Energetic and topological analysis of the reaction of Mo and Mo2 with NH3, C2H2, and C2H4 molecules

The Density functional theory has been applied to characterize the structural features of Mo(1,2)-NH(3),-C(2)H(4), and -C(2)H(2) compounds. Coordination modes, geometrical structures, and binding energies have been calculated for several spin multiplets. It has been shown that in contrast to the conserved spin cases (Mo(1,2)-NH(3)), the interaction between Mo (or Mo(2)) and C(2)H(4) (or C(2)H(2)) are the low-spin (Mo-C(2)H(4) and -C(2)H(2)) and high-spin (Mo(2)-C(2)H(4) and -C(2)H(2)) complexes. In the ground state of Mo(1,2)-C(2)H(4) and -C(2)H(2), the metal-center always reacts with the C-C center. The spontaneous formation of the global minima is found to be possible due to the crossing between the potential energy surfaces (ground and excited states with respect to the metallic center). The bonding characterization has been performed using the topological analysis of the Electron Localization Function. It has been shown that the most stable electronic structure for a pi-acceptor ligand correlates with a maximum charge transfer from the metal center to the C-C bond of the unsaturated hydrocarbons, resulting in the formation of two new basins located on the carbon atoms (away from hydrogen atoms) and the reduction of the number of attractors of the C-C basin. The interaction between Mo(1,2) and C(2)H(4) (or C(2)H(2)) should be considered as a chemical reaction, which causes the multiplicity change. Contrarily, there is no charge transfer between Mo(1,2) and NH(3), and the partners are bound by an electrostatic interaction.     

Comparative study of the bonding in the first series of transition metal 1:1 complexes M-L (M = Sc, ..., Cu; L = CO, N(2), C(2)H(2), CN(-), NH(3), H(2)O, and F(-))

The nature of the chemical bonding in the 1:1 complexes formed by the fourth period transition metals (Sc, ..., Cu) with 14 electrons (N(2), CN(-), C(2)H(2)) and 10 electrons (NH(3), H(2)O, F(-)) ligands has been investigated at the ROB3LYP/6-311+G(2d) level by the ELF topological approach. The bonding is ruled by the nature of the ligand. The 10 electrons and anionic ligands are very poor electron acceptors and therefore the interaction with the metal is mostly electrostatic and for all metal except Cr the multiplicity is given by the [Ar]c(n)() configuration of the metallic core (n = Z - 20). The electron acceptor ligands which have at least a lone pair form linear or bent complexes involving a dative bond with the metal and the rules proposed previously for monocarbonyls hold. In the case of ethyne, it is not possible to form a linear complex and the cyclic C(2)(v)() structure imposed by symmetry possesses two covalent M-C bonds, therefore the multiplicity is given by the local core configuration [Ar]c(n)() for all metals except Mn and Ni.     

Energetic and topological analyses of the oxidation reaction between Mo(n) (n = 1, 2) and N2O

The interaction between molybdenum, atom, and dimer, with nitrous oxide has been investigated using density functional theory. The analysis of the potential energy surfaces for both reactions has revealed that a single molybdenum atom can activate the N--O bond of N2O requiring a small activation energy. However, the presence of several intersystem crossings between three different spin states, namely, septet, quintet and triplet states, seems to be the major constraint to the Mo + N2O reaction. Contrarily, the low-lying excited states (triplet and quintet) do not participate in the reaction between the molybdenum dimer and N2O. The latter reaction fully evolves on the singlet spin surface. Three different regions have been distinguished along the pathway: formation of an adduct complex, formation of an inserted compound, and the N2 detachment. The connection between the two first regions has been characterized by the formation of a special complex in which the N--O bond is so weakened that it could be considered as a first step in the insertion process. It has been shown that the topological changes along the pathways provide a clear explanation for the geometrical changes that occur along the reaction pathway. In summary, the detachment of the N2 molecule is found to be kinetically an effective process for both reactions, owing to the high exothermicity and consequently to the high internal energy of the insertion intermediates. However, in the case of Mo atom, the reaction should be a slow process due to the presence of spin-forbidden transitions. These results fully agree with previous experimental works.     

Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations

This paper is devoted to considering the existence and uniqueness results for fuzzy fractional integral equations employing the method of upper and lower solutions. Moreover, the approach is followed to prove the existence of solutions for the fuzzy initial value problem of fractional integrodifferential equations involving Riemann–Liouville differential operators. The method is illustrated by two examples.     

EPR Studies of Tl0.5Pb0.5Sr1.6Ba0.4CaCu2?xRuxO7?δ Superconductor

Bulk superconducting samples of type Tl_0.5Pb_0.5Sr_1.6Ba_0.4CaCu_2−x Ru _x O_7−δ, (Tl, Pb)/Sr-1212, with 0.0 ≤ x ≤ 0.525 were prepared by the conventional one-step solid-state reaction technique. The prepared samples were investigated using X-ray powder diffraction, electrical resistivity and electron paramagnetic resonance (EPR) measurements. Enhancement of the phase formation, superconducting transition temperature T _c and hole carriers concentration P was observed up to x = 0.075. For x > 0.075, a reverse trend was observed. EPR spectra were measured at different temperatures (120–290 K) for all prepared samples. The number of spins N participating in the resonance and the paramagnetic susceptibility χ were calculated as a function of both Ru-content and temperature. N and χ increased as the Ru-content increased. A linear relationship between logN and 1/T was established, from which the activation energy E _a was calculated as a function of the Ru-content. The temperature dependence of χ was fitted according to Curie–Weiss type of magnetic behavior. Curie constant C, Curie temperature θ, the effective magnetic moment μ and the electronic specific heat γ were estimated as a function of the Ru-content.     

Vibrational spectra and structure of CH3Cl:NO complex: IR matrix isolation and DFT study

Infrared spectra of the CH(3)Cl:NO complex isolated in solid neon have been investigated. Most of the vibrational modes of the complex have been detected. The weak interaction between NO and CH(3)Cl in CH(3)Cl:NO is responsible for small shifts of the vibrational mode frequencies of both CH(3)Cl and NO molecules. The measured shifts range between -3.2 and + 3.8 cm(-1). On the basis of DFT calculations, different geometries have been explored for the complex, and it has been shown that the most stable structure is of C(1) symmetry. The calculated frequency shifts match well the experimental data.     

Reactivity of atomic cobalt with molecular oxygen: a combined IR matrix isolation and theoretical study of the formation and structure of CoO2

The reactivity of atomic cobalt toward molecular oxygen in rare gas matrices has been reinvestigated. Experiments confirm that Co atoms in their a(4)F ground state are inert toward O(2) in solid argon and neon but reactive in the b(4)F first excited state, in agreement with the previous gas-phase study of Honma and co-workers. The formation of CoO(2) starting from effusive beams of Co and O(2) has been followed by IR absorption spectroscopy, both in neon and argon matrices. Our observations show that only the dioxo form, OCoO, is stabilized in the matrix and that IR absorptions previously assigned to the peroxo and superoxo forms are due to other, larger species. The present data strongly support the linear geometry in rare gas matrices proposed by Weltner and co-workers. We report on measurements on all IR-active fundamental modes for (16)OCo(16)O, (18)OCo(18)O, and (16)OCo(18)O with additional combination transitions supplying anharmonicity correction. This allows for a 5.93 +/- 0.02 mdyne/A CoO harmonic bond force constant in solid neon. Using the empirical relationship previously optimized for the CoO diatomics, an approximate value for the CoO internuclear bond distance is proposed (1.615 +/- 0.01A). In light of recent theoretical studies predicting (2)A(1) or (6)A(1) electronic ground states, the geometry and electronic structure of the OCoO molecule has also been reconsidered. Calculations carried out at the CCSD(T)/6-311G(3df) level indicate a linear structure with an r(e) = 1.62 A bond distance, consistent with the experimental estimate. For later studies of larger systems, where CCSD(T) calculations become too time-consuming, an effective DFT-based method is proposed which reproduces the basic electronic and geometrical properties of cobalt dioxide. Quantitative results are compared to the experimental data and high-level results regarding bond length and frequencies. This DFT method is used to propose a reaction pathway.     

