RESUMEN

We investigate the physical basis, validity, and limitations of the minimum electrophilicity principle, MEP, which postulates that the sum of the electrophilicity indices, ∑ω, of the reaction products will be smaller than that of the reactants, Δω < 0. We present a much-improved understanding of the conditions for minimizing electrophilicity indices. Two indices, ω1 = (I + A)2/8(I - A) and ω2 = I·A/(I - A), are discussed, using ionization energies, I, and electron affinities, A, obtained from either ground-state (GS) or valence-state (VS) energies. The performances of ω1 and ω2 are compared for a wide range of chemical species from diatomic molecules, through large clusters to liquid water and solid crystals. New analytical arguments in support of MEP are found. Two new theorems are proved, and three new rules rationalize the changes Δω1 and Δω2 in association reactions, X + Y → XY. They explain why MEP is much more successful as a guiding rule than the maximum hardness postulate in such reactions. On the other hand, they also identify the increased electron affinity of the product as the reason for the rare but highly significant failures of MEP, e.g., in B2, C2, Si2, and CN. As a rule, electrophilicity is minimized in association reactions. However, both ω1 and ω2 are increased if the bond dissociation energy D(XY-) is larger than D(XY), which is equivalent to an increased product electron affinity. The large positive changes Δω1 and Δω2 in 2C → C2 exhibit a strong contrast to MEP. The changes in electrophilicity indices may help gain insights into the versatility of the chemistries of carbon and other elements. Solid-state double-exchange reactions are correctly assessed by Kaya's composite descriptor, somewhat less by ω2, but not at all by ω1. A wide class of failures of MEP is found as size-driven electrophilicity maximization, Δω > 0, e.g., in fullerenes, large metal clusters, and liquid water. Many electrophiles, especially superelectrophiles, show significantly larger electrophilicity indices than the largest index of their isolated atoms. The changes Δω1 and Δω2 provide important information on the reactivities of chemical systems; however, it appears that the minimum electrophilicity postulate cannot serve as a basis for a theory.

RESUMEN

The Periodic Table, and the unique chemical behavior of the first element in a column (group), were discovered simultaneously one and a half centuries ago. Half a century ago, this unique chemistry of the light homologs was correlated to the then available atomic orbital (AO) radii. The radially nodeless 1s, 2p, 3d, 4f valence AOs are particularly compact. The similarity of r(2s)≈r(2p) leads to pronounced sp-hybrid bonding of the light p-block elements, whereas the heavier p elements with n≥3 exhibit r(ns) ≪ r(np) of approximately -20 to -30 %. Herein, a comprehensive physical explanation is presented in terms of kinetic radial and angular, as well as potential nuclear-attraction and electron-screening effects. For hydrogen-like atoms and all inner shells of the heavy atoms, r(2s) ≫ r(2p) by +20 to +30 %, whereas r(3s)≳r(3p)≳r(3d), since in Coulomb potentials radial motion is more radial orbital expanding than angular motion. However, the screening of nuclear attraction by inner core shells is more efficient for s than for p valence shells. The uniqueness of the 2p AO is explained by this differential shielding. Thereby, the present work paves the way for future physical explanations of the 3d, 4f, and 5g cases.

RESUMEN

The conclusions of a recent Communication of Yoshida, Raebiger, Shudo, and Ohno published in this journal, that varying core orbital topologies with minuscule negative tails upon bond formation determine the different chemistries of carbon and silicon and affect ionization energies, excitation energies and bond properties of molecules, are now shown to be based on computational artifacts and oversimplified models. The all-electron wave function uniquely determines the observables, while its representation by one-electron orbital products depends on the details of the chosen approximation and therefore need to be considered with great care.

RESUMEN

The chemical potential is by definition constant in molecules, and electronic charge is in principle equilibrated by bonding. Does electronegativity offer the best scale to unify these principles? According to conceptual density functional theory (c-DFT), the electronegativity equalization (ENE) and chemical potential equalization (CPE) principles seem rigorous and identical. However, the operational formulations of CPE and ENE fail to validate this claim, and frequently dramatic deviations from equalization are reported. We here eliminate the deviations to a very large extent. The problems originate from (i) c-DFT's exclusive reference to ground states and violations of the Wigner-Witmer symmetry constraints for bonding, (ii) electron self-interaction and delocalization errors. The problems are solved, and much more accurate ENE and bond polarities are obtained by replacing the ground-state electronegativity (χGS ) by the valence-state electronegativity (χVS ) and its generalization, the valence-pair-affinity (VPA, αVP ). The VPA is a charge dependent pair-sharing potential connected to Ruedenberg's bond theory that emphasizes the role of electron pair-density. The performances of the valence-pair equilibration (VPEq) and c-DFT's operational CPE are compared for 89 molecules with very diverse bond characters, including the "exotic" dimers Be2 , Mg2 , B2 , C2 , and Mn2 . The accuracy of VPEq is about 9 times better than that of operational CPE. Without requiring ad hoc calibrations, the VPEq bond polarities agree very well with results of state-of-the-art population analyses, and charges derived from vibrational spectra. A paradigm shift emphasizing valence states seems in order for c-DFT. Electronegativity and the chemical potential should be regarded as separate properties. Copyright © 2018 Wiley Periodicals, Inc.

