Free Energy Correlation Research Articles

Glassy random matrix models.

This paper discusses random matrix models that exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues. The free energy and certain correlation functions of these models show differences for the different solutions. This study presents evidence for the presence of multiple solutions both analytically and numerically. As an example this paper discusses the double-well matrix model with potential V(M)=-(mu/2)M(2)+(g/4)M(4), where M is a random N x N matrix (the M(4) matrix model) as well as the Gaussian Penner model with V(M)=(mu/2)M(2)-t ln M. First this paper studies what these multiple solutions are in the large N limit using the recurrence coefficient of the orthogonal polynomials. Second it discusses these solutions at the nonperturbative level to bring out some differences between the multiple solutions. Also presented are the two-point density-density correlation functions, which further characterize these models in a different universality class. A motivation for this work is that variants of these models have been conjectured to be models of certain structural glasses in the high temperature phase.

Fragmentation reactions of protonated peptides containing phenylalanine: a linear free energy correlation in the fragmentation of H–Gly–Xxx–Phe–OH

The fragmentation reactions of a variety of protonated tri- and tetra-peptides containing phenylalanine have been examined using metastable ion studies and energy-resolved collision-induced dissociation studies. For peptides with the sequence H–Gly–Xxx–Phe–OH (Xxx=Gly,Ala,Val,Leu,Phe) the major primary fragmentation of MH + involves cleavage of the C-terminus amide bond to form either the b 2 ion or the y 1″ ion. For metastable ion fragmentation it is found that log([b 2]/[ y 1″]) increases linearly with the increase in the gas phase basicity of H–Xxx–OH. This linear free energy correlation is in contrast to the lack of such a correlation in the fragmentation of protonated H–Gly–Xxx–Gly–OH [J. Mass Spectrom. 30 (1995) 290]. When Phe is the central residue in tripeptides, the major primary fragmentation reaction involves formation of the b 2 ion which fragments further to the a 2 ion; at higher internal energies the a 2 ion fragments to give the phenylalanine immonium ion which becomes the dominant fragment. When Phe is in the N-terminus position, as in Phe–Gly–Gly–OH, the phenylalanine immonium ion is the dominant fragment and is formed, in part, directly by fragmentation of MH +. The fragmentation of the tetrapeptides H–Gly–Gly–Phe–Leu–OH, H–Phe–Gly–Gly–Phe–OH and H–Val–Ala–Ala–Phe–OH are more complex but show a substantial directional effect of the phenylalanine residue(s).

Intrinsic (Gas Phase) Thermodynamic Stability of 2-Adamantyl Cation. Its Bearing on the Solvolysis Rates of 2-Adamantyl Derivatives

The standard enthalpy of formation of gaseous 2-adamantyl chloride(2-Ad-Cl) was determined by calorimetric techniques. The standard Gibbs energy change for the chloride anion exchange between 1-adamantyl (1-Ad+) and 2-adamantyl (2-Ad+) cations in the gas phase was obtained by Fourier transform ion cyclotron resonance spectroscopy (FT ICR). Theoretical calculations at the G2(MP2) level were performed on these and other relevant species. This and data from the literature provided three highly consistent independent estimates of the relative stabilities of 2-Ad+ and 1-Ad+. This difference in gas-phase stability was compared to the differential structural effects on the rates of solvolysis of the corresponding chlorides and tosylates, and it was shown that the thermodynamic stability of the secondary cation is the leading factor determining the solvolytic reactivity of the precursors in the absence of solvent effects. Thus, under these conditions, the previously established linear free energy correlation between carbenium ion stability and solvolytic reactivity of bridgehead derivatives applies also to secondary derivatives.

Prediction of trace metal partitioning between minerals and aqueous solutions: a linear free energy correlation approach

