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Thermodynamic study of the complexation of trivalent actinide and lanthanide cations by ADPTZ, a tridentate N-donor ligand.

To better understand the bonding in complexes of f-elements by polydentate N-donor ligands, the complexation of americium(III) and lanthanide(III) cations by 2-amino-4,6-di-(pyridin-2-yl)-1,3,5-triazine (ADPTZ) was studied using a thermodynamic approach. The stability constants of the 1:1 complexes in a methanol/water mixture (75/25 vol %) were determined by UV-visible spectrophotometry for every lanthanide(III) ion (except promethium), and yttrium(III) and americium(III) cations. The thermodynamic parameters (DeltaH degrees , DeltaS degrees) of complexation were determined from the temperature dependence of the stability constants and by microcalorimetry. The trends of the variations of DeltaG degrees , DeltaH degrees , and DeltaS degrees across the lanthanide series are compared with published results for other tridentate ligands and confirm strongly ionic bonding in the lanthanide-ADPTZ complexes. Comparison of the thermodynamic properties between the Am- and Ln-ADPTZ complexes highlights an increase in stability of the complexes by a factor of 20 in favor of the americium cation. This difference arises from a more exothermic reaction enthalpy in the case of Am, which is correlated with a greater degree of covalency in the americium-nitrogen bonds. Quantum chemistry calculations performed on a series of trivalent actinide and lanthanide-ADPTZ complexes support the experimental results, showing a slightly greater covalence in the actinide-ligand bonds that originates from a charge transfer from the ligand sigma orbitals to the 5f and 6d orbitals of the actinide ion.

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Thermodynamics, kinetics, and dynamics of the two alternative aniomesolytic fragmentations of C-O bonds: an electrochemical and theoretical study.

Fragmentation reactions of radical anions (mesolytic cleavages) of cyanobenzyl alkyl ethers (intramolecular dissociative electron transfer, heterolytic cleavages) have been studied electrochemically. The intrinsic barriers for the processes have been established from the experimental thermodynamic and kinetic parameters. These values are more than 3 kcal/mol lower as an average than the related homolytic mesolytic fragmentations of radical anions of 4-cyanophenyl ethers. In the particular case of isomers 4-cyanobenzyl phenyl ether and 4-cyanophenyl benzyl ether, the difference in intrinsic barriers amounts to 5.5 kcal/mol, and this produces an energetic crossing where the thermodynamically more favorable process (homolytic) is the kinetically slower one. The fundamental reasons for this behavior have been established by means of theoretical calculations within the density functional theory framework, showing that, in this case, the factors that determine the kinetics are clearly different (mainly present in the transition state) from those that determine the thermodynamics and they are not related to the regioconservation of the spin density ("spin regioconservation principle"). Our theoretical results reproduce quite well the experimental energetic difference of barriers and demonstrate the main structural origin of the difference.

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Comparison of the kinetics and thermodynamics for methyl radical addition to C=C, C=O, and C=S double bonds.

The barriers, enthalpies, and rate constants for the addition of methyl radical to the double bonds of a selection of alkene, carbonyl, and thiocarbonyl species (CH(2)=Z, CH(3)CH=Z, and (CH(3))(2)C=Z, where Z = CH(2), O, or S) and for the reverse beta-scission reactions have been investigated using high-level ab inito calculations. The results are rationalized with the aid of the curve-crossing model. The addition reactions proceed via early transition structures in all cases. The barriers for addition of methyl radical to C=C bonds are largely determined by the reaction exothermicities. Addition to the unsubstituted carbon center of C=C double bonds is favored over addition to the substituted carbon center, both kinetically (lower barriers) and thermodynamically (greater exothermicities). The barriers for addition to C=O bonds are influenced by both the reaction exothermicity and the singlet-triplet gap of the substrate. Addition to the carbon center is favored over addition to the oxygen, also both thermodynamically and kinetically. For the thiocarbonyl systems, addition to the carbon center is thermodynamically favored over addition to sulfur. However, in this case, the reaction is contrathermodynamic, addition to the sulfur center having a lower barrier due to spin density considerations. Entropic differences among corresponding addition and beta-scission reactions are relatively minor, and the differences in reaction rates are thus dominated by differences in the respective reaction barriers.

