Bounds for the Kirchhoff index of regular graphs via the spectra of their random walks

Using probabilistic tools, we give tight upper and lower bounds for the Kirchhoff index of any d‐regular N‐vertex graph in terms of d, N, and the spectral gap of the transition probability matrix associated to the random walk on the graph. We then use bounds of the spectral gap of more specialized graphs, available in the literature, in order to obtain upper bounds for the Kirchhoff index of these specialized graphs. As a byproduct, we obtain a closed‐form formula for the Kirchhoff index of the d‐dimensional cube in terms of the first inverse moment of a positive binomial variable. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Theoretical and experimental study of the vertical excitation energies in the ionic and tautomeric forms of 4-aminomethylpyridine

4-Aminomethylpyridine (4-PAM) has been widely used as a model compound to elucidate the mechanisms of biological and biomedical action of the amino derivatives of vitamin B₆. By virtue of the presence of two ionizable groups (viz. a pyridine nitrogen and an amino function) in its structure, 4-PAM in solution occurs as various ionic and tautomeric forms in equilibrium. In this work, we optimized the geometries of such forms and found the protonation status of the ionizable groups in 4-PAM to affect the molecular geometry and frontier orbitals. In addition, we determined the experimental electronic excitation energies for each molecular species of 4-PAM from deconvoluted UV–vis spectra. The results thus obtained were compared with their theoretical counterparts as determined from TD-DFT calculations. Based on the outcome, the theoretical methodology used affords correct simulation of electronic excitation energies. The theoretical and experimental results showed that the deprotonation of the pyridine nitrogen has no effect on the energy of the first electronic transition, however it affects its intensity. Additionally, the deprotonation of both pyridine nitrogen and methylamino group increases the number of bands, by increasing the n–π^* transitions.     

Complexation of Hg2+ with α‐Lipoic and Dihydrolipoic Acids: Study by Differential Pulse Voltammetry on Rotating Au‐Disk Electrode and ESI‐MS

The complexation of the natural antioxidants α‐lipoic acid (ALA) and its reduced form dihydrolipoic acid (DHLA) with Hg²⁺ was investigated by a recently proposed differential pulse voltammetric (DPV) method using the rotating Au‐disk electrode. Complexation processes are proposed from the multivariate curve resolution by alternating least squares (MCR‐ALS) analysis of DPV titration data. Main complexes were both 1 : 1 Hg : ALA and Hg : DHLA, although the formation of 1 : 2 complexes can be also deduced. ALA and DHLA show different Hg²⁺‐binding patterns at different pH. Voltammetric findings are completed with the data obtained by electrospray ionization mass‐spectrometry (ESI‐MS), especially in negative mode.     

Quantification of Quercetin Using Glassy Carbon Electrodes Modified with Multiwalled Carbon Nanotubes Dispersed in Polyethylenimine and Polyacrylic Acid

This work reports the highly sensitive detection of quercetin using glassy carbon electrodes modified with multiwall carbon nanotubes (MWCNT) dispersed in polyethylenimine and poly(acrylic acid). The adsorptive stripping with square wave voltammetric transduction allowed the detection of 7.5 nM quercetin after 1.0 min accumulation at open circuit potential. The amperometric detection at 0.150 V is reported as an easier and simpler alternative to determine quercetin, with detection limits of 0.2 µM. The careful selection of the working conditions also made possible the detection of submicromolar levels of quercetin in the presence of excess of rutin. The proposed methodology was successfully used to quantify quercetin in onion samples.     

Global ab initio potential energy surfaces for the O2(3Σg-)+O2(3Σg-) interaction

Completely ab initio global potential energy surfaces (PESs) for the singlet and triplet spin multiplicities of rigid O(2)((3)Σ(g)(-))+O(2)((3)Σ(g)(-)) are reported for the first time. They have been obtained by combining an accurate restricted coupled cluster theory with singles, doubles, and perturbative triple excitations [RCCSD(T)] quintet potential [Bartolomei et al., J. Chem. Phys. 128, 214304 (2008)] with complete active space second order perturbation theory (CASPT2) or, alternatively, multireference configuration interaction (MRCI) calculations of the singlet-quintet and triplet-quintet splittings. Spherical harmonic expansions, containing a large number of terms due to the high anisotropy of the interaction, have been built from the ab initio data. The radial coefficients of these expansions are matched at long range distances with analytical functions based on recent ab initio calculations of the electric properties of the monomers [M. Bartolomei, E. Carmona-Novillo, M. I. Hernández, J. Campos-Martínez, and R. Hernández-Lamoneda, J. Comput. Chem. (2010) (in press)]. The singlet and triplet PESs obtained from either RCCSD(T)-CASPT2 or RCCSD(T)-MRCI calculations are quite similar, although quantitative differences appear in specific terms of the expansion. CASPT2 calculations are the ones giving rise to larger splittings and more attractive interactions, particularly in the region of the absolute minima (in the rectangular D(2h) geometry). The new singlet, triplet, and quintet PESs are tested against second virial coefficient B(T) data and, their spherically averaged components, against integral cross sections measured with rotationally hot effusive beams. Both types of multiconfigurational approaches provide quite similar results, which, in turn, are in good agreement with the measurements. It is found that discrepancies with the experiments could be removed if the PESs were slightly more attractive. In this regard, the most attractive RCCSD(T)-CASPT2 PESs perform slightly better than the RCCSD(T)-MRCI counterpart.     

