On the nature of the Møller-Plesset critical point

It has been suggested [F. H. Stillinger, J. Chem. Phys. 112, 9711 (2000)] that the convergence or divergence of M?ller-Plesset perturbation theory is determined by a critical point at a negative value of the perturbation parameter z at which an electron cluster dissociates from the nuclei. This conjecture is examined using configuration-interaction computations as a function of z and using a quadratic approximant analysis of the high-order perturbation series. Results are presented for the He, Ne, and Ar atoms and the hydrogen fluoride molecule. The original theoretical analysis used the true Hamiltonian without the approximation of a finite basis set. In practice, the singularity structure depends strongly on the choice of basis set. Standard basis sets cannot model dissociation to an electron cluster, but if the basis includes diffuse functions then it can model another critical point corresponding to complete dissociation of all the valence electrons. This point is farther from the origin of the z plane than is the critical point for the electron cluster, but it is still close enough to cause divergence of the perturbation series. For the hydrogen fluoride molecule a critical point is present even without diffuse functions. The basis functions centered on the H atom are far enough from the F atom to model the escape of electrons away from the fluorine end of the molecule. For the Ar atom a critical point for a one-electron ionization, which was not previously predicted, seems to be present at a positive value of the perturbation parameter. Implications of the existence of critical points for quantum-chemical applications are discussed.     

Are the solvent effects critical in the modeling of polyoxoanions?

DFT calculations were driven for a set of differently charged polyoxoanions in the gas phase and in solution. We have calculated and analyzed their geometries and orbital energies to trace simple rules of behavior regarding the modeling of anions in isolated form. We discuss the quality of the results depending on the molecular charge, q, and the size of the cluster in terms of the number of metal centers, m. When the q/m ratio reaches a value of approximately 0.8, DFT calculations for the isolated anion fail to describe the gap between the band of occupied oxo orbitals and the set of unoccupied orbitals delocalized among the metal atoms. In these cases the incorporation of the stabilizing external fields generated by the solvent through continuum models improves the geometries and orbital energies.     

Is the ring conformation the most critical parameter in lipase-catalysed acylation of cycloalkanols?

CAL-B catalysed the resolution of several five and six-membered cyclic beta-hydroxy esters efficiently with the exception of the cis-cyclohexanol (+/-)-4. When employing molecular modelling techniques the conformation turned out to be the most important determinant for their reactivity towards O-acetylation. In all cases, the R enantiomers reacted faster than the S enantiomers since the reactive intermediates of the former can adopt more favourable ring conformations and thus experience less steric hindrance in the active site. Furthermore, the minimised structure for the main conformer of R-4 showed that the axial hydrogens in the 3 and 5-positions with respect to the hydroxyl group prevent the enzymatic reaction.     

Can the speed of sound be used for detecting critical states of fluid mixtures?

The phenomenology of sound speeds in fluid mixtures is examined near and across critical lines. Using literature data for binary and ternary mixtures, it is shown that the ultrasound speed along an isotherm-isopleth passes through a minimum value in the form of an angular (or V-shaped) point at critical states. The relation between critical and pseudo-critical coordinates is discussed. For nonazeotropic fixed-composition fluid mixtures, pseudo-critical temperatures and pressures are found to be lower than the corresponding critical temperatures and pressures. The analysis shows that unstable pseudo-critical states cannot be detected using acoustic methods. The thermodynamic link between sound speeds and isochoric heat capacities is formulated and discussed in terms of p-Vm-T derivatives capable of being calculated using cubic equations of state. Based on the Griffiths-Wheeler theory of critical phenomena, a new specific link between critical sound speeds and critical isochoric heat capacities is deduced in terms of the rate of change of critical pressures and critical temperatures along the p-T projection of the critical locus of binary fluid mixtures. It is shown that the latter link can be used to obtain estimates of critical isochoric heat capacities from the experimental determination of critical speeds of sound. The applicability domain of the new link does not include binary systems at compositions along the critical line for which the rate of change in pressure with temperature changes sign. The new equation is combined with thermodynamic data to provide approximate numerical estimates for the speed of sound in two mixtures of carbon dioxide and ethane at different temperatures along their critical isochores. A clear decrease in the sound speed is found at critical points. A similar behavior is suggested by available critical heat capacity data for several binary fluid mixtures. Using an acoustic technique, the critical temperature and pressure were determined for three different mixtures of methane and propane, and compared with literature data obtained using conventional methods. It is concluded that acoustic-based techniques are reliable to determine, for the most part, critical surfaces of fluid mixtures. The remaining few cases where the present analysis cannot be applied could be tested by the thermodynamic calculation of critical sound speeds using crossover equations of state in conjunction with experimentally determined critical isochoric heat capacities.     

