Optimization and basis-set dependence of a restricted-open-shell form of B2-PLYP double-hybrid density functional theory.

The performance of the restricted-open-shell form of the double-hybrid density functional theory (DHDFT) B2-PLYP procedure has been compared with that of its unrestricted counterpart using the G3/05 test set. Additionally, the influence of basis set on the parametrization and performance of ROB2-PLYP, and the further improvement of ROB2-PLYP through augmentation with a long-range dispersion function, have been investigated. We find that, after optimization of the two empirical DHDFT parameters, the ROB2-PLYP method (HF exchange = 59% and MP2 correlation = 28%) performs slightly better than the corresponding UB2-PLYP method (HF exchange = 62% and MP2 correlation = 35%), with mean absolute deviations (MADs) from the experimental energies in the G3/05 test set of 9.1 and 9.9 kJ mol(-1), respectively, when the cc-pVQZ basis set is employed. Separate optimizations of the parameters for the RO and U procedures are crucial for a fair comparison. For example, for the G2/97 test set, ROB2-PLYP(53,27) and ROB2-PLYP(62,35) show MADs of 12.2 and 13.5 kJ mol(-1), respectively, compared with the 6.6 kJ mol(-1) for (the optimized) ROB2-PLYP(59,28). The performance of ROB2-PLYP deteriorates significantly as the basis-set size is decreased, reflecting the enhanced basis-set dependence of the MP2 contribution compared with standard DFT. We find that this deficiency can be partly overcome through reparametrization. However, when the basis set drops below triple-zeta, the improvements made on reoptimizing the ROB2-PLYP parameters are not sufficient to warrant their general use. We find that the dispersion- and BSSE-corrected ROB2-PLYP(59,28)-D HCP procedure performs significantly better than ROB2-PLYP(59,28) for the S22 test set of interaction energies in which dispersion interactions are particularly important, with the MAD falling from 6.1 to 1.6 kJ mol(-1). However, when the same D correction is applied to the G3/05 test set, the performance of ROB2-PLYP(59,28)-D deteriorates slightly compared with ROB2-PLYP(59,28), with the MAD increasing from 9.1 to 9.5 kJ mol(-1).

The influence of peripheral ligand bulk on nitrogen activation by three-coordinate molybdenum complexes--a theoretical study using the ONIOM method.

Electronic structure methods have been combined with the ONIOM approach to carry out a comprehensive study of the effect of ligand bulk on the activation of dinitrogen with three-coordinate molybdenum complexes. Calculations were performed with both density functional and CCSD(T) methods. Our results show that not only is there expected destabilization of the intermediate on the pathway due to direct steric interactions of the bulky groups, but also there is significant electronic destabilization as the size of the ligand increases. This latter destabilization is due to the inability of the molecule to accommodate a rotated amide group bound to the molybdenum once the amide reaches a certain size. This destabilization also leads to a clear preference for the triplet intermediate (rather than the singlet intermediate) for bulky substituents which is in agreement with experiment. Overall, the calculated reaction profile for the bulky substituents shows a good correlation with the available experimental data.

Oxidative addition of 2-substituted azolium salts to Group-10 metal zero complexes--a DFT study.

Generation of N-heterocyclic carbene (NHC) complexes [(dmpe)M(azol-2-ylidene)R] via the oxidative addition of a series of 2-substituted azolium salts to Group-10 zerovalent metal complexes has been investigated using density functional theory (2-R = H, Me, Ph; Azole = imidazole, thiazole, oxazole; M = Ni, Pd, Pt). Overall, platinum-based pathways result in the greatest enthalpies of reaction, but due to the reactive nature of Group-10 metals bearing the 1,2-bis(dimethylphosphino)ethane (dmpe) chelate, nickel and palladium species also have little trouble proceeding to stable products in the absence of a significant barrier. Imidazolium salts were found to be the most vulnerable to oxidative addition due to their low stabilisation energies when compared to the oxazolium and thiazolium species. Activation barriers show the general trend of phenyl > methyl > hydrido with regard to the azole 2-substituent, with no observed barrier for all but one of the 2-hydrido cases. Minimal barriers were found to exist in a number of cases for activation of a C(2)-CH3 bond suggesting that synthesis of alkyl-carbene complexes may be possible via this route under certain conditions, and therefore ionic liquids based on these substituted azolium salts may be active participants in catalytic reactions.

The influence of N-substitution on the reductive elimination behaviour of hydrocarbyl-palladium-carbene complexes--a DFT study.