The mobility in disordered molecular systems with energies given by a charge-induced dipoles interaction

We investigate the field dependence of the mobility in a model for a disordered molecular system containing spatial and energetic disorders. In this model we assign an isotropic polarizability to each site and take the site energies to be the site polarization energies, the interaction energy of a charge in the given site with the induced dipoles in the neighboring sites. This model was shown, in a previous publication, to contain short-ranged energetic correlations and we show in this work that this correlation produces a charge mobility proportional to the exponential of the square root of the applied field, the Poole-Frenkel dependence observed in various disordered organic materials, over a significant range of fields. We present an expression for the field dependence of the mobility in terms of the average intersite separation and of the isotropic polarizability of the electronic states, the two model parameters.     

Structural and atoms-in-molecules analysis of hydrogen-bond network around nitroxides in liquid water

In this study, we investigated the hydrogen-bond network patterns involving the NO moieties of five small nitroxides in liquid water by analyzing nanosecond scale molecular dynamics trajectories. To this end, we implemented two types of hydrogen-bond definitions, based on electronic structure, using Bader's atoms-in-molecules analysis and based on geometric criteria. In each definition framework, the nitroxide/water hydrogen-bond networks appear very variable from a nitroxide to another. Moreover, each definition clearly leads to a different picture of nitroxide hydration. For instance, the electronic structure-based definition predicts a number of hydrogen bonds around the nitroxide NO moiety usually larger than geometric structure-based ones. One particularly interesting result is that the strength of a nitroxide/water hydrogen bond does not depend on its linearity, leading us to question the relevance of geometric definition based on angular cutoffs to study this type of hydrogen bond. Moreover, none of the hydrogen-bond definitions we consider in the present study is able to quantitatively correlate the strength of nitroxide/water hydrogen-bond networks with the aqueous nitroxide spin properties. This clearly exhibits that the hydrogen-bonding concept is not reliable enough to draw quantitative conclusions concerning such properties.     

Full-dimensional quantum dynamics of vibrationally highly excited NHD2

We report on full-dimensional vibrational quantum dynamics of the highly excited ammonia isotopologue NHD(2) using a newly developed potential energy surface and the MCTDH program package. The calculations allow to realistically simulate an infrared laser induced stereomutation reaction at the pyramidal nitrogen atom in the femtosecond time domain. Our results allow for a thorough qualitative and quantitative understanding of infrared photoinduced stereomutation kinetics, the underlying quantum dynamics, and the reaction mechanisms. Comparison is made with a previous, reduced dimensionality study of the same reaction [R. Marquardt, M. Quack, I. Thanopulos, and D. Luckhaus, J. Chem. Phys. 118, 643 (2003)], and it is shown that slight variances of reduced spaces lead to significantly different kinetics. Because the quantum dynamics depends subtly on variances of reduced spaces, reduced dimensionality treatments are not reliable even for qualitative predictions of the stereomutation kinetics. The first direct comparison between the Multiconfigurational Time Dependent Hartree [M. H. Beck, A. Ja?ckle, G. A. Worth et al., Phys. Rep. 324, 1 (2000)] and Unimolecular Reactions Induced by Monochromatic Infrared Radiation [M. Quack and E. Sutcliffe, QCPE Bulletin 6, 98 (1986)] program packages on a specific, four dimensional quantum dynamical problem allows for their full validation in the present work.     

The applicability of three-dimensional aromaticity in BiSn(n)- Zintl analogues

Three-dimensional aromaticity is shown to play a role in the stability of deltahedral Zintl clusters and here we examine the connection between aromaticity and stability. In order to gain further insight, we have studied Zintl analogs comprised of bismuth doped tin clusters with photoelectron spectroscopy and theoretical methods. To assign aromaticity, we examine the ring currents induced around the cage by using the nucleus independent chemical shift. In the current study, BiSn(4)(-) is a stable cluster and fits aromatic criteria, while BiSn(5)(-) is found to fit antiaromatic criteria and has reduced stability. The more stable clusters exhibit an aromatic character which originates from weakly interacting s-states and bonding orbitals parallel to the surface of the cluster, while nonbonding lone pairs perpendicular to the surface of the cluster account for antiaromaticity and reduced stability. The effect of three-dimensional aromaticity on the electronic structure does not result in degeneracies, so the resulting variations in stability are smaller than those seen in conventional aromaticity.     

A Process to Produce Penicillin G Acylase by Surface-Adhesion Fermentation Using <Emphasis Type="Italic">Mucor griseocyanus</Emphasis> to Obtain 6-Aminopenicillanic Acid by Penicillin G Hydrolysis

The production of extracellular and mycelia-associated penicillin G acylase (maPGA) with Mucor griseocyanus H/55.1.1 by surface-adhesion fermentation using Opuntia imbricata, a cactus, as a natural immobilization support was studied. Enzyme activity to form 6-aminopencillanic acid (6-APA) from penicillin G was assayed spectrophotometrically. The penicillin G hydrolysis to 6-APA was evaluated at six different times using PGA samples recovered from the skim milk medium at five different incubation times. Additionally, the effect of varying the penicillin G substrate concentration level on the PGA enzyme activity was also studied. The maximum reaction rate, V _max, and the Michaelis constant, K _M, were determined using the Michaelis–Menten model. The maximum levels for maPGA and extracellular activity were found to be 2,126.50 international unit per liter (IU/l; equal to 997.83 IU/g of support) at 48 h and 755.33 IU/l at 60 h, respectively. Kinetics of biomass production for total biomass showed a maximum growth at 60 h of 3.36 and 2.55 g/l (equal to 0.012 g of biomass per gram of support) for the immobilized M. griseocyanus biomass. The maPGA was employed for the hydrolysis of penicillin G to obtain 6-APA in a batch reactor. The highest quantity of 6-APA obtained was 226.16 mg/l after 40-min reaction. The effect of substrate concentration on maPGA activity was evaluated at different concentrations of penicillin G (0–10 mM). K _M and V _max were determined to be 3.0 × 10⁻³ M and 4.4 × 10⁻³ mM/min, respectively.