Time dependence of the NMR line shape for systems with chemical exchange in a zero saturation limit

An expression has been derived for the time dependence of the NMR line shape for systems with many-site chemical exchange in the absence of spin-spin coupling, in a zero saturation limit. The dynamics of variation of the NMR line shape with time is considered in detail for the case of two-site chemical exchange. Mathematica programs have been designed for numerical simulation of the NMR spectra of chemical exchange systems. The analytical expressions obtained are useful for NMR line shape simulations for systems with photoinduced chemical exchange.     

Characterization of conformational exchange of a histidine side chain: protonation, rotamerization, and tautomerization of His61 in plastocyanin from Anabaena variabilis

A model describing conformational exchange of His 61 in plastocyanin from Anabaena variabilis is presented. A detailed picture of the exchange dynamics has been obtained using solution NMR relaxation measurements, chemical shift titrations, and structural information provided by a high-resolution crystal structure of the protein. A three-site model for chemical exchange that involves interconversion among the tautomeric and protonated forms of the histidine side chain with rates that are fast on the NMR chemical shift time scale can account for all of the data. In general, in the limit of fast exchange, it is not possible to obtain separate measures of chemical shift differences and populations of the participating states using NMR. However, we show here that when the data mentioned above are combined, it is possible to extract values of all of the parameters that characterize the exchange process, including rates, populations, and chemical shift changes, and to provide cross-validations that establish their accuracy. The methodology is generally applicable to the study of histidine side chain dynamics, which can play an important functional role in many protein systems.     

Use of exchange maximization to generate starting vectors for self-consistent field calculations on metal cluster/adsorbate systems

Localized molecular orbitals (LMOs) derived from exchange maximization with respect to all atom-centered basis functions in the basis set are shown to generate a good starting electronic field for self-consistent field calculations on extended systems such as metal clusters, for which well-defined chemical bonds are not present. Examples studied are a cluster of 20 Ni atoms and the Pt(97)CO, Ag(43)/H(3)CNON, Ag(91)/H(2)CO, and vinylidene/Ni metal cluster plus adsorbate systems. It is also shown that improved starting vectors can be obtained by remixing a subset of the LMOs with the largest exchange eigenvalues through diagonalization of the Fock matrix computed with a null electronic field. Employing only a subset of the exchange-maximized LMOs in the first iterations, and then gradually expanding the space in which the diagonalizations are carried out in succeeding cycles, is shown to be an effective means of guiding the SCF procedure to the converged full-basis solution.     

Calculation of two-dimensional infrared spectra of ultrafast chemical exchange with numerical Langevin simulations

We combine numerical Langevin simulations with numerical integration of the Schrodinger equation to calculate two-dimensional infrared spectra of ultrafast chemical exchange. This provides a tool to model and interpret such spectra of molecules undergoing chemical processes, such as isomerization and solvent exchange reactions. Two-dimensional infrared spectroscopy has already been used to extract reaction rates for ultrafast chemical reactions. We demonstrate that these spectra are not only sensitive to the rates, but also to the finite duration of the exchange. This is emphasised by comparing with the popular Kubo two-state jump models, which do not account for finite exchange times.     

Graph Methodology and Principles of Linear Nonequilibrium Thermodynamics in the Theory of Flow-Injection Analysis

It is shown that chemical, configurational, and informational properties of flow-injection systems can be interrelated with the use of the methodology of the graph theory. The main equation of the theory is derived using a mathematical expression of the transition paths from the analyte to the detection of a product of the analytical reaction. Examples of specific developments are discussed for redox reactions, ligand exchange reactions, and heterogeneous exchange reactions, with due regard to, the hidden peculiarities of their chemical mechanisms that are essential for flow analysis and also for on-line preconcentration by coprecipitation. It is also shown that the conditions obtained in a flow system correspond to the basic postulates of linear nonequilibrium thermodynamics, which provides a basis for a new approach to the theory of flow analysis. An example of a complexation reaction was used for discussing the possibility that a linear interrelation exists between flows and forces in a flow system, which corresponds to the Onsager reciprocal relation.     

Modelling of surface exchange reactions and diffusion in composites and polycrystalline materials

Abstract  Surface exchange reactions and chemical diffusion in composites, consisting of a dilute distribution of inclusions in a matrix, and polycrystalline materials have been modelled by application of both a square grain and a spherical grain model. The diffusion equations have been solved numerically by employing a finite element approach in the case of the square grain model and the Laplace transform method involving numerical Laplace inversion with respect to the spherical grain model. The boundary conditions refer to oxygen exchange reactions between a gas phase and a mixed ionically–electronically conducting ceramic sample within the linear response regime, i.e. small variations of the oxygen partial pressure. Diffusion profiles as well as the time dependence of the total amount of exchanged oxygen (relaxation curves) have been calculated. A necessary requirement for effective medium diffusion is proposed, and appropriate relations for the effective chemical surface exchange coefficient and the effective chemical diffusion coefficient are derived. On the contrary, when the time constant for diffusion from the matrix into the inclusions of a composite exceeds considerably the relaxation time for effective medium diffusion, relaxation curves with two separate time constants are observed. Analogously, in the case of polycrystalline materials the overall transport process is determined by slow (rate-limiting) bulk diffusion from the grain boundaries into the grains. Adequate formulae for the relaxation times are given based on analytical approximations of the solution functions to the diffusion equations. In addition, the spherical grain model is applied to interpret the re-oxidation kinetics of the positive temperature coefficient of resistivity (PTC) ceramics based on conductivity relaxation experiments. Graphical abstract        