A critical analysis of the effect of crosslinking on the linear viscoelastic behavior of styrene–butadiene rubber and other elastomers

The linear viscoelastic behavior in dynamic shear and tensile creep at temperatures from −30 to 70 °C is measured for an styrene–butadiene rubber (SBR) elastomer cured with dicumyl peroxide to crosslinking densities between 0 and 23.5 × 10⁻⁵ mol/cm³. The G′, G″, and tan δ isotherms are analyzed by time–temperature superposition (TTS), where the tan δ master curves are consistent with those of Mancke and Ferry. However, to achieve the TTS in the lightly crosslinked SBR systems, an anomalous vertical shift is required in the narrow temperature region from 10 to 30 °C. The vertical shift factor in this temperature region is not the standard from rubber elasticity. No anomalous behavior is detected in the equilibrium modulus, which is a linear function of temperature in accordance with the classical theory of rubber elasticity. In contrast to SBR, standard vertical shifts are required to effect TTS for uncrosslinked polybutadiene and an ethylene propylene diene monomer elastomer. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

How critical is the use of commercially available enzymes for selenium speciation?

The aim of this work was to check whether commercially available enzymes are pure enough to be used for selenium speciation analysis and the contribution that impurities could make to Se determination in real samples. For this purpose, twelve commercially available enzymes with different origins and classifications (protease, amylase, cellulase, lipase) were analysed. After the dissolution of the enzyme in water, the Se species were separated by ion exchange chromatography, with inductively coupled plasma mass spectrometry used as the detection system. The results showed that the Se content was significant in several cases. The highest value was obtained for β-amylase from barley, 3100 ng Se per g of enzyme. Speciation analysis showed that Se-methionine, selenite, selenate and some unknown compounds were present in several enzymes. In general, the Se species identified represented a small fraction of the total Se. For instance, only 17% of the total Se was determined for β-amylase from barley. On the other hand, about 100% of the total Se was identified in protease from Streptomyces griseus. Upon comparing the results from different lots of the same enzyme, not all of them were found to be comparable. Thus, the presence of selenium species in commercially available enzymes could be due to the preparation procedure used for the enzyme; they could be present as degradation products. Therefore, when determining selenium species in samples with low Se contents, attention should be paid to enzyme purity in relation to selenium compounds when an enzyme is used for hydrolysis.     

A critical study of the application of ultraviolet spectroscopy to the self-association of adenine,adenosine and 5′-AMP in aqueous solution

UV spectra of adenine, adenosine and 5′-AMP in aqueous solution have been measured over the concentration range 1 × 10⁻⁶−5 × 10⁻² M. The apparent molar absorptivity of these compounds changes upon concentration, showing two hypochromic effects at c < 5 × 10⁻³ M and c &>; 5 × 10⁻³ M, respectively, which may be explained in terms of self-association.A method for calculating self-association constants from these experimental data is developed, based on an association model in which the first hypochromic effect is interpreted in terms of formation of dimers, with an equilibrium constant K₂, and the second effect is interpreted in terms of formation of polymers, with an equilibrium constant K_n. The value of K₂ is of the order of magnitude of 10⁴ for the three compounds. The value of K_n is dependent on the model chosen for the analysis of the second effect, having an order of magnitude of 10².The features of the self-association model are discussed, as well as the method for calculating self-association parameters from experimental data.     

Application of the Wilson—Wegner expansion to represent vapor—liquid equilibrium surfaces of binary and ternary systems from the critical locus to the vapor pressure of the heavier component

The Torquato—Stell modification of the Wilson—Wegner expansion has been used to present and to represent the vapor—liquid equilibrium surfaces of several binary methane—alkane mixtures and one ternary system from the critical locus to the heavier component's vapor pressure within the experimental accuracy of the data. Inconsistent phase compositions are revealed without recourse to equations of state computations. Since the critical point of the mixtures are not precisely known, an isothermal regression analysis of the data is first used to obtain an improved estimate of the critical point of mixtures using the scaled expressions. Then, along isotherms, the phase compositions are analyzed in terms of the reduced proximity to the critical pressure. Subsequently, the entire compositional surfaces are presented in terms of both the reduced proximity to the critical pressure of the mixture and the reduced proximity to the critical temperature of the heavier component.     