Trace metal partitioning between authigenic minerals and aqueous solutions is of great interest to both geochemical and environmental communities. In this paper, we have developed a linear free energy correlation model that correlates metal partition coefficients with metal cation properties: −2.303 RT log K d + ΔG f,M Z+ 0 = a ∗ M H X Δ G n,M Z+ 0 + β ∗ M H X r M Z+ + b ∗ M H X where a ∗ M H X , β ∗ M H X , and b ∗ M H X are constants, which can be determined by a regression analysis. For isovalent metal partitioning, because of the constraint of K d = 1 for the host metal, this correlation can be also expressed as: −2.303 RT log K d = a ∗ M H X (Δ G n,M H Z+ 0 − Δ G n,M 0 ) + β ∗ M H X ( r M Z+ − r n,M H Z+ ) − (Δ G f,M Z+ 0 − Δ G 0 f,M H Z+ ). Host minerals from an isostructural family have the same linear free energy relationship, as long as the relationship is expressed as a function of the differences in cation properties between substituent and host metals. We have applied our model to both isovalent and non-isovalent metal partitioning in carbonate minerals. The model closely fits experimental data, demonstrating the robustness of the proposed linear free energy relationship. Using the model, we have predicted the partition coefficients of divalent and trivalent metals between various carbonate minerals and aqueous solutions. The differences between the predicted and experimental values are generally less than 1 logarithmic unit for divalent cations and less than 0.4 logarithmic unit for trivalent cations. Magnesite is predicted to have the largest partition coefficients among the carbonate minerals with a calcite structure and therefore, can be a good scavenger for toxic metals. The kinetic effect on metal partitioning can be described graphically by a “seesaw” line anchored at a host cation. To explain the rate dependence of partition coefficients, we have proposed a conceptual model that relates metal partitioning to surface adsorption. The conceptual model suggests that as the rate of host mineral precipitation increases, the ratio of substituent to host cation in a solid approaches what is in the adsorbed layer. The linear free energy correlation model developed in this paper provides a useful tool for systematizing the existing experimental data and for predicting unknown partition coefficients.

Application of a linear free energy correlation to actinide mononitrides

Application of a linear free energy correlation to actinide mononitrides

Dissociation of the peptide bond in protonated peptides.

The dissociation of the amide (peptide) bond in protonated peptides, [M + H](+), is discussed in terms of the structures and energetics of the resulting N-terminal b(n) and C-terminal y(n) sequence ions. The combined data provide strong evidence that dissociation proceeds with no reverse barriers through interconverting proton-bound complexes between the segments emerging upon cleavage of the protonated peptide bond. These complexes contain the C-terminal part as a smaller linear peptide (amino acid if one residue) and the N-terminal part either as an oxazolone or a cyclic peptide (cyclic amide if one residue). Owing to the higher thermodynamic stability but substantially lower gas-phase basicity of cyclic peptides vs isomeric oxazolones, the N-terminus is cleaved as a protonated oxazolone when ionic (b(n) series) but as a cyclic peptide when neutral (accompanying the C-terminal y(n) series). It is demonstrated that free energy correlations can be used to derive thermochemical data about sequence ions. In this context, the dependence of the logarithm of the abundance ratio log[y(1)/b(2)], from protonated GGX (G, glycine; X, varying amino acid) on the gas-phase basicity of X is used to obtain a first experimental estimate of the gas-phase basicity of the simplest b-type oxazolone, viz. 2-aminomethyl-5-oxazolone (b(2) ion with two glycyl residues).

Metal-centered redox chemistry of substituted cobalt phthalocyanines adsorbed on graphite and correlations with MO calculations and Hammett parameters. Electrocatalytic reduction of a disulfide

We have studied the metal-centered redox chemistry of unsubstituted cobaltphthalocyanine (CoPc) and the cobalt complexes of the substituted ligands, cobaltoctaethylhexyloxyphthalocyanine (CoOEHPc), cobalttetramethoxyphthalocyanine (CoMeOPc), cobalttetraneopentoxyphthalocyanine (CoTNPPc), cobalttetraaminophthalocyanine (CoTAPc), cobalttetrasulfonatophthalocyanine (CoTSPc) and cobalthexadecafluorophthalocyanine (CoPcF 16) adsorbed on ordinary pyrolytic graphite (OPG). These complexes exhibit two distinct metal-centered reversible redox processes attributed to the Co(II)/Co(I) and Co(III)/Co(II) couples. The redox potentials of these couples are shifted according to the electron withdrawing or donating character of the groups located at the periphery of the phthalocyanine ligand, as seen by comparison to molecular orbital theoretical calculations. Correlations between the redox potential and the Hammett parameters of the substituents provide good linear correlations. The slopes of the linear free energy correlations give values of 0.41 and 0.49 V σ −1 for the Co(III)/Co(II) and Co(II)/Co(I) redox couples, respectively. We have also tested the electrocatalytic activity of these adsorbed phthalocyanines for the reduction of 2-hydroxyethyldisulfide. A plot of log i (current density at constant potential) versus the Co(II)/Co(I) redox potential gives a linear correlation where the rate of the reaction increases with the driving force of the catalyst, suggesting that that the reaction takes place via an outer-sphere mechanism.

