Inner projection techniques for the low-cost handling of two-electron integrals in quantum chemistry

ABSTRACT

The density-fitting technique for approximating electron-repulsion integrals relies on the quality of auxiliary basis sets. These are commonly obtained through data fitting, an approach that presents some shortcomings. On the other hand, it is possible to derive auxiliary basis sets by removing elements from the product space of both contracted and primitive orbitals by means of a particular form of inner projection technique that has come to be known as Cholesky decomposition (CD). This procedure allows for on-the-fly construction of auxiliary basis sets that may be used in conjunction with any quantum chemical method, i.e. unbiased auxiliary basis sets. One key feature of these sets is that they represent the electron-repulsion integral matrix in atomic orbital basis with an accuracy that can be systematically improved. Another key feature is represented by the fact that locality of fitting coefficients is obtained even with the long-ranged Coulomb metric, as result of integral accuracy. Here we report on recent advances in the development of the CD-based density fitting technology. In particular, the implementation of analytical gradients algorithms is reviewed and the present status of local formulations – potentially linear scaling – is analysed in detail.     

Mathematical Analysis of the Jin-Neelin Model of El Niño-Southern-Oscillation

The Jin-Neelin model for the El Ni$\wt{\rm n}$o--Southern Oscillation (ENSO for short) is considered for which the authors establish existence and uniqueness of global solutions in time over an unbounded channel domain. The result is proved for initial data and forcing that are sufficiently small. The smallness conditions involve in particular key physical parameters of the model such as those that control the travel time of the equatorial waves and the strength of feedback due to vertical-shear currents and upwelling; central mechanisms in ENSO dynamics. From the mathematical view point, the system appears as the coupling of a linear shallow water system and a nonlinear heat equation. Because of the very different nature of the two components of the system, the authors find it convenient to prove the existence of solution by semi-discretization in time and utilization of a fractional step scheme. The main idea consists of handling the coupling between the oceanic and temperature components by dividing the time interval into small sub-intervals of length $k$ and on each sub-interval to solve successively the oceanic component, using the temperature $T$ calculated on the previous sub-interval, to then solve the sea-surface temperature (SST for short) equation on the current sub-interval. The passage to the limit as $k$ tends to zero is ensured via a priori estimates derived under the aforementioned smallness conditions.     

Behavior of extraframework Fe sites in MFI and MCM-22 zeolites upon interaction with N2O and NO

We report on the characterization of an isomorphously substituted Fe-MCM-22 sample containing both Fe and Al in framework positions (Si/Fe = 44, Si/Al = 25). XANES spectroscopy was used to study the evolution of Fe sites as a consequence of thermal activation at high temperature (1073 K) and subsequent oxidation with N2O. The results were compared to those obtained in the same conditions on a well-known Fe-silicalite sample (Si/Fe = 68, Si/Al = infinity). In both samples, thermal activation causes migration of a fraction of Fe ions from framework to extraframework positions, this migration being accompanied by a reduction of Fe3+ to Fe2+. Upon oxidation with N2O at 523 K, the two samples show a different behavior. While in Fe-silicalite practically all of the Fe2+ sites formed by thermal activation are reoxidized to Fe3+, in Fe-MCM-22 only a fraction of the extraframework iron sites is involved in the reoxidation process. The accessibility of the extraframework Fe sites was also investigated by using the NO molecule as a surface probe. Upon NO dosage on the sample, the modification of the pre-edge peak and of the edge position suggests an important charge release from the extraframework Fe2+ ions to the adsorbed molecules. This could be formalized with the formation of Fe3+(NO-) complexes, compatible (on the basis of the simple molecular orbital theory) with a bent NO geometry. The formation of a complex family of Fe2+ mono-, di-, and trinitrosyl complexes was also confirmed by FTIR spectroscopy. Similarly to what was observed in the oxidation experiments, the fraction of extraframework Fe sites able to interact with NO in Fe-MCM-22 sample is smaller than that in Fe-silicalite treated in the same conditions. This trend is explained with a major clustering of extraframework Fe sites in Fe-MCM-22 sample, as was also suggested by FTIR experiments. These results suggest that the dispersion of iron in zeolitic matrixes prepared by isomorphous substitution could also depend on the zeolitic structure.     

Synthesis of a laterally branched polyamine from alpha-methylene-gamma-butyrolactone

[reaction: see text] A polyamine derivative was prepared from alpha-methylene-gamma-butyrolactone. This method used Michael addition and lactone aminolysis followed by the nucleophilic substitution of the hydroxyl group by an azido group. The coupling of a lipophilic alkyne led to a polyamine that will be probed as a gene transfer agent.     

A Convergence Analysis of Gmres and Fom Methods for Sylvester Equations

We discuss convergence properties of the GMRES and FOM methods for solving large Sylvester equations of the form AX–XB=C. In particular we show the importance of the separation between the fields of values of A and B on the convergence behavior of GMRES. We also discuss the stagnation phenomenon in GMRES and its consequence on FOM. We generalize the issue of breakdown in the block-Arnoldi algorithm and explain its consequence on FOM and GMRES methods. Several numerical tests illustrate the theoretical results.     

