Probing Low-Energy Collective Nuclear Modes with Fast Neutrons

The low-energy, low-spin collective modes of nuclei that can be excited through inelastic scattering reactions with fast neutrons are reviewed. Recent studies of quadrupole, octupole, and multiphonon vibrations are described, and more exotic modes, including mixed-symmetry states, scissors mode states, and intruder excitations, are presented. The opportunities afforded through reactions with very energetic neutrons are considered, and a view to the future of nuclear structure studies with energetic neutrons is given.     

Scission of Carbon Monoxide Using TaR3, R=(N(tBu)Ph) or OSi(tBu)3: A DFT Investigation

The experimentally known reduction of carbon monoxide using a 3‐coordinate [Ta(silox)₃] (silox=OSi(tBu)₃) complex initially forms a ketenylidene [(silox)₃Ta? CCO], followed by a dicarbide [(silox)₃Ta? CC? Ta(silox)₃] structure. The mechanism for this intricate reaction has finally been revealed by using density functional theory, and importantly a likely structure for the previously unknown intermediate [(silox)₃Ta? CO]₂ has been identified. The analysis of the reaction pathway and the numerous intermediates has also uncovered an interesting pattern that results in CO cleavage, that being scission from a structure of the general form [(silox)₃Ta? C_nO] in which n is even. When n is odd, cleavage cannot occur. The mechanism has been extended to consider the effect of altering both the metal species and the ligand environment. Specifically, we predict that introducing electron‐rich metals to the right of Ta in the periodic table to create mixed‐metal dinuclear intermediates shows great promise, as does the ligand environment of the Cummins‐style 3‐coordinate amide structure. This latter environment has the added complexity of improved electron donation from amide rotation that can significantly increase the reaction exothermicity.     

General theory of domain decomposition: Indirect methods

According to a general theory of domain decomposition methods (DDM), recently proposed by Herrera, DDM may be classified into two broad categories: direct and indirect (or Trefftz‐Herrera methods). This article is devoted to formulate systematically indirect methods and apply them to differential equations in several dimensions. They have interest since they subsume some of the best‐known formulations of domain decomposition methods, such as those based on the application of Steklov‐Poincaré operators. Trefftz‐Herrera approach is based on a special kind of Green's formulas applicable to discontinuous functions, and one of their essential features is the use of weighting functions which yield information, about the sought solution, at the internal boundary of the domain decomposition exclusively. A special class of Sobolev spaces is introduced in which boundary value problems with prescribed jumps at the internal boundary are formulated. Green's formulas applicable in such Sobolev spaces, which contain discontinuous functions, are established and from them the general framework for indirect methods is derived. Guidelines for the construction of the special kind of test functions are then supplied and, as an illustration, the method is applied to elliptic problems in several dimensions. A nonstandard method of collocation is derived in this manner, which possesses significant advantages over more standard procedures. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 296–322, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10008     

Phosphine and solvent effects on oxidative addition of CH3Br to Pd(PR3) and Pd(PR3)2 complexes

The reaction between bromomethane CH(3)Br and Pd(0) phosphine complexes Pd(PR(3)) and Pd(PR(3))(2) resulting in the corresponding Pd(II) species Pd(PR(3))(CH(3))Br and Pd(PR(3))(2)(CH(3))Br was studied computationally with DFT methods. The oxidative addition can take place through two different mechanisms: concerted or S(N)2 transition state. The effect of a number of variables on the height of the barrier associated to each of these two mechanisms is systematically analyzed. The variables considered include the number of ligands on the metal (mono- or bis-phosphine), the nature of the phosphine (PF(3), PH(3), PMe(3) or PPh(3)), and the nature of the solvent (gas phase, tetrahydrofuran or dimethylformamide). A number of trends can be identified, resulting in a complex picture where the nature of the phosphine and the solvent can be tuned to favor one of the two possible mechanisms, with the corresponding stereochemical implications that can be extrapolated to the behaviour of more sophisticated substrates.     