RESUMEN

It has been overlooked that the change of hardness, η, upon bonding is intimately connected to thermochemical cycles, which determine whether hardness is increased according to Pearson's "maximum hardness principle" (MHP) or equalized, as expected by Datta's "hardness equalization principle" (HEP). So far the performances of these likely incompatible "structural principles" have not been compared. Computational validations have been inconclusive because the hardness values and even their qualitative trends change drastically and unsystematically at different levels of theory. Here I elucidate the physical basis of both rules, and shed new light on them from an elementary experimental source. The difference, Δη = Î· mol - <η at>, of the molecular hardness, η mol, and the averaged atomic hardness, <η at>, is determined by thermochemical cycles involving the bond dissociation energies D of the molecule, D + of its cation, and D - of its anion. Whether the hardness is increased, equalized or even reduced is strongly influenced by ΔD = 2D - D +  - D -. Quantitative expressions for Δη are obtained, and the principles are tested on 90 molecules and the association reactions forming them. The Wigner-Witmer symmetry constraints on bonding require the valence state (VS) hardness, η VS, instead of the conventional ground state (GS) hardness, η GS. Many intriguingly "unpredictable" failures and systematic shortcomings of said "principles" are understood and overcome for the first time, including failures involving exotic and/or challenging molecules, such as Be2, B2, O3, and transition metal compounds. New linear relationships are discovered between the MHP hardness increase Δη VS and the intrinsic bond dissociation energy D i . For bond formations, MHP and HEP are not compatible, and HEP does not qualify as an ordering rule.

RESUMEN

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.

RESUMEN

The new coordinate-dependent pseudopotential for Na2(+) by Kahros and Schwartz [J. Chem. Phys. 138, 054110 (2013)] is assessed and compared to the pseudopotential approach by Fuentealba et al. [Chem. Phys. Lett. 89, 418 (1982)] which incorporates the coordinate-dependent core-polarization potential by Müller and Meyer [J. Chem. Phys. 80, 3311 (1984)]. In contrast to the latter approach, the one by Kahros and Schwartz does not reproduce the accurately known experimental data and∕or high level theoretical results for Na2(+). The treatment of core polarization by Kahros and Schwartz neglects the dynamic polarization of atomic cores which is much more important for Na2(+) than the static one. On the other hand, the Kahros and Schwartz method heavily overestimates frozen-core corrections at the Hartree-Fock level by compounding them with artifacts of a superposition of non-norm-conserving pseudopotentials.

RESUMEN

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.

RESUMEN

Two gas-phase electrophilicity indices, ω(1) and ω(2), introduced by Parr, von Szentpály, and Liu are tested with respect to the recently proposed "principle of electrophilicity equalization." Although electronegativity is equalized in many cases, there is no functioning "hardness equalization principle" nor are the electrophilicity indices principally equalized during molecule formation: they cannot be generally expressed as the mean of the corresponding atomic indices. For large metal clusters and [n]fullerenes, both electrophilicity indices increase proportional to n(1/3) and n(1/2), respectively, as the hardness values converge to zero. Two "principles" are shown to be obsolete: the "geometric mean principle for hardness equalization" and the "principle of electrophilicity equalization", with the latter somewhat relying on the former. An appeal is made to exercise careful judgment before proposing and publishing new structural principles.

RESUMEN

The electronic stability of gas-phase dianions of arbitrary size, X(2-), is determined by the first universal method to calculate second electron affinities, A(2). The model expresses A(2,calc) = A(1) - (7/6)η(0) by the first electron affinity, A(1), and chemical hardness, η(0), of the neutral "grandparent" species. A comparison with 37 reference data of atoms, molecules, superatoms, and clusters yields A(2,ref) = 1.004A(2,calc) - 0.023 eV, with a mean unsigned deviation of MUD = 0.095 eV and a correlation coefficient of R = 0.9987. Predictions of second electron affinities are given for a further 24 species. The universality of the model is apparent from the broad variety of compounds formed by 30 diverse elements. The electronegativity and hardness of dianions are determined for the first time as χ(X(2-)) = A(2) and η(X(2-)) = (7/12)η(0), respectively. Pearson and Parr's operational assumption regarding the hardness of anionic bases for the hard-soft acid-base (HSAB) principle is rationalized, and predictions for hard and soft dianionic bases are presented. For trianions, first criteria and predictions for electronic stability are given and require A(1) > (7/4)η(0).

