ALBERT

Notes: Complexation constants with the macrocyclic azoniacyclophane CP44 and phenyl guest compounds with at least four fluorine atoms or alternatively protons at the ring were obtained by NMR shift titrations in water. The fluorinated compounds show free energies of complexation which are smaller by ΔΔG=3·4-7·7 kJ mol-1 in comparison with the protonated compounds. The NMR shifts induced upon 100% complexation (CIS values) were obtained simultaneously from non-linear least-squares fitting and indicate intra-cavity inclusion in all cases. The CIS values agree roughly with screening constants calculated from aromatic ring current and linear electric field effects, the latter resulting from the permanent charges at the host compound. Molecular mechanics calculations (CHARMm) indicate that intracavity inclusion is possible with all compounds with negligible strain induced (〈1 kJ mol-1) in the macrocycle upon complexation. In contrast, α-cyclodextrin can accommodate fluorinated phenyl compounds only at the rim of the cavity without larger strain. Preliminary data with α-cyclodextrin, obtained by competitive UV-visible titration with methyl orange, indicate again a smaller association free energy (ΔΔG=1·-7 kJ mol-1) for pentafluorphenol compared with normal phenol as guest. © 1997 John Wiley & Sons, Ltd.

Notes: The guest-binding behavior of two different cyclophane hosts, each being capable of providing a three-dimensionally extended hydrophobic cavity toward aromatic guests, was examined in aqueous media: a steroid cyclophane bearing four rigid cholate moieties and an octopus cyclophane having four flexible double-chain segments. Even though the binding constant for 2,7-dihydroxynaphthalene with the steroid cyclophane was comparable to that with the octopus cyclophane, the guest binding modes were very different from each other, as confirmed by 1H NMR spectroscopy. That is, the steroid cyclophane incorporates the guest into its rigid macrocyclic cavity with axial geometry whereas the octopus cyclophane provides a three-dimensional space created by the macrocyclic skeleton and the flexible hydrocarbon chains so that the long axis of the guest becomes more or less perpendicular to the molecular axis of the host upon complexation. Temperature-dependent molecular recognition by these hosts toward 8-anilinonaphthalene-1-sulfonate was examined by means of fluorescence spectroscopy. Characteristic differences in the guest-binding mode between these hosts were sensitively reflected in the thermodynamic entropy change on host-guest complexation and the temperature-dependent microscopic viscosity experienced by the guest at the binding site. © 1997 John Wiley & Sons, Ltd.

Notes: The recent surge of interest in the control of molecular organization in both the solution state (i.e. self-assembly) and the solid state (i.e. crystal engineering) has led researchers to recognize increasingly the importance of weak non-covalent interactions. The design and synthesis of an efficient molecular construction set are dependent upon a very close interplay between x-ray crystallography and synthetic chemistry. π-π Stacking interactions between π-donors, such as hydroquinone, resorcinol or dioxynaphthalene residues, and π-accepting ring systems, such as bipyridinium or π-extended viologen units, can govern the self-assembly of a variety of complexes and interlocked molecular compounds in both the solid and solution states. Non-covalent bonding interactions (i.e. π-π interactions) can be considered as information vectors: they define and rule the self-assembly processes that lead to the formation of the desired molecular and supramolecular architectures, and thereafter they still govern the dynamic processes occurring within the self-assembled structures and superstructures. The manner in which such molecules and supermolecules can contribute to an understanding of non-covalent interactions at both structural and superstructural levels is described, with reference to numerous examples of self-assembly processes in synthesis, of dynamic processes in the solution state, and of the packing of molecules and molecular complexes in the solid state. © 1997 John Wiley & Sons, Ltd.

Notes: ---Thirty ferrocene derivatives were prepared and their ability to form vesicles in aqueous solution when oxidized was assessed. The compounds included alkyl ferrocenylmethyl ether derivatives of the form C10H9FeCH2OR in which R=octyl, dodecyl, tetradecyl, hexadecyl, octadecyl and eicosanyl. One single-tailed amine derivative, C10H9FeCH2NR2, R=octadecyl, was studied. Alkylferrocene derivatives had the form C10H9FeR in which R=butyl, decyl, tetradecyl, hexadecyl, octadecyl, eicosanyl and docosanyl. Sixteen symmetrical 1,1′-disubstituted ferrocenes were also studied. Three ethers were of the form C10H8Fe-1,1′-(CH2OR),2, R=tetradecyl, hexadecyl and octadecyl. Four corresponding dialkyl derivatives of the form C10H8Fe-1,1′-R2, R=decyl, tetradecyl, hexadecyl and octadecyl, were assessed. Finally, a range of 1,1′-disubstituted ferrocene derivatives were analyzed. These all had the form C10H8Fe-1,1′-(COR)2, for which R has the following identities: octyl, tridecyl, pentadecyl and heptadecyl (ketones); heptadecyloxy, 3-cholesteryl and 3-cholestanyl (esters); and two amides, R=NHC18H37 and N(C18H37)2. The alkyl and ether derivatives could be readily oxidized and formed vesicular aggregates upon sonication. The ketones, esters and amides could be oxidized but the ferricenium derivatives did not form stable aggregates. An interesting observation is that the aggregates formed were vesicular whether the ferrocene derivative had one or two alkyl tails. © 1997 John Wiley & Sons, Ltd.

Notes: Non-covalent intermolecular forces have been recognized as a very important part of molecular interactions in complex biological systems. The fundamental functions of living matter such as transcription of genetic information in DNA, spatial arrangement of protein molecules, enzymatic functions or immunity system response are enabled owing to the presence of weak non-covalent forces based on hydrogen bonding interactions, van der Waals interactions, electrostatic interactions, hydrophobic effects, etc. Recently, among them so-called "cation-π" interactions have been proved to contribute to the overall binding process in various artificial or biological systems. Calix[n]arenes have emerged as an important family of molecules with promising applications in many branches of chemistry. Because of their suitable molecular preorganization with aromatic units being "concentrated' in a relatively small space, calix[n]arenes represent interesting compounds exhibiting an enhanced ability for cation-π interactions. The importance of such forces in calix[n]arene chemistry is demonstrated here on several recent examples. © 1997 John Wiley & Sons, Ltd.

Notes: ---Evidence is provided for the enormous role of hydrophobic interactions in aqueous solutions. It is concluded that complementary functions of hydrophilic and of hydrophobic species are in continuous operation and that these are a conditio sine qua non for the existence of the liquid. With regard to the supermolecular aggregations, hydrophobic interactions are operative on the highest hierarchic levels of the system organization, i.e. at the interface and at the holes around dissolved hydrophobic species. It is further emphasized that water is essential both for the unity and for the differentiation of each living organism. With regard to its role for the differentiation of the body, the hydrophobic interactions are of paramount importance, notably those provided by amphipathic solutes. The cell membrane is considered to be the result of interactions between the highest hierarchic levels of intracellular and extracellular water. The hydrophobic double layer provides the barriers for the separation of intracellular and extracellular water and at the same time the connections for recognition and for exchange of information between them. The DNA structures obtain conservative boundary conditions for their surrounding water systems which do not freeze at -60 °C. These water systems are dynamically superior to all other parts of the water system of the organism. It is suggested that more knowledge about the abilities of liquid water can be obtained by giving appropriate attention to its properties within the living body. © 1997 John Wiley & Sons, Ltd.

Notes: ---The standard Gibbs energy changes for the formation of 1:1 charge-transfer complexes between molecular iodine and several bases in solution at 25·0 °C [ΔG0l2(soln)] were determined experimentally. The bases were 2,2,2-trifluoro- ethylamine, cyclopropylamine and 1,1,3,3-tetramethylguanidine. These [ΔG0l2(soln)] values, determined in n-heptane, and also that for the formation of the 1:1 complex between 2,2,2-trifluoroethanethiol and molecular iodine in dichloromethane, were found to follow with excellent precision the correlation equations linking ΔG0l2(soln) and the intrinsic (gas-phase) basicities of N(sp3), N(sp2) and S(sp3) bases. These findings strongly support previous conclusions regarding the relationship between gas-phase and solution reactivity data. © 1997 John Wiley & Sons, Ltd.

Notes: Whenever hydrogen bonding is involved in molecular recognition, the possibility of a proton transfer from the donor to the acceptor arises. In most cases the pKa of the donor is far enough above the pKa of the conjugate acid of the acceptor for it to be clear that no proton transfer will occur. However, as the difference between the donor and acceptor pKas decreases, it can become difficult to predict whether a proton transfer will occur. Since most hydrogen bond-driven molecular recognition is studied in low dielectric solvents, non-aqueous titrations can be used to measure the pKas and therefore predict proton transfers. In this paper three studies which involved non-aqueous titrations are summarized. The first deals with distinguishing simple proton transfer from host-guest complex formation. The second involves measuring pKa shifts upon host-guest complex formation. The last is a study of the catalysis of a phosphoryl transfer. In all three scenarios the non-aqueous titration method gave results which would have been difficult to obtain by other means, and which proved crucial for a complete understanding of the molecular recognition process. © 1997 John Wiley & Sons, Ltd.

Notes: The benzene · · · hexafluorobenzene stacking interaction was evaluated at several levels of theory. At the MP2/6-31G** level, it is estimated that the interaction is stabilizing by approximately 3.7 kcal mol-1. Lower levels of theory perform poorly on this system. This is a fairly strong non-covalent interaction, suggesting this motif may be a valuable supramolecular synthon. © 1997 John Wiley & Sons, Ltd.

