Hammett Equation Research Articles

Mechanism of silver-mediated di-tert-butylsilylene transfer from a silacyclopropane to an alkene.

Kinetic studies of the reactions of cyclohexene silacyclopropane 1 and monosubstituted alkenes in the presence of 5 mol % of (Ph3P)2AgOTf suggested a possible mechanism for silver-mediated di-tert-butylsilylene transfer. The kinetic order in cyclohexene silacyclopropane 1 was determined to be one. Inverse kinetic saturation behavior (rate inhibition) was observed in monosubstituted alkene and cyclohexene concentrations. Saturation kinetic behavior in catalyst concentration was observed. A reactive intermediate, a silylsilver complex, was observed using low temperature 29Si NMR spectroscopy. Competition experiments between substituted styrenes and a deficient amount of 1 correlated well with the Hammett equation and provided a rho value of -0.62 +/- 0.02 using sigmap constants. These data support a mechanism involving reversible silver-promoted di-tert-butylsilylene extrusion from 1 followed by irreversible concerted electrophilic attack of the silylsilver intermediate on the alkene.

Bond Strengths of Toluenes, Anilines, and Phenols: To Hammett or Not

AbstractFor Abstract see ChemInform Abstract in Full Text.

Differential substrate behaviour of phenol and aniline derivatives during oxidation by horseradish peroxidase: kinetic evidence for a two-step mechanism

The catalytic constant (kcat) and the second-order association constant of compound II with reducing substrate (k5) of horseradish peroxidase C (HRPC) acting on phenols and anilines have been determined from studies of the steady-state reaction velocities (V0 vs. [S0]). Since kcat=k2k6/k2+k6, and k2 (the first-order rate constant for heterolytic cleavage of the oxygen–oxygen bond of hydrogen peroxide during compound I formation) is known, it has been possible to calculate the first-order rate constant for the transformation of each phenol or aniline by HRPC compound II (k6). The values of k6 are quantitatively correlated to the σ values (Hammett equation) and can be rationalized by an aromatic substrate oxidation mechanism in which the substrate donates an electron to the oxyferryl group in HRPC compound II, accompanied by two proton additions to the ferryl oxygen atom, one from the substrate and the other the protein or solvent. k6 is also quantitatively correlated to the experimentally determined 13C-NMR chemical shifts (δ1) and the calculated ionization potentials, E (HOMO), of the substrates. Similar dependencies were observed for kcat and k5. From the kinetic analysis, the absolute values of the Michaelis constants for hydrogen peroxide and the reducing substrates (KMH2O2 and KMS), respectively, were obtained.

Bond strengths of toluenes, anilines, and phenols: to hammett or not.

The Hammett equation correlates the effects of Y on many different chemical properties of YC(6)H(4)ZX families of compounds. One of the most surprising is that the Z-X bond dissociation enthalpy (BDE), a homolytic property, can be correlated for some 4-YC(6)H(4)ZX families with electrophilic substituent constants, sigma(p)(+)(Y), which were largely derived from the rates of the heterolytic S(N)1 solvolyses of para-substituted cumyl chlorides. Although there is no Hammett correlation of the C-X BDEs in 4-YC(6)H(4)CH(2)X (X = H, halide, OPh) families, there are good correlations of N-X BDEs with sigma(p)(+)(Y) in 4-YC(6)H(4)NHX (X = H, CH(3), OH, F) and excellent correlations of O-X BDEs with sigma(p)(+)(Y) in 4-YC(6)H(4)OX (X = H, CH(3), CH(2)Ph) families. The reasons for this varied behavior are discussed.

