Valence-State Atoms in Molecules. 6. Universal Ionic−Covalent Potential Energy Curves

Symmetry laws improve electronegativity equalization by orders of magnitude and call for a paradigm shift in conceptual density functional theory

The strict Wigner-Witmer symmetry constraints on chemical bonding are shown to determine the accuracy of electronegativity equalization (ENE) to a high degree. Bonding models employing the electronic chemical potential, μ, as the negative of the ground-state electronegativity, χ(GS), frequently collide with the Wigner-Witmer laws in molecule formation. The violations are presented as the root of the substantially disturbing lack of chemical potential equalization (CPE) in diatomic molecules. For the operational chemical potential, μ(op), the relative deviations from CPE fall between -31% ≤ δμ(op) ≤ +70%. Conceptual density functional theory (cDFT) cannot claim to have operationally (not to mention, rigorously) proven and unified the CPE and ENE principles. The solution to this limitation of cDFT and the symmetry violations is found in substituting μ(op) (i) by Mulliken's valence-state electronegativity, χ(M), for atoms and (ii) its new generalization, the valence-pair-affinity, α(VP), for diatomic molecules. Mulliken's χ(M) is equalized into the α(VP) of the bond, and the accuracy of ENE is orders of magnitude better than that of CPE using μ(op). A paradigm shift replacing the dominance of ground states by emphasizing valence states seems to be in order for conceptual DFT.

Chemical potential of molecules contrasted to averaged atomic electronegativities: alarming differences and their theoretical rationalization

We present the first large-scale empirical examination of the relation of molecular chemical potentials, μ(0)(mol) = -½(I(0) + A(0))(mol), to the geometric mean (GM) of atomic electronegativities, <χ(0)(at)>(GM) = <½(I(0) + A(0))(at)>(GM), and demonstrate that μ(0)(mol) ≠ -<χ(0)(at)>(GM). Out of 210 molecular μ(0)(mol)values considered more than 150 are not even in the range min{μ(0)(at)} < μ(0)(mol) < max{μ(0)(at)} spanned by the μ(0)(at) = -χ(0)(at) of the constituent atoms. Thus the chemical potentials of the large majority of our molecules cannot be obtained by any electronegativity equalization scheme, including the "geometric mean equalization principle", ½(I(0) + A(0))(mol) = <½(I(0) + A(0))(at)>(GM). For this equation the root-mean-square of relative errors amounts to SE = 71%. Our results are at strong variance with Sanderson's electronegativity equalization principle and present a challenge to some popular practice in conceptual density functional theory (DFT). The influences of the "external" potential and charge dependent covalent and ionic binding contributions are discussed and provide the theoretical rationalization for the empirical facts. Support is given to the warnings by Hinze, Bader et al., Allen, and Politzer et al. that equating the chemical potential to the negative of electronegativity may lead to misconceptions.

Born−Haber−Fajans Cycle Generalized: Linear Energy Relation between Molecules, Crystals, and Metals

Classical procedures to calculate ion-based lattice potential energies (U(POT)) assume formal integral charges on the structural units; consequently, poor results are anticipated when significant covalency is present. To generalize the procedures beyond strictly ionic solids, a method is needed for calculating (i) physically reasonable partial charges, delta, and (ii) well-defined and consistent asymptotic reference energies corresponding to the separated structural components. The problem is here treated for groups 1 and 11 monohalides and monohydrides, and for the alkali metal elements (with their metallic bonds), by using the valence-state atoms-in-molecules (VSAM) model of von Szentpály et al. (J. Phys. Chem. A 2001, 105, 9467). In this model, the Born-Haber-Fajans reference energy, U(POT), of free ions, M(+) and Y(-), is replaced by the energy of charged dissociation products, M(delta)(+) and Y(delta)(-), of equalized electronegativity. The partial atomic charge is obtained via the iso-electronegativity principle, and the asymptotic energy reference of separated free ions is lowered by the "ion demotion energy", IDE = -(1)/(2)(1 - delta(VS))(I(VS,M) - A(VS,Y)), where delta(VS) is the valence-state partial charge and (I(VS,M) - A(VS,Y)) is the difference between the valence-state ionization potential and electron affinity of the M and Y atoms producing the charged species. A very close linear relation (R = 0.994) is found between the molecular valence-state dissociation energy, D(VS), of the VSAM model, and our valence-state-based lattice potential energy, U(VS) = U(POT) - (1)/(2)(1 - delta(VS))(I(VS,M) - A(VS,Y)) = 1.230D(VS) + 86.4 kJ mol(-)(1). Predictions are given for the lattice energy of AuF, the coinage metal monohydrides, and the molecular dissociation energy, D(e), of AuI. The coinage metals (Cu, Ag, and Au) do not fit into this linear regression because d orbitals are strongly involved in their metallic bonding, while s orbitals dominate their homonuclear molecular bonding.

An empirical charge transfer potential with correct dissociation limits

The empirical valence bond (EVB) method [J. Chem. Phys. 52, 1262 (1970)] has always embodied charge transfer processes. The mechanism of that behavior is examined here and recast for use as a new empirical potential energy surface for large-scale simulations. A two-state model is explored. The main features of the model are: (1) explicit decomposition of the total system electron density is invoked; (2) the charge is defined through the density decomposition into constituent contributions; (3) the charge transfer behavior is controlled through the resonance energy matrix elements which cannot be ignored; and (4) a reference-state approach, similar in spirit to the EVB method, is used to define the resonance state energy contributions in terms of "knowable" quantities. With equal validity, the new potential energy can be expressed as a nonthermal ensemble average with a nonlinear but analytical charge dependence in the occupation number. Dissociation to neutral species for a gas-phase process is preserved. A variant of constrained search density functional theory is advocated as the preferred way to define an energy for a given charge.