On the convergence of FPT-DFT calculations of the Fermi contact contribution to NMR coupling constants

Calculations of the Fermi contact term of NMR couplings, J^FC(MN), using a single FC perturbation within the Finite Perturbation Theory-DFT frameworks are only reliable if they do not depend either on a) the size of the perturbation, and b) whether the perturbation is placed at the site of the M or N nucleus. In this short communication these two points are addressed by studying the ¹J^FC(MN) and ²J^FC(MN) linear response behavior in a set of small molecules. It is shown how such a linearity depends on the size of the finite perturbation, the basis set employed, and the chosen nucleus site. The dependence of SCF convergence requirements on the size of the perturbation is also discussed. Calculations are carried out employing the B3LYP and B3PW91 hybrid functionals and results are compared with both state-of-the-art calculations and experimental values. Received: 28 June 2000 / Accepted: 12 July 2000 / Published online: 23 November 2000     

Hypervalent triphenyl and diphenyl tin coordination compounds derived from 2-(1H-benzimidazol-2-yl)phenol

Reactions of 2-(1H-benzimidazol-2-yl)phenol (1) and SnPh₃Cl, SnPh₂Cl₂ and SnCl₄ were investigated. One tetracoordinated triphenyltin(IV) compound: triphenyltin-2-(1H-benzimidazol-2-yl)phenolate] (3) and its adducts: [O → Sn] dimethylsulfoxide triphenyltin-[2-(1H-benzimidazol-2-yl)phenolate] (4), [O → Sn] aqua triphenyltin-[2-(1H-benzimidazol-2-yl)phenolate] (5) [O → Sn] ethanol triphenyltin-[2-(1H-benzimidazol-2-yl)phenolate] (6), [N → Sn] pyridine triphenyltin-[2-(1H-benzimidazol-2-yl)phenolate] (7), where 1 acts as a monodentate ligand bound through the phenol oxygen, were obtained. In the pentacoordinated compounds 4-7, the tin atom has tbp geometry. The three phenyl groups are in equatorial positions, whereas the benzimidazole and the Lewis base are in apical positions. Two hexacoordinated tin compounds: diphenyltin-bis[2-(1H-benzimidazol-2-yl-κN)phenolate-κO] (8), dichlorotin-bis[2-(1H-benzimidazol-2-yl-κN)phenolate-κO] (9) bearing two bidentate ligands are reported. The coplanar ligands in 8 and 9 form six membered rings by oxygen and nitrogen coordination. The tin geometry is all-trans octahedral. In 8 the two phenyl groups, and in 9 the two chlorine atoms are perpendicular to the plane of the ligands. Compounds were identified in solution mainly by ¹H, ¹³C and ¹¹⁹Sn NMR and in the solid state by X-ray diffraction analysis.     

Planar tetracoordinate carbon versus planar tetracoordinate boron: the case of CB4 and its cation

In this study, we analyzed CB(4) and its cation, CB(4)(+). Using CCSD(T)/aug-cc-pVQZ//CCSD(T)/aug-cc-pVTZ quantum-chemical calculations, we found that the neutral molecule is in accord with the results of Boldyrev and Wang, having a C(s) global minimum with a planar tricoordinate carbon structure, contradicting previous studies. In contrast, CB(4)(+), which was reported by an early mass spectroscopic study, has a planar tetracoordinate carbon (ptC) atom, demonstrating that a modification of the charge can promote the stabilization of a ptC structure.     

Solvent effects in ionic liquids: empirical linear energy-density relationships

Multiparameter linear energy-density relationships to model solvent effects in room temperature ionic liquids (RTILs) are introduced and tested. The model incorporates two solvent dependent and two specific solute-solvent parameters represented by a set of electronic indexes derived from the conceptual density functional theory. The specific solute-solvent interactions are described in terms of the electronic chemical potential for proton migration between the anion or cation and the transition state structure of a specific reaction. These indexes provide a quantitative estimation of the hydrogen bond (HB) acceptor basicity and the hydrogen bond donor acidity of the ionic solvent, respectively. A sound quantitative scale of HB strength is thereby obtained. The solvent dependent contributions are described by the global electrophilicity of the cation and nucleophilicity of the anion forming the ionic liquid. The model is illustrated for the kinetics of cycloaddition of cyclopentadiene towards acrolein. In general, cation HB acidity outweighs the remaining parameters for this reaction.     

Simultaneous in situ generation of hydrogen peroxide and Fenton reaction over Pd-Fe catalysts

High mineralization degree of organic compounds can be achieved by a novel environmentally-friendly full heterogeneous Pd-Fe catalytic system, which involves in situ generation of hydrogen peroxide from formic acid and oxygen, and oxidation of organic compounds by Fenton process in a one-pot reaction.     