Structure‐Reactivity Relationships as Probes to Acetylcholinesterase Inhibition Mechanisms by Aryl Carbamates. II. Hammett‐Taft Cross‐Interaction Correlations

AbstractSubstituted phenyl‐N‐butyl carbamates (1) and p‐nitrophenyl‐N‐substituted carbamates (2) are characterized as “pseudo‐pseudo‐substrate” inhibitors of acetylcholinesterase. Since the inhibitors protonate in pH 7.0 buffer solution, the virtual inhibition constants (Ki's) of the protonated inhibitors can be calculated from the equation, ‐logKi' = ‐logKi ‐ pKa + 14. The ‐logKi' and logkc values for acetylcholinesterase inhibitions by carbamates 1 correlate with the Hammett equation (log(k/k0) = ρσ); moreover, those by carbamates 2 correlate with the Taft equation (log(k/k0) = ρ* σ*). With modified Hammett‐Taft cross‐interaction variations, multiple linear regressions of the ‐logKi' and logkc values of carbamates 1 and 2 give good correlations, and the cross‐interaction constants (ρXR) are 0.5 and 0.0, respectively. The ρXR value of 0.5 indicates that the carbamate O‐C(O)‐N‐R geometries for the transition states that lead to enzyme‐carbamate tetrahedral intermediates are all pseudo‐trans conformations. Therefore, the carbamate moiety of the inhibitors stretches along the active site gorge of the enzyme but does not bind in the acyl binding site pocket of the enzyme. Overall, the carbamate O‐C(O)‐N‐R geometries for carbamates 1 and 2, protonated carbamates 1 and 2, and the tetrahedral intermediate are all retained in pseudo‐trans conformations. The ρXR value of 0.0 suggests that the transition states that lead to the carbamyl enzymes are breaking C‐O bonds and are excluding the leaving groups, substituted phenols.

Differential substrate behaviour of phenol and aniline derivatives during oxidation by horseradish peroxidase: kinetic evidence for a two-step mechanism

The catalytic constant ( k cat) and the second-order association constant of compound II with reducing substrate ( k 5) of horseradish peroxidase C (HRPC) acting on phenols and anilines have been determined from studies of the steady-state reaction velocities ( V 0 vs. [S 0]). Since k cat= k 2 k 6/ k 2+ k 6, and k 2 (the first-order rate constant for heterolytic cleavage of the oxygen–oxygen bond of hydrogen peroxide during compound I formation) is known, it has been possible to calculate the first-order rate constant for the transformation of each phenol or aniline by HRPC compound II ( k 6). The values of k 6 are quantitatively correlated to the σ values (Hammett equation) and can be rationalized by an aromatic substrate oxidation mechanism in which the substrate donates an electron to the oxyferryl group in HRPC compound II, accompanied by two proton additions to the ferryl oxygen atom, one from the substrate and the other the protein or solvent. k 6 is also quantitatively correlated to the experimentally determined 13C-NMR chemical shifts ( δ 1) and the calculated ionization potentials, E (HOMO), of the substrates. Similar dependencies were observed for k cat and k 5. From the kinetic analysis, the absolute values of the Michaelis constants for hydrogen peroxide and the reducing substrates ( K M H 2O 2 and K M S), respectively, were obtained.

Substituent and solvent effects on electronic absorption spectra of some N-(substitutedphenyl)benzene sulphonamides

The effects of substituents and solvents have been studied through the absorption spectra of nearly 23 ortho- and para-N-(substitutedphenyl)benzene sulphonamides in the range of 200–400 nm. The effects of substituents on the absorption spectra of compounds under present investigation are interpreted by correlation of absorption frequencies with simple and extended Hammett equations. Effect of solvent polarity and hydrogen bonding on the absorption spectra are interpreted by means of Kamlet equation and the results are discussed.

QSPR/QSAR in N-[(dimethylamine)methyl] benzamides substituents groups influence upon electronic distribution and local anesthetics activity

It was determined, with a systematic mode, the carbonyl group frequency in the region of the infrared of N-[(dimethylamine)methyl] benzamides 4-substituted (set A) and their hydrochlorides (set B), that had its local anesthetical activity evaluated. The application of the Hammett equation considering the values of the absorption frequency of carbonyl group, ν CO, using the electronic constants σ, σ I, σ R, I and R leads to meaningful correlation. The nature and the contribution of substituent group electronic effects on the polarity of the carbonyl group was also analyzed. The use of the ν CO as an experimental electronic parameter for QSPR studies was validated.

Solvolysis of para-substituted cumyl chlorides. Brown and Okamoto's electrophilic substituent constants revisited using continuum solvent models.