FT-IR spectra of NaCl�CH2O in the region from near to beyond the critical state

Water and NaCl?CH₂O solutions and their molecular spectra at high temperatures and pressures were observed and examined using a new design of hydrothermal diamond anvil cell (HDAC) connected to both a light and an infrared microscope. We have modified the diamond window of the HDAC to have a wide angle to allow the infrared beam to pass the window. Fourier-transform infrared (FT-IR) spectra of NaCl?CH₂O?CD₂O were examined at high temperatures and pressures up to 850 °C and 3 GPa. The effect of increasing temperature on water spectra differed from that of increasing pressure. The O?CH stretching frequency of water molecules increases with increasing temperature (from 20 to 600 °C), and also with increasing salinity of the solution.     

Beta-phenyl quenching of triplet excited ketones: how critical is the geometry for deactivation?

The phenomenon of beta-phenyl quenching has been examined by laser-flash photolysis in a series of alpha- and/or beta-substituted ketones 4-8 with similar excited-state characteristics. It is found that alpha-substitution markedly increases the triplet lifetimes in contrast to beta-substitution. The force field calculations for the various staggered conformers of ketones 4-6 and 8-syn show that the lowest-energy conformation in all these ketones has the carbonyl group and the beta-phenyl ring gauche to each other. Despite this geometrical requirement, the longer lifetimes observed are interpreted as being due to the influence of the alpha-substituent on the rotational freedom of the planar benzoyl moiety as a whole. The experimental results are suggestive of the attainment of what appears to be a critical geometry for quenching. This scenario may be likened to Norrish type II reactions, where the alpha-substituent has long been known to suppress the elimination pathway and promote Yang cyclization. In addition, we have shown that the diastereomers of alpha,beta-disubstituted ketones exhibit distinct lifetimes.     

Are the asserted advantages of organic solvents in capillary electrophoresis real? A critical discussion

Background electrolytes (BGEs) prepared in pure organic solvents are common alternatives to aqueous BGEs in capillary electrophoresis. Several general advantages of organic solvents over water have been asserted in the literature, namely (i) organic solvents increase the separation selectivity; (ii) organic solvents increase the separation efficiency; (iii) high separation voltages and/or high BGE ionic strengths can be used in organic solvents due to lower electric current compared to water. Related assumptions are that (iv) due to higher field strengths applicable in organic solvents the analysis time is shorter than in aqueous BGEs, and (v) the solubility and/or stability of components (either analytes or BGE chemicals) is higher/better in organic solvents. In the present work, these asserted advantages were critically evaluated based on the physical principles of ion transport and zone dispersion in solution. The result was that many of the above-mentioned general advantages are overestimated or even inexistent; often they have no fundamental basis.     

Relationship between the density of supercritical CO_2 + ethanol binary system and its critical properties

The solvent strength and selectivity of supercritical fluids (SCF) can be greatly enhanced by addition of one or two entrainers into the system. The amount of entrainer added is usually less than 5% (mole fraction). However, even with such slight amount, solubility of organic solutes has been observed to increase by several orders magnitude[1]. Therefore, critical pressure and tem-perature data of these supercritical fluid + cosolvent systems are imperative for the reasonable design of effici…     

Anharmonic treatment of vibrational resonance polyads—the diborane: a critical case for numerical methods

Based on accurate computational results, the IR spectra of diborane B₂H₆ and its deuterated derivative B₂D₆ were experimentally revisited to reconsider or complete their band assignments. A pure, variational approach, developed in both mechanical and electrical anharmonicities, was applied to study the diborane molecule for which many uncertainties remain in the spectral IR assignment. This work, together with all the experiments on this system over recent decades, shows the difficulty of interpreting the spectral data, making it a “benchmark” ideal for testing the mathematical approaches for the implementation of vibrational codes.     

Use of normal boiling point correlations for predicting critical parameters of paraffins for vapour–liquid equilibrium calculations with the SRK equation of state

Correlations between normal boiling points and critical parameters (critical temperatures and critical pressures) and between normal boiling points and acentric factors of normal and branched paraffins in the range from C₇ to C₁₀₀ have been developed. These correlations can be used to quickly and easily compute critical properties that allow to reproduce closely, by means of the Soave–Redlich–Kwong (SRK) equation of state (EoS), the vapour pressure of pure compounds. In the range of 0.5–5 mmHg the values of vapour pressure calculated by means of the SRK EoS become less accurate and they can be improved using a different equation for the temperature-depending attractive parameter (i.e., the Mathias–Copeman alpha function) instead of the classical Soave function.     

