What Dominates the Error in the CaO Diatomic Bond Energy Predicted by Various Approximate Exchange–Correlation Functionals?

The crucial role of transient tri-coordinated oxygen in the flow of silicate melts

The transport properties of high-temperature silicate melts control magma flow and are crucial for a wide variety of industrial processes involving minerals. However, anomalous melt properties have been observed that cannot be explained by the traditional polymerization degree theory, which was derived based on quenched melts. Ab initio molecular dynamics (AIMD) simulations were conducted to investigate the flow mechanism of CaO-Al2O3-SiO2 melts under high temperature atmospheric conditions. By analyzing the dynamic structure of melted silicates and employing molecular orbital theory, we gained a fundamental understanding of the flow mechanism from a chemistry perspective. Transient tri-coordinated oxygen (TO) bonded with one Si and two Al atoms (SiOAl2) was found to be a pivotal intermediate in melt flow and atomic diffusion processes. Frequent chemical transition between TO in SiOAl2 and bridging oxygen (BO) dominated the fluidity of melted silicates. The presence of such transitions is facilitated by the unstable nature of [SiAlO2] 4-membered rings, which are susceptible to instability due to the intense repulsion between the O 2p lone pairs and the excessively bent O-Al-O angle. Additionally, the density of SiOAl2 type TO motif could serve as an indicator to determine the relationship between structure and fluidity. Our results challenge the traditional polymerization degree theory and suggest the need to reassess high-temperature liquid properties that govern processes in the Earth and industry by monitoring transient motifs.

Transition Metal Behavior of Heavier Alkaline Earth Elements in Doped Monocyclic and Tubular Boron Clusters

Quantum chemical calculations are carried out to design highly symmetric-doped boron clusters by employing the transition metal behavior of heavier alkaline earth (Ae = Ca, Sr, and Ba) metals. Following an electron counting rule, a set of monocyclic and tubular boron clusters capped by two heavier Ae metals were tested, which leads to the highly symmetric Ae2B8, Ae2B18, and Ae2B30 clusters as true minima on the potential energy surface having a monocyclic ring, two-ring tubular, and three-ring tubular boron motifs, respectively. Then, a thorough global minimum (GM) structural search reveals that a monocyclic B8 ring capped with two Ae atoms is indeed a GM for Ca2B8 and Ba2B8, while for Sr2B8 it is a low-lying isomer. Similarly, the present search also unambiguously shows the most stable isomers of Ae2B18 and Ae2B30 to be highly symmetric two- and three-ring tubular boron motifs, respectively, capped with two Ae atoms on each side of the tube. In these Ae-doped boron clusters, in addition to the electrostatic interactions, a substantial covalent interaction, specifically the bonding occurring between (n - 1)d orbitals of Ae and delocalized orbitals of boron motifs, provides the essential driving force behind their highly symmetrical structures and overall stability.