Notes: The linear free energy equationlogk′ = c + rR2 + sπ2H + a∑α2H + b∑β2 + vVxwas applied to the capacity factors for various sets of solutes on C18 stationary phases with aqueous methanol and acetonitrile eluents. Here, k′ are the capacity factors for a series of solutes with a given C18 phase and a given eluent, and R2, π2H, ∑α2H, ∑β2, Vx are parameters or descriptors of the solutes as follows: R2 is an excess molar refraction, π2H is the solute polarizability/dipolarity, ∑α2H and ∑β2 are the solute hydrogen-bond acidity and basicity and Vx is the solute volume. It is shown that although the regression coefficients r, s, a, b and v vary widely within the C18 column and mobile phase used, the ratios r/v, s/v, a/v and b/v are remarkably constant. Thus, for the retention of 25 series of solutes on six different C18 columns with 30-90% aqueous methanol as the eluent, all the 25 LFER equations can be combined into one general equation:logk′ = c + v(0.13 R2 - 0.32 π2H - 0.22 ∑α2H - 0.90 ∑β2O + 1.00 Vx)where only c and v vary from system to system. For 11 other phases for which data are available, the ratios v/A and (v + c)/A are constant, where A is the quantity of stationary phase per unit surface area. Similar results were found with C18 phases and aqueous acetonitrile as eluents. Although a first examination of equations based on the first equation above suggests that various C18 phases behave differently, for example the v coefficient, that is related to the observed hydrophobicity of a stationary phase relative to the mobile phase, varies considerably from phase to phase with the same eluent, a detailed analysis led to the conclusion that all the C18 phases examined have roughly the same hydrophobicity, when the v coefficients are corrected for the quantity of stationary phase per unit surface area. It is suggested that these corrected v coefficients, v/A and (v + c)/A, can be regarded as the ‘intrinsic’ phase hydrophobicity. © 1997 John Wiley & Sons, Ltd.

Notes: ---The mechanisms for chiral recognition by cyclodextrins (CDxs) are discussed. Examples of host-guest systems where the "lock-and-key mechanism" and the "three-point rule" are applicable are cited and discussed. Most results reported so far suggest that the ability of native CDxs and chemically modified CDxs to discriminate between enantiomers of guests having a central chirality is low in aqueous solutions. Small ΔΔG values for enantioselective complexation of CDxs with amino acids seem to be due to unpredictably small changes in the structures of the complexes of the guest enantiomers. Therefore, it is very difficult to prove the participation of hydrogen bonding in chiral recognition through the "three-point rule" in these systems. The use of the Coulomb interaction and the coordinate bonds as point interactions is discussed. CDxs might be good hosts to recognize axial chirality or helicity of guests. Hydrogen bonding in water is assumed in the recognition of the helicity of bilirubin. Very large ΔΔG values have been reported for the chiral recognition of the binaphthyl derivatives. Such a system seems to be a suitable model system to study the mechanism of chiral recognition by CDxs. © 1997 John Wiley & Sons, Ltd.

Notes: The rate data for the Menschutkin reaction between strongly activated Z-substituted benzyl p-toluenesulfonates and Y-substituted N,N-dimethylanilines in acetonitrile at 35 °C fit the equation, kobs  =  k1 + k2 [DMA], which is consistent with concurrent first- and second-order processes. The k1 and k2 values for each substrate were separated based on the above equation. The SN1 rate constant, k1, is unaffected by the nature of the nucleophile, whereas the SN2 rate constant, k2, increased with the electron-donating substituent of the N,N-dimethylaniline. The substituent effect on the k1 values is linearly correlated by the Yukawa-Tsuno equation with ρ  =  -5.2 and r  =  1.3. The unimolecular reaction can be regarded as a classical SN1 mechanism. In contrast, that on the k2 values shows an upward curvature when analyzed by the Brown σ+ treatment. These results are ascribed to the simultaneous and independent occurrence of SN1 and SN2 mechanisms in the present Menschutkin reaction. © 1998 John Wiley & Sons, Ltd.

Notes: No Abstract

Notes: Solution enthalpies of n-hexane, acetone, butan-2-one and octan-2-one in a series of tetrachloromethane-acetonitrile mixtures and the carbonyl stretching absorption frequencies in the IR spectra of these ketones were determined. It was found that over the whole range of concentrations (varying from neat tetrachloromethane up to neat acetonitrile) the solvation enthalpy of these compounds can be obtained additively from the contributions of the alkyl and carbonyl fragments. The solvent effect on the solvation enthalpy of the carbonyl group was found to be satisfactorily correlated with the corresponding IR frequency shifts of the C=O group. It was also found that the sensitivities of the carbonyl IR frequencies to the solvent composition are different for various ketones. From both IR and calorimetric data, the preferential solvation parameters were evaluated. The differences between the IR spectroscopic and calorimetric data are discussed. © 1998 John Wiley & Sons, Ltd.

Notes: In an effort to model solute-solvent interactions, the C=O stretching frequencies of five 1-substituted 2-pyrrolidinones and four other carbonyl-containing compounds were measured for 30 common solvents. These were then correlated with four empirical parameter sets and one theoretical (computational) parameter set. While an empirical parameter set gave the best correlation equations, the theoretical parameter equations are physically and statistically significant. Solvent volume, polarizability and hydrogen bond donor acidity (capacity) terms are significant in the correlation equations. © 1998 John Wiley & Sons, Ltd.

Notes: The P - S bond cleavage process in the hydroperoxidolysis of a model system for the nerve agent VX was studied using ab initio and semiempirical molecular orbital methods. Aqueous solvation effects were included through single-point calculations using the semiempirical SM5.2PD/A continuum solvation model and geometries optimized at the HF/MIDI! level of theory. The predominant pathway for P - S bond cleavage involves pseudorotation of a low-energy trigonal bipyramidal intermediate followed by apical ligand ejection. In aqueous solution, the free energy barriers for these processes are found to be 14.3 and 4.6 kcal mol-1, respectively, with electronic energies calculated at the MP2/cc-pVDZ//HF/MIDI! level of theory. By comparison with another continuum model of solvation (PCM), it is concluded that the SM5.2PD/A model performs well even for hypervalent phosphorus species, in spite of not having included any such molecules in the model's parameterization set. © 1998 John Wiley & Sons, Ltd.

Notes: N-Methyl-N-phenyl-tert-butylsulfenamide (MPSA) and morpholinyl-tert-butylsulfenamide (MOSA) were thermolyzed in a stirred-flow reactor at temperatures of 340-390 °C and pressures of 7-13 Torr, using toluene as carrier gas, at residence times of 0.3-1.3 s. Isobutene was formed in 99% yield through first-order reactions having the following Arrhenius parameters (A,s-1, Ea, kJ mol-1): MPSA, log A  =  12.41 ± 0.02, Ea  =  158.8 ± 0.2; MOSA, log A  =  12.91 ± 0.22, Ea  =  159 ± 3. It is proposed that the elimination of isobutene takes place by unimolecular reaction mechanisms involving polar, four-center cyclic transition states, forming S-unsubstituted thiohydroxylamines as co-products. Thermochemical parameters, estimated by semiempirical AM1 calculations, are reported for the latter and for the parent molecules. © 1998 John Wiley & Sons, Ltd.

Notes: A dynamic NMR study of the tautomerism of 2,2′-bisbenzimidazolyl in DMSO-d6 and a mechanistic interpretation of the process, based on a stepwise, single-proton transfer and formation of a zwitterionic intermediate, are presented. This interpretation is substantiated by semi-empirical calculations of the postulated intermediate and transition state, that yield results which are compared with previous studies on related aliphatic systems. © 1998 John Wiley & Sons, Ltd.

Notes: Acidities and bond dissociation energies (BDEs) of the N-H bond in two phenylsulfenylamides, PhSNHBz and PhSNH-t-Bu, and four phenylsulfenylanilides, 4-GC6H4NHSPh, where G  =  MeO, H, Br and CN, were measured in order to compare the effects of substituents on acidities and BDEs of N - H bonds with those of C - H bonds. The effects of PhS groups on acidities and BDEs in a series of C - H acids were found to be comparable to those on acidities and BDEs of PhS in a similar series of N - H acids. Comparisons were also made of the effects of changing the oxidation state of sulfur in the series PhS, PhSO and PhSO2 on the acidities and BDEs of adjacent N - H and C - H bonds in weak acids. Hammett-type plots of pKHA values for phenyl benzyl sulfones (4-GC6H4CH2SO2Ph) and phenylsulfenylanilides (4-GC6H4NHSPh) were linear vs σp- values. A linear plot was obtained and explained for a plot of BDE of the N - H bonds in remotely substituted phenylsulfonylanilides with σ+ values. Plots of BDEs vs Eox(A-) were also linear for 4-substituted phenylsulfenylanilides (4-GC6H4NHSPh), phenylsulfonylanilides (4-GC6H4NHSO2Ph) and phenyl benzyl sulfones (4-GC6H4CH2SO2Ph). © 1998 John Wiley & Sons, Ltd.

Notes: 17O NMR spectra of several α-diamides were obtained at natural isotopic abundance in acetonitrile solution in order to study the conformations of these compounds in solution. The 17O NMR shifts vary with the intercarbonyl dihedral angle α in a sense opposite to that observed for α-diketones. © 1998 John Wiley & Sons, Ltd.

