Dmitry Yu. Zubarev

Comprehensive analysis of chemical bonding in boron clusters.

We present a comprehensive analysis of chemical bonding in pure boron clusters. It is now established in joint experimental and theoretical studies that pure boron clusters are planar or quasi‐planar at least up to twenty atoms. Their planarity or quasi‐planarity was usually discussed in terms of π‐delocalization or π‐aromaticity. In the current article, we demonstrated that one cannot ignore σ‐electrons and that the presence of two‐center two‐electron (2c2e) peripheral BB bonds together with the globally delocalized σ‐electrons must be taken into consideration when the shape of pure boron cluster is discussed. The global aromaticity (or global antiaromaticity) can be assigned on the basis of the 4n + 2 (or 4n) electron counting rule for either π‐ or σ‐electrons in the planar structures. We showed that pure boron clusters could have double (σ‐ and π‐) aromaticity (B  3− , B4, B  5+ , B  62+ , B  7+ , B  7− , B8, B  82− , B  9− , B10, B  11+ , B12, and B  13+ ), double (σ‐ and π‐) antiaromaticity (B  62− , B15), or conflicting aromaticity (B5−,σ‐antiaromatic and π‐aromatic and B14, σ‐aromatic and π‐antiaromatic). Appropriate geometric fit is also an essential factor, which determines the shape of the most stable structures. In all the boron clusters considered here, the peripheral atoms form planar cycles. Peripheral 2c2e BB bonds are built up from s to p hybrid atomic orbitals and this enforces the planarity of the cycle. If the given number of central atoms (1, 2, 3, or 4) can perfectly fit the central cavity then the overall structure is planar. Otherwise, central atoms come out of the plane of the cycle and the overall structure is quasi‐planar.

Revealing Intuitively Assessable Chemical Bonding Patterns in Organic Aromatic Molecules via Adaptive Natural Density Partitioning

The newly developed adaptive natural density partitioning (AdNDP) method has been applied to a series of organic aromatic mono- and polycyclic molecules, including cyclopropenyl cation, cyclopentadienyl anion, benzene, naphthalene, anthracene, phenanthrene, triphenylene, and coronene. The patterns of chemical bonding obtained by AdNDP are consistent with chemical intuition and lead to unique, compact, graphic formulas. The resulting bonding patterns avoid resonant description and are always consistent with the point symmetry of the molecule. The AdNDP representation of aromatic systems seamlessly incorporates localized and delocalized bonding elements.

Deciphering Chemical Bonding in Golden Cages

The recently developed adaptive natural density partitioning (AdNDP) method has been applied to a series of golden clusters. The pattern of chemical bonding in Au(20) revealed by AdNDP shows that 20 electrons form a four-center-two-electron (4c-2e) bond in each of 10 tetrahedral cavities of the Au(20) cluster. This chemical bonding picture can readily explain the tetrahedral structure of the Au(20) cluster. Furthermore, we demonstrate that the recovered 4c-2e bonds corresponding to independent structural fragments of the cluster provide important information about chemically relevant fragmentation of Au(20). In fact, some of these bonds can be removed from the initial tetrahedral structure together with the associated atomic fragments, leading to the family of smaller gold clusters. Chemical bonding in the systems formed in such a manner is yet closely related to the bonding in the parental systems showing persistence of the 4c-2e bonding motif. Thus, the multicenter bonds in golden cages recovered by the AdNDP analysis correspond to the fragments that should be seen as building blocks of these chemical systems.

Carbon Avoids Hypercoordination in CB6-, CB62-, and C2B5-Planar Carbon-Boron Clusters

The structures and bonding of CB6-, C2B5-, and CB62- are investigated by photoelectron spectroscopy and ab initio calculations. It is shown that the global minimum structures for these systems are distorted heptacyclic structures. The previously reported hexacyclic structures with a hypercoordinate central carbon atom are found to be significantly higher in energy and were not populated under current experimental conditions. The reasons why carbon avoids hypercoordination in these planar carbon-boron clusters are explained through detailed chemical-bonding analyses.

Global minimum structure searches via particle swarm optimization.

Novel implementation of the evolutionary approach known as particle swarm optimization (PSO) capable of finding the global minimum of the potential energy surface of atomic assemblies is reported. This is the first time the PSO technique has been used to perform global optimization of minimum structure search for chemical systems. Significant improvements have been introduced to the original PSO algorithm to increase its efficiency and reliability and adapt it to chemical systems. The developed software has successfully found the lowest‐energy structures of the LJ26 Lennard‐Jones cluster, anionic silicon hydride Si2H  5− , and triply hydrated hydroxide ion OH− (H2O)3. It requires relatively small population sizes and demonstrates fast convergence. Efficiency of PSO has been compared with simulated annealing, and the gradient embedded genetic algorithm.