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Thermodynamic clarification of the curious ferric/potassium ion exchange accompanying the electrochromic redox reactions of prussian blue, iron(III) hexacyanoferrate(II).

The recent Glasser-Jenkins method for lattice-energy prediction, applied to an examination of the solid-state thermodynamics of the cation exchanges that occur in electrochromic reactions of Prussian Blue, provides incisive thermodynamic clarification of an ill-understood ion exchange that accompanies particularly the early electrochromic cycles. A volume of 0.246 +/- 0.017 nm(3) formula unit(-1) for the ferrocyanide ion, Fe(II)[(CN)(6)],(4-) is first established and then used, together with other formula unit-volume data, to evaluate the changes of standard enthalpy, entropy, and Gibbs energy in those ion-exchange reactions. The results impressively show by how much the exchange of interstitial Fe(3+) ions by alkali metal ions, usually exemplified by K+, is thermodynamically favored.

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Highly effective pincer-ligated iridium catalysts for alkane dehydrogenation. DFT calculations of relevant thermodynamic, kinetic, and spectroscopic properties.

The p-methoxy-substituted pincer-ligated iridium complexes, (MeO-(tBu)PCP)IrH(4) ((R)PCP = kappa(3)-C(6)H(3)-2,6-(CH(2)PR(2))(2)) and (MeO-(iPr)PCP)IrH(4), are found to be highly effective catalysts for the dehydrogenation of alkanes (both with and without the use of sacrificial hydrogen acceptors). These complexes offer an interesting comparison with the recently reported bis-phosphinite "POCOP" ((R)POCOP = kappa(3)-C(6)H(3)-2,6-(OPR(2))(2)) pincer-ligated catalysts, which also show catalytic activity higher than unsubstituted PCP analogues (Gottker-Schnetmann, I.; White, P.; Brookhart, M. J. Am. Chem. Soc. 2004, 126, 1804). On the basis of nu(CO) values of the respective CO adducts, the MeO-PCP complexes appear to be more electron-rich than the parent PCP complexes, whereas the POCOP complexes appear to be more electron-poor. However, the MeO-PCP and POCOP ligands are calculated (DFT) to show effects in the same directions, relative to the parent PCP ligand, for the kinetics and thermodynamics of a broad range of reactions including the addition of C-H and H-H bonds and CO. In general, both ligands favor (relative to unsubstituted PCP) addition to the 14e (pincer)Ir fragments but disfavor addition to the 16e complexes (pincer)IrH(2) or (pincer)Ir(CO). These kinetic and thermodynamic effects are all largely attributable to the same electronic feature: O --> C(aryl) pi-donation, from the methoxy or phosphinito groups of the respective ligands. DFT calculations also indicate that the kinetics (but not the thermodynamics) of C-H addition to (pincer)Ir are favored by sigma-withdrawal from the phosphorus atoms. The high nu(CO) value of (POCOP)Ir(CO) is attributable to electrostatic effects, rather than decreased Ir-CO pi-donation or increased OC-Ir sigma-donation.

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Thermodynamics of diamond nucleation on the nanoscale.

To have a clear insight into the diamond nucleation upon the hydrothermal synthesis and the reduction of carbide (HSRC), we performed the thermodynamic approach on the nanoscale to elucidate the diamond nucleation taking place in HSRC supercritical-fluid systems taking into account the capillary effect of the nanosized curvature of the diamond critical nuclei, based on the carbon thermodynamic equilibrium phase diagram. These theoretical analyses showed that the nanosize-induced interior pressure of diamond nuclei could drive the metastable phase region of the diamond nucleation in HSRC into the new stable phase region of diamond in the carbon phase diagram. Accordingly, the diamond nucleation is preferable to the graphite phase formation in the competing growth between diamond and graphite upon HSRC. Meanwhile, we predicted that 400 MPa should be the threshold pressure for the diamond synthesis by HSRC in the metastable phase region of diamond, based on the proposed thermodynamic nucleation on the nanoscale.

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Thermodynamics of rhodium hydride reactions with CO, aldehydes, and olefins in water: organo-rhodium porphyrin bond dissociation free energies.