Notes: The prototropic tautomerism of 8-azaadenine (azaade) was studied theoretically by means of ab initio methods, in both the gas phase and aqueous solution. A number of tautomeric forms were not included in the calculations after applying a stepwise elimination procedure based on both AM1 and HF/6-31G* energy values. The tautomers 9H-azaade, 8H-azaade and 7H-azaade survived to this elimination and their optimized geometries and energies were calculated at the MP2/6-31*//HF/6-31G* level. To include the solvent effects, two self-consistent reaction field method were used: (1) Onsager's SCRF with multipolar expansion up to the hexadecapolar term and (2) the isodensity polarizable continuum method (IPCM). Both methods produce similar results, although the latter represents better the situation in aqueous solution. The stability order in solution, 8H- 〉 9H- 〉 7H-azaade, differs slightly from that found in the gas phase, implying that in general the electrostatic effects in solution are important, but the intrinsic stability of these species in the gas phase overcomes the solvent effect. © 1998 John Wiley & Sons, Ltd.

Notes: No abstract.

Notes: Cyclic voltamograms of the solvatochromic dye 5-nitro-5′-dimethylamino-2,2′-bisthiophene (1), introduced recently as a sensitive π* probe, were recorded in different solvents. An EPR spectrum of the anionic radical of 1 in DMSO was obtained and compared with other spectra of analogous substituted bisthiophene radicals. It was found that the presence of a donor- acceptor pair of substituents in 1-⋅ reduces significantly the rotational barrier of the radical compared with the unsubstituted bithienyl radical anion 2-⋅. This is the result of an electronic repulsion between the donor ring fragment and the added electron in the coplanar radical, which does not exist in 2-⋅. © 1998 John Wiley & Sons, Ltd.

Notes: Reversed-phase high-performance liquid chromatography [LiChrosorb RP-18,UV detection at 254 nm and acetonitrile-water (86:14,v/v) as mobile phase] was applied to studies of the host-guest complexation of tetraalkylcalix[4]resorcinareneoctols and their upper rim phosphoryl, sulfonyl and dialkylaminomethyl derivatives with some aromatic guests in the mobile phase. It was shown that the formation of the inclusion complexes results in changes in the retention of aromatic guests and improves their separation. Stability constants of the complexes were calculated from the dependences of the l/k′ values of the aromatic guest on the concentration of the calix[4]resorcinarene in the mobile phase. The molecular structure of 4,6,16,18-tetrahydroxy-10,12,22,24-tetrakis(dipropoxyphosphoryloxy)-2,8,14,20-tetramethylcalix[4]resorcinarene (12) was determined. Crystal data for 12 are P21/n, a  =  16.708(9) Å, b  =  18.683(6) Å, c  =  20.243(5) Å, β  =  95.75(3)°, V  =  6287(4) Å3 and Z  =  4. Compound 12 exists in a boat conformation, in which two opposite unsubstituted resorcinol rings of the macrocyclic skeleton lie in the plane formed by four methine bridges and two diphosphorylated rings are perpendicular to the plane. © 1998 John Wiley & Sons, Ltd.

Notes: The boronic acid functional group has been incorporated into various biologically important compounds. In order to study this class of compounds better with molecular mechanics, five alkyl- and arylboronic acids were calculated using ab initio methods (Spartan) at the RHF/6-31G* level. MM3 force field parameters were developed based on the theoretically calculated geometries, vibrational spectra, and torsional profiles. © 1998 John Wiley & Sons, Ltd.

Notes: Rate coefficients were measured for the base-catalysed hydrolysis of a series of substituted 3-(phenoxy- or thiophenoxymethylene)-(Z)-1(3H)-isobenzfuranones (3-phenoxy- or thiophenoxymethylenephthalides) in 70% (v/v) aqueous dioxane at 30.0 °C, in addition to the carbonyl stretching frequencies in chloroform and tetrachloromethane following deconvolution and band separation, when required. The Hammett reaction constants for the alkaline hydrolysis of the 3-/4-substituted phenoxy and thiophenoxy series are ca 0.75 and 1.10, respectively. These results are related to electrostatic field and resonance effects. Successful correlations between the carbonyl stretching frequencies and substituent constants and the rates of alkaline hydrolysis were found. Computational studies using the semi-empirical AM1 method correctly model both the details of the mechanistic pathway and the substituent effects. © 1998 John Wiley & Sons, Ltd.

Notes: A new model of the inductive effect is proposed, allowing highly accurate theoretical calculations of inductive constants for a diversity of substituents, using a simple and readily available system of mathematics. According to this approach, the inductive effect of a substituent is considered in terms of the additive influence of its constituent atoms. A constant inherent capacity for inductive interaction with a reactive center (with a four-coordinate carbon atom chosen for such a center), represented by an atomic constant σA, is ascribed to each atom. Values of σA for a wide variety of atoms are determined, and their physical meaning is revealed to elucidate to a certain extent the physical nature of the inductive effect. In addition, the proposed model permits the convenient use in calculations of group constants σG characterizing the inductive power of groups. Values of σG are determined for molecular fragments that are most widely dealt with in organic chemistry, and the use of σA or σG constants and of their superposition is shown to have, in most cases, little or no effect on the accuracy and reproducibility of the results obtained. It is also shown that, in terms of the developed approach, the inductive effect of a substituent is closely associated with its conformation. Theoretical inductive constants were calculated for 427 organic, aromatic, organometallic and charged substituents, and they showed perfect correlation with the corresponding experimental values. © 1998 John Wiley & Sons, Ltd.

Notes: The kinetics of the oxidation of mandelic acid (MA) by permanganate in aqueous alkaline medium at a constant ionic strength of 1.0 mol dm-3 were studied spectrophotometrically. The reaction shows first-order kinetics in [permanganate ion] and fractional order dependences in [MA] and [alkali]. Addition of products, manganate and aldehyde have no significant effect on the reaction rate. An increase in ionic strength and a decrease in dielectric constant of the medium increase the rate. The oxidation process in alkaline medium under the conditions employed in the present investigation proceeds first by formation of an alkali permanganate complex, which combines with mandelic acid to form another complex. The latter decomposes slowly followed by a fast reaction between the free radical of mandelic acid and another molecule of permanganate to give products. The reaction constants involved in the mechanism were derived. There is good agreement between the observed and calculated rate constants under different experimental conditions. The reaction was studied at different temperatures and activation parameters were computed with respect to the slow step of the proposed mechanism. © 1998 John Wiley & Sons, Ltd.

Notes: Photo-reactions of tetrazolo[1,5-a]pyrimidine (1) with benzene (2a) and substituted benzenes (2b-f) in the presence of trifluoroacetic acid (TFA) gave 2-(2-, 3- and 4-substituted anilino)pyrimidines (3-5) together with 2-aminopyridine (6) and biphenyl (7) or diarylmethanes (8b, 8c and 8e). From the effect of heavy-atom solvent on the reactions, it is reasonable to assume that 3-5 are formed via a singlet species, but 6-8 via a triplet species. The intermediacy of 2-pyrimidylnitrenium ion is consistent with the evidence derived by the above effect, by a Hammett plot with ρ = -2.9 and by effects of solvent nucleophilicity and counter-anions. The selective exocyclic N-arylation giving 3-5 is discussed. © 1998 John Wiley & Sons, Ltd.

Notes: ---The reactions of aryliminodimagnesium [ArN(MgBr)2, IDMg] with p′-substituted p-cyanobenzophenones, 1-cyano-9-fluorenone, o-, m- and p-dicyanobenzenes and o-, m- and p-nitrobenzonitriles were examined, and the relative yields of products were referred to the previous results of electron spin resonance studies. The products of condensation with carbonyl and nitro groups and of addition to cyano groups were formed. From the variations of the yields caused by the molar ratio of the magnesium reagent versus substrates and by the substituents of both reactants, the preferred groups were determined. The groups of p- and m-substrates are consistent with the position of highest density of free electrons in the anion radicals, whereas those of the o-substrates are inconsistent. The consistency indicates competition of functional groups reflecting the relative ability of single electron acceptance from the reagent, whereas the inconsistency is ascribed to cooperation of neighbouring groups for σ-complexation with the Mg atom of the reagent. The categories of competition and cooperation are discussed in relation to fundamental features and general governing factors proposed for the IDMg reactions of monofunctional substrates. © 1997 John Wiley & Sons, Ltd.

Notes: Although the electronic contribution to the strength of a H-bond is unaffected by isotopic substitution, the heavier mass of deuterium compared with protium lowers some of the vibrational frequencies in the complex. The binding energy of the complex, which includes zero-point and thermal vibrational energies, can thus be altered by several tenths of a kcal mol-1 by H/D substitution. Ab initio calculations are used to analyze this phenomenon in a number of common organic functional groups that are prone to form H-bonds: hydroxyl, carboxyl and amide, both self-complexing as homodimers and with water molecules as partners. It is found that any site of D-substitution increases the complexation energy; however, the bridging sites show a stronger preference for D over H than do the non-bridging, or terminal, sites. Hence D-bonding can be considered to be stronger than H-bonding in these functional groups. Of the groups considered, the energetic preference for D over H is greater in the hydroxyl group, so deuterium would be expected to gravitate toward solvent water molecules in isotopic scrambling experiments. The increments in H-bonding energy resulting from each site of substitution are addititve in cases of multiple substitution. © 1997 John Wiley & Sons, Ltd.