Comment on “Instability of the Al42− ‘All-Metal Aromaticʼ Ion and Its Implications”

Lambrecht, Fleig, and Sommerfeld1 recently presented study on implications of instability of Al4. In their thorough ab initio investigation they showed that the Al4 dianion is metastable with a very short lifetime of 9 fs. They also demonstrated that the adequate description of the dianion requires the admixture of scattering solutions to the bound-state wave functions. Thus, they made a conclusion that calculations of molecular properties can give essentially arbitrary results for such ill-defined systems. The instability of isolated Al4 toward electron autodetachment was recognized in our first publication on this system.2 Nevertheless, we performed geometry optimization, calculated harmonic frequencies and analyzed chemical bonding in this system using B3LYP and CCSD(T) methods with compact 6-311+G* basis set. Though we agree that accurate description of this dianion requires taking the continuum (unbound) states Al4 + free e into account, we still believe that our calculations of molecular properties of Al4 performed with compact basis set do make sense. It is common in chemistry to partition complex systems into simpler “building blocks”. For example, all inorganic salts are usually represented by the simplest stoichiometric ratio of cations and anions, even though some of these anions may not be stable in the isolated form. When theoreticians run calculations of such unstable anions, they try to model properties of these objects in the condensed phase, where these objects are stabilized by the external field. Within the same conceptual framework, we considered Al4 as a building block of electronically stable systems such NaAl4 or Na2Al4. In this case calculations of Al4 with compact basis sets serve for modeling purposes because the bound state of individual Al4 is an adequate model of the Al4 in stabilizing environment such as in NaAl4 or Na2Al4 species. This is because the compact basis sets used in our calculations adequately describe the part of the potential energy surface inside the repulsive Coulomb barrier. This part of the potential energy surface should not be significantly affected by the external field of Na+ cation as we show below. When Al4 is stabilized by the external field, the “tails” of continuum solutions can be disregarded. To prove our statement and validate this modeling approach, we compare properties (obtained at B3LYP with compact 6-311+G* basis set) of bound state description of isolated Al4 with corresponding properties of Al4 in the electronically stable NaAl4 and Na2Al4 species where perfect square shape of Al4 unit is preserved (Figure 1 and Table 1). In Figure 1b we presented localized description of chemical bonding in Al4, NaAl4, and Na2Al4 using newly developed Adaptive Natural Density Partitioning method.3 One can see that Al4 unit has four lone pairs (one on each Al atom) and three delocalized four center two electron (4c-2e) bonds in each species. Three 4c-2e bonds are responsible for double (σand π-) aromaticity in this model system. Sodium cations only introduce relatively small perturbations in this description due to the charge transfer but do not change it qualitatively. On the basis of this chemical bonding analysis, we can expect that other molecular properties of the model dianion Al4 will remain close to those of Al4 unit within electronically stable NaAl4 and Na2Al4 species. Indeed, comparison of interatomic distances (Figure 1a), harmonic vibrational frequencies and corresponding force constants (Table 1) confirms this expectation. This good agreement is the criterion for choosing specific compact basis set for modeling purposes. When Na cations are coordinated so that Al4 unit looses its perfect square shape (cations coordinated to an edge of the square), perturbations are higher as one should expect, though the qualitative picture of bonding and square-like geometric structure is approximately preserved. * Corresponding author. E-mail: a.i.boldyrev@usu.edu. Figure 1. (a) Optimized geometries (Al-Al distances are in Å) and (b) localized nc-2e bonds (obtained by the AdNDP) for Al4 (D4h, 1A1 g), NaAl4 (C4V, A1), and Na2Al4 (D4h, A1 g). All calculations are performed at B3LYP/6-311+G*. J. Phys. Chem. A 2008, 112, 7984–7985 7984

On the Structure and Chemical Bonding of Si62- and Si62- in NaSi6- Upon Na+ Coordination