Brown and Okamoto (J. Am. Chem. Soc. 1958, 80, 4979) derived their electrophilic substitutent constants, sigma(p)+, from the relative rates of solvolysis of ring-substituted cumyl chlorides in an acetone/water solvent mixture. Application of the Hammett equation to the rates for the meta-substituted cumyl chlorides, where there could be no resonance interaction with the developing carbocation, gave a slope, rho(+) = -4.54 ( identical with 6.2 kcal/mol free energy). Rates for the para-substituted chlorides were then used to obtain sigma(p)+ values. We have calculated gas-phase C-Cl heterolytic bond dissociation enthalpy differences, Delta BDE(het) (= BDE(het)(4-YC(6)H(4)CMe(2)Cl) - BDE(het)(C(6)H(5)CMe(2)Cl)), for 16 of the 4-Y substituents employed by Brown and Okamoto. The plot of Delta BDE(het) vs sigma(p)+ gave rho(+) (SD) = 16.3 (2.3) kcal/mol, i.e., a rho(+) value roughly 2.5 times greater than experiment. Inclusion of solvation (water) energies, calculated using three continuum solvent models, reduced rho(+) and SD. The computationally least expensive model used, SM5.42R (Li et al. Theor. Chem. Acc. 1999, 103, 9) gave the best agreement with experiment. This model yielded rho(+) (SD) = 7.7 (0.9) kcal/mol, i.e., a rho(+) value that is only 24% larger than experiment.

Hammett Equation and Generalized Pauling's Electronegativity Equation

Substituent interaction energy (SIE) was defined as the energy change of the isodesmic reaction X-spacer-Y + H-spacer-H --> X-spacer-H + H-spacer-Y. It was found that this SIE followed a simple equation, SIE(X,Y) = -ksigma(X)sigma(Y), where k was a constant dependent on the system and sigma was a certain scale of electronic substituent constant. It was demonstrated that the equation was applicable to disubstituted bicyclo[2.2.2]octanes, benzenes, ethylenes, butadienes, and hexatrienes. It was also demonstrated that Hammett's equation was a derivative form of the above equation. Furthermore, it was found that when spacer = nil the above equation was mathematically the same as Pauling's electronegativity equation. Thus it was shown that Hammett's equation was a derivative form of the generalized Pauling's electronegativity equation and that a generalized Pauling's electronegativity equation could be utilized for diverse X-spacer-Y systems. In addition, the total electronic substituent effects were successfully separated into field/inductive and resonance effects in the equation SIE(X,Y) = -k(1)F(X)F(Y) - k(2)R(X)R(Y) - k(3)(F(X)R(Y) + R(X)F(Y)). The existence of the cross term (i.e., F(X)R(Y) and R(X)F(Y)) suggested that the field/inductive effect was not orthogonal to the resonance effect because the field/inductive effect from one substituent interacted with the resonance effect from the other. Further studies on multi-substituted systems suggested that the electronic substituent effects should be pairwise and additive. Hence, the SIE in a multi-substituted system could be described using the equation SIE(X1, X2, ..., Xn) = Sigma(n-1)(i=1)Sigma(n)(j=i+1)k(ij)sigma(X)isigma(X)j.

Validity of the Hammett equation for isolated molecules: basicity of 3- and 4-substituted benzonitriles

Atomic and electronic energies of 27 3- and 4-substituted benzonitriles and of their protonated forms were calculated within the framework of density functional theory (DFT) at the B3LYP/6-311 + G(d,p) level. The substituent effects were expressed by isodesmic homodesmotic reactions, separately for the molecule of benzonitrile [eqn. (7)], for the protonated form [eqn. (8)] and for the resulting basicity [eqn. (6)]. With several molecules, actual site of protonation may be ambiguous and was determined in most cases from the energies of both protonated forms. In particular 4-aminobenzonitrile, 3-formylbenzonitrile and both nitrobenzonitriles are protonated on the CN group, while 3-aminobenzonitrile and both dimethylaminobenzonitriles on the substituent. The behaviour of methylsulfonylbenzonitriles is still doubtful. The validity of the Hammett equation was tested by correlation with the energies of equally substituted benzoic acids. It holds within the gradually extended range of validity with gradually decreased accuracy: Strictly speaking, it is valid only for meta derivatives; para derivatives with acceptor substituents can be still included at the cost of accuracy but para donors deviate significantly. The DFT model is not the best for the protonated nitriles. From several models tested, best agreement with the experimental gas-phase basicities was achieved with MP2/6-311 + G(d,p) but for the purpose of testing the Hammett equation the DFT model is good when only relative energies are compared.