Transition-Metal Chemistry of the Heavier Alkaline Earth Atoms Ca, Sr, and Ba

ConspectusAlkaline earth elements beryllium, magnesium, calcium, strontium, and barium with an ns² valence-shell configuration are usually classified as main-group elements that belong to the s-block atoms. For a long time, the elements were considered to be rather chemically uninteresting atomic species due to preconceived ideas about bonding, structure, and reactivity. They typically use the two ns valence electrons in forming ionic salt compounds with the metal in a formal oxidation state of +2. For the heavier alkaline earth atoms, calcium, strontium, and barium, their (n - 1)d atomic orbitals (AOs) are empty but lie close in energy to the valence np orbitals. Earlier theoretical investigations have already suggested that these elements can employ the (n - 1)d AOs to some extent to form polar bonds in divalent species in which the alkaline earth metal centers are sufficiently positively charged. The d orbital involvement increases from Ca to Sr and markedly in Ba. Thus, barium has been termed an honorary transition metal.Recently, molecular complexes of Ca, Sr, and Ba were prepared in the gas phase and in a low-temperature solid neon matrix and were detected by infrared spectroscopy. An analysis of the electronic structures of [Ba(CO)]⁺, [Ba(CO)]^-, saturated coordinated octacarbonyls [M(CO)₈] and [M(CO)₈]⁺, isoelectronic dinitrogen complexes [M(N₂)₈] and [M(N₂)₈]⁺, and the tribenzene complexes [M(Bz)₃] (M = Ca, Sr, Ba) revealed that the metal-ligand bonding can be straightforwardly discussed using the traditional Dewar-Chatt-Duncanson (DCD) model as in classical transition-metal complexes. The metal-ligand bonds can be explained with metal → ligand π back donation from occupied metal (n - 1)d AOs to vacant antibonding π molecular orbitals of the ligands with concomitant σ donation from occupied MOs of the ligands to vacant metal d orbitals of the alkaline earth atoms. In addition, heteronuclear Ca-Fe carbonyl cation complexes were also produced in the gas phase. Bonding analysis of the coordination saturated [CaFe(CO)₁₀]⁺ complex implies that it can be described by the bonding interactions between a [Ca(CO)₆]²⁺ fragment and an [Fe(CO)₄]^- anion fragment in forming a Fe → Ca d-d dative bond. The nature of metal-ligand and metal-metal bonding was quantitatively elucidated by the energy decomposition analysis in conjunction with the natural orbitals for the chemical valence (EDA-NOCV) method, which indicate that the (n - 1)d AOs of the alkaline earth metals are the dominant orbitals participating in the covalent interactions, just as typical transition metals. The results indicate that the heavier alkaline earth elements have a much richer covalent chemistry than previously thought. These findings, along with earlier studies, suggest that the heavier alkaline earth atoms Ca, Sr, and Ba should be classified as transition metals rather than main group atoms in the periodic table of the elements. This interesting structural chemistry, together with some recently reported examples of spectacular reactivity, establishes these elements as exciting and promising research targets in current research.

Small Amount Makes a Big Difference: Critical (n - 1)d Valence Orbitals of Heavy Alkaline Earth Metals inside Cage Clusters

Heavy alkaline earth metals (Aes) are usually considered to engage in chemical bonding by donating the two electrons on ns atomic orbitals (AOs). In this work, a series of typical endohedrally doped cage clusters Ae@cage (Ae = Ca, Sr, Ba; cage = C₃₂, C₇₄, C₉₄, B₄₀, Si₂₀, Sn₁₂, Au₁₆) were thoroughly investigated by means of density functional theory calculations. We found that their occupied molecular orbitals have ∼1 to 14% contributions from Ae-(n - 1)d AOs due to electron back-donation from the cage. Though the amount is small, it is hard to ignore: with the d orbitals, all these endohedral clusters exhibit obviously shortened Ae-cage distances, greatly enhanced encapsulation stabilities, changed highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps, and much lowered Ae valences far from ideal +2. Evidently, the valence orbitals of Ca/Sr/Ba in these systems should include both ns and (n - 1)d. By disclosing the critical role of unnoticed metal orbitals, our work provides completely new insights into the cluster field.

The Valence Orbitals of the Alkaline-Earth Atoms

Quantum chemical calculations of the alkaline-earth oxides, imides and dihydrides of the alkaline-earth atoms (Ae=Be, Mg, Ca, Sr, Ba) and the calcium cluster Ca6 H9 [N(SiMe3 )2 ]3 (pmdta)3 (pmdta=N,N,N',N'',N''-pentamethyldiethylenetriamine) have been carried out by using density functional theory. Analysis of the electronic structures by charge and energy partitioning methods suggests that the valence orbitals of the lighter atoms Be and Mg are the (n)s and (n)p orbitals. In contrast, the valence orbitals of the heavier atoms Ca, Sr and Ba comprise the (n)s and (n-1)d orbitals. The alkaline-earth metals Be and Mg build covalent bonds like typical main-group elements, whereas Ca, Sr and Ba covalently bind like transition metals. The results not only shed new light on the covalent bonds of the heavier alkaline-earth metals, but are also very important for understanding and designing experimental studies.

