John Emsley

β-diketone interactions: Part 5. Solvent effects on the keto ⇋ enol equilibrium

Abstract The keto ⇋ enol equilibrium of pentane-2,4-dione (PD) has been measured in 21 solvents at infinite dilution and a linear free energy relationship (LFER) tested against four solvent polarity vectors: ϵ, ET, π* and A + B. The best correlation coefficient is found for A + B. Similarly 3-methyl-pentane-2,4-dione (MePD) has been studied in 14 solvents and 3-ethylpentane-2,4-dione (EtPD) in six. The results suggest that the cyclic hydrogen bonding of the enol remains intact in all the solvents studied.

β-diketone interactions: Part 10. The structure and properties of 3-(2′,4′-dimethoxyphenyl)pentane-2,4-dione; enol ring symmetry and other hydrogen bond parameters

Abstract The X-ray crystal structure of the title compound shows it to be the enol tautomer and with two molecules in the unit cell, with hydrogen bond lengths, R (O··O), of 2.446 and 2.474 A. These and other hydrogen bond parameters (δ, Δδ(H-D) and ν OHO ) of similar compounds are compared and attempts made to relate them to Q , which is derived from the bond asymmetry of the enol ring.

β-Diketone interactions Part 12. The structure and properties of 3-(3′,4′,5′- trimethylphenyl)-pentane-2,4-dione, C14H18O2; the hydrogen-bond energy of the enol tautomers of β-diketones☆

Abstract The X-ray crystal structure of 3-(3′,4′,5′-trimethylphenyl) pentane-2,4-dione shows it to be the enol tautomer, with a hydrogen bond length R O&…o of 2.460 A, and the enol ring remarkably symmetrical indicating a strong hydrogen bond. The hydrogen-bond energy is estimated to be 110±10 kJ mol −1 , a value derived from the infra-red spectrum. In CDCl 3 solutin 8% of the keto tautomer is present.

β-diketone interactions: Part 7. X-Ray molecular structure of 3-(4′-biphenyl)pentane-2,4-dione reveals an enol tautomer with a very strong hydrogen bond

Abstract A new derivative of pentane-2,4-dione has been made, 3-(4′-biphenyl)pentane-2,4-dione, which exists predominantly (98.5%) as the enol tautomer in CDCl 3 solution and in the solid state. An X-ray crystal structure reveals a very short hydrogen bond whose vibrations are characterized as broad bands at 1600, 1380 and 960 (± 20) cm −1 in the infrared. The hydrogen bond energy of this bond probably exceeds 100 kJ mol −1 .

Hydrogen bonding between free fluoride ions and water molecules: two X-ray structures

Abstract The structures of two copper complexes, [Cu(cyclam) (H2O)2]F2·4H2O (cyclam = 1,4,8,11-tetraazacyclotetradecane) and [Cu(en)2(H2O)2]F2·4H2O (en=ethylenediamine), are reported, in which the fluoride ions within their lattices are solvated by four water molecules attached by strong hydrogen bonds. The configurations of these and other “free” [F(H2O)n]− groupings are compared, and the strength of the hydrogen bonds discussed.

THE STRUCTURE OF myo-INOSITOL HEXAPHOSPHATE IN SOLUTION: 31P N.M.R. INVESTIGATION

Abstract Changes in the 31P n.m.r. spectrum of myo-inositol hexaphosphate at different pH reveal that the conformation of this molecule varies with its degree of protonation. Above pH 12 it has the equatorial structure (Ie), below it has the axial conformation (Ia) which it retains to pH 5 when it reverts to le on the addition of a seventh proton. These changes are explained by strong hydrogen bonding between phosphate groups. There is also evidence that at low pH (2) the molecule again reverts to la.

