The catalytic activity of a series of ruthenium(II) complexes in azide-alkyne cycloadditions has been evaluated. The [Cp*RuCl] complexes, such as Cp*RuCl(PPh 3) 2, Cp*RuCl(COD), and Cp*RuCl(NBD), were among the most effective catalysts. In the presence of catalytic Cp*RuCl(PPh 3) 2 or Cp*RuCl(COD), primary and secondary azides react with a broad range of terminal alkynes containing a range of functionalities selectively producing 1,5-disubstituted 1,2,3-triazoles; tertiary azides were significantly less reactive. Both complexes also promote the cycloaddition reactions of organic azides with internal alkynes, providing access to fully-substituted 1,2,3-triazoles. The ruthenium-catalyzed azide-alkyne cycloaddition (RuAAC) appears to proceed via oxidative coupling of the azide and alkyne reactants to give a six-membered ruthenacycle intermediate, in which the first new carbon-nitrogen bond is formed between the more electronegative carbon of the alkyne and the terminal, electrophilic nitrogen of the azide. This step is followed by reductive elimination, which forms the triazole product. DFT calculations support this mechanistic proposal and indicate that the reductive elimination step is rate-determining.

The detailed reaction mechanism for the reduction of CO2 to CO catalyzed by (NHC)Cu(boryl) complexes (NHC = N-heterocyclic carbene) was studied with the aid of DFT by calculating the relevant intermediates and transition state structures. Our DFT calculations show that the reaction occurs through CO2 insertion into the Cu-B bond to give a Cu-OC(=O)-boryl species (i.e., containing Cu-O and C-B bonds), and subsequent boryl migration from C to O, followed by alpha-bond metathesis between pinB-Bpin (B2pin2, pin = pinacolate = OCMe2CMe2O) and (NHC)Cu(OBpin). The overall reaction is exergonic by 38.0 kcal/mol. It is the nucleophilicity of the Cu-B bond, a function of the very strong alpha-donor properties of the boryl ligand, rather than the oxophilicity of boron, which determines the direction of the CO2 insertion process. The boryl migration from C to O, which releases the product CO, is the rate-determining step and involves the "vacant" orbital orbital on boron. The (NHC)Cu(boryl) complexes show unique activity in the catalytic process. For the analogous (NHC)Cu(alkyl) complexes, the CO2 insertion into the Cu-C bond giving a copper acetate intermediate occurs with a readily achievable barrier. However, the elimination of CO from the acetate intermediate through a methyl migration from C to O is energetically inaccessible.

DFT calculations have been carried out to study the insertion reactions of alkenes into the Cu-B bond in (NHC)Cu(boryl) complexes (NHC ) N-heterocyclic carbene). The nature of the insertion reactions and the relevant regiochemistry have been examined along with β-hydride eliminations, which are followed by reinsertion of the alkene into the Cu-H bond. Hyperconjugation (i.e., π bonding) between the Cu-C σ bond and the "empty" p z orbital on boron has been identified as the cause of the unexpectedly small Cu-C-B angle found experimentally by X-ray diffraction in R-borylalkyl Cu(I) complexes.

The detailed mechanism for the diboration of aldehydes catalyzed by (NHC)Cu(boryl) complexes (NHC = N-heterocyclic carbene) was studied with the aid of DFT by calculating the relevant intermediates and transition states. The results show that the catalyzed diboration occurs through aldehyde insertion into Cu-B to give a Cu-O-C(boryl) species followed by sigma-bond metathesis with a diboron reagent. It is the "electron-richness", that is, the nucleophilicity of the Cu-boryl bond, which gives rise to a small insertion barrier and determines the direction of insertion. The results of our calculations also explain the formation of the product, observed experimentally, from the stoichiometric reaction of (IPr)Cu-Bpin (IPr = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene) with mesitylaldehyde. In the absence of a diboron reagent, the insertion intermediate having a Cu-O-C(boryl) linkage isomerizes to the thermodynamically preferred Cu-C-O(boryl) isomer via a boryl migration to the metal-bonded oxygen through an S(E)2-like transition state. We have also studied the catalyzed diboration of 2-pyridinecarboxaldehyde, which gives the unexpected reductive coupling product 1,2-di-2-pyridyl-1,2-bis(pinacolboroxy)ethane. The insertion intermediate, which contains a coordinated pyridyl group, isomerizes easily to a 1,2-dihydropyridine form, preventing its metathesis with a diboron reagent to give the expected diboration product as observed for other aldehyde substrates.

Ruthenium clusters of up to 64 atoms were studied using density-functional theory with a plane wave basis set. The simple cubic structure was found to be the most stable structure in the formation of small ruthenium clusters. A strong trend of trimer formation was also observed in the linear ruthenium clusters. All the ruthenium clusters investigated in this work are ferromagnetic with large magnetic moments and have small energy gaps between the highest occupied and the lowest unoccupied molecular orbitals. A quantitative correlation was established between the energetic, electronic, and magnetic properties of ruthenium clusters and the cluster size and structure. Our analysis showed that the atoms in similar bonding environments have similar binding energies. On the basis of this analysis, estimations were made on the binding energy for certain planar and simple cubic ruthenium clusters. The estimated binding energies are in good agreement with those from the density-functional theory calculations.

Molybdenum clusters consisting of 2-55 atoms were investigated using density functional theory calculations with a plane-wave basis set. The results show that the linear and planar molybdenum clusters have a strong tendency to form dimers. This tendency results in the formation of alternate short and long bonds within a linear cluster, in which the strength of these short bonds is covalent. Therefore, the linear and planar Mo clusters exhibit significant nonmetallic characteristics. Furthermore, the linear and planar Mo clusters show a strong even-odd effect in binding energy with the even-numbered clusters being more stable than their neighboring odd-numbered clusters. On the other hand, the even-odd effect in the energy gap between the highest occupied and the lowest unoccupied molecular orbitals, i.e., the HOMO-LUMO energy gap, for the linear and the planar clusters is different. The odd-numbered linear clusters and even-numbered planar clusters have larger HOMO-LUMO energy gaps than their corresponding neighboring clusters.

DFT calculations have been carried out to study the reactivity difference of B 2 cat 2 and B 2 pin 2 in the diboration reaction of alkenes catalyzed by carbene-ligated copper(I) complexes. The higher reactivity of B 2 cat 2 versus B 2 pin 2 in this reaction results largely from the enhanced electrophilicity/Lewis acidity of the former, which significantly lowers the barrier in the product-forming transmetalation step. Transmetalation reactions of B 2 cat 2 and B 2 pin 2 with (NHC)Cu-OMe have also been investigated, and the relative barriers are much closer than with analogous Cu-R systems.

Heteroatom and -hydrogen eliminations of the model complexes [L 2 PdCH 2 CH 2 X] + (L 2 ) H 2 PCH 2 -CH 2 PH 2 ; X ) halides, OMe, OH, OAc) were studied using density function theory calculations at the B3LYP level. Our calculations indicate that for the complexes where X ) Cl, Br, and I -heteroatom eliminations are thermodynamically and kinetically more favorable. For the complexes where X ) F, OH, OMe, and OAc, -hydrogen elimination is kinetically more favorable than -heteroatom elimination. However, the products (hydride-olefin complexes) formed from the kinetically favorable -hydrogen elimination are thermodynamically unstable relative to the pre-eliminated species (Pd-alkyl containing a -X to metal dative bond). Implications of these results on the palladium-catalyzed reactions have been discussed.