Optimizing the rank position of the DMU as secondary goal in DEA cross-evaluation

Cross-efficiency evaluation is an extension of Data Envelopment Analysis (DEA) that permits not only the determination of a ranking of Decision Making Units (DMUs) but also the elimination of unrealistic weighting schemes, thereby rescinding the necessity for the inclusion of individual judgements in the models. The main deficiency of the procedure is the non-uniqueness of the optimal weights, which results in the peer evaluations dependences, for instance, on the software used to determine DMU’s efficiencies. This shortfall justifies the inclusion of secondary goals in order to determine cross-efficiency values. In this paper a new proposal of a secondary goal is studied. The idea is related with that proposed in Wu et al. (2009), in which the objective is the optimization of the rank position of the DMU under evaluation. In the procedure proposed here, an incentive to break level-pegging ties between alternatives is introduced by considering that efficiency scores induce a weak order of alternatives. The model is illustrated with a preference-aggregation application.     

Predicting the reaction mechanism of nucleophilic substitutions at carbonyl and thiocarbonyl centres of esters and thioesters

In nucleophilic substitution reactions at carbonyl centres, there are two possible channels. The first one occurs when the attack of nucleophilic agents takes place simultaneously with the departure of the nucleofuge. This process is named as concerted. The second possibility is the formation of a reaction intermediate, typically a tetrahedral intermediate from which the nucleofuge departs after passing through a second transition state. This second mechanism is defined as stepwise. Whether a concerted or stepwise mechanism is to be expected for a given reaction depends on several factors. Among these determinants are the nucleophilicity of the attacking group, the leaving group ability of the nucleofuge, and the solvent, which affects both the stability of the intermediate or the transition states involved. The role of the electrophilic centre can however become an important factor that can determine the reaction mechanism. In this work we show that the group nucleophilic Fukui function model may be used to rationalize and to predict the reaction mechanism of the title compounds towards alicyclic amines. In general, when the electrophilic carbon centre is attached to the soft sulfur atom, the reaction mechanism is predicted to follow a stepwise route. When the electrophilic carbon atom is attached to a harder oxygen centre, the reaction mechanism is determined by chemical substitution at the nucleofuge moiety. Experimental verification for a set of four substrates is presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Sizing the BFGS and DFP updates: Numerical study

In this study, we develop and test a strategy for selectively sizing (multiplying by an appropriate scalar) the approximate Hessian matrix before it is updated in the BFGS and DFP trust-region methods for unconstrained optimization. Our numerical results imply that, for use with the DFP update, the Oren-Luenberger sizing factor is completely satisfactory and selective sizing is vastly superior to the alternatives of never sizing or first-iteration sizing and is slightly better than the alternative of always sizing. Numerical experimentation showed that the Oren-Luenberger sizing factor is not a satisfactory sizing factor for use with the BFGS update. Therefore, based on our newly acquired understanding of the situation, we propose a centered Oren-Luenberger sizing factor to be used with the BFGS update. Our numerical experimentation implies that selectively sizing the BFGS update with the centered Oren-Luenberger sizing factor is superior to the alternatives. These results contradict the folk axiom that sizing should be done only at the first iteration. They also show that, without sufficient sizing, DFP is vastly inferior to BFGS; however, when selectively sized, DFP is competitive with BFGS.This research was supported in part by NSF Cooperative Agreement No. CCR-88-09615, AFOSR Grant 89-0363, DOE Grant DEFG05-86-ER25017, and AR0 Grant 9DAAL03-90-G-0093. This paper was presented at the ICIAM 91 International Conference, Washington DC, July 1991.The authors thank all those individuals who took part in the lively discussions concerning this material following the ICIAM 91 presentation. These discussions influenced the current version of the paper. The first author also thanks Maria Cristina Maciel for assistance and support during the earlier stages of the research.This author is currently a Graduate Student in the Mathematics Department, University of California at Riverside, Riverside, California, and has participated in the Summer Student Visitor Program at the Center for Research in Parallel Computation of Rice University for the past two years.     

Transmission mechanisms of inter-proton long-range couplings in substituted anisoles

Inter-proton long-range and ring couplings were measured in o-anisaldehyde and in seven disubstituted anisoles. In order to investigate the transmission mechanisms of long-range couplings with the methoxy group, partially restricted molecular orbital (PRMO) calculations were carried out within the FPT-INDO method on o-anisaldehyde. σ- and π-electron, and through-space transmitted components were separated. For the energetically favoured trans-OMe conformation a through-space component was found for the couplings of the methyl protons with the ortho-proton, and it was found that its sign, as well as its magnitude, depends on their relative positions. If free rotation, however, is assumed for the methyl group, the averaged value for this coupling constant is negative.     

The use of partially restricted molecular orbitals to investigate transmission mechanisms of spin-spin coupling constants. I. Theσ andπ contributions within the FPT INDO method

Partially restricted INDO MO Calculations have been carried out to separate the -electron contributions to spin-spin coupling constants in ethylene, butadiene, benzene and toluene. Results reproduce very well known trends such as the pathway invariance, the alternation in sign and the methyl group replacement rule.Comisión de Investigaciones Científicas (CIC, Pcia.Bs.As.) fellow.