Tetra(p-sulfonato-phenyl) porphyrin rhodium hydride ([(TSPP)Rh-D(D2O)](-4)) (1) reacts in water (D2O) with carbon monoxide, aldehydes, and olefins to produce metallo formyl, alpha-hydroxyalkyl, and alkyl complexes, respectively. The hydride complex (1) functions as a weak acid in D2O and partially dissociates into a rhodium(I) complex ([(TSPP)Rh(I)(D2O)](-5)) and a proton (D+). Fast substrate reactions of 1 in D2O compared to reactions of rhodium porphyrin hydride ((por)Rh-H) in benzene are ascribed to aqueous media promoting formation of ions and supporting ionic reaction pathways. The regioselectivity for addition of 1 to olefins is predominantly anti-Markovnikov in acidic D2O and exclusively anti-Markovnikov in basic D2O. The range of accessible equilibrium thermodynamic measurements for rhodium hydride substrate reactions is substantially increased in water compared to that in organic media through exploiting the hydrogen ion dependence for the equilibrium distribution of species in aqueous media. Thermodynamic measurements are reported for reactions of a rhodium porphyrin hydride in water with each of the substrates, including CO, H2CO, CH3CHO, CH2=CH2, and sets of aldehydes and olefins. Reactions of rhodium porphyrin hydrides with CO and aldehydes have nearly equal free-energy changes in water and benzene, but alkene reactions that form hydrophobic alkyl groups are substantially less favorable in water than in benzene. Bond dissociation free energies in water are derived from thermodynamic results for (TSPP)Rh-organo complexes in aqueous solution for Rh-CDO, Rh-CH(R)OD, and Rh-CH2CH(D)R units and are compared with related values determined in benzene.

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Thermodynamics of alpha-Cyclodextrin-p-Nitrophenyl Glycoside Complexes. A Simple System To Understand the Energetics of Carbohydrate Interactions in Water.

Thermodynamic studies of the binding of a series of p-nitrophenyl glycosides (PNPGly) of varying stereochemistry to alpha-cyclodextrin (alpha-CD) were performed at three different temperatures (25, 35, and 42 degrees C) using a microcalorimetric technique. The system p-nitrophenol (PNP) at pH = 3 and alpha-CD was also studied for the sake of comparison. All these complexes were found to be enthalpy driven with a favorable enthalpic term clearly dominant over an unfavorable entropic term. A clear enthalpy-entropy compensation effect was observed at all the temperatures, with a slope close to unity (alpha = 1.02) and an intercept TDeltaS degrees (o) = 2.91 kcal mol(-)(1). This thermodynamic pattern is in agreement with those usually found for lectin-carbohydrate associations and for the binding processes of several host-guest systems. This pattern is explained in terms of the contribution of primarily two driving forces: the van der Waals interactions between the host and the guest, and the solvation/desolvation processes which accompany the association reaction. The presence of the carbohydrate molecule in the PNP ring causes a slight destabilization of the complex at 25 degrees C with respect to the alpha-CD-PNP (pH = 3) complex, although a different behavior has been observed depending on the axial/equatorial configuration of the glycoside and the temperature. This behavior is modulated by the stereochemistry of the glycoside. Differences were observed between the deoxy-derivatives (LAra and LFuc) and those derivatives with a hydroxymethyl group (Glc, Gal, Man). DeltaC(p) degrees values were obtained from the dependency of DeltaH degrees on temperature (=( partial differentialDeltaH degrees / partial differentialT)(p)). These values are small and negative except for alphaMan complex. For the latter complex, discrepancy between the calorimetric and the calculated van't Hoff enthalpies was observed. Parallels are drawn between the thermodynamics of our model and those proposed for carbohydrate-protein associations.

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Tautomeric equilibrium of pyridoxine in water. Thermodynamic characterization by 13C and 15N nuclear magnetic resonance

