Efficient implementation of the analytic second derivatives of Hartree–Fock and hybrid DFT energies: a detailed analysis of different approximations

In this paper, various implementations of the analytic Hartree–Fock and hybrid density functional energy second derivatives are studied. An approximation-free four-centre implementation is presented, and its accuracy is rigorously analysed in terms of self-consistent field (SCF), coupled-perturbed SCF (CP-SCF) convergence and prescreening criteria. The CP-SCF residual norm convergence threshold turns out to be the most important of these. Final choices of convergence thresholds are made such that an accuracy of the vibrational frequencies of better than 5 cm^?1 compared to the numerical noise-free results is obtained, even for the highly sensitive low frequencies (<100–200 cm^?1). The effects of the choice of numerical grid for density functional exchange–correlation integrations are studied and various weight derivative schemes are analysed in detail. In the second step of the work, approximations are introduced in order to speed up the computation without compromising its accuracy. To this end, the accuracy and efficiency of the resolution of identity approximation for the Coulomb terms and the semi-numerical chain of spheres approximation to the exchange terms are carefully analysed. It is shown that the largest performance improvements are realised if either Hartree–Fock exchange is absent (pure density functionals) and otherwise, if the exchange terms in the CP-SCF step of the calculation are approximated by the COSX method in conjunction with a small integration grid. Default values for all the involved truncation parameters are suggested. For vancomycine (176 atoms and 3593 basis functions), the RIJCOSX Hessian calculation with the B3LYP functional and the def2-TZVP basis set takes ～3 days using 16 Intel® Xeon® 2.60GHz processors with the COSX algorithm having a net parallelisation scaling of 11.9 which is at least ～20 times faster than the calculation without the RIJCOSX approximation.     

Molecular Size and Electronic Structure Combined Effects on the Electrogenerated Chemiluminescence of Sulfurated Pyrene‐Cored Dendrimers

The electrochemistry, photophysics, and electrochemically generated chemiluminescence (ECL) of a family of polysulfurated dendrimers with a pyrene core have been thoroughly investigated and complemented by theoretical calculations. The redox and luminescence properties of dendrimers are dependent on the generation number. From low to higher generation it is both easier to reduce and oxidize them and the emission efficiency increases along the family, with respect to the polysulfurated pyrene core. The analysis of such data evidences that the formation of the singlet excited state by cation–anion annihilation is an energy‐deficient process and, thus, the ECL has been justified through the triplet–triplet annihilation pathway. The study of the dynamics of the ECL emission was achieved both experimentally and theoretically by molecular mechanics and quantum chemical calculations. It has allowed rationalization of a possible mechanism and the experimental dependence of the transient ECL on the dendrimer generation. The theoretically calculated Marcus electron‐transfer rate constant compares very well with that obtained by the finite element simulation of the whole ECL mechanism. This highlights the role played by the thioether dendrons in modulating the redox and photophysical properties, responsible for the occurrence and dynamics of the electron transfer involved in the ECL. Thus, the combination of experimental and computational results allows understanding of the dendrimer size dependence of the ECL transient signal as a result of factors affecting the annihilation electron transfer.     

From Ion‐Like Ethylzinc Aluminates to [EtZn(arene)2]+[Al(ORF)4]− Salts

Attempts to prepare previously unknown simple and very Lewis acidic [RZn]⁺[Al(OR^F)₄]^? salts from ZnR₂, AlR₃, and HO?R^F delivered the ion‐like RZn(Al(OR^F)₄) (R=Me, Et; R^F=C(CF₃)₃) with a coordinated counterion, but never the ionic compound. Increasing the steric bulk in RZn⁺ to R=CH₂CMe₃, CH₂SiMe₃, or Cp*, thus attempting to induce ionization, failed and led only to reaction mixtures including anion decomposition. However, ionization of the ion‐like EtZn(Al(OR^F)₄) compound with arenes yielded the [EtZn(arene)₂]⁺[Al(OR^F)₄]^? salts with arene=toluene, mesitylene, or o‐difluorobenzene (o‐DFB)/toluene. In contrast to the ion‐like EtZn(η³‐C₆H₆)(CHB₁₁Cl₁₁), which co‐crystallizes with one benzene molecule, the less coordinating nature of the [Al(OR^F)₄]^? anion allowed the ionization and preparation of the purely organometallic [EtZn(arene)₂]⁺ cation. These stable materials have further applications as, for example, initiators of isobutene polymerization. DFT calculations to compare the Lewis acidities of the zinc cations to those of a large number of organometallic cations were performed on the basis of fluoride ion affinity. The complexation energetics of EtZn⁺ with arenes and THF was assessed and related to the experiments.     

Meeting Report: Ten Years of Atomic and Molecular Science at Elettra

On the 31^st of May and the 1^st of June, 2007, a workshop to celebrate 10 years of atomic and molecular science was held at Elettra. The occasion marked the 10^th anniversary since the first beamtime was officially allocated to a user at the Gas Phase beamline, namely George King of Manchester University. As a satisfied user, King was not only present, but had beamtime during the workshop.     

A 1H NMR Study of the Kinetics of the Reaction of Diisocyanates with Ethlene Oxide-Dimethylsiloxane-Ethylene Oxide Block Copolymer

The reaction of pure 2–4 and 2–6 tolylene diisocyanate with an OH terminated ethylene oxide-dimethylsiloxane-ethylene oxide ABA block copolymer was carried out directly in a n.m.r. tube. The kinetic of the reaction was studied by ¹H nmr spectroscopy.     

Distance rendering and perception of nearby virtual sound sources with a near-field filter model

Headphone rendering of nearby virtual sound sources represents to date an open issue in 3-D audio, due to a number of technical challenges and temporal requirements involved in the measurement of individual Head-Related Transfer Functions (HRTFs). In order to tackle this problem, we propose a filter model of near-field effects based on the Distance Variation Function (Kan et al., 2009). Thanks to its simple structure and low order, the model can be applied to any far-field virtual auditory display to yield a realistic and computationally efficient near-field compensation of spectral and binaural effects. The model is subjectively evaluated in two psychophysical experiments where the relative distance of pairs of virtually rendered sound sources is judged. Results show that even though sound intensity overshadows subtler near-field effects when it is available as a cue for distance, the model is capable of offering relative distance information of near lateral virtual sources when intensity cues are removed. Furthermore, performances of the model in relative distance rendering are compared to those of alternative near-field rendering methods available in the literature.