The Grunewald–O'Halloran Conjecture for Nilpotent Lie Algebras of Rank ≥1

Grunewald and O'Halloran conjectured in 1993 that every complex nilpotent Lie algebra is the degeneration of another, nonisomorphic, Lie algebra. We prove the conjecture for the class of nilpotent Lie algebras admitting a semisimple derivation, and also for 7-dimensional nilpotent Lie algebras. The conjecture remains open for characteristically nilpotent Lie algebras of dimension grater than or equal to 8.     

A general nonlinear Fokker-Planck equation and its associated entropy

A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence of external forces. Such an equation is characterized by a nonlinear diffusion term that may present, in general, two distinct powers of the probability distribution. Herein, we calculate the stationary-state distributions of this equation in some special cases, and introduce associated classes of generalized entropies in order to satisfy the H-theorem. Within this approach, the parameters associated with the transition rates of the original master-equation are related to such generalized entropies, and are shown to obey some restrictions. Some particular cases are discussed.     

Taming the Antiferromagnetic Beast: Computational Design of Ultrashort Mn−Mn Bonds Stabilized by N-Heterocyclic Carbenes

The development of complexes featuring low-valent, multiply bonded metal centers is an exciting field with several potential applications. In this work, we describe the design principles and extensive computational investigation of new organometallic platforms featuring the elusive manganese-manganese bond stabilized by experimentally realized N-heterocyclic carbenes (NHCs). By using DFT computations benchmarked against multireference calculations, as well as MO- and VB-based bonding analyses, we could disentangle the various electronic and structural effects contributing to the thermodynamic and kinetic stability, as well as the experimental feasibility, of the systems. In particular, we explored the nature of the metal-carbene interaction and the role of the ancillary η⁶ coordination to the generation of Mn₂ systems featuring ultrashort metal-metal bonds, closed-shell singlet multiplicities, and positive adiabatic singlet-triplet gaps. Our analysis identifies two distinct classes of viable synthetic targets, whose electrostructural properties are thoroughly investigated.     

Troubleshooting time-dependent density-functional theory for photochemical applications: oxirane

The development of analytic-gradient methodology for excited states within conventional time-dependent density-functional theory (TDDFT) would seem to offer a relatively inexpensive alternative to better established quantum-chemical approaches for the modeling of photochemical reactions. However, even though TDDFT is formally exact, practical calculations involve the use of approximate functional, in particular the TDDFT adiabatic approximation, the use of which in photochemical applications must be further validated. Here, we investigate the prototypical case of the symmetric CC ring opening of oxirane. We demonstrate by direct comparison with the results of high-quality quantum Monte Carlo calculations that, far from being an approximation on TDDFT, the Tamm-Dancoff approximation is a practical necessity for avoiding triplet instabilities and singlet near instabilities, thus helping maintain energetically reasonable excited-state potential energy surfaces during bond breaking. Other difficulties one would encounter in modeling oxirane photodynamics are pointed out.     

Optimized effective potentials from electron densities in finite basis sets

The Wu-Yang method for determining the optimized effective potential (OEP) and implicit density functionals from a given electron density is revisited to account for its ill-posed nature, as recently done for the direct minimization method for OEP's from a given orbital functional [T. Heaton-Burgess, F. A. Bulat, and W. Yang, Phys. Rev. Lett. 98, 256401 (2007)]. To address the issues on the general validity and practical applicability of methods that determine the Kohn-Sham (local) multiplicative potential in a finite basis expansion, a new functional is introduced as a regularized version of the original work of Wu and Yang. It is shown that the unphysical, highly oscillatory potentials that can be obtained when unbalanced basis sets are used are the controllable manifestation of the ill-posed nature of the problem. The new method ensures that well behaved potentials are obtained for arbitrary basis sets.     

Liquid phase behavior of perfluoroalkylalkane surfactants

We have performed a combined experimental and theoretical study of the thermodynamic properties of semifluorinated alkanes. In particular, the liquid density of perfluorohexylhexane (F6H6) and perfluorohexyloctane (F6H8) has been measured as a function of temperature from 273.15 to 353.15 K and at four temperatures as a function of pressure up to 600 bar. The results were interpreted using the SAFT-VR equation of state. The perfluoroalkylalkanes were modeled as heterosegmented diblock chains using parameters for the alkyl and perfluoroalkyl segments developed in earlier work. Through this simple approach, we are able to predict the thermodynamic behavior of the perfluoroalkylalkanes studied without fitting to any experimental data for the systems being studied.     

Ansa-tris(allyl) complexes of alkali metals: tripodal analogues of cyclopentadienyl and ansa-metallocene ligands

Alkali metal complexes of two types of ansa-tris(allyl) ligand are reported; a monoanionic ansa-tris(allyl) ligand containing tin(II) is formally valence isoelectronic to the cyclopentadienyl ligand and a trianionic ansa-tris(allyl) ligand containing silicon(IV) is formally valence isoelectronic to an ansa-metallocene ligand; the potential wider use of these tripodal ligands in coordination chemistry is discussed.     

Markov chain modeling of polymer translocation through pores

We solve the Chapman-Kolmogorov equation and study the exact splitting probabilities of the general stochastic process which describes polymer translocation through membrane pores within the broad class of Markov chains. Transition probabilities, which satisfy a specific balance constraint, provide a refinement of the Chuang-Kantor-Kardar relaxation picture of translocation, allowing us to investigate finite size effects in the evaluation of dynamical scaling exponents. We find that (i) previous Langevin simulation results can be recovered only if corrections to the polymer mobility exponent are taken into account and (ii) the dynamical scaling exponents have a slow approach to their predicted asymptotic values as the polymer's length increases. We also address, along with strong support from additional numerical simulations, a critical discussion which points in a clear way the viability of the Markov chain approach put forward in this work.     

Speciation of the Vanadium (III) Complexes with 6-Methylpicolinic Acid,Salicylic Acid and Phthalic Acid

The complex species formed in aqueous solutions (25 °C, I=3.0 mol⋅dm⁻³ KCl ionic medium) between the V(III) cation and the ligands 6-methylpicolinic acid (MePic, HL), salicylic acid (H₂Sal, H₂L) and phthalic acid (H₂Phtha, H₂L) have been studied by potentiometric and spectrophotometric measurements. Application of the least-squares computer program LETAGROP to the experimental emf(H) data, taking into account the hydrolytic species and hydrolysis constants of V(III), indicates that under the employed experimental conditions the complexes [VL]²⁺, [V(OH)L]⁺, [V(OH)₂L], [V(OH)₃L]⁻, [VL₂]⁺, [VL₃] and [V₂OL₄] form in the vanadium(III)–MePic system. Were observed the complexes [VL]⁺, [VL₂]⁻, [V(OH)L₂]²⁻ and [VL₃]³⁻ in the vanadium(III)–H₂Sal system, and the species [VHL]²⁺, [VL]⁺, [V(OH)L], [VHL₂], [VL₂]⁻, [V(OH)L₂]²⁻, [V(OH)₂L₂]³⁻ and [VL₃]³⁻ in the vanadium(III)–H₂Phtha system. The stability constants of these complexes were determined by potentiometric measurements, and spectrophotometric measurements were made in order to perform a qualitative characterization of the complexes formed in aqueous solution.