compactness and Γ-convergence for Ginzburg-Landau type functionals. We only assume that the potential is continuous and positive definite close to one circular well, but allow large zero sets inside the well. We show that the relaxation of the assumptions does not change the results to leading order unless the energy is very large.

The Sylvester (d + 2)-points problem deals with the probability S(K) that d + 2 random points taken from a convex compact subset K of Rd are not the vertices of any convex polytope and asks for which sets S(K) is minimal or maximal. While it is known that ellipsoids are the only minimizers of S(K), the problem of the maximum is still open, unless d = 2. In this paper we study generalizations of...

Various exchange and correlation functionals have been examined in density-functional calculations for obtaining reliable optimized structures for dicationic binuclear ruthenocenes bridged by an unsaturated compound, which has a characteristic fulvene-type structure. First, we have performed extensive calculations for ruthenocene (RuCp2) in D5h symmetry. It has been found that the Ru-Cp optimiz...

We compare the definability of total functionals over the reals in two functional-programming approaches to exact real-number computation: the extensional approach, in which one has an abstract datatype of real numbers; and the intensional approach, in which one encodes real numbers using ordinary datatypes. We show that the type hierarchies coincide up to second-order types, and we relate this...

We report the results of theoretical calculations on the optimized structures and relative energies between the D4d and D2 symmetry structures for double-decker type phthalocyanine compounds, Ti(Pc)2, Ti(Pc)2(+), Sn(Pc)2, Sn(Pc)2(+), Sc(Pc)2 and Sc(Pc)2(+), using eighteen types of functionals: B3LYP, B3PW91, B3P86, PBE1PBE, BHandHLYP, BPW91, BP86, M06, M06-2x, M06-HF, M06L, LC-BPW91, LC-ωPBE, C...

A general scheme for systematically modeling long-range corrected (LC) hybrid density functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochemistry, kinetics, and noncovalent interactions, when compared with common hybrid density functionals. The qualitative failures of the commonly used hybrid density functionals in some "difficult problems," such...

We present and discuss the results of calculations of the CaF2 bulk and surface electronic structure. These are based on the ab initio Hartree–Fock (HF) method with electron correlation corrections and on Density Functional Theory (DFT) calculations with different exchange-correlation functionals, including hybrid exchange techniques. Both approaches use the localised Gaussian-type basis set. A...

A set of 41 metal-ligand bond distances in 25 third-row transition-metal complexes, for which precise structural data are known in the gas phase, is used to assess optimized and zero-point averaged geometries obtained from DFT computations with various exchange-correlation functionals and basis sets. For a given functional (except LSDA) Stuttgart-type quasi-relativistic effective core potential...