D-Amino acid oxidase: new findings.

The most recent research on D-amino acid oxidases and D-amino acid metabolism has revealed new, intriguing properties of the flavoenzyme and enlighted novel biotechnological uses of this catalyst. Concerning the in vivo function of the enzyme, new findings on the physiological role of D-amino acid oxidase point to a detoxifying function of the enzyme in metabolizing exogenous D-amino acids in animals. A novel role in modulating the level of D-serine in brain has also been proposed for the enzyme. At the molecular level, site-directed mutagenesis studies on the pig kidney D-amino acid oxidase and, more recently, on the enzyme from the yeast Rhodotorula gracilis indicated that the few conserved residues of the active site do not play a role in acid-base catalysis but rather are involved in substrate interactions. The three-dimensional structure of the enzyme was recently determined from two different sources: at 2.5-3.0 A resolution for DAAO from pig kidney and at 1.2-1.8 A resolution for R. gracilis. The active site can be clearly depicted: the striking absence of essential residues acting in acid-base catalysis and the mode of substrate orientation into the active site, taken together with the results of free-energy correlation studies, clearly support a hydrid transfer type of mechanism in which the orbital steering between the substrate and the isoalloxazine atoms plays a crucial role during catalysis.

Driving force effects in proton coupled electron transfer

The rates of reduction of the nickel(III) oxime–imine complexes, [NiIII(Me2L)]+ and [NiIII(Me2LH)]2+ by the corresponding iron(II) species are determined. Comparisons with rates calculated with the use of Marcus theory reveal that reactions of [FeII(Me2LH)]+, where the electron transfer product is the highly acidic [FeIII(Me2LH)]2+, show rate enhancements of several orders of magnitude. These are ascribed to a strong coupling of the electron transfer with the concomitant, thermodynamically favorable proton transfer. A free energy correlation supports this conclusion.

New mechanistic insights into the reactivity of the R2 protein of E. coli ribonucleotide reductase (RNR)

Further to a linear free-energy correlation of cross-reaction rate constants k 12 for the reaction of eight organic radicals (OR), e.g. MV + , from methyl viologen, with cytochrome c(III), we consider here similar studies for the reduction of the R2 protein of Escherichia coli ribonucleotide reductase, which has Fe III 2 and Tyr redox components. The same two techniques of pulse radiolysis and stopped-flow were used. Cross-reaction rate constants (22 °C) at pH 7.0, I=0.100 M (NaCl), were determined for the reduction of active-R2 with the eight ORs, reduction potentials E 0 1 from −0.446 to +0.194 V. Samples of active-R2 have an Fe III 2 met-R2 component, which in the present studies was close to 40%. Concurrent reactions have to be taken into account for the five most reactive ORs, corresponding to reduction of the Fe III 2 of met-R2 and then of active-R2. Separate experiments on met-R2 reproduced the first of these rate constants, which on average is ∼66% larger than the second rate constant. A single Marcus free-energy plot of log k 12−0.5 log 10 f versus − E 0 1/0.059 describes all the data and the slope of 0.54 is in satisfactory agreement with the theoretical value of 0.50. Such behaviour is unexpected since the Tyr is a much stronger oxidant ( E 0∼1.0 V versus NHE) as compared to Fe III 2 ( E 0 close to zero). X-ray structures of the met- and red-R2 states have indicated that electroneutrality of the ∼10 Å buried active site is maintained. Proton transfer is therefore proposed as a rapid sequel to electron transfer. Other reactions considered are the much slower conventional time-range reductions of active-R2 with hydrazine and dithionite. For these reactions one and/or two-equivalent changes are possible. With both reductants, met-R2 reacts about four-fold faster than active-R2, and as with the ORs the less strongly oxidising Fe III 2 component is reduced before the Tyr .

