Variational evaluation of correlation functions for lattice electrons in high dimensions

We present a general formalism for the diagrammatic calculation of correlation functions for Hubbard-type models in terms of projected wave functions. It is shown that in the limit of high spatial dimensionsd only diagrams with bubble-structure remain. This causes correlation functions to have an overall RPA-type form ind. Exact evaluations are performed for the Gutzwiller wave function. Nearest neighbor correlations are shown to be proportional to their value in the non-interacting case, i.e. are renormalized. However, their absolute value is only of order 1/d. Hence this wave function does not describe spin correlations adequately in high dimensions. The asymptotic behavior of the spin-correlation function is extracted and is found to have a scaling form similar tod=1. Assuming this form to hold in all dimensions we show that the Brinkman-Rice transition only occurs ind=. Finite orders of perturbation theory in 1/d around this singular point are not sufficient to remove the transition.     

Hindered rotation in an "exploded" biphenyl

The first cases of hindered rotation around the triple bond in simple diphenylacetylenes were observed, including that in chiral 2,2'-bis(trimethylsilyl)-6,6'-bis(dimethylthexylsilyl)diphenylacetylene.     

Potential routes to cyclobuta[1,2-C] cyclopropabenzene

The CpCo(CO)₂-catalyzed cyclization of 1-trimethylsilyl-1, 5-hexadiyne (4) with propargyltetrahy-dropyranylether (5 leads to the formation of both possible regioisomers of the benzocyclobutene product: 3-trimethylsilyl-4-tetrahydropyranyloxymethylbenzocyclobutene (6) and the corresponding 5-tetrahydropyranyloxymethyl-isomer 7. On the other hand, cyclization of the same diyne with 3-(trimethylsilyloxy) propyne (10) gave only the 3,4-disubstituted product as the free alcohol 11. Compound 6 was iododesilylated, the ether hydrolyzed, and the alcohol tosylated to give 4-iodo-5-tosyloxymethylbenzocyclobutene 13, also obtainable more directly from 11 by treatment with ICI and tosylation. Iodide 13 could be reacted with n-butyllithium to give a variety of products incorporating the n-butylgroup and derived from crosscoupling of the carbon skeleton of starting material. The title compound 1 may be an intermediate en route to the observed products, but was not detected. Several thermal elimination routes to 1 from appropriately 4,5-substituted benzocyclobutenes were unsuccessful. Flash vacuum thermolysis of 11 furnished the silyloxyderivative 21 through elimination of methane.