Calix[4]arenes with one and two N-linked imidazolium units as precursors of N-heterocyclic carbene complexes. Coordination chemistry and use in Suzuki-Miyaura cross-coupling

The calix[4]arene-imidazolium salts 5-(3-butyl-1-imidazolylium)-25,26,27,28-tetrabenzyloxy-calix[4]arene bromide (cone) (2), and 5,11-bis(3-alkyl-1-imidazolylium)-25,26,27,28-tetrabenzyloxycalix[4]arene diiodide (cone) (R = methyl, 3a; R = n-butyl, 3b) have been synthesised. Reaction of 2 in dioxane with PdCl(2) in the presence of CsCO(3) and KBr (80 °C, 24 h) gives the carbene complex trans-[PdBr(2)(calix-monocarbene)(2)] (14), containing two N-heterocyclic carbene ligands derived from 2 (yield: 63%). Repeating the reaction in pyridine instead of dioxane gives the mixed pyridine-carbene complex trans-[PdBr(2)(calix-carbene)(pyridine)] (15) in 75% yield. Treatment of the bis-imidazolium salt 3a with [Pd(OAc)(2)] affords a chelate complex, trans-[PdI(2){calix-bis(carbene)}] (16), in which a metallo-(bis-carbene) fragment caps the upper rim of the calixarene basket. Complex 16, as well as its analogue 17, obtained from 3b, display apparent C(s)-symmetry in solution. This is not the case in the solid state, a single X-ray diffraction study carried out for 16 revealing a pinced cone structure for the calixarene skeleton, which reduces the symmetry to C(1). The chelate complex 17 shows poor activity in Suzuki-Miyaura cross-coupling of phenyl boronic acid and p-tolyl halides, an observation that suggests the presence of a strained metallocyclic unit preventing easy stereochemical rearrangement to an active species. Unlike 17, complexes 14 and 15 show good activities in cross-coupling. A comparative study using the carbene precursor 1-butyl-3-(2,6-diisopropylphenyl)imidazolium bromide (18), which is devoid of the receptor fragment, strongly suggests that the carbene ligands of 14 and 15 operate typically as bulky NHC-ligands.     

Cavitand supported tetraphosphine: cyclodextrin offers a useful platform for Suzuki-Miyaura cross-coupling

The cyclodextrin-tetraphosphine hybrid coined α-Cytep allows turnover numbers up to 340,000,000,000 and turnover frequencies up to 1,000,000,000 h(-1) to be reached in Suzuki-Miyaura reactions. These exceptional figures are clearly linked to the outstanding longevity of the reactive species induced by the ligand α-Cytep and illustrates the rising potential of cyclodextrins in catalytic applications.     

Calix[6]arene‐Based Cascade Complexes of Organic Ion Triplets Stable in a Protic Solvent

Herein we report a D_3h‐symmetric tail‐to‐tail bis‐calix[6]arene 3 featuring two divergent cavities triply connected by ureido linkages. This calix[6]tube was synthesized by a domino Staudinger/aza‐Wittig reaction followed by a macrocyclization reaction. This process also afforded a C_2h‐symmetric isomer that represents a rare example of a self‐threaded rotaxane based on calix[6]arene subunits. The binding properties of 3 have been evaluated by NMR studies. Thus, bis‐calix[6]arene 3 is able to bind simultaneously two neutral ureido guests through an induced‐fit process. The guests are located in the cavities and are recognized through multiple hydrogen‐bonding interactions with the ureido bridges. Host 3 can also simultaneously bind multiple ions and is especially efficient for the complexation of organic ion triplets. The anion is recognized through hydrogen‐bonding interactions at the ureido binding site and is thus located between the two ammonium ions accommodated in the cavities. The resulting [1+1+2] quaternary complexes represent rare examples of cascade complexes with organic cations. These complexes are unique: 1) They are stable even in a markedly protic solvent, 2) the recognition of the ion triplets proceeds in a cooperative way through an induced‐fit process and with a high selectivity, linear cations and doubly charged anions being particularly well recognized, 3) the ions are bound as contact ion triplets thanks to the closeness of the three binding sites, 4) the cationic guests can be exchanged and thus mixed [1+1+1+1] complexes can be obtained, 5) the ureido linkers wrapped around the anion adopt a helical shape and the resulting chirality is sensed by the cations. In other words, bis‐calix[6]arene 3 presents a selective inner tunnel in which multiple guests such as organic ion triplets can be aligned in a cooperative way through induced‐fit processes.     

The initial single yeast cell adhesion on glass via optical trapping and Derjaguin-Landau-Verwey-Overbeek predictions

We used an optical tweezer to investigate the adhesion of yeast Saccharomyces cerevisiae onto a glass substrate at the initial contact. Micromanipulation of free-living objects with single-beam gradient optical trap enabled to highlight mechanisms involved in this initial contact. As a function of the ionic strength and with a displacement parallel to the glass surface, the yeast adheres following different successive ways: (i) Slipping and rolling at 1.5 mM NaCl, (ii) slipping, rolling, and sticking at 15 mM NaCl, and (iii) only sticking at 150 mM. These observations were numerous and reproducible. A kinetic evolution of these adhesion phenomena during yeast movement was clearly established. The nature, range, and relative intensity of forces involved in these different adhesion mechanisms have been worked out as a quantitative analysis from Derjaguin-Landau-Verwey-Overbeek (DLVO) and extended DLVO theories. Calculations show that the adhesion mechanisms observed and their affinity with ionic strength were mainly governed by the Lifshitz-van der Waals interaction forces and the electrical double-layer repulsion to which are added specific contact forces linked to "sticky" glycoprotein secretion, considered to be the main forces capable of overcoming the short-range Lewis acid-base repulsions.