Mechanistic Implications of a Linear Free-Energy Correlation of Rate Constants for the Reduction of Active- and Met-R2 Forms ofE. coliRibonucleotide Reductase with Eight Organic Radicals

Cross-reaction rate constants k12 (22 °C) at pH 7.0 have been determined for the reduction of FeIII2 and tyrosyl-radical-containing active-R2 from E. coli ribonucleotide reductase with eight organic radicals (OR), e.g., MV•+ from methyl viologen. The more reactive OR's were generated in situ using pulse radiolysis (PR) techniques, and other OR's were generated by prior reduction of the parent with dithionite, followed by stopped-flow (SF) studies. In both procedures it was necessary to include consideration of doubly-reduced parent forms. Values of k12 are in the range 109 to 104 M-1 s-1 and reduction potentials Eo1 for the OR vary from −0.446 to +0.194 V. Samples of E. coli active-R2 also have an FeIII2 met-R2 component (with no Tyr•), which in the present work was close to 40%. From separate experiments met-R2 gave similar k12 rate constants (on average 66% bigger) to those for active-R2, suggesting that reduction of the FeIII2 center is the common rate-limiting step. A single Marcus free-energy plot of...

Structural chemistry of polycyclic heteroaromatic compounds. Part 10: photoelectron spectra and electronic structures of 1-substituted 1 H-benzotriazoles

The electronic structures of 1 H-benzotriazole ( 1) and its 1-substituted derivatives 2– 20 have been investigated by ultraviolet photoelectron spectroscopy and quantum chemical methods. The conformational properties of some compounds were studied by semi-empirical and B3LYP calculations. For the alkenyl derivative 14 a twisted conformation was ascertained both from IP values and calculations, and in the amino derivative 20 the amino group is twisted by 90° which is reflected by the absence of n/π interactions. With only a few exceptions, the ionization potentials corresponding to the five occupied π MOs (π 1–π 5) and the two n(N) orbitals of the 1 H-benzotriazole unit (Bt 1) could be determined and assigned for 1– 20. Linear free energy correlations of the IPs related to these orbitals with inductive substituent parameters σ I and F were satisfactory except for IP(π 3). The energies of π and n MOs—except for π 3—are thus affected primarily by the substituent's electronegativity. The different behaviour of π 3 is caused by direct interactions with substituent orbitals. For some substituents for which no σ I or F parameters were known these could be determined from their IPs by correlation analysis.

Universality, frustration, and conformal invariance in two-dimensional random Ising magnets

We consider long, finite-width strips of Ising spins with randomly distributed couplings. Frustration is introduced by allowing both ferromagnetic and antiferromagnetic interactions. Free energy and spin-spin correlation functions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponents $\ensuremath{\gamma}/\ensuremath{\nu},$ $\ensuremath{\alpha}/\ensuremath{\nu},$ and $\ensuremath{\nu}$ to be obtained, whenever a second-order transition is present. Low-temperature ordering persists for suitably small concentrations of frustrated bonds, with a transition governed by pure-Ising exponents. Contrary to the unfrustrated case, subdominant terms do not fit a simple, logarithmic-enhancement form. Our analysis also suggests a vertical critical line at and below the Nishimori point. Approaching this point along either the temperature axis or the Nishimori line, one finds nondiverging specific heats. A percolationlike ratio $\ensuremath{\gamma}/\ensuremath{\nu}$ is found upon analysis of the uniform susceptibility at the Nishimori point. Our data are also consistent with frustration inducing a breakdown of the relationship between correlation-length amplitude and critical exponents, predicted by conformal invariance for pure systems.

Linear free energy correlations in mass spectrometry

Linear free energy correlations have played a major role in the development of physical organic chemistry and have led to many of the now widely used concepts of reactivity. This paper reviews the application of linear free energy correlations to the field of gas-phase ion chemistry. The results indicate that many of the concepts developed to systematize liquid-phase properties and reactivities are applicable to gas-phase ionic systems. Copyright © 1999 John Wiley & Sons, Ltd.

Linear free energy correlations in mass spectrometry†Presented, in part, at the 46th ASMS Conference on Mass Spectrometry and Allied Topics, Orlando, FL, June 1998.

Linear free energy correlations in mass spectrometry†Presented, in part, at the 46th ASMS Conference on Mass Spectrometry and Allied Topics, Orlando, FL, June 1998.

Evidence for a charge-transfer intermediate in the catalytic epoxidation of alkenes by ruthenium complexes: a comparison between electrochemical and kinetic data

The catalytic oxidation of various olefins by iodosobenzene in the presence of the diphosphino complexes of ruthenium(II) [RuCl(LL) 2]PF 6, where LL is 1,3-bis(diphenylphosphino)propane (DPP) or 1-diphenylphosphino-2-(2′-pyridyl)ethane (PPY), gives rise to epoxides, obeying the Michaelis–Menten kinetic law. The calculated kinetic parameters ( K m) follow a free energy correlation with the one-electron oxidation potentials of the olefins, measured in the reaction conditions, thus suggesting that the reaction intermediate of the epoxidation is substantially charge-transfer in character.