Achieving C-N bond cleavage in dinuclear metal cyanide complexes

Cleavage of cyanide is more difficult to achieve compared to dinitrogen and carbon monoxide, even though these species contain triple bonds of greater strength. In this work, we have used computational methods to investigate thermodynamic and mechanistic aspects of the C-N bond cleavage process in [L(3)M-CN-M'L(3)] systems consisting of a central cyanide unit bound in an end-on fashion to two terminal metal tris-amide complexes. In these systems, [M] is a d(3) transition metal from the 3d, 4d, 5d, or 6d series and groups 4 through 7, and [L] is either [NH(2)], [NMe(2)], [N(i)PrPh], or [N(t)BuAr]. A comparison of various models for the experimentally relevant [L(3)Mo-CN-MoL(3)] system has shown that while the C-N cleavage step appears to be an energetically favourable process, a large barrier exists for the dissociation of [L(3)Mo-CN-MoL(3)]((-)) into [L(3)Mo-C]((-)) and [N-MoL(3)], which possibly explains why C-N bond scission is not observed experimentally. The general structural, bonding, and thermochemical trends across the transition metal series investigated, indicate that the systems exhibiting the greatest degree of C-N activation, and most favourable energetics for C-N cleavage, also possess the most favourable electronic properties, namely, a close match between the relevant π-like orbitals on the metal-based and cyanide fragments. The negative charge on the cyanide fragment leads to significant destabilization of the π* level which needs to be populated through back-donation from the metal centres in order for C-N bond scission to be achieved. Therefore, metal-based systems with high-lying d(π) orbitals are best suited to C-N cleavage. In terms of chemical periodicity, these systems can be identified as the heavier members within a group and the earlier members within a period. As a consequence, Mo complexes are not well suited to cleaving the C-N bond, whereas the Ta analogues are the most favourable systems and should, in principle, be capable of cleaving cyanide under relatively mild conditions. An important conclusion from this work is that a successful strategy for achieving cleavage of multiply-bonded, and relatively unreactive, molecular fragments, may simply lie in tuning the electronic structures and orbital interactions by judicious choice of metal sites and ligand groups.     

Theoretical investigation into the mechanism of reductive elimination from bimetallic palladium complexes

Reductive elimination of C-Cl and C-C bonds from binuclear organopalladium complexes containing Pd-Pd bonds with overall formal oxidation state +III are explored by density functional theory for dichloromethane and acetonitrile solvent environments. An X-ray crystallographically authenticated neutral complex, [(L-C,N)ClPd(μ-O(2)CMe)](2) (L = benzo[h]quinolinyl) (I), is examined for C-Cl coupling, and the proposed cation, [(L-C,N)PhPd(1)(μ-O(2)CMe)(2)Pd(2)(L-C,N)](+) (II), examined for C-C coupling together with (L-C,N)PhPd(1)(μ-O(2)CMe)(2)Pd(2)Cl(L-C,N) (III) as a neutral analogue of II. In both polar and nonpolar solvents, reaction from III via chloride dissociation from Pd(2) to form II is predicted to be favored. Cation II undergoes Ph-C coupling at Pd(1) with concomitant Pd(1)-Pd(2) lengthening and shortening of the Pd(1)-O bond trans to the carbon atom of L; natural bond orbital analysis indicates that reductive coupling from II involves depopulation of the d(x(2)-y(2)) orbital of Pd(1) and population of the d(z(2)) orbitals of Pd(1) and Pd(2) as the Pd-Pd bond lengthens. Calculations for the symmetrical dichloro complex I indicate that a similar dissociative pathway for C-Cl coupling is competitive with a direct (nondissociative) pathway in acetonitrile, but the direct pathway is favored in dichloromethane. In contrast to the dissociative mechanism, direct coupling for I involves population of the d(x(2)-y(2)) orbital of Pd(1) with Pd(1)-O(1) lengthening, significantly less population occurs for the d(z(2)) orbital of Pd(1) than for the dissociative pathway, and d(z(2)) at Pd(2) is only marginally populated resulting in an intermediate that is formally a Pd(1)(I)-Pd(2)(III) species, (L-Cl-N,Cl)Pd(1)(μ-O(2)CMe)Pd(2)Cl(O(2)CMe)(L-C,N) that releases chloride from Pd(2) with loss of Pd(I)-Pd(III) bonding to form a Pd(II) species. A similar process is formulated for the less competitive direct pathway for C-C coupling from III, in this case involving decreased population of the d(z(2)) orbital of Pd(2) and strengthening of the Pd(I)-Pd(III) interaction in the analogous intermediate with η(2)-coordination at Pd(1) by L-Ph-N, C(1)-C(2).     

Proton–neutron structure of the N=52 nucleus Zr

Following the successful identification of mixed-symmetric one- and two-phonon states in the N=52 nuclei ⁹⁴Mo and ⁹⁶Ru, we have performed a photon scattering experiment on the N=52 isotone ⁹²Zr. Experimental data and shell model calculations show that both, single particle and collective degrees of freedom are present in the low-lying levels of ⁹²Zr. The second excited quadrupole state shows the signatures of the one-phonon mixed-symmetric 2⁺ state, while calculations and data indicate an almost pure neutron configuration for the 2⁺₁ state, in contradiction with the F-spin symmetric limit. Furthermore, two strong dipole excitations, which are candidates for the two-phonon quadrupole–octupole coupled E1 excitation and for the mixed-symmetric 1⁺ two-phonon state, were observed.     

Quasar red shifts

The results of techniques developed in earlier papers are used in a discussion of the quasar red shifts. An expression with the form of a kinetic energy arises in relation to the probability distribution of red shifts. Agreement with the Hoyle & Burbridge (1966) red shift data at the time of writing is statistically significant, the correlation coefficient being 0·82.