Atomic Radii Scale and Related Size Properties from Density Functional Electronegativity Formulation Mihai V. Putz, ² Nino Russo,* and Emilia Sicilia Dipartimento di Chimica and Centro di Calcolo ad Alte Prestazioni per Elaborazioni Parallele e Distribuite-Centro d’Eccellenza MIUR, UniVersita ` della Calabria, Via Pietro Bucci, I-87030 ArcaVacata di Rende (CS), Italy ReceiVed: NoVember 19, 2002; In Final Form: May 2, 2003 Assuming the Mulliken electronegativity density functional theory (DFT) formulation as the primary structural information on atomic systems, we propose a new atomic radii quantitative definition and scale. The radii scale based on DFT first principles is further used to evaluate the atomic diamagnetic susceptibility, polarizability, and chemical hardness. A new chemical hardness expression in terms of atomic radius is also given. The investigated quantities show that periodic trends prove the reliability of the proposed radii definition. Moreover, the proposed method to calculate size of atoms is useful for the theoretical prediction of several size-dependent physicochemical properties. 1. Introduction The evaluation of periodic properties is a fruitful research field starting from 1869 when Mendeleev proposed the periodic table of elements. 1 One of the most important periodic concepts is, certainly, the atomic size or radius. Indeed, it is very useful in explaining many chemical and physical characteristics of the elements and in predicting their reactivity behavior. The history of atomic radii evaluation is rich and exciting and starts from the beginning of the modern chemistry. Briefly, we are reminded of the pioneering works of Bragg, Goldschmidt, Zachariasen, Pauling, and Slater. 2-6 From an experimental point of view, the atomic radii of some elements can be obtained from X-ray or from spectroscopic measurements, but their reliability is often questionable because of the experimental conditions (e.g., crystal type, allotropic modifications, coordination number, tempera- ture). Because of the importance of the prediction of the internuclear distances into a molecule and between different molecules, many attempts have been made to fix radii values such that a sum of two of them is able to reproduce their distance, no matter the kind of bond existing between the considered atoms. Unfortunately, a plethora of scales has appeared, and a very long series of terms has been introduced to indicate the radius in different environmental conditions. As a consequence, the possibility to estimate theoretically this periodic property is very advantageous because it does not depend on the given physical conditions. From a theoretical viewpoint, some atomic radii scales have been proposed on the basis of several quantum mechan- ical tools going from self-consistent field (SCF) to density functional theories (DFT). 7-15 In a very recent work of Ghosh and Biswas, a detailed literature survey on this matter is reported. 16 With the introduction of DFT of many electrons systems, many useful qualitative chemical concepts (e.g., chemical potential, and chemical hardness and softness) have found a rigorous quantitative definition. 12 In this context, the chemical potential, μ, is defined as the first derivative of the energy with respect to the change of the number of the electrons, N, and is ultimately identified with the negative of electronegativity, l. 17 Because electronegativity measures the tendency of atoms to attract bonding electrons to themselves at their valence shell, it is also related to the outer orbitals and then to the size. Therefore, a definition of electronegativity obtained in the framework of DFT and properly correlated with the atomic radius can provide a quantitatively rigorous atomic radii scale. With the purpose to obtain “constant” atomic radii useful to describe any bonding situation, we propose in this work a new atomic radii scale computed by using the electronegativity formulation based on a new approach, which employs the chemical action concept 18 and the Slater-type orbitals for the considered elements. 2. Method and Computational Details 2.1. Atomic Radii and Electronegativity. The relation between atomic radii and electronegativity is obtained starting from the electronegativity formulation, 18 derived from the first principles of DFT. In this context, we define the atomic radius as the limit until which an electron can be added to an atom from infinity, due to its electronegativity. In the DFT framework, the analytical expression introduced to evaluate electronegativity is given, according to the work of Garza and Robles, 19 in terms of the local response function, L(x): with x, F, and V being the position vector, electronic density, * To whom correspondence should be addressed. Telephone: +39-0984- 492106. Fax: +39-0984-492044. E-mail: nrusso@unical.it. ² Permanent address: Chemistry Department, West University of Timi- soara, Str. Pestalozzi No. 16, Timisoara, RO-1900, Romania. L(x) ) ∇F(x) [-∇V(x)] (1) 5461 J. Phys. Chem. A 2003, 107, 5461-5465 10.1021/jp027492h CCC: $25.00 © 2003 American Chemical Society Published on Web 06/17/2003