Effect of para Substitution on Dissociation of N-Phenylbenzenesulfonamides

The reaction of substituted anilines and benzenesulfonyl chlorides has been used to prepare 49 substituted N-phenylbenzenesulfonamides of general formula 4-X-C6H4SO2NHC6H4-Y-4'. Their purity was checked by elemental analysis. The substituents X and Y include H, CH3, CH3O, Cl, Br, CN, and NO2. The dissociation constants of all compounds were determined by potentiometric titration in methanol, acetonitrile, N,N-dimethylformamide, and pyridine. The obtained dissociation constants, pKHA, were correlated with various sets of substituent constants. It was found that the effects of substituents X and Y on the dissociation are best described by using the Hammett equation with σp constants and the Yukawa-Tsuno equation with σp- and σp constants, respectively. This result confirms the direct conjugation of Y substituent with the reaction centre. The explained variability using the additive model was above 96% in all the solvents used. The data also provided information about the transmission effect of the SO2 group. The average dissociation constants were further processed by the latent variables methods, principal components and conjugated deviations analyses.

Reactivity of p-Substituted Benzaldoximes in the Cleavage of p-Nitrophenyl Acetate: Kinetics and Mechanism

Eleven p-substituted benzaldoximes (p-XC6H4CH=NOH, where X = H, CH3, CF3, F, Cl, Br, OCH3, N(CH3)2, COOCH3, CN, NO2) have been synthesized and their dissociation constants determined in 10% (v/v) aqueous dioxane at 35 °C. Under the same conditions, the pseudo-first order rate constants kobs of their reactions with p-nitrophenyl acetate (PNPA) were measured at pH values from 7.8 to 10.8 and at concentrations coxime ranging from 0 to 4.00 × 10-3 mol l-1. The kinetic model and mechanism of the said reaction was proposed by means of mathematical statistical modelling of the dependences of kobs on pH and coxime. The mechanism involves a pre-equilibrium (k-1/k1) in which PNPA forms a tetrahedral intermediate (THI) with the deprotonated form of oxime. In the given medium, THI is in equilibrium with the non-reactive conjugated acid THIH (dissociation constant Ka,THIH) which is stabilized by intramolecular hydrogen bond. Depending on pH, the rate-limiting step consists either in formation of THI from educts (pH < pKa,oxime) or in its spontaneous (k2) and oxime-catalyzed (k3, general acid catalysis) decomposition to products (pH > pKa,oxime). Evaluation of substituent effects on dissociation constants (Ka,oxime) of the oximes showed that there is no direct conjugation between the substituent and the reaction centre (the found reaction constant ρ(Ka,oxime) = 0.91). The transmission coefficient of the transfer of these effects through C=N-O grouping corresponds approximately to one bond. The reaction constants in the Hammett equation obtained from the regression model are: ρ(k-1Ka,THIH/k1) = 1.29, ρ(k2Ka,THIH) = 0.20 and ρ(k3Ka,THIH) = 0.67. These reaction constants have been discussed with the regard to the reaction mechanism suggested.

N-benzoylimido complexes of palladium. Synthesis, structural characterisation and structure-reactivity relationship.

