Solvent impact on the planarity and aromaticity of free and monohydrated zinc phthalocyanine: a theoretical study

A theoretical investigation on the planarity of molecular structure of zinc phthalocyanine (ZnPc) and its aromaticity has been performed using B3LYP and M06-2X density functionals combined with selected Pople-type basis sets. The effect of the applied calculation method on the optimized structure of ZnPc and ZnPc???H₂O, both in the gas phase and in the polar solvent, was analyzed. To quantify the aromaticity of the ZnPc and ZnPc???H₂O complexes, both the geometric and magnetic criteria, i.e., Harmonic Oscillator Model of Aromaticity (HOMA) index and the nucleus-independent chemical shift (NICS) values at the centers or 1 Å above the centers of structural subunits, were calculated. The energies of highest energy occupied molecular orbital (HOMO) and lowest energy unoccupied molecular orbital (LUMO) and energy gaps were also estimated. The results show that the free ZnPC molecule is flat in the gas phase and nonplanar in the polar environments (DMSO and water). ZnPC???H₂O is nonpolar in the gas phase and polar solvent which is in agreement with recent X-ray reports. Both HOMA and NICS indexes indicate the presence of highly aromatic macrocycle and benzene rings while these parameters for pyrrolic ring are significantly smaller than in free pyrrole. The presence of polar solvents practically does not change aromaticity of the ring subunits of the studied compounds.     

Spin‐orbit ZORA and four‐component Dirac–Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange‐correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin‐orbit zeroth‐order regular approximation Hamiltonian in combination with the large Slater‐type basis set QZ4P as well as with the four‐component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization‐consistent basis sets aug‐pcSseg‐4 for He, Ne and Ar, aug‐pcSseg‐3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero‐point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.     

DFT calculation of structures and NMR chemical shifts of simple models of small diameter zigzag single wall carbon nanotubes (SWCNTs)

Linearly conjugated benzene rings (acenes), belt‐shape molecules (cyclic acenes) and model single wall carbon nanotubes (SWCNTs) were fully optimized at the unrestricted level of density functional theory (UB3LYP/6‐31G*). The models of SWCNTs were selected to get some insight into the potential changes of NMR chemical shift upon systematic increase of the molecular size. The theoretical NMR chemical shifts were calculated at the B3LYP/pcS‐2 level of theory using benzene as reference. In addition, the change of radial breathing mode (RBM), empirically correlated with SWCNT diameter, was directly related with the radius of cyclic acenes. Both geometrical and NMR parameters were extrapolated to infinity upon increase in the studied systems size using a simple two‐parameter mathematical formula. Very good agreement between calculated and available experimental CC bond lengths of acenes was observed (RMS of 0.0173 Å). The saturation of changes in CC bond lengths and ¹H and ¹³C NMR parameters for linear and cyclic acenes, starting from 7–8 conjugated benzene rings, was observed. The ¹³C NMR parameters of individual carbon atoms from the middle of ultra‐thin (4,0) SWCNT formed from 10 conjugated cyclic acenes differ by about 130 ppm from the corresponding open end carbon nuclei. Copyright © 2011 John Wiley & Sons, Ltd.     

Some questions related to modeling in cellular biology

Several years ago, we decided to switch our main focus of interest toward the field of modeling cellular biology. Several reasons motivated this move: first cellular and molecular biology offer a fantastic new source of physical and mathematical problems. Second, to understand the function of cellular microdomains, modeling and computer simulations are necessary tools to organize and structure experimental observations. We review here some questions we have started to address.     

Partial Star Products: A Local Covering Approach for the Recognition of Approximate Cartesian Product Graphs

This paper is concerned with the recognition of approximate graph products with respect to the Cartesian product. Most graphs are prime, although they can have a rich product-like structure. The proposed algorithms are based on a local approach that covers a graph by small subgraphs, so-called partial star products, and then utilizes this information to derive the global factors and an embedding of the graph under investigation into Cartesian product graphs.     

Biodegradable polyhydroxybutyrate as a polyol for elastomeric polyurethanes

In the proposed work, new elastomeric bio-polyol based polyurethanes (bio-PUs) with specific mechanical properties were prepared by a one-shot process without the presence of a solvent. Commercial non-degradable polyether polyol derived from petrochemical feed stock was partly (in the amount of 1 mass %, 5 mass %, and 10 mass %) substituted by the biodegradable polyhydroxybutyrate (PHB). Morphology of elastomeric PU composites was evaluated by scanning electron microscopy and mechanical properties of the prepared samples were obtained by both tensile measurements and prediction via the Mooney-Rivlin equation. Electron microscopy proved that the prepared materials have the character of a particle filled composite material, where PHB particles are regular with their size of about 1?C2 ??m in diameter. Tensile measurements demonstrated that the Young??s modulus, tensile stress at break, and tensile strain at break of each sample increase with the increase of the volume fraction of the filler. From the measured stress-strain data, the first and the second term of the Mooney-Rivlin equation were calculated. The obtained constants were applied to recalculate the stress-strain curves. It was found that the Mooney-Rivlin equation corresponds well with the stress-strain behavior of the prepared specimens.     

Experimental and theoretical studies on corals. I. Toward understanding the origin of color in precious red corals from Raman and IR spectroscopies and DFT calculations

An attempt to explain the origin of the vivid red color in precious pink and red corals was undertaken. Raman and IR spectroscopies were applied to characterize white, pink and red corals. The position of the Raman signal near 1500 cm⁻¹ of some corals and pearls was associated by several authors with the presence of the mixture of all‐trans‐polyenic pigments, containing 6–16 conjugated CC bonds or β‐carotenoids. This hypothesis was examined theoretically by performing extensive B3LYP‐DFT calculations of vibrational spectra of the model polyenic compounds. The B3LYP/6‐311++G** predicted positions of the dominating Raman mode depend on the number of CC units (Cn parameter) and can be accurately predicted for larger systems from a simple nonlinear fit. The DFT‐predicted Raman activities of these modes are extremely sensitive to Cn, and sharply increase with the number of double bonds. This implies a presence of only—two to three polyenes differing slightly in the number of CC units as the source of color in pink and red corals. Copyright © 2009 John Wiley & Sons, Ltd.