Theoretical and experimental investigations of electrostatic effects on acetylcholinesterase catalysis and inhibition

The role of electrostatics in the function of acetylcholinesterase (AChE) has been investigated by both theoretical and experimental approaches. Second-order rate constants (kE=kcat/Km) for acetylthiocholine (ATCh) turnover have been measured as a function of ionic strength of the reaction medium for wild-type and mutant AChEs. Also, binding and dissociation rate constants have been measured as a function of ionic strength for the respective charged and neutral transition state analog inhibitors m-(N,N,N-trimethylammonio)trifluoroacetophenone (TMTFA) and m-(t-butyl)trifluoroacetophenone (TBTFA). Linear free-energy correlations between catalytic rate constants and inhibition constants indicate that kE for ATCh turnover is rate limited by terminal binding events. Comparison of binding rate constants for TMTFA and TBTFA attests to the sizable electrostatic discrimination of AChE. Free energy profiles for cationic ligand release from the active sites of wild-type and mutant AChEs have been calculated via a model that utilizes the structure of T. californica AChE, a spherical ligand, and energy terms that account for electrostatic and van der Waals interactions and chemical potential. These calculations indicate that EA and EI complexes are not bound with respect to electrostatic interactions, which obviates the need for a ‘back door’ for cationic ligand release. Moreover, the computed energy barriers for ligand release give linear free-energy correlations with log(kE) for substrate turnover, which supports the general correctness of the computational model.

Ureas and amides as dipolar aprotic solvents in highly basic media. The dependence of kinetic basicity on solvent composition

The basicity of dipolar aprotic solvent–water–HO– systems with amides and ureas as the organic component has been studied kinetically because previous information is not available, excluding some H– values measured for aqueous dimethylformamide (DMF) and tetramethylurea (TMU). It was found that the increase in basicity with the mole fraction of organic component is at least of the same magnitude as in aqueous dimethyl sulfoxide (DMSO). For instance, in the detritiation of chloroform-t the slopes of the plots log(k2/mol–1 dm3 s–1) vs.x(urea) varied between 11.4–14.6 (as compared to 11.0 in aqueous DMSO) when TMU and cyclic ureas, 1,3-dimethylimidazolidin-2-one (DMI) and 1,3-dimethyl-3,4,5,6-tetrahydropyrimidin-2(1H)-one (DMPU), were used as the organic component in solvent mixture. In aqueous TMU acidity functions H– were extrapolated from kinetic results using linear free energy correlations. Agreement with literature values was evident. This method was also used to extrapolate the H– values in aqueous DMPU. On the basis of present work aqueous ureas can be recommended as solvents in highly basic media. The utility of amides, dimethylformamide and dimethylacetamide, is limited by their instability in basic water solutions.

ChemInform Abstract: Linear Free Energy Correlations in Liquid‐Phase Catalytic Hydrogenation of Aromatic Compounds

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Substituent effects on the electrochemical oxidation ofN,N?,N?-triphenyl-1,3,5-triaminobenzenes

Correlation analysis of the oxidation potentials of a series of N,N′,N″-triphenyl-1,3,5-triaminobenzenes (TPABs) substituted at the para positions of the outer phenyl rings shows a linear free energy relationship with resonance-enhanced substituent parameters (σ+). Reaction parameters (ρ+) for oxidation of TPABs were found to be −1.53, −1.45 and −1.34 (per substituent) in methylene chloride, acetonitrile and propylene carbonate respectively. The resonance enhancement and small magnitude of the ρ+ values are related to a significant but weak delocalization of charge onto the outer phenyl rings in the molecular orbitals of radical cations resulting from the oxidation of TPABs. Data on the oxidation of p-substituted triphenylamines were treated similarly and gave a ρ+ value of −3.27 (per substituent) in acetonitrile, greater than that for TPABs owing to a more significant delocalization of charge onto the phenyl rings in the molecular orbitals of the corresponding radical cations. To demonstrate their predictive value, these linear free energy correlations were used to estimate the oxidation potentials of similarly substituted N,N,N′,N′,N″,N″-hexaphenyl-1,3,5-triaminobenzenes, which are of interest as building blocks for molecular magnetic materials. © 1998 John Wiley & Sons, Ltd.