Double Hybrid Functionals and the Π-System Bond Length Alternation Challenge: Rivaling Accuracy of Post-HF Methods

Predicting accurate bond length alternations (BLAs) in long conjugated oligomers has been a significant challenge for electronic-structure methods for many decades, made particularly important by the close relationships between BLA and the rich optoelectronic properties of π-delocalized systems. Here, we test the accuracy of recently developed, and increasingly popular, double hybrid (DH) functionals, positioned at the top of Jacobs Ladder of DFT methods of increasing sophistication, computational cost, and accuracy, due to incorporation of MP2 correlation energy. Our test systems comprise oligomeric series of polyacetylene, polymethineimine, and polysilaacetylene up to six units long. MP2 calculations reveal a pronounced shift in BLAs between the 6-31G(d) basis set used in many studies of BLA to date and the larger cc-pVTZ basis set, but only modest shifts between cc-pVTZ and aug-cc-pVQZ results. We hence perform new reference CCSD(T)/cc-pVTZ calculations for all three series of oligomers against which we assess the performance of several families of DH functionals based on BLYP, PBE, and TPSS, along with lower-rung relatives including global- and range-separated hybrids. Our results show that DH functionals systematically improve the accuracy of BLAs relative to single hybrid functionals. xDH-PBE0 (N4 scaling using SOS-MP2) emerges as a DH functional rivaling the BLA accuracy of SCS-MP2 (N5 scaling), which was found to offer the best compromise between computational cost and accuracy the last time the BLA accuracy of DFT- and wave function-based methods was systematically investigated. Interestingly, xDH-PBE0 (XYG3), which differs to other DHs in that its MP2 term uses PBE0 (B3LYP) orbitals that are not self-consistent with the DH functional, is an outlier of trends of decreasing average BLA errors with increasing fractions of MP2 correlation and HF exchange.

Calibration of the length of a chain of single gold atoms

Using a scanning tunnelling microscope or mechanically controllable break junction it has been shown that it is possible to control the formation of a wire made of single gold atoms. In these experiments an interatomic distance between atoms in the chain of ∼3.6 Å was reported which is not consistent with recent theoretical calculations. Here, using precise calibration procedures for both techniques, we measure the length of the atomic chains. Based on the distance between the peaks observed in the chain length histogram we find the mean value of the interatomic distance before chain rupture to be 2.5±0.2 Å. This value agrees with the theoretical calculations for the bond length. The discrepancy with the previous experimental measurements was due to the presence of He gas, that was used to promote the thermal contact, and which affects the value of the work function that is commonly used to calibrate distances in scanning tunnelling microscopy and mechanically controllable break junctions at low temperatures.

Palladium(II) complexes with a phosphino-oxime ligand: synthesis, structure and applications to the catalytic rearrangement and dehydration of aldoximes

The treatment of [PdCl2(COD)] (COD = 1,5-cyclooctadiene) with 1 and 2 equivalents of 2-(diphenylphosphino)benzaldehyde oxime in dichloromethane at room temperature led to the selective formation of [PdCl2{κ2-(P,N)-2-Ph2PC6H4CH[double bond, length as m-dash]NOH}] (1) and [Pd{κ2-(P,N)-2-Ph2PC6H4CH[double bond, length as m-dash]NOH}2][Cl]2 (2), respectively, which represent the first examples of Pd(II) complexes containing a phosphino-oxime ligand. These compounds, whose structures were fully confirmed by X-ray diffraction methods, were active in the catalytic rearrangement of aldoximes. In particular, using 5 mol% complex 1, a large variety of aldoximes could be cleanly converted into the corresponding primary amides at 100 °C, employing water as solvent and without the assistance of any cocatalyst. Palladium nanoparticles are the active species in the rearrangement process. In addition, when the same reactions were performed employing acetonitrile as solvent, selective dehydration of the aldoximes to form the respective nitriles was observed. For comparative purposes, the catalytic behaviour of an oxime-derived palladacyclic complex has also been briefly evaluated.