High order linear initial-value problems and Schauder bases

In this paper we approximate the solution of a linear initial-value problem, making use of a Schauder basis for certain Banach space associated with such a differential problem. In addition, we apply that results in order to calculate numerically the response from a structure modelled by a three degree-of-freedom mass–damper–spring system.     

Substituted m-phenylene bridges as strong ferromagnetic couplers for Cu(II)-bridge-Cu(II) magnetic interactions: new perspectives

Based on a combined theoretical-experimental study, we propose that substituted m-phenylene ligands (m-N-Phi-N) can act as tuneable strong ferromagnetic couplers connecting Cu(II) ions; a new complex presenting that bridge with J close to +15 cm(-1) has been suggested and synthesized.     

Complexation of the Non-steroidal Anti-inflammatory Drug Nabumetone with Modified and Unmodified Cyclodextrins

The inclusion of the anti-inflammatory drug, Nabumetone, in -, - and hydroxypropyl--cyclodextrin (CDs) is studied using UV-VIS absorption and steady-state fluorescence emission. Binding constants and thermodynamic parameters of complex formation are determined by spectrofluorimetry. The inclusion phenomena of Nabumetone with the three cyclodextrins is compared with that of the well known similar anti-inflammatory drug Naproxen. In the case of Nabumetone pronounced differences are observed in the complexation process with each cyclodextrin whereas the respective Naproxen complexes are nearly identical. ¹H-NMR experiments show that the inclusion process in Nabumetone can occur either through the substituents in the -2 (butanone) or -6 (methoxy) positions in the naphthalene ring.     

New results for the OH (nu = 0,j = 0) + CO (nu = 0,j = 0) --> H + CO2 reaction: Five- and full-dimensional quantum dynamical study on several potential energy surfaces

Full- [six-dimensional (6-D)] and reduced-dimensional [five-dimensional (5-D)] quantum wave packet calculations have been performed for the title reaction to obtain reaction probabilities deriving from the ground rovibrational states of OH and CO with total angular momentum J = 0. Three potential energy surfaces (PES) are studied, namely, those of Bradley and Schatz (BS), Yu, Muckerman, and Sears (YMS), and Lakin, Troya, Schatz, and Harding (LTSH). 6-D calculations are performed only for the BS PES, while 5-D results are reported for all three PES'. The 6-D results obtained in the present work improve on those previously reported, since a larger vibrational basis and a better representation of the OH and CO bonds has been introduced. In particular, we now employ a generalized Lanczos-Morse discrete variable representation for both the OH and CO vibrations. In a further improvement, the generalized discrete variable representation of the CO vibration is based on different CO intramolecular potentials for the asymptotic and product grids employed in our projection formalism. This new treatment of the vibrational bases allows for a large reduction in computation time with respect to our previous implementation of the wave packet method, for a given level of accuracy. As a result, we have been able to extend the range of collision energies for which we can obtain converged 6-D results to a higher energy (0.8 eV) than was possible before (0.5 eV). The comparison of the new 6-D and previous 5-D results for the BS PES shows good agreement of the general trend in the reaction probabilities over all collision energies considered (0.1-0.8 eV), while our previous 6-D calculation showed reaction probabilities that differed from the 5-D results by up to 10% between 0.5 and 0.8 eV. The 5-D reaction probabilities reveal interesting trends for the different PES'. In particular, at low energies (< 0.2 eV) the LTSH PES gives rise to much larger reactivity than the other PES', while at high energies (> 0.3 eV) its reaction probability decreases with respect to the BS and YMS PES', being more than a factor of 2 smaller at 0.8 eV. A 5-D calculation on a modified version of the LTSH surface shows that the van der Waals interaction in the entrance channel, which is not correctly described in the other PES' is largely responsible for its larger reactivity at low energies. The large difference between the 5-D reaction probabilities for the YMS and LTSH PES' serves to emphasize the importance of the van der Waals interaction for the reactivity at low energies, because most of the stationary point energies on the YMS and LTSH PES are rather similar, being in line with high-level ab initio information.     

