From Classical Density Functionals to Adiabatic Connection Methods. The State of the Art.

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Abstract

This contribution is devoted to the impact of density functional (DF) theory in the field of computational chemistry. After a short discussion of the theoretical background, the attention is focussed on the role played by exchange and correlation functionals in determining the overall performances of DF methods. The theoretical behavior of the most common exchange functionals, like those proposed by Becke in 1988 and by Perdew and Wang in 1991, will be compared with that of more recent proposals. A particular attention will be devoted to high-gradient low density regions, which dominate weak non covalent interactions. An analysis of the most common correlation functionals, e.g. those introduced by Lee, Yang and Parr and by Perdew and Wang in 1991, will be also carried out. Next, the most recent development of DF theory, namely the adiabatic connection methods (ACMs), will be treated. The numerical performances of the most recent ACM approaches will be examined in detail, with special reference to the development of new parameter-free ACMs. Finally, some results obtained on a standard molecular data set and on some “delicate” chemical systems will be discussed.

Section snippets

INTRODUCTION

The quantum mechanical approach to chemistry has two long standing goals. The first one is the a-priori prediction of the structure, properties and reactivity of molecules formed by atoms of the whole periodic table. The second, and not less ambitious, objective is the interpretation of the above results in terms of chemical concepts, such as bond energies, inductive effects and electronegativity, for example. Thanks to the impressive development of computer power and to the implementation of

The Kohn-Sham approach

Density functional (DF) theory rests on the two theorems of Hohenberg-Kohn (HK) [13]. The first of these states that for systems with a nondegenerate ground state and a given electron-electron interaction there is a one-to-one mapping between the external (local) potential and the ground state wave function as well as the diagonal one-electron density. Therefore the wave function is uniquely determined by the one-electron density, i.e. it is a functional of the density, and so are all

Covalent interactions

The so called G2 set of molecules is nowadays considered a standard for the validation of new quantum chemical approaches [72]. Table V collects an error statistic for several quantum mechanical approaches concerning the geometric and thermodynamic parameters of 32 molecules belonging to the G2 set, together with dipole moments and harmonic vibrational frequencies.

From these data, it is clear that all the GGA methods provide geometric parameters with comparable accuracies, the error ranging

Conclusion

The present contribution explores the reliability of current density functionals concerning a number of structural, thermodynamic, kinetic and spectroscopic properties. Together with local and gradient corrected functionals, hybrid models including some Hartree-Fock exchange have been also considered.

A very important point is that, contrary to methods based on a Hartree-Fock zero-order wave function, those rooted in the Kohn-Sham approach appear equally reliable for closed- and open-shell

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