The μ₃Model of Acids and Bases: Extending the Lewis Theory to Intermetallics

Abstract

A central challenge in the design of new metallic materials is the elucidation of the chemical factors underlying the structures of intermetallic compounds. Analogies to molecular bonding phenomena, such as the Zintl concept, have proven very productive in approaching this goal. In this Article, we extend a foundational concept of molecular chemistry to intermetallics: the Lewis theory of acids and bases. The connection is developed through the method of moments, as applied to DFT-calibrated Hückel calculations. We begin by illustrating that the third and fourth moments (μ(3) and μ(4)) of the electronic density of states (DOS) distribution tune the properties of a pseudogap. μ(3) controls the balance of states above and below the DOS minimum, with μ(4) then determining the minimum's depth. In this way, μ(3) predicts an ideal occupancy for the DOS distribution. The μ(3)-ideal electron count is used to forge a link between the reactivity of transition metals toward intermetallic phase formation, and that of Lewis acids and bases toward adduct formation. This is accomplished through a moments-based definition of acidity which classifies systems that are electron-poor relative to the μ(3)-ideal as μ(3)-acidic, and those that are electron-rich as μ(3)-basic. The reaction of μ(3) acids and bases, whether in the formation of a Lewis acid/base adduct or an intermetallic phase, tends to neutralize the μ(3) acidity or basicity of the reactants. This μ(3)-neutralization is traced to the influence of electronegativity differences at heteroatomic contacts on the projected DOS curves of the atoms involved. The role of μ(3)-acid/base interactions in intermetallic phases is demonstrated through the examination of 23 binary phases forming between 3d metals, the stability range of the CsCl type, and structural trends within the Ti-Ni system.

Perceiving molecular themes in the structures and bonding of intermetallic phases: the role of Hückel theory in an ab initio era

“…A detailed examination of the dependence of the DOS curve shape on μ 3 and μ 4 leads quickly to the conclusion that μ 4 controls the depth of this pseudogap, while the number of states above and below the gap is determined by μ 3 . 34 Already, then, in the third moment we have found a measure of how well a DOS distribution is suited to its population by electrons. This is shown in Fig.…”

“…By exploring how the total energy of the DOS curve with a particular BF depends on μ 3 and μ 4 , we have found that ideal values of μ 3 occur for other BFs as well. 34 For a given BF value, the lowest total energy is obtained for a DOS distribution consisting of a simple pair of δ-functions, with the area under the lower energy peak being just sufficient to accept all electrons in the system.…”

“…Following ref. 34, let us examine how well the ideal relationship between μ 3 and BF is borne out for the first row transition metal elements. We begin by performing DFT-calibrated Hückel calculations on each of these metals in its elemental structure (hcp for Sc, Ti and Co; bcc for V, Cr and Fe; the α-Mn type for Mn; fcc for Ni and Cu 60 ), then we extract from the calculation a d-only, low-order moment model, from which a total energy is calculated.…”

“…In our first paper on the μ 3 acid-base model, we demonstrated this through analyzing the formation of 23 intermetallic phases. 34 Here, we will focus on just one class of phases that appear in the binary systems of firstrow transition metals: the Laves phases, an immense family of compounds which crystallize in the MgCu 2 type, the MgZn 2 type, or intergrowths of the two.…”

“…28 The program takes the output of the widely-used Vienna ab initio Simulation Package (VASP), [29][30][31] and uses the VASP band energies and density of states (DOS) curves to work toward an optimal reproduction of these properties with simple or extended Hückel calculations made with YAeHMOP. 32,33 After showing the quality of the fits produced by this program, we will then demonstrate some new theoretical approaches that DFT-calibrated Hückel models make possible: the μ 3 -acidity 34 and μ 2 -Hückel chemical pressure analyses, 35,36 which translate the molecular concepts of Lewis acids/bases, and electronic/steric competition, respectively, into the intermetallic context. The application of the first of these methods will be illustrated in understanding the stability range of one important class of intermetallic compounds, the Laves phases as exemplified by the MgCu 2 structure type (Fig.…”