Elongation of β-hydroxyenones by cross-metathesis

Enantioenriched aldol products derived from enones are notoriously difficult to prepare due to their sensitivity to retro-aldolisation, elimination and the requirement of a large excess of the enone donor for their preparation. However, some success has been obtained for the preparation of aldol products derived from methylvinylketone and pentenone using zinc-dinuclear catalysts or catalytic antibodies. Herein, we describe how simple first-generation hydroxyenones can be easily elongated by alkene exchange with structurally diverse olefinic partners in the presence of Ru-based metathesis catalysts allowing for the preparation of aldol products difficult to access by direct aldolisation. The data suggest that even though unprotected aldols are suitable for these cross-metathesis reactions, silyl-protected β-hydroxyenones generally afforded the desired elongated products in much higher chemical yields.     

Polymeric Schiff Bases. III. Some Prototype Exchange Reactions of Schiff Bases

The amine moiety in Schiff bases can be exchanged quantitatively by another amine to yield new Schiff bases if the volatility of the replacing amine is lower than the derived amine, thereby allowing the latter to distilled from the reaction mass. This amine exchange was shown to be quantitative also for diamines and di-Schiff bases. Similarly, quantitative conversions were found for aldehydes and acetal exchanges with Schiff bases for both monofunctional and difunctional reactants. The bis exchange, involving two complementary Schiff bases, was quantitative also when the reactants were so selected that one of the new derived Schiff bases could be removed by distillation. The bis exchange was demonstrated with mono and di-Schiff bases.

Mechanisms are suggested for these Schiff base exchange reactions: attempts to isolate the proposed intermediates physically were unsuccessful; however spectroscopic evidence indicates the formation of intermediate compounds.

The Schiff base exchanges involving polyfunctional reactants are of interest in the synthesis of polymers.     

Density functional perturbational orbital theory of spin polarization in electronic systems. II. Transition metal dimer complexes

We present a theoretical scheme for a semiquantitative analysis of electronic structures of magnetic transition metal dimer complexes within spin density functional theory (DFT). Based on the spin polarization perturbational orbital theory [D.-K. Seo, J. Chem. Phys. 125, 154105 (2006)], explicit spin-dependent expressions of the spin orbital energies and coefficients are derived, which allows to understand how spin orbitals form and change their energies and shapes when two magnetic sites are coupled either ferromagnetically or antiferromagnetically. Upon employment of the concept of magnetic orbitals in the active-electron approximation, a general mathematical formula is obtained for the magnetic coupling constant J from the analytical expression for the electronic energy difference between low-spin broken-symmetry and high-spin states. The origin of the potential exchange and kinetic exchange terms based on the one-electron picture is also elucidated. In addition, we provide a general account of the DFT analysis of the magnetic exchange interactions in compounds for which the active-electron approximation is not appropriate.     

Separating degenerate (1)H transitions in methyl group probes for single-quantum (1)H-CPMG relaxation dispersion NMR spectroscopy

A relaxation dispersion pulse scheme is presented for quantifying chemical exchange processes in proteins that exploits 1H chemical shifts as probes of changes in conformation. The experiment selects 1H single-quantum magnetization from the I = 1/2 manifolds of the methyl group, which behave like AX spin systems, while suppressing coherences that derive from the 3/2 manifold that are extremely sensitive to pulse imperfections and that would otherwise severely compromise the accuracy of the experiment. The utility of the sequence is first demonstrated with an application to a protein system that is known not to undergo chemical exchange and flat dispersion profiles are obtained. Subsequently, the methodology is applied to study the folding of a G48M mutant of the Fyn SH3 domain that has been shown previously to undergo exchange between folded and unfolded states on the millisecond time scale.     

On the combined use of discrete solvent models and continuum descriptions of solvent effects in ligand exchange reactions: a case study of the uranyl(VI) aquo ion

Modeling of the solvent is important when using quantum chemical methods for the assignment of mechanisms from experimental studies of the exchange of water between metal aquo ions and the bulk solvent. In the present study, we have investigated if and how the mechanisms for water exchange in the UO₂(OH₂) ₅ ²⁺ –H₂O system is affected by the choice of chemical models for the second coordination sphere and physical models for describing the cavity in conductor-like polarizable continuum (CPCM) models. In the first case, we have compared models with one and five waters in the second coordination sphere. For both models, we have compared cavities in which each atom is assigned one spherical cavity and one in which the water molecules are described by a single spherical cavity (the United Atom model). There are significant differences in the relative energy of dissociative and associative intermediates; however, they are not large enough to affect the conclusion that the water exchange proceeds through an associative/interchange mechanism.     