The reductive elimination of 2-hydrocarbyl-imidazolium salts from hydrocarbyl-palladium complexes bearing N-heterocyclic carbene (NHC) ligands represents an important deactivation route for catalysts of this type. We have explored the influence that carbene N-substituents have on both the activation energy and the overall thermodynamics of the reductive elimination reaction using density functional theory (DFT). Given the proximity of the N-substituent to the three-centred transition structure, steric bulk has little influence on the activation barrier and it is electronic factors that dominate the barriers' magnitude. Increased electron donation from the departing NHC ligand acts to stabilise the associated complex against reductive elimination, with stability following the trend: Cl < H < Ph < Me < Cy < iPr < neopentyl < tBu. The intimate involvement of the carbene p pi-orbital in determining the barrier to reductive elimination means N-substituents that are capable of removing pi-density (e.g. phenyl) act to promote a more facile reductive elimination.

Influence of geometry on reductive elimination of hydrocarbyl-palladium-carbene complexes.

The influence of spectator ligand bite angle and the twist angle of the carbene on the reductive elimination of N-heterocyclic carbenes (NHCs) from palladium bis-phosphine complexes has been investigated using density functional theory. The spectator bite angle was found to have a significant influence on both the activation energy (E(act)) and the enthalpy of reaction. Widening of the bite angle was found to lower E(act) and increase the enthalpy of reaction. In contrast, rotation of the carbene with respect to the PdL(2) plane was found to have little influence on E(act). At carbene twist angles approaching 0 degrees however, relief of the increased steric strain provides a considerable driving force for the decomposition reaction.

Ligand rotation in [Ar(R)N]3M-N2-M'[N(R)Ar]3(M, M' = MoIII, NbIII; R = iPr and tBu) dimers.

Earlier calculations on the model N2-bridged dimer (micro-N2)-{Mo[NH2]3}2 revealed that ligand rotation away from a trigonal arrangement around the metal centres was energetically favourable resulting in a reversal of the singlet and triplet energies such that the singlet state was stabilized 13 kJ mol(-1) below the D(3d) triplet structure. These calculations, however, ignored the steric bulk of the amide ligands N(R)Ar (R =iPr and tBu, Ar = 3,5-C6H3Me2) which may prevent or limit the extent of ligand rotation. In order to investigate the consequences of steric crowding, density functional calculations using QM/MM techniques have been performed on the Mo(III)Mo(III) and Mo(III)Nb(III) intermediate dimer complexes (mu-N(2))-{Mo[N(R)Ar]3}2 and [Ar(R)N]3Mo-(mu-N2)-Nb[N(R)Ar]3 formed when three-coordinate Mo[N(R)Ar]3 and Nb[N(R)Ar]3 react with dinitrogen. The calculations indicate that ligand rotation away from a trigonal arrangement is energetically favourable for all of the ligands investigated and that the distortion is largely electronic in origin. However, the steric constraints of the bulky amide groups do play a role in determining the final orientation of the ligands, in particular, whether the ligands are rotated at one or both metal centres of the dimer. Analogous to the model system, QM/MM calculations predict a singlet ground state for the (mu-N2)-{Mo[N(R)Ar]3}2 dimers, a result which is seemingly at odds with the experimental triplet ground state found for the related (mu-N2)-{Mo[N(tBu)Ph]3}2 system. However, QM/MM calculations on the (mu-N2)-{Mo[N(tBu)Ph]3}2 dimer reveal that the singlet-triplet gap is nearly 20 kJ mol(-1) smaller and therefore this complex is expected to exhibit very different magnetic behaviour to the (mu-N2)-{Mo[N(R)Ar]3}2 system.

Nitrogen activation via three-coordinate molybdenum complexes: comparison of density functional theory performance with wave function based methods.

Obtaining an accurate theoretical model for the activation of dinitrogen by three-coordinate molybdenum amide complexes (e.g. Mo(NH2)3) is difficult due to the interaction of various high- and low-spin open-shell complexes along the reaction coordinate which must be treated with comparable levels of accuracy in order to obtain reasonable potential energy surfaces. Density functional theory with present-day functionals is a popular choice in this situation; however, the dinitrogen activation reaction energetics vary substantially with the choice of functional. An assessment of the reaction using specialized wave function based methods indicates that although current density functionals in general agree qualitatively on the mechanistic details of the reaction, a variety of high-level electron correlation methods (including CCSD(T), OD(T), CCSD(2), KS-CCSD(T), and spin-flip CCSD) provide a consistent but slightly different representation of the system.