Directed metalation/ligand coupling approach to the enantioselective synthesis of 1,1′-binaphthyls

Introduction of a 2-isopropoxycarbonyl or 2-NN-dimethylcarbamoyl group into homochiral 1-p-tolyl- or 1-t-butyl-sulfinylnaphthalenes, via directed metalation reaction, followed by ligand coupling reaction with 1-naphthylmagnesium bromide, furnished atropisomeric 1,1′-binaphthyls in 82–95% enantiomeric excess (e.e.).     

The delocalisation energy of benzene and the non-empirical MO theory

Algebraic expressions for the vertical Delocalisation Energy (DE) of benzene are derived from non-empirical MO theory. For comparison with early work in the π-electron approximation, and ultimately with Hückel theory, the results are formulated in terms of a core resonance integral,β, and π-electronic repulsion integrals. All integral values are inferred from the results ofab initio SCF calculations. Two expressions are derived, which refer to two ways of forming the localised π MOs: one where three pairs of adjacent atomic orbitals are selected from a set of six orthogonalised orbitals; and another where a non-orthogonal set of atomic orbitals is used. The first expression is formally similar to an expression originally derived by Pople from a different point of view and with many approximations. This expression gives too large a magnitude for DE when used with anab initio value ofβ. The second expression gives a result much closer to an empirical value of DE and shows that the main reason for DE being about 50% of 2β rather than 2β is the stabilising effect of overlap in the localised structure, and that the less important factor is the inclusion of electronic repulsion.     

On the calculation of the satellite peaks observed in the high energy photoelectron spectra of small molecules

The shake-up peaks which are observed to high binding energy of the main photoionization peak in the high energy photoeletron spectra of CO (carbon and oxygen core holes), H₂O and NH₃ have been interpreted by an extension of the singly excited configuration interaction method used previously in the study of the low-lying excited states of these molecules. The results obtained provide a good interpretation of the experimental spectra of these molecules in terms of many shake-up states. It is concluded that relaxed orbitals and an extensive basis set, including diffuse functions, should be used in the calculations in order to obtain good results.     

Connected components of arithmetic graphs

Let . LetG _m (R) be the graph whose vertices are the numbers 1, 2, ...,m and whose edges are all pairs {a, b} such thata+br (modm) for somerR. LetC _m (R) be the number of connected components ofG _m (R). Letd be the greatest common divisor ofm and the differencesr _j –r _j or allr _i ,r _j R. ThenC _m (R) is equal to (i) (d+1)/2 ifd is odd, (ii)d/2 ifd is even andr is odd for allrR, or (iii) (d/2)+1 ifd is even andr is even for allrR.This research was supported in part by the National Science Foundation under grant No. MCS78-07908.     

Synthesis and structure of FeRu3(CO)13(μ-PPh2)2; A “64-electron” cluster complex with a planar triangulated rhomboidal array of metal atoms

The species FeRu₃(CO)₁₃(μ-PPH₂)₂, synthesized from Ru₃(CO)₁₂ and Fe(CO)₄(Ph₂PPPh₂),has been characterized both spectroscopically and via a single-crystal X-ray structural analysis. This complex crystallizes in the centrosymmetric triclinic space group P$\text{1}$ [No. 2, C_i¹] with a  10.066(3), b  12.899(3), c  17.003(4) Å, α  111.89(2), β  91.02(2), γ  102.00(2)°, V  1992.7(9) ų, Z  2, ?(obsd)  1.79(2) g cm^-3 and ?(calcd)  1.82 cm^-3. Diffraction data were collected with a Syntex P2₁ automated four-circle diffractometer and the structure was refined to R_F  6.0% and R_WF  3.6% for all 5213 reflections (R_F  3.8%, R_WF  3.6% for those 4140 reflections with |F_o|> 3σ(|F_o|).The metal atoms define a planar triangulated rhombus, with atoms Ru(1) and Ru(2) at the bridgehead, and Fe(1) and Ru(3) at the acute apices. Fe(1) is linked to four terminal carbonyl ligands and is associated with the heteronuclear bonds Fe(1)Ru(1)  2.861(1) Å and Fe(1)Ru(2)  2.868(1) Å. The ruthenium atoms are each bonded to three terminal carbonyl groups. The retheniumruthenium distances are Ru(1)Ru(2)  3.098(1), Ru(1)Ru(3)  3.147(1), and Ru(2)Ru(3)  3.171(1) Å. The structure is completed by Ph₂P bridges across the Ru(1)Ru(3) and Ru(2)(ru(3) vectors (<Ru(1)P(1)Ru(3)  84.89(5)° and <Ru(2)P(2)Ru(3)  85.56(6)°).     

The reaction π−p → K0Σ0 up to 2375 MeV/c

Differential cross-section and polarization measurements for the reaction π^?p → K⁰Σ⁰ are presented from 1395 to 2375 MeV/c incident beam momentum. The polarization data from an earlier experiment, from thershold to 1334 MeV/c, have been re-analysed by an improved method leading to a substantial reduction in the errors.     

Liebig's alkaloid analyses: the uncertain route from content to molecular formulae

Liebig's 1831 paper that describes a new apparatus for the analysis of organic compounds and the results of several analyses using the apparatus is a justly famous contribution to the evolution of modern chemistry. In this paper, I look at the three separate components of Liebig's combustion apparatus that collect the water, carbon dioxide and nitrogen released by the combustion of six alkaloids. Gravimetric data included in the paper reveal that very accurate results could be obtained for water by absorption in a calcium chloride tube, and even better results for carbon dioxide resulted from use of the Kaliapparat. Volumetric measurement of nitrogen gave very poor results despite Liebig's efforts to improve it. Inaccuracies in nitrogen measurement made consistent construction of accurate molecular formulae for nitrogenous substances impossible, and only fortuitous decisions intended to bring molecular formulae into agreement with measured combining weights gave formulae in agreement with modern ones, as in the case for quinine.     

A functional equation arising from multiplication of quantum integers

For the quantum integer [n]_q=1+q+q²+?+qⁿ⁻¹ there is a natural polynomial multiplication such that [m]_q⊗_q[n]_q=[mn]_q. This multiplication leads to the functional equation f_m(q)f_n(q^m)=f_mn(q), defined on a given sequence of polynomials. This paper contains various results concerning the construction and classification of polynomial sequences that satisfy the functional equation, as well open problems that arise from the functional equation.