Reaction kinetics of hydrogen abstraction from polycyclic aromatic hydrocarbons by H atoms

We studied how the PAH structure, site, and size affect the rate constants of hydrogen abstraction reactions of PAH systematically.

MN15: A Kohn-Sham global-hybrid exchange-correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions

Kohn-Sham density functionals are widely used; however, no currently available exchange-correlation functional can predict all chemical properties with chemical accuracy. Here we report a new functional, called MN15, that has broader accuracy than any previously available one. The properties considered in the parameterization include bond energies, atomization energies, ionization potentials, electron affinities, proton affinities, reaction barrier heights, noncovalent interactions, hydrocarbon thermochemistry, isomerization energies, electronic excitation energies, absolute atomic energies, and molecular structures. When compared with 82 other density functionals that have been defined in the literature, MN15 gives the second smallest mean unsigned error (MUE) for 54 data on inherently multiconfigurational systems, the smallest MUE for 313 single-reference chemical data, and the smallest MUE on 87 noncovalent data, with MUEs for these three categories of 4.75, 1.85, and 0.25 kcal mol-1, respectively, as compared to the average MUEs of the other 82 functionals of 14.0, 4.63, and 1.98 kcal mol-1. The MUE for 17 absolute atomic energies is 7.4 kcal mol-1 as compared to an average MUE of the other 82 functionals of 34.6 kcal mol-1. We further tested MN15 for 10 transition-metal coordination energies, the entire S66x8 database of noncovalent interactions, 21 transition-metal reaction barrier heights, 69 electronic excitation energies of organic molecules, 31 semiconductor band gaps, seven transition-metal dimer bond lengths, and 193 bond lengths of 47 organic molecules. The MN15 functional not only performs very well for our training set, which has 481 pieces of data, but also performs very well for our test set, which has 823 data that are not in our training set. The test set includes both ground-state properties and molecular excitation energies. For the latter MN15 achieves simultaneous accuracy for both valence and Rydberg electronic excitations when used with linear-response time-dependent density functional theory, with an MUE of less than 0.3 eV for both types of excitations.

MN15-L: A New Local Exchange-Correlation Functional for Kohn-Sham Density Functional Theory with Broad Accuracy for Atoms, Molecules, and Solids

Kohn-Sham density functional theory is widely used for applications of electronic structure theory in chemistry, materials science, and condensed-matter physics, but the accuracy depends on the quality of the exchange-correlation functional. Here, we present a new local exchange-correlation functional called MN15-L that predicts accurate results for a broad range of molecular and solid-state properties including main-group bond energies, transition metal bond energies, reaction barrier heights, noncovalent interactions, atomic excitation energies, ionization potentials, electron affinities, total atomic energies, hydrocarbon thermochemistry, and lattice constants of solids. The MN15-L functional has the same mathematical form as a previous meta-nonseparable gradient approximation exchange-correlation functional, MN12-L, but it is improved because we optimized it against a larger database, designated 2015A, and included smoothness restraints; the optimization has a much better representation of transition metals. The mean unsigned error on 422 chemical energies is 2.32 kcal/mol, which is the best among all tested functionals, with or without nonlocal exchange. The MN15-L functional also provides good results for test sets that are outside the training set. A key issue is that the functional is local (no nonlocal exchange or nonlocal correlation), which makes it relatively economical for treating large and complex systems and solids. Another key advantage is that medium-range correlation energy is built in so that one does not need to add damped dispersion by molecular mechanics in order to predict accurate noncovalent binding energies. We believe that the MN15-L functional should be useful for a wide variety of applications in chemistry, physics, materials science, and molecular biology.

Nonseparable exchange–correlation functional for molecules, including homogeneous catalysis involving transition metals

A gradient approximation, GAM, to the exchange–correlation functional of Kohn–Sham theory with broad performance for metal and nonmetal bond energies and weak interactions is reported.