Benzoyl azides, ArC(O)N3, 2, (Ar = phenyl or substituted phenyl), react with [Pd2Cl2(dppm)2], 1, [dppm = bis(diphenylphosphino)methane] with the formation of novel [Pd2Cl2(mu-NC(O)Ar)(dppm)2], 3, benzoylnitrene complexes that were structurally characterised by multinuclear magnetic resonance and IR spectroscopy and, in several instances, by single crystal X-ray diffraction. As shown by crystallographic studies, the C2P4Pd2 rings adopt extended twist-boat conformations with methylene groups bending towards the bridging benzoylimido moieties. X-ray diffraction studies have revealed the chiral nature of the imido complexes, the chiral element being the propeller-like C2P4Pd2 ring. Structural data accumulated on complexes 3 such as short C-N distances (1.32 A), elongated C=O bonds (1.30 A) as well as the outstandingly high barrier to internal rotation around the N-C(O) linkage (88.3 kJ mol(-1)) are in line with extensive ppi-ppi interaction between the bridging nitrogen and the carbonyl carbon atoms. Theoretical calculations indicate an electron shift from the dimer towards the apical nitrogen atom, which, in turn, facilitates the donation of electrons towards the carbonyl moiety. To elucidate the structure-reactivity relationship of benzoyl azides towards 1, crystallographic and solution IR spectroscopic studies were carried out on a series of para-substituted benzoyl azides. The reaction obeys the Hammett equation. The large positive value of the reaction constant indicates that the azides act as electrophiles in the reaction studied. The enhanced reactivity of 2-nitrobenzoyl azide has been attributed to a decreased conjugation of the phenyl and carbonyl moieties in this reagent.

AM1 and PM3 semi-empirical study of the Diels–Alder reaction between N-, P-, O- and S-substituted aromatic heterocyclic five-membered rings with acrolein

A semi-empirical study of the effect of substituent on the HOMO–LUMO energies of the 3,4-disubstituted five-membered heterocyclic aromatic compounds, the equilibrium constants of the Diels–Alder reaction of N-, P-, O- and S-substituted heterocyclic five-membered aromatic rings with acrolein and the enthalpy change of the reactions, gave results in accordance with the familiar Diels–Alder reaction. A linear correlation was found between E HOMO and E LUMO of the diene and σ p and σ m of Hammett equation. The log of the equilibrium constant calculated from the computed enthalpy and entropy of the reactions at 298 K, and the reaction enthalpy itself, also correlated with σ p and σ m, as expected for linear free energy relationships.

Validação de ½C=O como descritor estrutural de caráter eletrônico para aplicação em estudos de QSAR/QSPR

Com o propósito de validar o uso da freqüência de absorção do grupo carbonila, ½C=O , na região do infravermelho como descritor estrutural de caráter eletrônico para aplicação em estudos de QSAR/QSPR, este trabalho teve como objetivo correlacionar quantitativamente a estrutura química de compostos benzidrazídicos para-substituídos com o efeito eletrônico de grupos substituintes do anel benzênico. A validação foi obtida através da aplicação da equação de Hammett adaptada para freqüência de absorção no IV utilizando-se o Billin Program, versão 98. Aplicaram-se as constantes de substituintes de Hammett, Ãp, ÃI e ÃR, e as constantes N e O de Swain e Lupton, observando-se excelente correlação entre a constante Ãp e ½C=O possibilitando, inclusive, quantificar separadamente a influência dos efeitos indutivo e de ressonância sobre a polaridade do grupo carbonila de grupos substituintes na série de compostos estudados.

Hydroxide-catalysed decomposition of benzoquinone-imine dyes

A comparative kinetic study of the hydroxide-catalysed decomposition of benzoquinone-imine dyes such as 4-[(4-hydroxyphenyl)imino]-2,5-cyclohexadien-1-one (indophenol, IP), 2,6-dichloro-4-[(4-hydroxyphenyl)imino]-2,5-cyclohexadien-1-one ( DCIP), 2,6-dibromo-4-[(4-hydroxyphenyl)imino]-2,5-cyclohexadien-1-one ( DBIP), and 2,6-dibromo-4-[(4-hydroxy-3-methoxyphenyl)imino]-2,5-cyclohexadien-1-one ( DBMIP) was carried out. The kinetic data are consistent with nucleophilic addition of hydroxide anions to the imine carbon (step 1), followed by cleavage of the resulting carbinolamine intermediate (step 2). The reactivity for step 1 increases in the order IP < DCIP < DBIP < DBMIP, whereas the reactivity order for step 2 is DBIP < DCIP < DBMIP < IP. Application of the Hammett equation to the rate values corresponding to IP, DCIP and DBIP renders ρ values of (0.72±0.01) and (−0.46±0.03) for steps 1 and 2, respectively.