Photoelectron spectroscopy was combined with ab initio calculations to elucidate the structure and bonding in Si6 2- and NaSi6 -. Well-resolved electronic transitions were observed in the photoelectron spectra of Si6 - and NaSi6 - at three photon energies (355, 266, and 193 nm). The spectra of NaSi6 - were observed to be similar to those of Si6 - except that the electron binding energies of the former are lower, suggesting that the Si6 motif in NaSi6 - is structurally and electronically similar to that in Si6 -. The electron affinities of Si6 and NaSi6 were measured fairly accurately to be 2.23+/-0.03 eV and 1.80+/-0.05 eV, respectively. Global minimum structure searches for Si6 2- and NaSi6 - were performed using gradient embedded genetic algorithm followed by B3LYP, MP2, and CCSDT calculations. Vertical electron detachment energies were calculated for the lowest Si6 - and NaSi6 - structures at the CCSD(T)/6-311+G(2df), ROVGF/6-311+G(2df), UOVGF/6-311+G(2d), and time-dependent B3LYP/6-311+G(2df) levels of theory. Experimental vertical detachment energies were used to verify the global minimum structure for NaSi6 -. Though the octahedral Si6 2-, analogous to the closo form of borane B6H6 2-, is the most stable form for the bare hexasilicon dianion, it is not the kernel for the NaSi6 - global minimum. The most stable isomer of NaSi6 - is based on a Si6 2- motif, which is distorted into C2v symmetry similar to the ground state structure of Si6 -. The octahedral Si6 2- coordinated by a Na+ is a low-lying isomer and was also observed experimentally. The chemical bonding in Si6 2- and NaSi6 - was understood using natural bond orbital, molecular orbital, and electron localization function analyses.

Thermal Decomposition of Pentacene Oxyradicals

The energetics and kinetics of the thermal decomposition of pentacene oxyradicals were studied using a combination of ab initio electronic structure theory and energy-transfer master equation modeling. The rate coefficients of pentacene oxyradical decomposition were computed for the range of 1500-2500 K and 0.01-10 atm and found to be both temperature and pressure dependent. The computational results reveal that oxyradicals with oxygen attached to the inner rings are kinetically more stable than those with oxygen attached to the outer rings. The latter decompose to produce CO at rates comparable to those of phenoxy radical, while CO is unlikely to be produced from oxyradicals with oxygen bonded to the inner rings.

Pathways to soot oxidation: reaction of OH with phenanthrene radicals.

Energetics and kinetics of the oxidation of possible soot surface sites by hydroxyl radicals were investigated theoretically. Energetics were calculated by employing density functional theory. Three candidate reactions were selected as suitable prototypes of soot oxidation by OH. The first two, OH + benzene and OH + benzene-phenol complex, did not produce pathways that lead to substantial CO expulsion. The third reaction, OH attack on the phenanthrene radical, had multiple pathways leading to CO elimination. The kinetics of the latter reaction system were determined by solving the master equations with the MultiWell suite of codes. The barrierless reaction rates of this system were computed using the VariFlex program. The computations were carried out over the ranges 1500-2500 K and 0.01-10 atm. At higher temperatures, above 2000 K, the oxidation of phenanthrene radicals by OH followed a chemically activated path. At temperatures lower than 2000 K, chemical activation was not sufficient to drive the reaction to products; reaction progress was impeded by intermediate adducts rapidly de-energizing before reaching products. In such cases, the reaction system was modeled by treating the accumulating adducts as distinct chemical species and computing their kinetics via thermal decomposition. The overall rate coefficient of phenanthrene radical oxidation by OH forming CO was found to be insensitive to pressure and temperature and is approximately 1 × 10(14) cm(3) mol(-1) s(-1). The oxidation of phenanthrene radicals by OH is shown to be controlled by two main processes: H atom migration/elimination and oxyradical decomposition. H atom migration and elimination made possible relatively rapid rearrangement of the aromatic edge to form oxyradicals with favorable decomposition rates. The reaction then continues down the fastest oxyradical pathways, eliminating CO.

A Diffusion Monte Carlo Study of the O−H Bond Dissociation of Phenol†

The homolytic O-H bond dissociation energy (BDE) of phenol was determined from diffusion Monte Carlo (DMC) calculations using single determinant trial wave functions. DMC gives an O-H BDE of 87.0 +/- 0.3 kcal/mol when restricted Hartree-Fock orbitals are used and a BDE of 87.5 +/- 0.3 kcal/mol with restricted B3LYP Kohn-Sham orbitals. These results are in good agreement with the extrapolated B3P86 results of Costa Cabral and Canuto (88.3 kcal/mol), the recommended experimental value of Borges dos Santos and Martinho Simões (88.7 +/- 0.5 kcal/mol), and the G3 (88.2 kcal/mol), CBS-APNO (88.2 kcal/mol), CBS-QB3 (87.1 kcal/mol) results of Mulder.