Evaluation of a combination of local hybrid functionals with DFT-D3 corrections for the calculation of thermochemical and kinetic data

Due to their position-dependent exact exchange admixture, local hybrid functionals offer a higher flexibility and thus the potential for more universal and accurate exchange correlation functionals compared to global hybrids with a constant admixture, as has been demonstrated in previous work. Yet, the local hybrid constructions used so far do not account for the inclusion of dispersion-type interactions. As a first exploratory step toward a more general approach that includes van der Waals-type interactions with local hybrids, the present work has added DFT-D3-type corrections to a number of simple local hybrid functionals. Optimization of only the s(8) and s(r,6) parameters for the S22 set provides good results for weak interaction energies but deteriorates the excellent performance of the local hybrids for G3 atomization energies and for classical reaction barriers. A combined optimization of the two DFT-D3 parameters with one of the two parameters of the spin-polarized local mixing function (LMF) of a local hybrid for a more general optimization set provides simultaneously accurate dispersion energies, improved atomization energies, and accurate reaction barriers, as well as excellent alkane protobranching ratios. For other LMFs, the improvements of such a combined optimization for the S22 energies have been less satisfactory. The most notable advantage of the dispersion-corrected local hybrids over, for example, a B3LYP-D3 approach, is in the much more accurate reaction barriers.     

Numerical range of operators acting on Banach spaces

The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small weighted Hardy space has zero.     

Topologically Mixing and Hypercyclicity of Tuples

In this paper,we characterize conditions under which a tuple of bounded linear operators is topologically mixing.Also,we give conditions for a tuple to be hereditarily hypercyclic with respect to a tuple of syndetic sequences.     

Crossed graphene: Stability and electronic structure

Carbon has always attracted attention due to its rich chemistry and the almost complementary properties of the natural phases graphite and diamond. While graphite is a highly anisotropic semi‐metal, diamond shows high hardness and thermal conductivity and is a wide‐gap insulator. With the discovery of graphene, fullerenes, and carbon nanotubes which resemble properties of the two crystalline phases, research on those and novel carbon materials emerged. Since carbon is forming different covalent bonds, there is a multitude of possibilities to create new structures by just combining sp, sp², and sp³ bonded carbon. Here we report on the discovery of a new sp² and sp³ bonded carbon structure which can be seen as a crossed graphene structure providing hybrid properties of graphene and diamond by means of an evolutionary algorithm.

     

A thermochemically competitive local hybrid functional without gradient corrections

Following the suggestion of local hybrid functionals with position-dependent exact-exchange admixture [J. Jaramillo, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 1068 (2003)], a functional that mixes only local and exact exchange plus local correlation has been constructed. With a simple local mixing function for the position dependence, this Lh-SVWN functional provides atomization energies for the G2-1 set that are competitive with currently available state-of-the-art functionals like, e.g., B3LYP. This is achieved without generalized gradient approximations for exchange or correlation.     

MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

Let M? be the operator of multiplication by?on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral prope...     

Generalized-gradient exchange-correlation hole obtained from a correlation factor ansatz

The Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy is employed as reference point for the construction of an angle-averaged exchange-correlation hole. First, we develop a new model for the PBE exchange hole. In contrast to the previous model [Ernzerhof and Perdew, J. Chem. Phys. 109, 3313 (1998)], it contains an atomic exchange hole, similar to the Becke-Roussel model [Becke and Roussel, Phys. Rev. A 39, 3761 (1989)]. A correlation factor, i.e., a function multiplying the exchange hole, is proposed that turns the exchange into an exchange-correlation hole. The correlation factor has a simple form and is determined through a number of known conditions that should be satisfied by a generalized-gradient exchange-correlation hole.     

Property of reflexivity for multiplication operators on Banach function spaces

In this paper, we give conditions under which the powers of the multiplication operator \(M_{z}\) are reflexive on a Banach space of functions analytic on a plane domain.