The critical re-evaluation of the aromatic/antiaromatic nature of Ti3(CO)3: a missed opportunity?

The nature of bonding and aromaticity of Ti(3)(CO)(3), a mill-shaped metal-carbonyl complex, is studied carefully. A unique bonding mechanism between metal and carbonyl groups is found in this species. Ti(3)(CO)(3) is an example of a metal-carbonyl complex with prominent metal to carbonyl donation. Moreover, it is proven that not only is Ti(3)(CO)(3) not an antiaromatic complex but also it is the first synthesized example of d-block, σ+π aromatic species. A quick survey among the first row of transition metals in the periodic table shows that other local minima with similar structures and aromaticity are present and Ti(3)(CO)(3) is the first synthesized species of an unknown family.     

How does the critical point change during a chemical reaction in supercritical fluids? A study of the hydroformylation of propene in supercritical CO(2).

An understanding of homogeneous catalysis in supercritical fluids requires a knowledge of the phase behavior and the variation in critical point as the reaction proceeds. In this paper, the critical temperatures, T(c) and pressures, P(c), have been measured for a considerable number of mixtures representing the various stages of the hydroformylation reaction of propene in supercritical CO(2) and different reactant concentrations. Critical point data have also been measured for all of the binary mixtures of the components (CO(2), H(2), CO, propene, n- and isobutyraldehyde) which are not available from the literature or can be deduced from published data. We use the stoichiometry of the reacting system to simplify greatly the phase behavior problem by defining a path through the otherwise multidimensional "phase space". Satisfactory modeling of the data (0.3% in T(c) and 3.0% in P(c)) has been achieved using the Peng-Robinson equation of state and ignoring all binary interactions which do not involve CO(2). The model is used to explore the strategies needed to avoid phase separation in continuous and batch reactions. At a given temperature, a batch reactor may need to be run under much higher pressures than a flow reactor if single-phase conditions are to be preserved throughout the course of the reaction. Most of the critical point data were measured acoustically, but a selection of points were validated using more traditional view-cell procedures.     

Density,viscosity and electrical conductivity of isobutyric acid–water with added ions in the critical regions

Density, viscosity and electrical conductivity of the six concentrated binary ionic mixtures of isobutyric acid–water with X M [KCl] at the critical concentrations were measured as functions of temperature (ΔT = T ? T _c ≤ 2 K) and at various compositions, X, in the critical regions. The molar volumes have been calculated from their densities. The molar volume data dependence of viscosity and conductivity has been fitted to an equation similar to the Vogel–Tammann–Fulcher (VTF) based on the free volume model. The concentration of ions (K⁺, Cl^?), dependence of the Vogel temperature, the intrinsic volume and the transport properties are primarily governed by the existence of intermolecular interactions.     

Near critical electrolytes: Are the charge-charge sum rules obeyed?

In an electrolyte solution the charge-charge structure factor obeys S(ZZ)(k;T,ρ)=0+ξ(Z,1) (2)k(2)-ξ(Z,2) (4)k(4)+? , where ξ(Z, 1) and ξ(Z, 2) are the second- and fourth-moment charge-charge correlation lengths depending on the temperature T and the overall ion density ρ. The vanishing of the leading term, the first Stillinger-Lovett (SL) sum rule, simply reflects bulk electroneutrality. The second SL rule, or second-moment condition, dictates that ξ(Z, 1) = ξ(D), where the Debye screening length ξ(D) is proportional to T/ρ. In this paper we present results from grand canonical Monte Carlo simulations of a fully size and charge symmetric 1:1 (finely-discretized) hard-sphere electrolyte, or restricted primitive model. By design, electroneutrality is imposed during the simulations, so satisfying the first sum rule automatically. However, careful finite-size scaling analyses of extensive histogram reweighted data indicate that the second-moment condition is violated at criticality, ξ(Z,1) (c) exceeding ξ(D) (c) by approximately 8%. It is also found that ξ(Z,2) (4) diverges to +∞ as T → T(c) in a manner closely mirroring the density-density fluctuations, S(NN)(0). These findings contradict generalized Debye-Hu?ckel theory and also the exactly soluble charge-symmetric spherical models, both of which support the second-moment condition at criticality and the finiteness of the fourth-moment. Nevertheless, the observed behavior is strikingly similar to that of the charge-asymmetric spherical models.