Asunto(s)

RESUMEN

Surprising and useful linear relationships between the atomization enthalpies of molecules and the cohesion enthalpies of crystals are found by shifting the thermochemical reference zero from elements to free atoms. Although the reference shift looks extremely simple, such atom-based thermochemistry (ABT) offers a direct way to calculate and predict the standard atomization enthalpy of molecules, Delta(at) H degrees(g), or solids, Delta(at) H degrees(s), with good accuracy (J. Am. Chem. Soc. 2008, 130, 5962-5973). It appears that referencing to atoms is able to provide a new unifying perspective. For group 12 metal chalcogenides, ME with M = Zn, Cd, Hg, E = O, S, Se, Te, Po, diabatic bond dissociation enthalpies, Dd298, with reference to the 1D2 state of the chalcogen atoms are mandated, in order to analyze the bond strengths properly (Mol. Phys. 2007, 105, 1139-1155). In this case, ABT implies a 2-fold reference shift (i) from formation enthalpies to atomization enthalpies and (ii) from standard atomization enthalpies to diabatic atomization enthalpies. An excellent linear relationship is found between the Dd298(ME) values and the corresponding diabatic atomization enthalpy of the solids, Delta(at) Hd(ME, s). The regression line is Delta(at) Hd(ME, s, calc) = 2.2717Dd298(ME) + 148.1 kJ mol-1 with the correlation coefficient R = 0.9996, the standard deviation (SD) = 4.2 kJ mol-1 and a mean unsigned deviation (MAD) = 3.7 kJ mol-1. Updated and corrected gas phase standard enthalpies of formation, Delta(f) H degrees(g), are presented for all 15 group 12 metal chalcogenides, and their lack of correlation with the formation enthalpies of the crystals, Delta(f) H degrees(s), is documented. The standard sublimation enthalpies, Delta(subl) H degrees, are reported for the first time. Recent accurate theoretical Dd298 values for the group 12 metal polonides, MPo, are taken to derive the first prediction for the standard atomization, formation, and sublimation enthalpies of their solids.

RESUMEN

In atom-based thermochemistry (ABT), state functions are referenced to free atoms, as opposed to the thermochemical convention of referencing to elements in their standard state. The shift of the reference frame reveals previously unrecognized linear relationships between the standard atomization enthalpies Delta(at)H(o)(g) of gas-phase diatomic and triatomic molecules and Delta(at)H(o)(s) of the corresponding solids for large groups of materials. For 35 alkali and coinage-metal halides, as well as alkali metal hydrides, Delta(at)H(o)(s) = 1.1203 Delta(at)H(o)(g) + 167.0 kJ mol(-1) is found; the standard error is SE = 16.0 kJ mol(-1), and the correlation coefficient is R = 0.9946. The solid coinage-metal monohydrides, CuH(s), AgH(s), and AuH(s), are predicted to be unstable with respect to the formation from the metals and elemental hydrogen by an approximately constant standard enthalpy of formation, Delta(f)H(o)(s) approximately +80 +/- 20 kJ mol(-1). Solid AuF is predicted to be marginally stable, having Delta(f)H(o)(s) = -60 +/- 50 kJ mol(-1) and standard a Gibbs energy of formation Delta(f)G(o)(s) approximately -40 +/- 50 kJ mol (-1). Triatomic alkaline-earth dihalides MX2 obey a similar linear relationship. The combined data of altogether 51 materials obey the relationship Delta(at)H(o)(s) = 1.2593 Delta(at)H(o)(g) + 119.9 kJ mol(-1) with R = 0.9984 and SE = 18.5 kJ mol(-1). The atomization enthalpies per atom of 25 data pairs of diatoms and solids in the groups 14-14, 13-15, and 2-16 are related as Delta(at)H(o)(s) = 2.1015 Delta(at)H(o)(g) + 231.9 kJ mol(-1) with R = 0.9949 and SE = 24.0 kJ mol(-1). Predictions are made for the GeC, GaSb, Hf2, TlN, BeS, MgSe, and MgTe molecules and for the solids SiPb, GePb, SnPb, and the thallium pnictides. Exceptions to the rule, such as SrO and BaO, are rationalized. Standard enthalpies of sublimation, Delta(subl)H(o) = Delta(at)H(o)(s) - Delta(at)H(o)(g), are calculated as a linear function of Delta(at)H(o)(g) profiting from the above linear relationships, and predictions for the Delta(subl)H(o) of the thallium pnictides are given. The validity of the new empirical relationships is limited to substances where at least one of the constituent elements is solid in its standard state. Reasons for the late discovery of such relationships are given, and a meaningful ABT is recommended by using Delta(at)H(o) as an important ordering and reference state function.

RESUMEN

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.