Notes: ---This paper describes how empirical free energy and/or enthalpy values for hydrogen binding strength are derived from thousands of corresponding measurements between H-bond donors and acceptors, mostly in carbon tetrachloride, and how they can be used to construct common scales or factor values (increments) also for other reactions involving electron donor and acceptor ability of functions. The corresponding databases and programs (HYBOT) allow one to predict thermodynamic values for experimentally unknown equilibria, including also ionophore complexes with crown ethers or cryptands. Applications in QSAR involve the prediction of lipophilicity from any structure on the basis of only two variables, e.g. 234 systems are described this way with a correlation coefficient r=0·96. Similarly, permeabilities and some biological properties such as narcotic activities of chemicals and anti-HIV-1 activity of some porphyrins are evaluated. © 1997 John Wiley & Sons, Ltd.

Notes: ---The cooperative nature of non-covalent interactions which give rise to inclusion complexes involving cyclobis(paraquat-p-phenylene), 14+, and related cyclophane derivatives, 24+-44+, with substituted 1,4-phenyl and 4,4′-biphenyl guests has been studied by spectroscopic techniques and ab initio and semiempirical molecular orbital methods. Inclusion complex formation and stability are primarily determined by the combination of two main interaction modes involving aromatic stacking of the guest within the cyclophane cavity and external interactions between guest side arms and the exterior of the cyclophane. A balance between cavity and external forces results in supramolecular association and is shown to change depending upon the functionality and substitution of the guest. Cavity binding was probed using 1,4-phenyl and 4,4′-biphenyl guests, where for the 1,4-phenyl guests the primary basis for energy stabilization with 14+ is found to be short-range stabilizing electrostatic forces complemented by small amounts of polarizability and charge-transfer. In contrast, the cavity binding between substituted 4,4′-biphenyl guests and 14+ is determined by almost equal contributions of polarizability and electrostatics. The effect of solvent is shown to have only a small effect on the computed geometry of 14+ complexes, but its impact upon binding energies is substantial. The first solvation shell of the cyclophanes is computationally approximated by 12 acetonitriles and satisfies the requirements of the 16 relatively acidic protons on the bipyridinium groups. Good correlations between the computed (with solv ation) and experimental 14+ binding energies are found. The degree of linear correlation improves substantially when the comparison between computed and experimentally observed binding energies is restricted to structurally similar (number of aromatic rings, number of substituents and position of substitution) molecular guests. Furthermore, computed molecular properties, such as polarizability, maximum hardness, softness and electronegativity of the isolated guests, correlate well with 14+ binding energies based upon the same requirement of guest similarity. The non-covalent forces associated with the external cyclophane interactions were studied with guest molecules built from symmetrical 1,4-extensions of hydroquinone composed of aliphatic or ethyleneoxy side arms. In particular, side arm length and functionality, and the position and type of heteroatoms along the chain, were systematically varied to define the external interactions between the guest side arms and different host cyclophanes. Specifically, the ethyleneoxy linkages are shown to provide a large chelate and cooperative effect which direct the binding with 14+. In order to probe further the special geometric and electronic character of 14+, we have synthesized and tested a new supramolecular host, 24+, similar to 14+ but where a pentacycloundecane unit replaces one of the xylyl groups. Both experimental and computed data on the new host emphasize the ideal geometry and electronic nature of the 14+ molecular receptor for aromatic guests. The inclusion complexes discussed in this paper are important not only because they, or similar entities, are the main components of many rotaxanes, catenanes and other switchable molecules, but because the intermolecular interactions involved, such as electrostatics, polarizability and charge-transfer, are ubiquitous in supramolecular chemistry. The information reported on the specific interactions involving the 14+-44+ molecular receptors with substituted aromatic guests can also be extended by analogy to many systems of broad interest. © 1997 John Wiley & Sons, Ltd.

Notes: A series of esters derived from 3-methyl-2,4-diphenyl-3-azabicyclo[3.3.1]nonan-9α-ol (1) was synthesized and studied by 1H and 13C NMR spectroscopy, and the crystal structure of 3-methyl-2,4-diphenyl-9α-(3,5-dimethylbenzoyloxy)-3-azabicyclo[3.3.1]nonane (2) was determined by x-ray diffraction. The compounds studied display in CDCl3 a preferred flattened chair-chair conformation. This bicycle conformation is similar to that found for 2 in the crystal state. Pharmacological assays on mice were performed to evaluate drug-induced behavioral alteration, peripheral or central acute toxicity and analgesic activity. © 1998 John Wiley & Sons, Ltd.

Notes: Photo-induced electron donor-acceptor reactions between 1-cyanonaphthalene (CNN) and norbornadiene (N) generate products of several structure types. Methanol adducts (1-3) formed in polar solvents are rationalized via the radical cation, N+·, and stereospecific (exo-) nucleophilic attack by methanol. In less polar solvents, CNN and N form [2 + 2]-cycloadducts, exclusively on the exo-face of N. In non-polar solvents containing methanol, CNN, N and methanol combine to form 1:1:1 adducts, containing the sensitizer on the endo- and the methoxy groups on the exo-face. The formation of these products is rationalized via the trapping of encounter complexes of different geometries. Any rearrangement of the norbornenyl system can be eliminated, since neither tricyclyl nor 7-methoxynorbornenyl structures are formed. Apparently, the alcohol captures an endo-encounter complex of CNN and N by attack from the exo-face, similar to the attack of methanol on N+·. © 1998 John Wiley & Sons, Ltd.

Notes: Semiempirical, ab initio and DFT investigations on the mechanism of the Diels-Alder reactions of a set of masked dienes (ring-fused dienes), viz. o-quinodimethane, anthracene and α-vinylnaphthalene, with ethylene, and reactions of α-vinylnaphthalene with maleic anhydride and p-benzoquinone were performed with a view to understanding the role of masking factors on the activation and reaction energies. The reactions were found to occur in a concerted fashion through synchronous transition states (TSs) in the first two reactions and through asynchronous TS in the other case. Of the compounds studied, o-quinodimethane is the most reactive diene both in a kinetic and a thermodynamic sense. α-Vinylnaphthalene reacts faster with maleic anhydride than p-benzoquinone, as expected, and two possible stereoselective TSs, one endo and the other exo, have been located for the reactions of α-vinylnaphthalene with the above dienophiles. Calculations show that the relative gain or loss of aromatic stabilization of the benzonoid ring in the transition state and in the product seems to play a major role in the kinetic and thermodynamic control of these reactions. © 1998 John Wiley & Sons, Ltd.

Notes: Infrared spectra of all isomers of polymethyl-substituted benzoic acids were recorded in the carbonyl and hydroxyl regions in tetrachloromethane at various concentrations and interpreted in terms of conformation. According to a plot of ν(C=O) of the monomeric form vs Hammett substituent constants σ, these compounds may be classified into two classes. Derivatives with none or only one methyl group in the ortho position are concluded to exist in an equilibrium of two planar conformations, unless the equilibrium is degenerate. Derivatives with two ortho-situated methyl groups are concluded to take up one non-planar conformation. These findings are supported by the shape of the hydroxyl and carbonyl bands, which are unsymmetrical in the former class, although they could not be reliably separated into bands pertinent to the individual conformers. This conclusion is at variance with the common interpretation which has invariably ascribed to these and similar ortho derivatives non-planar conformations with a variable torsional angle. © 1998 John Wiley & Sons, Ltd.

Notes: Barrier heights for P - C bond homolysis in P-hydroxy-P-methyl-P,P-dioxophosphoranyl and P,P,P-trihydroxy-P-methylphosphoranyl were calculated using well correlated levels of electronic structure theory. The best estimate for the difference in barriers between the two indicates that homolysis is more facile for P,P,P-trihydroxy-P-methylphosphoranyl by roughly 9 kcal mol-1. This result suggests that bacterial pathways leading to P - C bond cleavage in organophosphonate derivatives will preferentially proceed via initial one-electron reduction of substrates rather than oxidation. © 1998 John Wiley & Sons, Ltd.

Notes: The peculiarities of [8+2] cycloaddition reactions of indolizines with dienophiles are reviewed. Quantum chemical SINDO1, AM1 and ab initio calculations of transition states were performed for [8+2] cycloaddition reactions of indolizine and 6-nitroindolizine with a series of alkenes with donor and acceptor groups. The calculations predict a dipolar cycloaddition mechanism (electrophilic addition and ring closure) for reactions of indolizine and 6-nitroindolizine with nitroethylene. For the reaction of 6-nitroindolizine with N,N-dimethylaminoethylene, the predicted mechanism corresponds to a previously unknown ‘inverse’ dipolar cycloaddition (nucleophilic addition and ring closure). © 1998 John Wiley & Sons, Ltd.

Notes: Gas-phase nucleophilic substitution reactions of Y-benzyl chlorides with X-phenoxide and X-thiophenoxide nucleophiles were investigated theoretically using the PM3 semi-empirical MO method. The Leffler-Grunwald rate-equilibrium and Brønsted correlations predict that the degree of bond formation in the transition state (TS) is approximately 45 and 40% on the reaction coordinate for the phenoxides and thiophenoxides, respectively. For a weaker nucleophile, a later TS is obtained with an increased bond making and breaking. The variation of the TS structure with substituents in the nucleophile is thermodynamically controlled and is well correlated by rate-equilibrium relationships. In contrast, the TS variation (a tighter TS) with substituent (for a stronger acceptor Y) in the substrate is dependent only on variations of the intrinsic barrier and so cannot be correlated by such thermodynamically based rate-equilibrium relationships. The gas phase ρX and ρY values are much greater in magnitude than those in solution. A similar gas-phase theoretical cross-interaction constant, ρXY (ca -0.60), is obtained for both phenoxides and thiophenoxides, which is in good agreement with the experimental value (-0.62) for the thiophenoxide reactions in MeOH at 20.0 °C. The oxy and sulfur anion bases lead to a similar TS structure, but a lower reactivity for the former is due to a greater endothermicity of the reaction. A relatively wide range variation of the reaction energies, ΔG°, can be ascribed to the loss of resonance stabilization of anion nucleophiles upon product formation. © 1998 John Wiley & Sons, Ltd.

