An effective scaling frequency factor method for scaling of harmonic vibrational frequencies: Application to 1,2,4-triazole derivatives

Scaling of harmonic frequencies of a molecule is one of the methods of improving the agreement between the calculated from a quadratic force field and experimental vibrational spectrum. An application of the recently proposed effective scaling frequency factor (ESFF) method to the complicated 1,2,4-triazole derivatives is presented. The calculations are based on the DFT/B3LYP/6-311G** quadratic force fields. It is shown that the ESFF method is capable of providing the high-quality spectra with regard to the scaled frequencies, comparable to these obtained with the well-established scaled quantum mechanical (SQM) force field method. Using the recommended scaling factors for the 11-parameter calculations, the RMS value obtained for a set of 293 vibrational modes of four compounds is only 8.7 and 8.5 cm^?1, for SQM and ESFF, respectively, provided the hydrogen bonded CO bond was excluded from the general non-hydrogen XX stretch group, and the scaling factor attributed to this bond was optimized. The new, 9-parameter set of scaling factors provides SQM- and ESFF-scaled frequencies that are of comparable quality to those of the 11-parameter calculations. In addition, it provides (on average) more reliable band splittings in the middle region of the spectrum, and the order of the scaled frequencies corresponds to that of the experimental bands. The straightforward application of the ESFF method to estimate the value of the scaled frequency is also presented.     

Excitation energies through the locally renormalized equation-of-motion formalism: singles and doubles model

The stationary conditions obtained from approximate coupled-cluster functional derived from the numerator-denominator connected expansion (NDC) [K. Kowalski and P. Piecuch, J. Chem. Phys. 122, 074107 (2005)] are employed to calculate the linear response of cluster amplitudes. A simple scheme that involves singly and doubly excited amplitudes, termed locally renormalized equation-of-motion approach with singles and doubles (LR-EOMCCSD), is compared with other excited-state methods that include up to two-body operators in the wave function expansion. In particular, the impact of the local denominators on the excitation energies is discussed in detail. Several benchmark calculations on the CH(+), C(2), N(2), O(3), and ClOCl molecules are presented to illustrate the performance of the LR-EOMCCSD approach.     

How to compare power towers?

Lithuanian Mathematical Journal - We provide various tools that give an answer to the following question: given two distinct finite tower powers with entries at least 1 and (possibly) different...     

Clar Rules the Electronic Properties of 2D π-Conjugated Frameworks: Mind the Gap

The key electronic properties of a family of 2D frameworks structurally convergent with holey graphenes were studied. The bandgap of these materials decreases monotonically with size, showing a common trend with anthracenes and kekulenes. This was rationalized by Clar's sextet rule, which reveals a direct relationship between the molecular systems and the 2D frameworks. In addition, a detailed benchmark against experimental data showcased the high quality of the models, which reproduce accurately available electronic properties. Overall, it was shown that DFT can be used to screen and understand the intrinsic bandgaps and electrochemistry potentials for technological applications prior to the synthesis of π-conjugated porous materials.     

Electroactive Organic Building Blocks for the Chemical Design of Functional Porous Frameworks (MOFs and COFs) in Electronics

Electroactive organic molecules have received a lot of attention in the field of electronics because of their fascinating electronic properties, easy functionalization and potential low cost towards their implementation in electronic devices. In recent years, electroactive organic molecules have also emerged as promising building blocks for the design and construction of crystalline porous frameworks such as metal–organic frameworks (MOFs) and covalent-organic frameworks (COFs) for applications in electronics. Such porous materials present certain additional advantages such as, for example, an immense structural and functional versatility, combination of porosity with multiple electronic properties and the possibility of tuning their physical properties by post-synthetic modifications. In this Review, we summarize the main electroactive organic building blocks used in the past few years for the design and construction of functional porous materials (MOFs and COFs) for electronics with special emphasis on their electronic structure and function relationships. The different building blocks have been classified based on the electronic nature and main function of the resulting porous frameworks. The design and synthesis of novel electroactive organic molecules is encouraged towards the construction of functional porous frameworks exhibiting new functions and applications in electronics.     

Scaling laws of complex band random matrices

We study a model of complex band random matrices capable of describing the transitions between three different ensembles of Hermitian matrices: Gaussian orthogonal, Gaussian unitary and Poissonian. Analyzing numerical data we observe new scaling relations based on the generalized localization length of eigenvectors. We show that during transitions between canonical ensembles of random matrices the changes of statistical properties of eigenvalues and eigenvectors are correlated.     

A new concept for the noncovalent binding of a ruthenium-based olefin metathesis catalyst to polymeric phases: preparation of a catalyst on Raschig rings

A new concept for noncovalent immobilization of a ruthenium olefin metathesis catalyst is presented. The 2-isopropoxybenzylidene ligand of a Hoveyda-Grubbs carbene is further modified by an additional amino group (7) and immobilization is achieved by treatment with sulfonated polystyrene forming the corresponding ammonium salt. In this novel strategy for the immobilization of ruthenium-based metathesis catalysts, the amino group plays a two-fold role, being first an active anchor for immobilization and second, after protonation, activating the catalysts (electron donating to electron withdrawing activity switch). The polymeric support was prepared by precipitation polymerization which led to small bead sizes (0.2-2 microm) and large surface areas. Compared to commercial resins this tailor-made phase showed superior properties in immobilization of complex 7. This concept of immobilization was applied to glass-polymer composite megaporous Raschig rings. Ru catalyst 7 on Raschig rings was used under batch conditions in various metathesis reactions, including ring-closing (RCM), cross- (CM) and enyne metathesis, to give products of high chemical purity with very low ruthenium contamination levels (21-102 ppm). The same ring can be used for up to 6 cycles of metathesis.