A remarkable temperature dependence on the 13C NMR and 15N NMR chemical shifts of pyridoxine in water (pH = 7.0) has been observed. C-3, C-6, and N-1 were the most sensitive nuclei to the temperature effect. This dependence has been explained on the basis of an equilibrium shift thermally induced between the neutral and the dipolar form of this molecule. The thermodynamic characterization of tautomeric equilibria that interconvert quickly on the NMR time scale can be carried out from the observed average 13C NMR and 15N NMR chemical shifts at different temperatures (5-90 degrees C). We have developed a new method for the estimation of the thermodynamic parameters of a given equilibrium by fitting the experimental data to a theoretical curve. This new method allows us to improve the fitting results on our previously proposed methodology. We show that there are linear correlations between the average chemical shifts obtained from different nuclei at the same temperature. This indicates that the parameters of the pure forms are related among them. We have carried out a simultaneous multiple function curve fitting of all data obtained from the most sensitive signals together using these linear correlations as restricted conditions in order to diminish the number of independent parameters to fit. To test the new methodology, we have studied the thermodynamics of the tautomeric equilibrium of pyridoxine in water. We have obtained delta H degree values ranging from -23.6 +/- 1.3 to -25.8 +/- 1.7 kJ/mol for this equilibrium depending on the used data set. This kind of methodology has, among others, the following advantages: It allows the use of a great number of experimental points from different signals in the fitting process, it yields very precise and accurate values of the tautomeric process, and it allows the resolution of the problem with only 13C NMR data in some cases saving NMR time.

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Theoretical studies on the vibrational spectra, thermodynamic properties, detonation properties, and pyrolysis mechanisms for polynitroadamantanes.

To look for high energy density materials (HEDM), the relationships between the structures and the performances of polynitroadamantanes (PNAs) were studied. The assigned infrared spectra of PNAs obtained at the density functional theory (DFT) B3LYP/6-31G level were used to compute the thermodynamic properties on the basis of the principle of statistical thermodynamics. The thermodynamic properties are linearly related with the number of nitro groups as well as with the temperatures. Detonation properties of PNAs were evaluated by using the Kamlet-Jacobs equation based on the calculated densities and heats of formation for titled compounds, and it is found that only when the number of nitro groups of PNA is equal to or more than eight can it be possible for PNAs to be used as HEDMs. The relative stabilities of PNAs were studied by the pyrolysis mechanism using the UHF-PM3 method. The homolysis of the C-NO2 bond is predicted to be the initial step of thermal decomposition. The activation energies (Ea) for the homolysis decrease with the number of nitro groups being increased on the whole. The stability order of dinitroadamantane isomers derived from the interactions among nitro groups is consistent with what is determined by Ea. The relations between the Ea's and the electronic structure parameters were discussed. In combination with the stability, PNA (1,2,3,4,5,6,7,8,9,10-) is recommended as the target of HEDM with insensitivity.

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Kinetic and thermodynamic assessments of the mediator-template assembly of nanoparticles.

The understanding of kinetic and thermodynamic factors governing the assembly of nanoparticles is important for the design and control of functional nanostructures. This paper describes a study of the kinetic and thermodynamic factors governing the mediator-template assembly of gold nanoparticles into spherical assemblies in solutions. The study is based on spectrophotometric measurements of the surface plasmon (SP) resonance optical property. Gold nanoparticle cores ( approximately 5 nm) encapsulated with tetraoctylammonium bromide shells were studied as a model system. The mediator-template assembly involves a thioether-based multidentate ligand (e.g., MeSi(CH2SMe)3) which functions as a mediator, whereas the tetraoctylammonium bromide capping molecules function as template agents. On the basis of the temperature dependence of the SP optical property in the mediator-template assembly process, the kinetic and thermodynamic parameters such as the reaction rate constant and reaction enthalpy have been determined. The results led to two important findings. First, the mediator-template assembly of nanoparticles is an enthalpy-driven process. Second, the enthalpy change (-1.3 kcal/mol) is close to the magnitude of the van der Waals interaction energy for alkyl chains and the condensation energy of hydrocarbons. Implications of the findings to the understanding of the interparticle interactions have also been discussed.

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Thermal vacancy effects on the thermodynamic properties and stability of fullerites.

We study the influence of thermal vacancies on equilibrium thermodynamic properties of the high-temperature phase of fullerites taking into account the strong anharmonicity of the lattice vibrations. Treating a crystal with point defects as a quasi-multicomponent system and using the correlative method of the unsymmetrized self-consistent field and the Girifalco interaction potential for the molecular subsystem, we have obtained the vacancy formation parameters for the C(60) fullerite. We also take into account the divacancies. The influence of the lattice defects on the specific heats of fullerites is negligible, since a dominant contribution to them is given by intramolecular degrees of freedom. We have calculated the contributions of vacancies to various thermodynamic properties, the volume thermal expansion coefficient, the isothermal bulk modulus, and the components of the isothermal elastic tensor, depending on the temperature and pressure. Near the estimated triple point, these contributions run to more than 10% and increase still further at a metastable region. We also discuss the influence of defects on the thermodynamic stability of fullerites.