Notes: Os(VIII) and Ru(III) catalysis of the periodate oxidation of acetaldehyde in aqueous alkaline medium was investigated. The catalytic efficiency is Ru(III)〈Os(VIII). The product of oxidation in both cases is acetate and IO3-. The stoichiometry is the same in both catalyzed reactions, i.e. [IO4-]:[CH3CHO] = 1:1. Probable mechanisms are proposed and discussed. The reaction constants involved in the mechanisms are derived. © 1998 John Wiley & Sons, Ltd.

Notes: Rate constants of solvolysis of α-tert-butyl(2-naphthyl)methyl chloride (1), 9-fluorenyl chloride (2) and a series of monosubstituted benzhydryl chlorides (3) in a wide range of solvents were measured. Grunwald-Winstein-type correlation analysis of log k for 2 and 3 against YBnCl, with or without nucleophilicity N, yielded less satisfactory linear correlations than that against log k(1). A new scale of solvent ionizing power, YxBnCl, for the correlation of solvolytic reactivities of benzylic chlorides with extended charge delocalization based on log k(1) was developed. Application to the mechanistic study suggested the solvolysis of 2 and 4-nitrobenzhydryl chloride were non-limiting. Hammett plots against σ+ constants exhibited more negative ρ values in less nucleophilic solvents. In a benzhydryl chloride containing a strong deactivating substituent, such as 4-nitro, the positive charge delocalizes mainly over the unsubstituted ring in the cationic transition state. The uneven charge distribution was also confirmed by Mulliken population analysis at the level of the RHF/6-31G*//RHF/3-21G(*) basis set for cations. Comparison of the results of correlation analysis using the equation log(k/k0) = mY vs the equation log(k/k0) = mY+hI, and using the equation log(k/k0) = mY+lN vs the equation log(k/k0) = mY+lN+hI indicated the use of YBnCl or YxBnCl could give a better understanding of solvolytic mechanisms than the combinatorial use of YCl and I. © 1998 John Wiley & Sons, Ltd.

Notes: Solvent effects on the wavenumber of the maximum of the longest wavelength electronic absorption band of all-trans-β-carotene were determined in 34 solvents. Together with results from previous studies, a data set for 51 solvents, mostly non-hydrogen bond donors, was constructed. This information was analyzed in terms of reaction field models and also showed its value for correlation purposes when used either alone or in combination with standard empirical solvent polarity-polarizability scales. © 1998 John Wiley & Sons, Ltd.

Notes: The UHF-SCF-AM1 MO method was applied to the study of two kinds of pyrolysis reactions of six nitro derivatives of phenols (homolysis reaction by rupture of the C - NO2 bond into radicals and isomerization reaction involving phenolic hydrogen transferring to oxygen on the NO2 group). The molecular geometries of reactants, transition states and products were fully optimized. The potential energy curves and activation energies were first obtained. The results show that this category of compounds is more easily initiated via isomerization reactions than by homolysis reactions. The parallel relationship among the Wiberg bond order of the pyrolysis-initiation H - O bond in the molecule of a reactant, the activation energy of the isomerization reaction breaking the H - O bond and impact sensitivity of the reactant gives ‘the principle of the smallest bond order’ (PSBO) powerful support. The sensitizing effect of a phenol group was elucidated based on calculation results. The different influences of OH and NO2 groups on the heat of formation of a molecule are discussed. © 1998 John Wiley & Sons, Ltd.

Notes: Phthalic anhydride was detected spectrophotometrically in the hydrolysis of o-carboxybenzohydroxamic acid (OCBA) in CH3CN-H2O solvent containing 0.03 mol dm-3 HCl. Pseudo-first-order rate constants (k1) for hydrolysis of OCBA are almost independent of the change in CH3CN content from 10 to 80% (v/v) in mixed aqueous solvents. The rate constants k1 are more than 10-fold larger than the corresponding rate constants for hydrolysis of phthalamic acid. These observations are explained in terms of a mechanism slightly different from the mechanism for hydrolysis of phthalamic acid. The activation parameters, ΔH* and ΔS*, are not affected appreciably by an increase in CH3CN content from 10 to 80% in mixed aqueous solvents. © 1998 John Wiley & Sons, Ltd.

Notes: A preferential solvation model that takes into account the enhancement of the structure of water when small amounts of alcohol are added was applied to solvatochromic data for binary mixtures of water with 2-methylpropan-2-ol, propan-2-ol, ethanol and methanol. Application of the model allows the calculation of the effect of the enhancement of the water structure on solvatochromic solvent properties. It is demonstrated that the enhancement of water structure increases the solvent dipolarity/polarizability and hydrogen-bond donor acidity and decreases the solvent hydrogen-bond acceptor basicity. The effect decreases in the order 2-methylpropan-2-ol-water, propan-2-ol-water, ethanol-water and methanol-water. © 1998 John Wiley & Sons, Ltd.

Notes: The coordination of a resonance-stabilized hydrocarbon cation and anion yielded a series of unprecedented hydrocarbons, which are susceptible to thermal heterolytic cleavage of carbon-carbon σ bonds in polar media, generating the original ions under reversible conditions. When the component ions were sufficiently stabilized, some ion pairs were even isolated as solids, thus providing the first examples of hydrocarbon salts. The direct observation of the heterolysis by means of spectroscopy permitted reliable thermodynamic treatments of the observed degree of ionic dissociation. Correlation of the free energy of heterolysis with solvent dielectric constants and parameters of ion stabilities such as pKHA, pKR+ and redox potentials revealed the importance of the thermodynamic stabilities of ions, the degree of solvation and steric congestion in the starting molecule as major controlling factors in the heterolysis. © 1998 John Wiley & Sons, Ltd.

Notes: Solvolyses of the N,N-diphenylcarbamoylpyridinium ion are subject to specific and/or general base catalysis, which can be eliminated by addition of perchloric acid or increased, especially in fluoroalcohol-containing solvents, by addition of pyridine. The uncatalyzed solvolyses in aqueous methanol and aqueous ethanol involve a weakly nucleophilically assisted (l  =  0.22) heterolysis and the solvolyses in the pure alcohols are anomalously slow. © 1998 John Wiley & Sons, Ltd.

Notes: The effects of micelles of cetyltrimethylammonium bromide (CTABr), tetradecyltrimethylammonium bromide (TTABr), sodium dodecyl sulfate (SDS) and polyoxyethylene 10 lauryl ether (C12E10) on the rates of alkaline hydrolysis of securinine were studied at a constant [-OH] (0.05 M). An increase in the total concentrations of CTABr, TTABr, SDS and C12E10 from 0.0 to 0.2 M causes a decrease in the observed pseudo-first-order rate constants (kobs) by factors of ca 2.5, 3, 7 and 4, respectively. The observed data are explained in terms of pseudophase and pseudophase ion-exchange (PIE) models of micelle. The binding constants, KS, of securinine with SDS, C12E10, CTABr and TTABr micelles are 32.4, 14.8, 22.1, and 9.1 M-1, respectively. The magnitudes of the second-order rate constants, kM, for the reactions in the micellar pseudophase are negligible compared with the corresponding rate constant, kW, for the reaction occurring in the aqueous pseudophase for CTABr, TTABr, SDS and C12E10. © 1998 John Wiley & Sons, Ltd.

Notes: 2-Methylindole (2-MI) is adsorbed on the surface of colloidal CdS particles with an adsorption intensity of 0.6 × 103 dm3 mol-1. A new emission band at 530 nm is produced by forming an exciplex between excited CdS and 2-MI and the red emission due to CdS is simultaneously quenched. The emission maxima of green bands for different indoles increase in the order indole 〈 tryptophan 〈 2-MI 〈 3-MI and are observed at 508, 520, 530 and 540 nm, respectively. The shift in emission maxima is related to the oxidation potential of these substrates. The irradiation of an aerated reaction mixture containing CdS and 2-MI with visible light induces the oxidation of adsorbed 2-MI by photogenerated holes to produce 2-methyl-3-indolinone and 2-acetamidobenzaldehyde. The latter product is formed due to oxidative C - C bond cleavage of the pyrrole ring. The reactivity of trapped holes towards the adsorbed 2-MI is evidenced by a decrease in the lifetime of the red emission of CdS in the presence of 2-MI. In this reaction the possibility of the participation of singlet oxygen is ruled out. A general mechanism of CdS-induced oxidation of indoles is discussed. © 1998 John Wiley & Sons, Ltd.

Notes: The solid-state molecular structure and the conformational behaviour in solution of the 12-membered crown dithioether 8-methyl-1,4-dioxa-7,10-dithiacyclododecane-5,12-dione were studied by x-ray crystallography, 1H and 13C NMR spectroscopy and molecular mechanics. The conformational rigidity of some constituent structural fragments allowed a detailed analysis of the structure and distribution of the conformers. A protocol for studies of multiconformational equilibrium was developed by means of the combined use of structure calculations and dynamic NMR measurements. © 1998 John Wiley & Sons, Ltd.