The Counterion Effect on the Assembly of Coordination Networks of Cationic (η3‐Allyl)palladium Complexes Containing 3,5‐Dimethyl‐4‐nitro‐1H‐pyrazole

Two new (η³‐allyl)palladium complexes containing the ligand 3,5‐dimethyl‐4‐nitro‐1H‐pyrazole (Hdmnpz) were synthesized and characterized as [Pd(η³‐C₃H₅)(Hdmnpz)₂]BF₄ ( 1 ) and [Pd(η³‐C₃H₅)(Hdmnpz)₂]NO₃ ( 2 ). The structures of these compounds were determined by single‐crystal X‐ray diffraction to evaluate the intermolecular assembly. Each complex exhibits similar coordination behavior consistent with cationic entities comprised of two pyrazole ligands coordinated with the [Pd(η³‐C₃H₅)]⁺ fragment in an almost square‐planar coordination geometry. In 1 , the cationic entities are propagated through strong intermolecular H‐bonds formed between the pyrazole NH groups and BF ions in one‐dimensional polymer chains along the a axis. These chains are extended into two‐dimensional sheet networks via bifurcated H‐bonds. New intermolecular interactions established between NO₂ and Me substituents at the pyrazole ligand of neighboring sheets give rise to a three‐dimensional network. By contrast, compound 2 presents molecular cyclic dimers formed through N? H???O H‐bonds between two NO counterions and the pyrazole NH groups of two cationic entities. The dimers are also connected to each other through C? H???O H‐bonds between the remaining O‐atom of each NO ion and the allyl CH₂ H‐atom. Those interactions expand in a layer which lies parallel to the face (101).     

A solvent-controlled switch of manganese complex assemblies with a beta-diketonate-based ligand

The coordination properties of the new polynucleating ligand H(3)L1 (1,3-bis(3-oxo-3-phenylpropionyl)-2-hydroxy-5-methylbenzene) with Mn(II/III) are described. Depending on the solvent used, the reaction of H(3)L1 with Mn(OAc)(2) yields either of the two new multinuclear assemblies [Mn(2)(HL1)(2)(py)(4)] (1) and [Mn(3)(HL1)(3)] (2), as revealed by X-ray crystallography. The structure of 2 is remarkable in that it shows a unique asymmetric triple-stranded helicate. Complexes 1 and 2 can be interconverted by controlling the solvent of the reaction system, and therefore, this ensemble constitutes an interesting externally addressable switch. In the presence of Mn(III)/pyridine, partial degradation of H(3)L1 occurs via oxidative cleavage, and the new complex [Mn(2)(L2)(2)(py)(4)] (3) is formed. The crystal structure of this complex has shown the fully deprotonated form of the new donor H(3)L2 (3-(3-oxo-3-phenylpropionyl)-5-methylsalicylic acid). From the same reaction, the Mn(II) complex 1 is also obtained. A rational synthesis of H(3)L2 is reported, and this has been used to prepare 3 in high yields, directly from its components. Variable-temperature magnetic susceptibility (chi(m)) measurements were performed on complexes 1-3 under a magnetic field of 1 kG. The data for each complex were fit to the appropriate chi(m) vs T theoretical equation, respectively. In 1, the Mn(II) ions are uncoupled, with g = 2.01. The data from 2 were fit by assuming the presence of an exchange coupled Mn(II)...Mn(II) pair next to a magnetically isolated Mn(II) center. The fit gave J = -2.75 cm(-1), g(12) = 1.97, and g(3) = 1.92, respectively. In 3, two models fit the experimental data. In the most satisfactory, the Mn(III) ions are coupled antiferromagnetically with J = -1.48 cm(-1) and g = 1.98 and a term for weak ferromagnetic intermolecular exchange is included with zJ' = 0.39 cm(-1). The other model contemplates the presence of two uncoupled zero field split Mn(III) ions.     

Local aromaticity of [n]acenes, [n]phenacenes, and [n]helicenes (n = 1-9)

The local aromaticity of the six-membered rings in three series of benzenoid compounds, namely, the [n]acenes, [n]phenacenes, and [n]helicenes for n = 1-9, has been assessed by means of three probes of local aromaticity based on structural, magnetic, and electron delocalization properties. For [n]acenes our analysis shows that the more reactive inner rings are more aromatic than the outer rings. For [n]phenacenes, all indicators of aromaticity show that the external rings are the most aromatic. From the external to the central ring, the local aromaticity varies in a damped alternate way. The trends for the [n]helicene series are the same as those found for [n]phenacenes. Despite the departure from planarity in [n]helicenes, only a very slight loss of aromaticity is detected in [n]helicenes as compared to the corresponding [n]phenacenes. Finally, because of magnetic couplings between superimposed six-membered rings in the higher members of the [n]helicenes series, we have demonstrated that the NICS indicator of aromaticity artificially increases the local aromaticity of their most external rings.     