Going one better than nature

rearranging them to form the other one. Hilbert’s third problem asked whether such a proof could be devised for tetrahedra. But his real interest was in the metamathematical question of whether the use of calculus was necessary. This was the first of his problems to be solved. In 1902, Max Dehn showed that calculus was needed. Two of Hilbert’s problems have, famously, had metamathematical solutions. His first problem was to prove or disprove Cantor’s continuum hypothesis, which is the statement that there is no infinite set larger than the set of positive integers but smaller than the set of real numbers. Thanks to Kurt Gödel (in 1938) and Paul Cohen (in 1963), it is now known that this statement can be neither proved nor disproved. Hilbert’s tenth problem asks for a systematic method for deciding which Diophantine equations have solutions. (Diophantine equations are polynomial equations whose solutions are required to be integers.) Building on the work of many mathematicians, Yuri Matiyasevich proved in 1970 that there was no such method. Results such as these have had a profound effect on the philosophy of mathematics. The author of any mathematical book aimed at the general reader has to decide what background knowledge to assume, and Gray, like many others, is not consistent in his demands. This can be seen from a quick inspection of his ‘boxes’, those receptacles much loved of popular science publishers, which contain illustrations and (necessarily inadequate) explanations of some of the technical points in the text. That said, it would be misleading to describe this book as popular science. Two indications of its serious intent are that its title does not make silly use of the words ‘history’ or ‘biography’, and that we learn next to nothing about Hilbert’s personal life. (For example, I still do not know whether he ever married.) As for the intended readership, at least some exposure to university-level mathematics is essential to appreciate the book properly. My one complaint (apart from a few minor quibbles) is that Gray’s prose contains far too many clumsily constructed sentences that I had to read twice. Here is one example from a long list: apparently, Hermann Minkowski thought it “unlikely that any polynomial in several variables which was never negative was expressible as a sum of squares”. Surely, several of them are, one wonders, before realizing that the word “any” is supposed to be understood, unnaturally, as “every”. This sort of writing lessens the pleasure of reading the book, which nevertheless remains illuminating and highly recommended. ■ W. Timothy Gowers is in the Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 OWB, UK. Going one better than nature?

The hydrogen bonding of ligand fluoride: the X-ray crystal structure of difluoro(2,2′:6′,2″-terpyridine)copper(II) trihydrate

Abstract The X-ray crystal structure of the title compound shows it to be [Cu(terpy)F 2 ]·3H 2 O (terpy= 2,2′:6′,2″-terpyridine) with a pentacoordinate copper in a square pyramidal configuration. The basal Cuue5f8F bond is the shortest such bond so far reported (1.862- (4) A). The hydrogen bonds between the apical fluoride and lattice waters are among the shortest known with R(F··O) of 2.595 and 2.598 A.

Diaquabis(1,3-diaminopropane)copper(II) difluoride: X-ray structure reveals short hydrogen bonds between ligand waters and lattice fluorides

Abstract The X-ray crystal structure of [Cu(pn) 2 (H 2 O) 2 ]F 2 , (pn=1,3-diaminopropane) provides a rare example of short hydrogen bonds between ligand waters and lattice fluorides with R(Fue5f8O)=2.644 and 2.678 A

β-diketone interactions: Part 4. The structures and properties of 1,3-diphenyl-2-methylpropane-1,3-dione, C16H14O2, and 1,3-diphenyl-2-(4-methoxyphenyl)propane-1,3-dione, C22H18O3☆

Abstract The X-ray crystal structures of 1,3-diphenyl-2-methylpropane-1,3-dione and 1,3-diphenyl-2-(4-methoxyphenyl)propane-1,3-dione show them both to adopt cis -diketo (Z,Z) conformations with carbonyl—carbonyl dihedral angles of 89.0(3)° (2-methyl derivative), and 85.5(4)° and 77.7(4)° for the two molecules in the asymmetric unit of the 2-(4-methoxyphenyl) derivative. These are the first acyclic β-diketones with an α-hydrogen to be reported which do not have an enol configuration in the solid state.