Notes: Transition metal-catalyzed decomposition of phenyliodonium and diphenylsulfonium ylides was investigated with regard to application in asymmetric carbenoid reactions. Phenyliodonium ylides react in the presence of Rh(II) catalysts with the same selectivity in inter- and intramolecular cyclopropanations as the corresponding diazo compounds, and intramolecular CH insertions proceed with identical enantioselectivities. With diphenylsulfonium ethoxycarbonylmethylide the Cu(I)-catalyzed cyclopropanation of olefins affords trans/cis ratios and asymmetric inductions identical with those of diazo compounds, but with Rh(II) catalysts some small, although significant, selectivity variations occur, which are ascribed to coordination of diphenyl sulfide to one of the coordination sites of the catalyst. © 1998 John Wiley & Sons, Ltd.

Notes: Application of the principles of physical organic chemistry to the construction of molecule-based magnets is discussed. Not only the magnetic structures of conventional magnets but also secondary and tertiary structures of biopolymers are instrumental in the molecular design. © 1998 John Wiley & Sons, Ltd.

Notes: In the direct investigation of reactive intermediates it is particularly valuable to use a combination of several spectroscopic techniques. This commentary highlights recent examples, using primarily flash vacuum thermolysis for the generation of the intermediates, and matrix IR spectroscopy in conjunction with gas-phase mass spectrometric methods for their identification. The examples include nitrile imines, nitrile ylides, nitrile sulfides and selenides, dinitrogen sulfide and several novel cumulenes (X=C=C=Y, RN=C=C=C=X). © 1998 John Wiley & Sons, Ltd.

Notes: Hydrophobically modified polyelectrolytes (polysoaps) are a unique class of water-soluble polymers containing distinct hydrophobic and hydrophilic regions. Above a certain concentration, polysoaps form intramolecular and intermolecular aggregates in aqueous solution. They have attracted much attention not only for their ability to mimic some functions demonstrated by biopolymers but also for their important industrial applications. This review highlights some interesting features of novel non-cross-linked and cross-linked poly(alkylmethyldiallylammonium halides) that have been described in recent years. © 1998 John Wiley & Sons, Ltd.

Notes: Efforts to developed detailed insights into the structure and function of the molecules of memory, thought and sensory perception - physical organic chemistry on the brain - are described. By combining more conventional chemical tools with a number of techniques adapted from modern biology, it is now possible to perform systematic structure-function studies on the integral membrane proteins that play a central role in molecular neurobiology. There are substantial challenges associated with such studies, but we believe the potential payoff is considerable. © 1998 John Wiley & Sons, Ltd.

Notes: Hydrogens located at activated positions in electrophilic arenes, e.g. ortho and para hydrogens in nitrobenzenes, can be replaced with a nucleophile moiety provided there is at least one nucleofuge X connected to the nucleophilic centre. As the group really leaving in this hydrogen substitution process is not the hydride anion but X, the reaction has been named vicarious nucleophilic substitution of hydrogen (VNS). The concepts on the mechanism of the reaction and their experimental background are presented. Reactivity and orientation - the fundamental questions concerning synthetical applications of VNS - are discussed in light of the supposed mechanistic picture.

Notes: No Abstract

Notes: An essential feature of the concept of aromaticity has been the stability and lack of reactivity of aromatics relative to that of other unsaturated compounds. Contrary to this general experience, high and unusual reactivity is encountered when simple, monocyclic benzene rings are bent by short bridges into a boat-shaped conformation, as is the case in small [n] paracyclophanes (n ≤ 8) and [n]metacyclophanes (n ≤ 7). This is illustrated, mostly with examples taken from the authors' own work, for thermal and photochemical behavior and reactions with electrophiles, nucleophiles and dienophiles. © 1998 John Wiley & Sons, Ltd.

Notes: A decade's worth of work is reviewed: building on the demonstrated prowess of heterogeneous catalysis in industrial organic chemistry, the author's laboratory devised efficient catalysts for a number of organic reactions, based on aluminosilicates such as clays and zeolites. This review also spells out, at a time when creative research is overshadowed by imitative research, some of the methodological musts that also happen to characterize physical organic chemistry: the devising of experiments so that accurate numerical data can be obtained; the importance of remote, interdisciplinary connections; the need for estrangement from stereotypic preconceptions that may obscure the true explanations for the phenomena; and the over-riding need for concerning oneself only, or at least predominantly, with the important facts that nature tells, if one cares to listen. © 1998 John Wiley & Sons, Ltd.

Notes: The advantage of adding more structure-diagnostic information to the simple detection of flash photolytically generated transient species by changes in UV-visible light absorbance is illustrated by a case study involving the mandelic acid keto-enol system. An early report based on preliminary evidence proposed that flash photolysis of phenyldiazoacetic acid produces the enol of mandelic acid by hydration of phenylhydroxyketene, itself generated by a photo-Wolff reaction of the diazo acid. Further examination, however, shows that this is only a minor route, and that the major pathway is a new enol-forming reaction involving what appears to be hydration of a carboxycarbene formed by dediazotization of the diazo compound. Hydration of phenylhydroxyketene is nevertheless the reaction by which mandelic acid enol is generated when esters of benzoylformic acid are the flash photolysis substrates. These mechanisms, and also identification of the enol as a tranisent species, are supported by detailed arguments involving acid-base catalysis, solvent isotope effects, and the use of oxygen-18 as a tracer. The work produces a keto-enol equilibrium constant for the mandelic acid system, pKE  =  16.19, and also acidity constants of the enol ionizing as an oxygen acid, pKEa  =  6.39, and the keto isomer ionizing as a carbon acid, pKKa  =  22.57. The bearing of these results on the enzyme-catalyzed racemization of mandelic acid is discussed. © 1998 John Wiley & Sons, Ltd.

Notes: Benzaldehyde in THF reacts with lithium metal to give the expected reduction product, benzyl alcohol, plus benzoin and benzyl as minor products. The kinetics of the overall reaction as well as the partial rate coefficients of the several steps have been determined under various reaction conditions. It was found that adsorption on the surface and electron transfer from the lithium to benzaldehyde are the slow steps. The experimental results show interesting surface effects, and evidence for significant radical intermediates, which were characterized by their epr spectra and trapping experiments, results useful to gain insight into the mechanisms of these and other related reactions. © 1997 John Wiley & Sons, Ltd.

Notes: ---Based on MD simulations, the structures of Eu3+ and EuCl3 complexes of bipyridine-substituted calixarenes in different environments (in vacuo and in acetonitrile and water solutions) were modelled. The data account for the differences in their luminescence properties. The role of the calixarene platform, preorganization of the ligands, and an explicit account of counterions in different environments are analysed. © 1997 John Wiley & Sons, Ltd.

Notes: ---Stochastic molecular dynamics simulations were used to determine the enantiomer retention orders of moderately polar analytes binding to permethylated β-cyclodextrin, a popular chiral stationary phase used in gas chromatography. It is found that averaging over multiple trajectories, each of which are lengthy, is required to faithfully reproduce experiment. From the simulations we find the major binding domain to be the interior of the macrocycle rather than the exterior with most analytes having a preference for associating to the primary rim rather than to the secondary rim. It is also found that the intermolecular forces responsible for holding the complexes together are the short range dispersion forces, and that the enantiodifferentiating forces of the competing diastereomeric complexes are dominated by the van der Waals contributions to the intermolecular energy. © 1997 John Wiley & Sons, Ltd.

Notes: The use of effective core potentials in the calculation of the geometrical parameters of the ferrocene molecule and its heavier analogs is reported. It is shown that a critical factor in these calculations is the efective core-core (ECC) potential and, in the absence of ECCs for first-row atoms that are involved in short bonds, calculations of the geometrical parameters are not reliable. Good agreement with experimental geometries may be obtained by using the Los Alamos ECPs for atoms of the second and higher rows of the periodic table at the MP2 level. DFT calculations have been performed and found to give numerical results comparable to MP2 in the same basis. © 1995 John Wiley & Sons, Inc.

Notes: In this article, we report an efficient computational procedure for electron scattering matrix elements in the previously developed cubic-grid Gaussian basis sets. The Green function matrix elements derived for the cubic-grid basis set are simpler and easier to calculate than are those available in the literature for conventional Gaussian basis sets. Special features of the cubic-grid basis sets may also be exploited for a very efficient computation of Coulomb and exchange integrals. Inelastic scattering amplitudes for vibrational excitations may be efficiently calcualted in the harmonic approximation by numerical differention of the T-matrix elements. © 1995 John Wiley & Sons, Inc.

Notes: Previously developed cubic-grid basis sets of various sizes were used for the calculation of cross sections for elastic and inelastic electron scattering by the He and Ne atoms and the H2O molecule by the T-matrix expansion method. The aim was to test the invariance of calculated cross sections with respect to the translation of the target molecule and to examine the effect of basis-set size on the results. We also present a simple procedure for accounting for long-range interactions from the part of space that lies outside the volume that contains the cubic-grid basis set. © 1995 John Wiley & Sons, Inc.

Notes: Atomic charge and momentum densities of 91 atoms (He—U) are classified in terms of their L1, L2, and entropic measures of distance from the densities of the preceding atoms. The relationship between these distances and the first ionization energies is also considered. © 1995 John Wiley & Sons, Inc.

Notes: The subject of this article is the self-consistent-field (SCF) treatment of low-lying molecular vibrations in molecules subject to solvent effects and light atom migration. The analyses use a Cartesian Gaussian basis and Gaussian functional expansions of potential energy operators. The objective of the work was to establish approximate and practical methods of analysis of vibrational degrees of freedom in molecules that build on and compare well with the highly accurate treatments of vibrations in small molecular systems of the past decade. An application to a system in which hydrogen bonding contributes the major anharmonic effect illustrates the method. © 1995 John Wiley & Sons, Inc.