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Sensitivity analysis of thermodynamic properties of liquid water: a general approach to improve empirical potentials.

A sensitivity analysis of bulk water thermodynamics is presented in an effort to understand the relation between qualitative features of molecular potentials and properties that they predict. The analysis is incorporated in molecular dynamics simulations and investigates the sensitivity of the Helmholtz free energy, internal energy, entropy, heat capacity, pressure, thermal pressure coefficient, and static dielectric constant to components of the potential rather than the parameters of a given functional form. The sensitivities of the properties are calculated with respect to the van der Waals repulsive and the attractive parts, plus short- and long-range Coulomb parts of three four site empirical water potentials: TIP4P, Dang-Chang and TTM2R. The polarization sensitivity is calculated for the polarizable Dang-Chang and TTM2R potentials. This new type of analysis allows direct comparisons of the sensitivities for different potentials that use different functional forms. The analysis indicates that all investigated properties are most sensitive to the van der Waals repulsive, the short-range Coulomb and the polarization components of the potentials. When polarization is included in the potentials, the magnitude of the sensitivity of the Helmholtz free energy, internal energy, and entropy with respect to this part of the potential is comparable in magnitude to the other electrostatic components. In addition similarities in trends of observed sensitivities for nonpolarizable and polarizable potentials lead to the conclusion that the complexity of the model is not of critical importance for the calculation of these thermodynamic properties for bulk water. The van der Waals attractive and the long-range Coulomb sensitivities are relatively small for the entropy, heat capacity, thermal pressure coefficient and the static dielectric constant, while small changes in any of the potential contributions will significantly affect the pressure. The analysis suggests a procedure for modification of the potentials to improve predictions of thermodynamic properties and we demonstrate this general approach for modifying potentials for one of the potentials.

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Design of oxygen reduction bimetallic catalysts: ab-initio-derived thermodynamic guidelines.

The Gibbs free energies of key elementary steps for the electrocatalytic oxygen reduction reaction (ORR) are calculated with B3LYP type of density functional theory: O2 + M + H+ + e- (0 eV) --> HOO-M (deltaG1), HOO-M + M --> HO-M + O-M (deltaG2), O2 + 2M + H+ + e- (0 eV) --> O-M + HO-M (deltaG3), and HO-M + O-M + 3H+ + 3e- (0 eV) --> 2H2O + 2M (deltaG4), where H+ is modeled as H3(+)O(H2O)3 and M stands for the adsorption site of a metal catalyst modeled by a single metal atom as well as by an M3 cluster. Taking Pt as a reference, deltaG4 is plotted against deltaG1 for 17 metals from groups V to XII. It is found that no single metal has both deltaG1 and deltaG4 more negative than Pt, although some of them have either more negative deltaG1 or more negative deltaG4. This enables us to explain thermodynamically why no other single metal catalyzes the ORR as effectively as Pt does. Moreover, a thermodynamic analysis reveals that the signs of delta deltaG (the difference between deltaG of other metals and deltaG of Pt) strongly correlate with the valence electronic structure of metals, i.e., delta deltaG1 < 0 and delta deltaG4 > 0 for metals M with vacant valence d orbitals, whereas delta deltaG1 > 0 and delta deltaG4 < 0 for metals M' with fully occupied valence d orbitals. Thus, a simple thermodynamic rule for the design of bimetallic catalysts for the ORR is proposed: couple a metal M (delta deltaG1 < 0) with a second metal M' (delta deltaG4 < 0) to form an alloy catalyst MM'3. The rationale behind this selection is based on M being more efficient for the rate-determining step, i.e., for the formation of the adsorbed species M-OOH, while M' can enhance the reductions of O and OH in the last three electron-transfer steps.

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Thermodynamic stability of fluid-fluid phase separation in binary athermal mixtures: the role of nonadditivity.

