The two-dimensional anharmonic oscillator: The microwave spectrum of silyl isocyanate,SiH3NCO

The J + 1 ← J transitions (J = 2, 3, 4, 5, and 6) in the microwave spectrum of SiH₃NCO have been assigned for the vibrational ground state and for the vibrational states v₁₀ = 1, 2, and 3. The results for v₁₀ = 0 confirm earlier work. The vibration-rotation constants show a remarkable variation with v₁₀ and l₁₀. To a large extent the anomalous behavior of these constants has been explained in terms of a strongly anharmonic potential function for the ν₁₀ vibrational mode.     

Government Incentive Contracts with Private Enterprise: Some Lessons from the Channel Tunnel

Some of the dangers of the sub-optimisation which may arise when governments and private companies enter into joint ventures are illustrated in this study of the financial arrangements for construction and operation of the Channel tunnel (the project abandoned in 1975). The governments wanted the tunnel to be operated as a commercial (profit-motivated) venture, but gave the private company partners financial incentives to adopt policies in conflict with this target. The paper analyses this conflict and suggests a form of contract which retains desirable incentives but avoids the conflict of interest.     

Gerüstverbindungen mit beweglichen LaIII‐Kationen: Synthesen,Kristallstrukturen und Strukturdynamik der Lanthan(III)‐Eisen(II)‐Sulfid‐Halogenide La53Fe12S90X3 (X = Cl,Br, I)

Framework Compounds with Mobile La^III Cations: Syntheses, Crystal Structures and Structural Dynamics of the Lanthanum(III) Iron(II) Sulfide Halides La₅₃Fe₁₂S₉₀X₃ (X = Cl, Br, I) Black crystals of La₅₃Fe₁₂S₉₀X₃ (X = Cl, Br, I) were synthesized from La₂S₃ and FeS in a reactive LaX₃ flux at 1320 K. The structures were determined by single‐crystal X‐ray diffraction. The compounds are isostructural, crystallizing in the rhombohedral space group with Z = 1 (La₅₃Fe₁₂S₉₀Cl₃: a = 14.0154(7), c = 21.888(1) Å, V = 3723.5(3) ų; La₅₃Fe₁₂S₉₀Br₃: a = 14.0048(9), c = 22.040(2) Å, V = 3743.6(4) ų; La₅₃Fe₁₂S₉₀I₃: a = 13.9805(8), c = 22.108(2) Å, V = 3742.2(4) ų). The structure adopted is a stuffed variant of the La₅₂Fe₁₂S₉₀ structure type. [Fe^II₂S₉] dimers of face‐sharing octahedra are linked by face‐ and vertex‐sharing bi‐ or tri‐capped [La^IIIS_6+n] trigonal prisms, forming a three‐dimensional framework containing cuboctahedral cavities of two sizes. The larger cavities, which remain empty in the structure of La₅₂Fe₁₂S₉₀, are filled by halide ions in La₅₃Fe₁₂S₉₀X₃. The smaller cavities accommodate numerous sites for disordered lanthanum cations, modelling a network of diffusion pathways through the structure. An analogous picture is obtained from the calculation of the periodic nodal surface (PNS): The PNS separates a labyrinth containing the framework atoms from a labyrinth containing the mobile lanthanum cations. Molecular dynamic simulations confirm a strong coupling between the motions of the mobile lanthanum ions and the neighbouring sulfide ions.     