Notes: This article presents methods for computing matrix elements with Cartesian Gaussian wave functions of potential energy operators that depend on functions of the form (r-r0)n exp[-a(r - r0)] as well as matrix elements of the class of polynomial many-body potentials developed by Murrell et al. The matrix elements arise in the analyses of anharmonic vibrations in molecules. © 1995 John Wiley & Sons, Inc.

Notes: The extension of the PPP Hamiltonian for alternant cyclic polyenes to noninteger values of the pseudomomentum by imposing modified boundary conditions is discussed in detail. It is shown that a computer program for periodic boundary conditions can be easily adapted to the new boundary conditions. Full CI computations are carried out for some low-lying states of the PPP model of altemant cyclic polyenes (CH)N, (N even) at half-filling. The energy values obtained by using periodic (Bloch) and antiperiodic (Möbius) orbitals are used to perform energy extrapolations for N → ∞. © 1995 John Wiley & Sons, Inc.

Notes: General formalism for evaluation of multiparticle integrals involving J̌2 and J̌z operators over explicitly correlated Cartesian Gaussian functions is presented. The integrals are expressed in terms of the general overlap integrals. An explicitly correlated Cartesian Gaussian function is a product of spherical orbital Gaussian functions, powers of the Cartesian coordinates of the particle, and exponential Gaussian factors, which depend on interparticular distances. This development is relevant to both adiabatic and nonadiabatic calculations of energy and properties of multiparticle systems. © 1995 John Wiley & Sons, Inc.

Notes: The molecular g-tensors for the molecules NO2, CO2-, C3H5, H2CO+, and NF3+ are calculated at the unrestricted Hartree-Fock (UHF) level using the Rayleigh-Schrödinger perturbation approach. All one-electron terms have been evaluated, including the relativistic mass correction, the one-electron spin-Zeeman gauge correction, and a second-order term involving the spin-orbit coupling and the orbital-Zeeman interaction. The relative importance of the first-order terms is found to be quite substantial. For first-row molecules, their total contribution is often of the same order of magnitude as of the second-order contribution, in some instances even larger. A study on the basis-set dependence of these g-tensors has been conducted. At this level, the most important basis-set criterion is shown to be a satisfactory description of the valence regions. Finally, the gauge dependence of these g-tensor calculations has been systematically studied. This dependence seems to be substantially reduced for basis sets which include polarization functions. © 1995 John Wiley & Sons, Inc.

Notes: A scaling procedure is used for the force constants generated by the SINDO1 method in internal coordinates to achieve better agreement with experimental frequencies of molecules. The procedure is subsequently used to calculate frequency shifts for adsorbed molecules. The results for CO2 and CO adsorption at NaCl cluster surfaces are in good agreement with experimental data. © 1995 John Wiley & Sons, Inc.

Notes: Ab initio self-consistent-field calculations are reported for electronic states of beryllium clusters comprised of 93, 105, 111, and 123 atoms. The respective clusters correspond to coordination shells 12-15 of a central Be atom with internuclear separations derived from the lattice constants of the bulk metal. Ab initio effective core potentials have been employed to replace the 1 s electrons, thereby reducing the complexity of the calculations. In addition, use of the full D3h point group symmetry of the clusters results in a substantial reduction of the numbers of two-electron integrals that must be computed and processed. Binding energies, orbital energies, electric field gradient, nuclear-electrostatic potential, diamagnetic shielding constant, second moments, and Mulliken populations are calculated for selected electronic states. Calculated binding energies when compared among the different clusters as well as to smaller and larger fragments from earlier studies provide evidence for the onset of convergence to the Hartree-Fock limit of the bulk. Lowest-state ionization potentials are consistently above and agree to within 14% of the experimental workfunction. The net charge on the central beryllium atom decreases toward zero. The variability of observed bulklike behavior for the different properties indicates that the transition between cluster and bulklike behavior is not sharp and depends on the quantity of interest. © 1995 John Wiley & Sons, Inc.

Notes: The discrete variable representation method (DVR) is applied to the calculation of the J = 0 vibrational energy levels of the ground electronic state of nitrogen dioxide, a molecule which shows a large amplitude bending vibration. The Hamiltonian is expressed in Johnson hyperspherical coordinates and developed on a DVR basis set for each coordinate. A successive diagonalization-truncation method is applied which gives accurate values for the energy levels up to ≃ 7000 cm-1. © 1995 John Wiley & Sons, Inc.

Notes: A procedure for finding transition states ( TS) that does not require the evaluation of the second derivatives during the search is proposed. The procedure is based on connecting a series of points representing products Pi and reactants Ri and taking conservative steps along the difference vector from Pi toward Ri and from Ri toward Pi until the two points coalesce. Although the points Po and Ro represent the product and reactant specifically, other Pi and Ri are determined by minimization in hyperplanes perpendicular to Pi -1 and Ri-1. We apply this technique to six well-known potential functions and compare these results with those obtained from other well-known procedures. © 1995 John Wiley & Sons, Inc.

Notes: Potential energy curves for the ground and low-lying excited states of the AH2+ (A = Mg - Ar) dications have been calculated using high-level ab initio methods with large atomic orbital basis sets. Quasi-bound potential energy curves with local minima and deprotonation barriers have been found for most of the dications studied. The energies, tunneling lifetimes, and widths of the quasi-bound states have been calculated by numerical solution of the radial Schrodinger equation using the Numeov method. All these dications except ArH2+ have low-lying states which support quasi-bound vibrational states. The ArH2+ dication has a 2∏i potential energy curve with a minimum so shallow that it does not support any quasi-bound vibrational states. Results of our calculations are compared with previous ab initio calculations and available experimental data. © 1995 John Wiley & Sons, Inc.

Notes: A bond-energy formula deduced by means of the Hellmann-Feynman theorem is applied to selected simple hydrocarbons. The required potentials at the nuclei are calculated with the help of large basis-set expansions including polarization functions. The carbon-carbon bond energy of ethane is evaluated at ∼ 70 kcal mol-1. The CC bond energies of ethane, ethylene, acetylene, benzene, and cyclopropane are approximately in a ratio of 1: 2.0: 3.0: 1.65 1.0. Limitations and possible improvements in future applications of this energy formula are discussed. © 1995 John Wiley & Sons, Inc.

Notes: Ab initio molecular orbital (MO) calculations with the 3-21G and 6-31G basis sets are carried out on a series of complexes of NH3 with Li+, C≡N-, LiCN, and its isomer LiNC. The BSSE-corrected interaction energies, geometrical parameters, internal force constants, and harmonic vibrational frequencies are evaluated for 15 species. Complexes with trifurcated (C3v) structures are calculated to be saddle points on the potential energy surfaces and have one imaginary frequency each. Calculated energies, geometrical parameters, internal force constants, and harmonic vibrational frequencies of the various species considered are discussed in terms of the nature of association of LiCN with ammonia. The vibrational frequencies of the relevant complexed species are compared with the experimental frequencies reported earlier for solutions of lithium cyanide in liquid ammonia. © 1995 John Wiley & Sons, Inc.

Notes: When two electronic potentials present an avoided crossing, the adiabatic approximation breaks down in the energy region near to the crossing. In particular, the correspondence between exact energy levels of the two-state system and the adiabatic levels of the lower and upper adiabatic potentials becomes ambiguous. This implies that the term “nonadiabatic effect,” used for the difference between exact and adiabatic energy eigenvalues, loses its meaning in the crossing regime unless an unambiguous way of assigning an adiabatic to an exact level is defined. This is important in order to investigate where nonadiabatic schemes, such as the generator coordinate approximation, fit in between the adiabatic approximation and quasi-exact approaches. © 1995 John Wiley & Sons, Inc.

Notes: The application of the Σ-separation method to the calculation of multicenter two-electron molecular integrals with Slater-type basis functions is reported. The approach is based on the approximation of a scalar component of the two-center atomic density by a two-center expansion over Slater-type functions. A least-squares fit was used to determine the coefficients of the expansion. The angular multipliers of the atomic density were treated exactly. It is shown that this approach can serve as a sufficiently accurate and fast algorithm for the calculation of multicenter two-electron molecular integrals with Slater-type basis functions. © 1995 John Wiley & Sons, Inc.

Notes: The intersystem crossing (ISC) between the lowest triplet and singlet states occurring in the reaction of atomic oxygen with ethylene was studied. The importance of spin-orbit coupling (SOC) in oxirane biradicals (ĊR′R″ - CRR* - Ȯ) is stressed through calculations where the spin-orbit matrix elements over the full Breit-Pauli SOC operator has been obtained in the singlet-triplet crossing region. The calculations are performed with a multiconfigurational linear response approach, in which the spin-orbit couplings are obtained from triplet response functions using differently correlated singlet-reference-state wave functions. Computational results confirm earlier semiempirical predictions of the spin-orbit coupling as an important mechanism behind the ring opening of oxiranes and addition of oxygen O(3P) atoms to alkenes. © 1995 John Wiley & Sons, Inc.

Notes: We consider a crystal as partitioned into a localized molecular cluster (containing a defect or not) and an embedding region. Within the Hartree-Fock formalism, an expression is derived for an effective potential due to the embedding region of crystal. This potential is part of the cluster Fock operator and requires input from a perfect crystal calculation. Special features of the derivative are rigorous inclusion of cluster-embedding overlap and orthogonality between single-electron states of the embedding region and the function-space manifold of the cluster; physically correct normalization of the Fock eigenstates; and a nontrivial total-energy algorithm. Computational requirements are qualitatively compared with those for an isolated cluster. The method allows for intracluster (and intraembedding) correlation and can be adapted straightforwardly to local density functional approaches. Fundamental aspects of the embedding problem are addressed in a general formulation that is, nevertheless, oriented toward explicit calculations. © 1995 John Wiley & Sons, Inc.