We studied the thermodynamic stability of fluid-fluid phase separation in binary nonadditive mixtures of hard-spheres for moderate size ratios. We are interested in elucidating the role played by small amounts of nonadditivity in determining the stability of fluid-fluid phase separation with respect to the fluid-solid phase transition. The demixing curves are built in the framework of the modified-hypernetted chain and of the Rogers-Young integral equation theories through the calculation of the Gibbs free energy. We also evaluated fluid-fluid phase equilibria within a first-order thermodynamic perturbation theory applied to an effective one-component potential obtained by integrating out the degrees of freedom of the small spheres. A qualitative agreement emerges between the two different approaches. We also addressed the determination of the freezing line by applying the first-order thermodynamic perturbation theory to the effective interaction between large spheres. Our results suggest that for intermediate size ratios a modest amount of nonadditivity, smaller than earlier thought, can be sufficient to drive the fluid-fluid critical point into the thermodinamically stable region of the phase diagram. These findings could be significant for rare-gas mixtures in extreme pressure and temperature conditions, where nonadditivity is expected to be rather small.

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Ab initio theoretical study of temperature and density dependence of molecular and thermodynamic properties of water in the entire fluid region: autoionization processes.

The temperature and density dependence of the molecular and thermodynamic properties of water is investigated theoretically by means of the ab initio electronic structure theory combined with the reference interaction site model method, so-called RISM-SCF. We consider the autoionization process (H2O + H2O right harpoon over left harpoon H3O+ + OH-) by regarding H2O, H3O+, and OH- as "solute" molecules in an aqueous solution and evaluate molecular geometry, electronic structure, solvation structure, and the ionic product of water (pKw) of these species as functions of thermodynamic conditions. In our previous paper, we calculated these properties by using essentially the same method in a wide range of density values (0.6-1.4 g/cm3). However, the calculation was limited at rather higher density (>0.6 g/cm3) due to the difficulty of convergence, which is inherent to the hypernetted-chain (HNC) closure. The problem is overcome in this study by employing the Kovalenko-Hirata (KH) closure which hybridizes the HNC and the mean-spherical approximation (MSA). Here, we present the results for the thermodynamic range of densities from 0.025 to 1.0 g/cm3 and for temperatures from 300 to 800 K including the supercritical point.

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The pi-pi stacked geometries and association thermodynamics of quinacridone derivatives studied by 1H NMR.

The pi-pi stacked associations of three N,N'-di(n-butyl) quinacridone derivatives, widely used dopants in organic light-emitting diodes, with different sizes of substituents were investigated in solution at various temperatures by (1)H NMR spectroscopy. The pi-pi stacked geometries were estimated by both the magnitudes of peak shifts with concentration and the directions of peak shifts induced by polar solvents. Two patterns of geometries with different pi-pi interaction strengths were found to coexist in solution for all the three samples. In both of the patterns, the preferential orientation of the stacking is the approach of the carbonyl groups on one molecule to the nitrogen atoms on the stacked partner, which makes the pi-deficient aromatic atoms interact with both pi-rich and pi-deficient aromatic atoms of the stacked partner to maximize the electrostatic complementarity. Differently, whereas the molecules in one pattern are face-to-face stacked in a parallel fashion and slip two rings relative to one another along with the long axis of the conjugated ring systems, the molecules in the other are either face-to-face stacked in an antiparallel fashion with slight slipping between layers or stacked in a turning fashion. Both association constants obtained by fitting the dilution curves and thermodynamic parameters obtained from van't Hoff analyses revealed unexpectedly three thermodynamic processes of aggregations for all the three samples in the temperature region of 298-213 K. The size of substituents on the outer aromatic rings significantly influences the pi-pi stacked structures and association thermodynamics.

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Thermodynamic analysis of the chemical exchange of beta-phosphorylated cyclic nitroxides by using two-dimensional (temperature versus magnetic field) simulation of ESR spectra: the impact of labile solvent-solute interactions on molecular dynamics.

A complete thermodynamic characterization of the chair-to-chair interconversion in beta-diphosphorylated piperidine-N-oxyl radicals was achieved by means of the analysis of temperature-dependent ESR spectra. A new two-dimensional simulation method was developed with the coordinates temperature and magnetic field, in which the entire set of spectra was simulated simultaneously by adjusting the coefficients in the power expansion, giving the temperature-dependent ESR parameters and the thermodynamic and kinetic parameters determining the site populations and exchange rates, respectively. The new method promotes elimination of the ambiguities inherent in the spectroscopic determination of thermodynamic parameters. Labile solvent-solute interactions can strongly influence the chemical exchange, producing a complex network of symmetric and asymmetric interconversions. The solvent dependence of magnetic relaxation was also analyzed.

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