Rh III- and Ir III-catalyzed asymmetric transfer hydrogenation of ketones in water

Asymmetric transfer hydrogenation (ATH) of ketones by formate in neat water is shown to be viable with Rh-TsDPEN and Ir-TsDPEN catalysts, derived in situ from [Cp*MCl2]2 (M=Rh, Ir) and TsDPEN. A variety of ketones were reduced, including nonfunctionalized aryl ketones, heteroaryl ketones, ketoesters, and unsaturated ketones. In comparison with Ir-TsDPEN and the related Ru II catalyst, the Rh III catalyst is most efficient in water, affording enantioselectivities of up to 99 % ee at substrate/catalyst (S/C) ratios of 100-1000 even without working under an inert atmosphere. The aqueous phase reduction is shown to be highly pH-dependent; the optimum pH windows for TOF greater than 50 mol mol(-1) h(-1) for Rh- and Ir-TsDPEN are 5.5-10.0 and 6.5-8.5, respectively. Outside the pH window, the reduction becomes slow or stagnant depending on the pH. However, the enantioselectivities erode only under acidic conditions. At a higher S/C ratio, the aqueous ATH by Rh-TsDPEN is shown to be product- as well as byproduct-inhibited; the product inhibition appears to stem at least partly from the reaction being reversible. The aqueous phase reduction is simple, efficient and environmentally benign, thus presenting a viable alternative for asymmetric reduction.     

Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization

We describe and test an implementation, using a basis set of Chebyshev polynomials, of a variational method for solving scattering problems in quantum mechanics. This minimum error method (MEM) determines the wave function Psi by minimizing the least-squares error in the function (H Psi - E Psi), where E is the desired scattering energy. We compare the MEM to an alternative, the Kohn variational principle (KVP), by solving the Secrest-Johnson model of two-dimensional inelastic scattering, which has been studied previously using the KVP and for which other numerical solutions are available. We use a conjugate gradient (CG) method to minimize the error, and by preconditioning the CG search, we are able to greatly reduce the number of iterations necessary; the method is thus faster and more stable than a matrix inversion, as is required in the KVP. Also, we avoid errors due to scattering off of the boundaries, which presents substantial problems for other methods, by matching the wave function in the interaction region to the correct asymptotic states at the specified energy; the use of Chebyshev polynomials allows this boundary condition to be implemented accurately. The use of Chebyshev polynomials allows for a rapid and accurate evaluation of the kinetic energy. This basis set is as efficient as plane waves but does not impose an artificial periodicity on the system. There are problems in surface science and molecular electronics which cannot be solved if periodicity is imposed, and the Chebyshev basis set is a good alternative in such situations.     

Spectral-product methods for electronic structure calculations

Progress is reported in development, implementation, and application of a spectral method for ab initio studies of the electronic structure of matter. In this approach, antisymmetry restrictions are enforced subsequent to construction of the many-electron Hamiltonian matrix in a complete orthonormal spectral-product basis. Transformation to a permutation-symmetry representation obtained from the eigenstates of the aggregate electron antisymmetrizer is seen to enforce the requirements of the Pauli principle ex post facto, and to eliminate the unphysical (non-Pauli) states spanned by the product representation. Results identical with conventional use of prior antisymmetrization of configurational state functions are obtained in applications to many-electron atoms. The development provides certain advantages over conventional methods for polyatomic molecules, and, in particular, facilitates incorporation of fragment information in the form of Hermitian matrix representatives of atomic and diatomic operators which include the non-local effects of overall electron antisymmetry. An exact atomic-pair expression is obtained in this way for polyatomic Hamiltonian matrices which avoids the ambiguities of previously described semi-empirical fragment-based methods for electronic structure calculations. Illustrative applications to the well-known low-lying doublet states of the H₃ molecule in a minimal-basis-set demonstrate that the eigensurfaces of the antisymmetrizer can anticipate the structures of the more familiar energy surfaces, including the seams of intersection common in high-symmetry molecular geometries. The calculated H₃ energy surfaces are found to be in good agreement with corresponding valence-bond results which include all three-center terms, and are in general accord with accurate values obtained employing conventional high-level computational-chemistry procedures. By avoiding the repeated evaluations of the many-centered one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices in the antisymmetric basis states commonly employed in conventional calculations, and by performing the required atomic and atomic-pair calculations once and for all, the spectral-product approach may provide an alternative potentially efficient ab initio formalism suitable for computational studies of adiabatic potential energy surfaces more generally. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.