NaCu(II)4] cluster from alkali template assembly of two asymmetric end-on azido-bridged [Cu(II)2] units

The cluster [NaCu4L2(N3)2](ClO4) [1; H3L is 2-(2'-hydroxyphenyl)-1,3-bis[3'-aza-4'-(2'-hydroxyphenyl)prop-4'-en-1'-yl]-1,3-imidazolidine] has been synthesized and structurally characterized. Complex 1 is formed by the template assembly of two [Cu2L(N3)] neutral fragments through their weak oxophilic interactions with a central Na+ cation as observed in metallacrowns. The cluster exhibits a combination of ferro- and antiferromagnetic interactions. End-on N3- bridging of copper ions within the [Cu(II)2] units facilitates stabilization of S = 1 magnetic subunits that mutually cancel via antiferromagnetic coupling as mediated by the O...Na+...O bridges.     

Structure and Dynamics of Oligonucleotides in the Gas Phase

By combining ion‐mobility mass spectrometry experiments with sub‐millisecond classical and ab initio molecular dynamics we fully characterized, for the first time, the dynamic ensemble of a model nucleic acid in the gas phase under electrospray ionization conditions. The studied oligonucleotide unfolds upon vaporization, loses memory of the solution structure, and explores true gas‐phase conformational space. Contrary to our original expectations, the oligonucleotide shows very rich dynamics in three different timescales (multi‐picosecond, nanosecond, and sub‐millisecond). The shorter timescale dynamics has a quantum mechanical nature and leads to changes in the covalent structure, whereas the other two are of classical origin. Overall, this study suggests that a re‐evaluation on our view of the physics of nucleic acids upon vaporization is needed.     

Aggregation of [Cu(II)4] building blocks into [Cu(II)8] clusters or a [Cu(II)4]infinity chain through subtle chemical control

Coordination complexes of the ligand H3L [1,3-bis(3-oxo-3-phenylpropionyl)-2-hydroxy-5-methylbenzene] with Cu(II) are reported. Clusters showing various nuclearities or modes of supramolecular organization have been prepared by slightly changing the reaction conditions and have been crystallographically characterized. The reaction of H3L with one equivalent of Cu(OAc)2 in DMF yields the dinuclear complex [Cu2(HL)2(dmf)2] (1). Reaction in MeOH of H3L with an increased amount of metal, in the form of Cu(NO3)2, and excess strong base (nBu4NOH) affords the cluster [Cu8(L)2(OMe)8(NO3)2] (2). Complex 2 is a dimer of two linear [Cu4] arrays bridged by methoxide ligands, where the polynucleating ligand is fully deprotonated. The [Cu4]2 clusters are linked to each other by NO3- bridges to form one-dimensional coordination polymers. The link between [Cu8] units and their relative spatial positioning can be modified by changing the anion of the Cu(II) salt, as demonstrated by the synthesis of the cluster polymers [Cu8(L)2(OMe)8Cl2] (3) and [Cu8(L)(OMe)7.86Br2.14] (4), where only NO3- has been replaced by Cl- or Br-, respectively. Similarly, when ClO4- is used, compound [Cu8(L)2(OMe)8(ClO4)2(MeOH)4] (5) can be isolated. It contains independent [Cu8] units. A slight change in the stoichiometry of the reaction leading to 2 affords the related complex catena-[Cu4(L)(OMe)3(NO3)2(H2O)0.36] (6). This polymer contains essentially the same [Cu4] moiety as 2, albeit organized in a completely different arrangement. Each [Cu4] unit in 6 is linked by OMe- ligands to two such equivalent groups to form an infinite chain. Magnetic susceptibility measurements reveal weak antiferromagnetic exchange between Cu(II) centers in 1 (J = -0.73 cm(-1)) and strong antiferromagnetic coupling within [Cu4] chains in 2, 5, and 6 (most negative J values of -113.8 and -177.3 cm(-1) for 2 and 6, respectively).