槲皮素在溶液中的化学交换和自扩散运动

通过对溶于氘代二甲亚砜（DMSO d6）中的槲皮素的自扩散系数和槲皮素羟基质子与溶剂中水质子之间的交换速率常数的NMR测量,研究了交换速率常数与扩散系数随温度和含水量的变化情况.结果表明,化学交换与扩散系数是相互独立的两种运动,活泼质子的化学交换并不需要通过槲皮素分子的扩散而进行.但是活泼质子的表观扩散系数却显著地受化学交换的影响.当以活泼质子为对象时,这种影响需要引起足够的重视.     

Ion exchange properties of crystalline bismuth molybdenum hydrous oxide and its intercalates: Equilibrium and kinetics of UO 2 2+ ions on the crystals

The sorption of uranyl ions on crystalline bismuth molybdenum hydrous oxide and its intercalates were investigated from point of view of both equilibrium and kinetics. Ion exchange isotherms of uranyl ions on the crystals were obtained, and ionic sieve effect was employed to describe the characteristics of ion exchange isotherms. The best fitting for sorption of uranyl ions on BMHO was achieved by means of the Langmuir isotherm, while the Freundlich isotherm appeared to best fit for its intercalates. The slightly negative free-energy change indicates that, thermodynamically, the crystals behave less favourable for uranyl ions. The equation derived from S_N2 chemical reactions was proved to fit the rate curves, and the rate constants were determined. The comparison between the calculated and observed pH values as a function of time further verified the chemical reaction mechanism.     

A Markov model for relaxation and exchange in NMR spectroscopy

A two-state Markov noise process for lattice fluctuations and chemical exchange dynamics is used to derive a stochastic Liouville equation describing the evolution of the spin-density operator in nuclear magnetic resonance spectroscopy. Relaxation through lattice fluctuations and chemical exchange processes is incorporated into the theory at the same fundamental level, and the results are valid for all time scales provided that lattice fluctuations are much faster than chemical exchange kinetics. Time-scale separation emerges as an essential feature from the lowest-order perturbation expansion of the average resolvent in the Laplace domain.     

Spin-echo NMR studies of chemical exchange in cyclohexane,dioxane and water

Prevously derived equations for NMR chemical-exchange effects are used in proton spin-echo studies at 60 and 90 MHz of the chair-to-chair isomerisation of cyclohexane, dioxane and proton chemical exchange of water. The isomerisation rates are found to be 2.5 × 10⁶ and 1.8 × 10⁶ for cyclohexane and dioxane respectively and the proton exchange rate in water is found to be 1.9 × 10⁶s^?1. The rates are compared with the results of several previous studies at low fields.     

Accuracy of SUPREX (stability of unpurified proteins from rates of H/D exchange) and MALDI mass spectrometry-derived protein unfolding free energies determined under non-EX2 exchange conditions

Described here is the impact of so-called non-EX2 exchange behavior on the accuracy of protein unfolding free energies (i.e., DeltaG u values) and m values (i.e.,-deltaDeltaG u/delta[denaturant] values) determined by an H/D exchange and mass spectrometry-based technique termed stability of unpurified proteins from rates of H/D exchange (SUPREX). Both experimental and theoretical results on a model protein, ubiquitin, reveal that reasonably accurate thermodynamic parameters for its folding reaction can be determined by SUPREX even when H/D exchange data is collected in a non-EX2 regime. Not surprisingly, the theoretical results reported here on a series of hypothetical protein systems with a wide range of biophysical properties show that the accuracy of SUPREX-derived DeltaG u and m values is compromised for many proteins when analyses are performed at high pH (e.g., pH 9) and for selected proteins with specific biophysical parameters (e.g., slow folding rates) when analyses are performed at lower pH. Of more significance is that the experimental and theoretical results reveal a means by which problems with non-EX2 exchange behavior can be detected in the SUPREX experiment without prior knowledge of the protein's biophysical properties. The results of this work also reveal that such problems with non-EX2 exchange behavior can generally be minimized if appropriate H/D exchange times are employed in the SUPREX experiment to yield SUPREX curve transition midpoints at chemical denaturant concentrations less than 2 M.     

A model investigation of ab initio geometries for identity and nonidentity substitution with three‐center four‐ and three‐electron transition states

With the van't Hoff model derived from the dynamics of a regular tetrahedron in which the interstitial carbon changes its position from tetrahedral into a trigonal (bi)pyramidal configuration, the introduction of dimensionless ratio numbers (R) can serve to localize significant points on the principal reaction coordinate. These numbers are expressed as R(d) and R(n) based on transition state geometries and the number of electrons involved in the three‐center bonding, respectively. Using this concept, we obtain a model for the evaluation of different ab initio calculations based on identity and nonidentity substitution reactions for three‐center four‐ and three‐electron bonding transition states. Similar ratio numbers have been derived for proton exchange reactions. The reactions under investigation show clearly that in spite of the differences in chemical outcome the transition steps reduced to the first principles of chemical bonding are similar. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011