Linear Free-Energy Relationships in the Protonation Equilibria and Acid–Base Catalysed Reaction of 4-Substituted Benzohydroxamic Acids

Abstract As part of our investigations on the structure-reactivity relationships in protonation and hydrolysis of hydroxamic acids, we have now studied a series of 4-substituted benzohydroxamic acids (4-X-C6H4.CO.NH(OH), with X = H, Me, OMe, Cl, Br, F and NO2) in aqueous sulfuric acid. Good correlation was observed pointing out the validity of the Hammett equation. The protonation constant, ionization constant and rate constant for acid- and base-catalysed hydrolysis reactions seems are to be related in a linear free-energy (LEER) fashion.

Mechanism of di-tert-butylsilylene transfer from a silacyclopropane to an alkene.

Kinetic and thermodynamic studies of the reactions of cyclohexene silacyclopropane 1 and monosubstituted alkenes suggested a possible mechanism for di-tert-butylsilylene transfer. The kinetic order in cyclohexene silacyclopropane 1 and cyclohexene were determined to be 1 and -1, respectively. Saturation kinetic behavior in monosubstituted alkene concentration was observed. Competition experiments between substituted styrenes and a deficient amount of di-tert-butylsilylene from 1 correlated well with the Hammett equation and provided a rho value of -0.666 +/- 0.008, using sigma(p) constants. These data supported a two-step mechanism involving reversible di-tert-butylsilylene extrusion from 1, followed by irreversible concerted electrophilic attack of the silylene on the monosubstituted alkene. Eyring activation parameters were found to be DeltaH++ = 22.1 +/- 0.9 kcal.mol(-1) and DeltaS++ = -15 +/- 2 eu. Competition experiments between cycloalkenes and allylbenzene determined cycloalkenes to be more efficient silylene traps (k(rel) =1.3, DeltaDeltaG++ = 0.200 kcal.mol(-1)). A summary of the data resulted in a postulated reaction coordinate diagram. The mechanistic studies enabled rational modification of reaction conditions that improved the synthetic utility of silylene transfer. Removal of the volatile cyclohexene from the reaction mixture into an evacuated headspace led to the formation of previously inaccessible cyclohexene-derived silacyclopropanes.

Kinetics and Mechanism of Oxidation of Dimethyl Sulphoxide by Mono- and Di-Substituted N,N-Dichlorobenzenesulphonamides in Aqueous Acetic Acid

In an effort to introduce N,N-dichloroarylsulphonamides of different oxidising strengths, four mono- and five di-substituted N,N-dichlorobenzenesulphonamides are prepared, characterised and employed as oxidants for studying the kinetics of oxidation of dimethyl sulphoxide (DMSO) in 50% aqueous acetic acid. The reactions show first order kinetics in [oxidant], fractional to first order in [DMSO] and nearly zero order in [H+]. Increase in ionic strength of the medium slightly increases the rates, while decrease in dielectric constant of the medium decreases the rates. The results along with those of the oxidation of DMSO by N,N-dichlorobenzenesulphonamide and N,N-dichloro-4- methylbenzenesulphonamide have been analysed. Effective oxidising species of the oxidants employed in the present oxidations is Cl+ in different forms, released from the oxidants. Therefore the introduction of different substituent groups into the benzene ring of the oxidant is expected to affect the ability of the reagent to release Cl+ and hence its capacity to oxidise the substrate. Significant changes in the kinetic and thermodynamic data are observed in the present investigations with change of substituent in the benzene ring. The electron releasing groups such as CH3 inhibit the ease with which Cl+ is released from the oxidant, while electron-withdrawing groups such as Cl enhance this ability. The Hammett equation, log kobs = −3.19 + 1.05 σ , is found to be valid for oxidations by all the p-substituted N,N-dichlorobenzenesulphonamides. The substituent effect on the energy of activation, Ea and log A for the oxidations is also analysed. The enthalpies and free energies of activation correlate with an isokinetic temperature of 320 K.