Notes: An efficient procedure for third-order electron propagator calculations of ionization energies and electron affinities is reported. Diagonal self-energy expressions that are suitable for large molecules are empolyed. The outer-valence Green's function method also is implemented. An integral transformation program for direct and semidirect algorithms is modified to store only nonzero integrals according to Abelian point group symmetry. Contributions to self-energy matrix elements that depend on electron repulsion integrals with four virtual orbital indices are computed in a direct way. Intermediate batches of integrals are created by sort procedures while avoiding storage of transformed integrals in the main memory. This method permits calculation of electron binding energies for C72- with a 231 atomic orbital basis and for Zn(C5H5)2 with a 220 atomic orbital basis on an IBM RISC/6000 Model 550. During these calculations, the CPU is engaged approximately 90% of the time. © 1995 John Wiley & Sons, Inc.

Notes: The intermolecular potentials for the X 2σ and A2Π states of Li… Ar were studied by a variety of multiconfiguration, single-configuration, and perturbation methods (CASPT2). The A 2Π excited state was calculated to have a well depth of 811 cm-1 at an internuclear separation of 2.59 Å, in excellent agreement with the 810 cm-1 derived from experimental data. A smaller well of 77 cm-1 was found for the X 2σ ground state at an intermolecular separation of 4.8 Å. These results are in better agreement with experimental results than were the previously reported pseudopotential calculations. The comparison of CI calculation with the CAPST2 results shows that the latter is able to give good results for interacting metal-rare gas systems. © 1995 John Wiley & Sons, Inc.

Notes: This article is a brief review of the work formalism of electronic structure, its recent developments, and the results of its application to spherically symmetric and nonspherical density atoms. The formalism, which is founded in Schrödinger theory, is derived by physical arguments based on Coulomb's law. The fundamental quantity in the formalism is the pair-correlation density that constitutes the nonlocal quantum-mechanical source charge distribution giving rise to both a local potential representing electron correlations as well as the electron interaction energy. The potential is the work done to move an electron in the force field of the pair-correlation density and the energy the interaction energy between the electronic and pair-correlation densities. (For systems for which the curl of the force field may not vanish, the potential is obtained from the irrotational component of the field, the solenoidal component being neglected). The differential equation governing the system is a Sturm-Liouville equation, and as such, the exact wave function can in principle be obtained as an infinite linear combination of Slater determinants of the self-consistently determined spin-orbitals of the occupied and virtual states. The correctness of the interpretation for the local potential representing electron interaction is evidenced as follows: In the Pauli-correlated and central field approximations, ground-state energies of atoms (2 He -86Rn) lie within 50 ppm of those of Hartree-Fock theory, differing by less than 10 ppm for atoms with Z 〉 35. The densities thus generated clearly exhibit atomic shell structure and also satisfy the Kato-Steiner electron-nucleus cusp condition to 2 ppm. Another attribute of the formalism is that the asymptotic structure of the potential (when both Pauli and Coulomb correlations are considered) is that of the Pauli-correlated approximation. This is rigorously the case as shown for the He atom for which the potential vanishes in the classically forbidden region, the potential there being the exchange potential. As such, it is meaningful to compare the highest occupied eigenvalue of the differential equation in the Pauli-correlated approximation to experiment. A comparison for atoms and atomic ions of this eigenvalue to experimental ionization potentials and electron affinities show them to be consistently superior to the corresponding eigenvalue of Hartree-Fock theory. Transition energies determined from eigenvalue differences are also superior to those obtained from total energy calculations via Hartree-Fock theory when compared to experiment. Further, by considering the carbon atom in one of its degenerate ground states for which the curl of the field due to the Fermi hole does not vanish, it is shown that the solenoidal component of the field is negligible and two orders of magnitude smaller than is the irrotational component. Thus, the approximation of obtaining a path-independent potential for nonspherical density systems from the irrotational component of the field is accurate. Finally, Coulomb correlation effects can be incorporated within the work formalism in practice via the configuration interaction approximation. The self-consistent orbitals thus obtained explicitly incorporate the effects of both Pauli and Coulomb correlations in their structure because the source charge from which they are generated is a pair-correlation density. Furthermore, these orbitals possess the correct asymptotic structure since they are also generated by a potential that is local. The work formalism also provides a physical interpretation for the local potential representing electron correlations of Kohn-Sham density functional theory. Further, the exchange potential of the work formalism satisfies analytically two requisite conditions of the Kohn-Sham theory exchange potential. These are the scaling requirement and the sum rule relating the exchange energy to its functional derivative. The work formalism also leads to a deeper understanding of electron correlations in various approximations within Kohn-Sham theory. For example, it can be rigorously shown that the pair-correlation density in the local density approximation contains a term proportional to the gradient of the density. Thus, in contrast to the Kohn-Sham theory interpretation that electron correlations in this approximation are those of the uniform electron gas assumed valid locally, we learn that the nonuniformity of the electronic density is, in fact, explicitly accounted for by the approximation. This then explains the accuracy of the approximation. © 1995 John Wiley & Sons, Inc.

Notes: The aziridine analogues of the epoxide metabolites of carcinogenic polycyclic aromatic hydrocarbons have greater mutagenic potency than the epoxides. Like their well-studied analogues, the aziridines undergo a pH-dependent decomposition that leads to a reactive carbocation intermediate. In aqueous solution the nucleophile with which the carbocation generally reacts is water. The kinetics of this pH-dependent reaction have been experimentally characterized by others. Although the effect of DNA on this reaction has not been studied, we hypothesize that, like their epoxide analogues, the aziridine derivatives of polycyclic aromatic hydrocarbons undergo a DNA-catalyzed reaction leading through a carbocation to either a DNA-adduct or a hydrolysis product. Using Poisson-Boltzmann calculations in conjunction with Metropolis Monte Carlo simulations and energy-minimized conformations, we predict the DNA-dependence of the acidcatalyzed decomposition of the K-region aziridine, phenanthrene[9,10]imine. © 1995 John Wiley & Sons, Inc.

Notes: A QSAR analysis of a series of Valproic Acid (vpa) derivatives is given, which shows the importance of hydrophobic and electronic effects as determinants of the anticonvulsivant activity. The statistical analysis allows one to infer that the electron acceptor capability of the carboxylic carbon atom may guide electrostatic interactions of the molecules with the receptor site, in those cases where the lipophilic requirements are satisfied. Both the anticonvulsivant activity and the calculated lipophilic parameters (log P values) are taken from the literature, whereas the electronic descriptors result from Intermediate Neglect of Differential Overlap calculations at the Configuration Interaction level, (INDO/S-CI parametrization), for the most stable conformers of each derivative. The protein environment is modeled as a dielectric continuum in a Self-Consistent Reaction Field approach. The conformational analysis is based on AMI calculations. © 1995 John Wiley & Sons, Inc.

Notes: A new form of second-order multireference perturbation theory coupled with finite-field perturbation theory is applied to evaluate some one-electron molecular properties. Several possible definitions of the zeroth-order Hamiltonian are considered and results tested against bench-mark full CI calculations. © 1995 John Wiley & Sons, Inc.

Notes: The correlation present in the nondegenerate ground state of an interacting Fermi system is discussed in terms of reduced density matrices and their cumulant expansion. By generalizing a result obtained for the interacting uniform electron gas (correlation induced exchange-hole narrowing), possible measures of the correlation strength in terms of natural occupation numbers (the eigenvalues of the true one-particle density matrix) are introduced. These quantities-the v-order nonidempotency and the information entropy of the natural occupation numbers-result from the correlated many-body wave function and characterize the ground-state correlation in addition to the usual correlation energy. The uniform electron gas serves as a first illustrative example. © 1995 John Wiley & Sons, Inc.

Notes: In the present work, we reexamined the gradient expansion of the exchange energy of an electron gas with a slowly varying charge density. We stay within the exchange-only approximation of Sharp, Horton, Talman, and Shadwick but go to second order in the deviation from the homogeneous limit. The coefficient of the lowest-order gradient correction is obtained analytically both for a bare and a screened Coulomb interaction - the former yielding the value previously obtained by Kleinman numerically and by Engel and Vosko analytically. A screened Coulomb interaction gives Sham's coefficient in the limit of infinite screening length. The cause of the difference between the coefficients of Kleinman and Sham is clearly exhibited. The coefficients of the two next highest-order gradient corrections, one of which originates in second-order response theory, is shown to diverge as the screening length becomes large. The bare Coulomb interaction gives finite coefficients of which the one originating from linear response is obtained analytically and differs from the presumably correct result obtained by Engel and Vosko. This discrepancy demonstrates the extreme sensitivity of the analytical expressions to different regularization procedures. We suggest that coefficients should rather be chosen according to the performance of the resulting gradient approximations in weakly perturbed electron gases. © 1995 John Wiley & Sons, Inc.

Notes: The focal point of the present work is the single-particle kinetic energy density tensor in D dimensions. This quantity enters both differential and various integral forms of the virial theorems, which are again set up in D dimensions. Major new results lie in (i) demonstrating that, by one-dimensional quadrature, it is possible to construct the Pauli potential directly from the kinetic energy tensor, without the need for functional differentiation and (ii) generating the gradient expansion for the kinetic energy tensor, in D dimensions. © 1995 John Wiley & Sons, Inc.