Vibrational spectra and structures of H2O-NO, HDO-NO, and D2O-NO complexes. An IR matrix isolation and DFT study

The IR spectra of H2O+NO, HDO+NO, and D2O+NO, isolated in solid neon at low temperature have been investigated. Concentration effects and detailed vibrational analysis of deuterated and partially deuterated species allowed identification of three 1:1 HDO-NO species, two 1:1 D2O-NO species, and only one 1:1 H2O-NO complex. From comparison between the experimental spectra and the results of DFT calculations, it appeared that two different types of weakly bound complexes between water and nitric oxide can be formed in a neon matrix. The first species is a 1:1 complex where bonding occurs between water hydrogen and nitric oxide nitrogen, in which OH-N and OD-N intermolecular bonds are engaged. For this complex only DOD-NO, HOD-NO, and DOH-NO isotopic species have been experimentally detected and no IR bands of HOH-NO were observed. This result could be explained by the fact that the dissociation energy of HOH-NO is lower than those of DOD-NO, HOD-NO and DOH-NO. For the second detected 1:1 H2O-NO complex and its isotopic variants, the H2O-NO potential surface was explored systematically at the B3LYP level, but no stable species corresponding to the complex could be calculated. The structure of the second observed 1:1 H2O-NO complex results from columbic attractions between water and nitric oxide and could be stabilized only in matrix, probably by interaction between NO, water and (Ne)n.     

A Topological Study of the Ferromagnetic “No-Pair Bonding” in Maximum-Spin Lithium clusters: n+1Li n (n=2–6)

The nature of the bonding between lithium atoms, in low-spin and maximum-spin clusters, was investigated using the topological electron localization function (ELF) approach. The maximum-spin clusters are especially intriguing since their bonding is sustained without having even a single electron pair! Hence this type of bonding had been called “no-pair ferromagnetic-bonding” [Danovich, Wu, Shaik J Am Chem Soc 121:3165 (1999); Glokhovtsev, Schleyer Isr J Chem 33: 455 (1993); de Visser, Danovich, Wu, Shaik J Phys Chem A 106:4961 (2002)]. The following conclusions were reached in the study: (a) In the ground state of Li _n , covalent bonding between Li atoms is accounted by the presence of the disynaptic valence basins, which exhibit a significant degree of inter-basin delocalization. (b) Except for the ³Li₂ case, the valence basins of all maximum-spin clusters are populated by unpaired electrons. The valence basins are located off Li–Li axis (or Li–Li–Li plane), so that their spatial distribution minimizes the mutual Pauli repulsion and screens the electrostatic repulsion between the Li cores. The inter-basin delocalization is rather high, thereby indicating that the unpaired electrons are virtually delocalized over all the valence basins. (c) The ELF analysis shows that Li atoms in the low-spin clusters are bonded by “two-center two-electron” and “three-center two-electron” bonds. (d) In the maximum-spin species, bonding is sustained by “two-center one-electron” and “three-center one-electron” bonds. The latter picture is complementary to the valence bond picture [Danovich, Wu, Shaik J Am Chem Soc 121 3165 (1999); de Visser, Danovich, Wu, Shaik J Phys Chem A 106: 4961 (2002)], in which the bicentric ferromagnetic-bonding is delocalized over all the short Li–Li contacts, by the mixing of the ionic structures and other nonredundant structures into the repulsive high-spin covalent structure in which all the electrons populate the 2s atomic orbitals, i.e., the configuration. In such a manner bonding can be sustained from “purely ferromagnetic interactions” without electron pairing.Dedicated to Jean-Paul Malrieu, a friend and a poet-scientist