Monomeric oxovanadium(IV) compounds of the general formula cis-[V(IV)(=O)(X)(L(NN))(2)](+/0) [X = OH(-), Cl(-), SO(4)(2)(-) and L(NN) = 2,2'-bipyridine (bipy) or 4,4'-disubstituted bipy

Reaction of [V(IV)OCl(2)(THF)(2)] in aqueous solution with 2 equiv of AgBF(4) or AgSbF(6) and then with 2 equiv of 2,2'-bipyridine (bipy), 4,4'-di-tert-butyl-2,2'-bipyridine (4,4'-dtbipy), or 4,4'-di-methyl-2,2'-bipyridine (4,4'-dmbipy) affords compounds of the general formula cis-[V(IV)O(OH)(L(NN))(2)]Y [where L(NN) = bipy, Y = BF(4)(-) (1), L(NN) = 4,4'-dtbipy, Y = BF(4)(-) (2.1.2H(2)O), L(NN) = 4,4'-dmbipy, Y = BF(4)(-) (3.2H(2)O), and L(NN) = 4,4'-dtbipy, Y = SbF(6)(-) (4)]. Sequential addition of 1 equiv of Ba(ClO(4))(2) and then of 2 equiv of bipy to an aqueous solution containing 1 equiv of V(IV)OSO(4).5H(2)O yields cis-[V(IV)O(OH)(bipy)(2)]ClO(4) (5). The monomeric compounds 1-5 contain the cis-[V(IV)O(OH)](+) structural unit. Reaction of 1 equiv of V(IV)OSO(4).5H(2)O in water and of 1 equiv of [V(IV)OCl(2)(THF)(2)] in ethanol with 2 equiv of bipy gives the compounds cis-[V(IV)O(OSO(3))(bipy)(2)].CH(3)OH.1.5H(2)O (6.CH(3)OH.1.5H(2)O) and cis-[V(IV)OCl(bipy)(2)]Cl (7), respectively, while reaction of 1 equiv of [V(IV)OCl(2)(THF)(2)] in CH(2)Cl(2) with 2 equiv of 4,4'-dtbipy gives the compound cis-[V(IV)OCl(4,4'-dtbipy)(2)]Cl.0.5CH(2)Cl(2) (8.0.5CH(2)Cl(2)). Compounds cis-[V(IV)O(BF(4))(4,4'-dtbipy)(2)]BF(4) (9), cis-[V(IV)O(BF(4))(4,4'-dmbipy)(2)]BF(4) (10), and cis-[V(IV)O(SbF(6))(4,4'-dtbipy)(2)]SbF(6) (11) were synthesized by sequential addition of 2 equiv of 4,4'-dtbipy or 4,4'-dmbipy and 2 equiv of AgBF(4) or AgSbF(6) to a dichloromethane solution containing 1 equiv of [V(IV)OCl(2)(THF)(2)]. The crystal structures of 2.1.2H(2)O, 6.CH(3)OH.1.5H(2)O, and 8.0.5CH(2)Cl(2) were demonstrated by X-ray diffraction analysis. Crystal data are as follows: Compound 2.1.2H(2)O crystallizes in the orthorhombic space group Pbca with (at 298 K) a = 21.62(1) A, b = 13.33(1) A, c = 27.25(2) A, V = 7851(2) A(3), Z = 8. Compound 6.CH(3)OH.1.5H(2)O crystallizes in the monoclinic space group P2(1)/a with (at 298 K) a = 12.581(4) A, b = 14.204(5) A, c = 14.613(6) A, beta = 114.88(1) degrees, V = 2369(1), Z = 4. Compound 8.0.5CH(2)Cl(2) crystallizes in the orthorhombic space group Pca2(1) with (at 298 K) a = 23.072(2) A, b = 24.176(2) A, c = 13.676(1) A, V = 7628(2) A(3), Z = 8 with two crystallographically independent molecules per asymmetric unit. In addition to the synthesis and crystallographic studies, we report the optical, infrared, magnetic, conductivity, and CW EPR properties of these oxovanadium(IV) compounds as well as theoretical studies on [V(IV)O(bipy)(2)](2+) and [V(IV)OX(bipy)(2)](+/0) species (X = OH(-), SO(4)(2)(-), Cl(-)).     

On the formality of equivariant classifying spaces

Partially supported by NSF MCS 7701623     

Optimization of Conical Wings in Hypersonic Flow

A method of calculation is presented to determine conical wing shapes that minimize the coefficient of (wave) drag, C _D, for a fixed coefficient of lift, C _L, in steady, hypersonic flow. An optimization problem is considered for the compressive flow underneath wings at a small angle of attack δ and at a high free-stream Mach number M _∞ so that hypersonic small-disturbance (HSD) theory applies. A figure of merit, F=C _D/C _L ^3/2, is computed for each wing using a finite volume discretization of the HSD equations. A set of design variables that determine the shape of the wing is defined and adjusted iteratively to find a shape that minimizes F for a given value of the hypersonic similarity parameter, H= (M _∞δ)⁻², and planform area. Wings with both attached and detached bow shocks are considered. Optimal wings are found for flat delta wings and for a family of caret wings. In the flat-wing case, the optima have detached bow shocks while in the caret-wing case, the optimum has an attached bow shock. An improved drag-to-lift performance is found using the optimization procedure for curved wing shapes. Several optimal designs are found, all with attached bow shocks. Numerical experiments are performed and suggest that these optima are unique. Received 1 May 1998 and accepted 14 October 1998     

A parallel multi-configuration self-consistent field algorithm

A scalable multi-configuration self-consistent field (MCSCF) algorithm is described. The method for optimizing the orbital and configurational parameters is based upon the two-step Newton–Raphson approach with an augmented orbital Hessian matrix. A single copy of the two-electron integrals in the molecular orbital basis is distributed over the memory of all processors. Storage of the augmented Hessian is avoided by re-computing its elements as needed. A replicated data approach is used to parallelize the configuration interaction step. Scalability to 1024 processors is demonstrated.