Investigation of the concentration dependence of mass transfer coefficients in reversed-phase liquid chromatography

In order to investigate the concentration dependence of mass transfer coefficients in RPLC, experimental breakthrough curves obtained by staircase frontal analysis (FA) were fitted to the simplified models such as multiplate (MP) model, equilibrium dispersive (ED) model, and transport model, and the sophisticated models such as lumped pore diffusion (POR) model and general rate (GR) model. The MP model was used to obtain the initial guesses of the parameters of the ED and the transport models. Then the best values were obtained by minimizing the differences between theoretical and experimental values with a nonlinear fitting procedure. The values of the parameters of the POR and the GR models can be calculated by using the expressions derived from the plate height equations, which was further validated by using the fitting method. It was found that the mass transfer coefficients would depend on the solute concentration. This can be ascribed to the surface diffusivity, which correlates with the concentration and is lumped into the mass transfer coefficients for both simplified and sophisticated models.     

Influence of the substituted side group on the molecular structure and electronic properties of TPP and related implications on organic zeolites use

Tris(o-phenylenedioxy)cyclotriphosphazene (TPP) became a compound of choice to investigate the structural features of organic zeolite and their potential applications. Different TPP-like materials are studied in this Letter from the electron-donor (E-D) capacity viewpoint, since this was reported as a stabilizing parameter of the TPP-Lewis acid inclusion compound up to high temperatures. On the basis of DFT-PBE0/6-31G(d,p) calculations, the results reported herein show a tight dependence of the E-D of the entire molecule on that of the side group. It was shown that both the O/NH substitution and the extension of the phenylenedioxyl group with an aromatic ring significantly enhance the E-D. As a result, the corresponding clathrates, including some reported ones, may also be exploited for the same issue, with an even wider range of operating temperatures when trapping compounds of Lewis acidity character comparable to that of I2. Furthermore, it was concluded that these two strategies may significantly enhance the E-D capacity without altering the tolerance of TPP-like host materials to the guest molecules.     

Second-order many-body perturbation study of solid hydrogen fluoride under pressure

A linear-scaling, embedded-fragment, second-order many-body perturbation (MP2) method with basis sets up to aug-cc-pVTZ is applied to the antiparallel structure of solid hydrogen fluoride and deuterium fluoride under 0-20 GPa of ambient pressure. The optimized structures, including the lattice parameters and molar volume, and phonon dispersion as well as phonon density of states (DOS), are determined as a function of pressure. The basis-set superposition errors are removed by the counterpoise correction. The structural parameters at 0 GPa calculated by MP2 agree accurately with the observed, making the predicted values at higher pressures a useful pilot for future experiments. The corresponding values obtained by the Hartree-Fock method have large, systematic errors. The MP2/aug-cc-pVDZ frequencies of the infrared- and Raman-active vibrations of the three-dimensional solids are in good agreement with the observed and also justify previous vibrational analyses based on one-dimensional chain models; the non-coincidence of the infrared and Raman mode pairs can be explained as factor-group (Davydov) splitting. The exceptions are one pair of modes in the librational region, for which band assignments based on a one-dimensional chain model need to be revised, as well as the five pseudo-translational modes that exist only in a three-dimensional treatment. The observed pressure dependence of Raman bands in the stretching region, which red-shift with pressure, is accounted for by theory only qualitatively, while that in the pseudo-translational region is reproduced with quantitative accuracy. The present calculation proves to be limited in explaining the complex pressure dependence of the librational modes. The hydrogen-amplitude-weighted phonon DOS at 0 GPa is much less structured than the DOS obtained from one-dimensional models and may be more realistic in view of the also broad, structureless observed inelastic neutron scattering spectra. All major observed peaks can be straightforwardly assigned to the calculated peaks in the DOS. With increasing pressure, MP2 predicts further broadening of bands and breach of the demarcation between the pseudo-translational and librational bands.     

Insights into the cycloaddition reaction mechanism between ketenimine and unsaturated hydrocarbon: A theoretical study

The cycloaddition reaction mechanisms between interstellar molecule ketenimine and unsaturated hydrocarbon (ethyne and ethylene) have been systematically investigated employing the second-order Møller-Plesset perturbation theory (MP2) method. Geometry optimizations and vibrational analyses have been performed for the stationary points on the potential energy surfaces of the system. The calculated results show that it can be produced the five-membered cyclic carbene intermediates through pericyclic reaction processes between ketenimine and ethyne (or ethylene). For the reaction between ketenimine and ethyne, through the following H-transferred processes, carbene intermediate can be isomerized to the pyrrole compounds. For the reaction between ketenimine and ethylene, carbene intermediate can be isomerized to the pyrroline compounds. The present study is helpful to understand the reactivity of nitrogenous cumulene ketenimine and the formation of prebiotic species in interstellar space.     

Quantum-chemical studies of methyl and silyl torsional frequencies and the structures of disilylsulphide and trisilylphosphine

Torsional frequencies of methyl and silyl groups occurring in a range of molecules have been calculated by HF, B3LYP and MP2 methods using several basis sets. Linear correlations between calculated and observed values are derived and used to predict unobserved or dubious frequencies. The current experimental value for the E torsion in trimethylphosphine is questioned. The relative merits of the B3LYP and MP2 methods are explored. MP2 calculations can show wide variation with respect to basis set. In cases where two or more silyl groups are attached to a common atom, as in disilylsulphide (SiH3)2S, disilylmethane (SiH3)2CH2, trisilylmethane (SiH3)3CH and tetrasilylmethane (SiH3)4C, marked differences occur between B3LYP and MP2 estimates. These may be linked to concomitant differences in conformation or potential barrier restraining internal rotation. In disilylmethane the B3LYP results agree much better with experiment than those from the MP2 method. HF and B3LYP calculations for disilylsulphide and trisilylphosphine give normal C2v and C3v equilibrium structures, respectively, but in MP2 structures the silyl groups are twisted through 6-13 degrees yielding C2 and C3 configurations. It may be possible to distinguish between these structures through the observation of isolated SiH stretching frequencies in the spectra of fully deuterated materials. Dispersion forces could contribute to the twisting calculated by the MP2 method. Further studies of the microwave and vibrational spectra of disilylsulphide and trisilylphosphine isotopomers are needed.     

Application of a single model to study the adsorption kinetics of prednisolone on six carbonaceous materials

The knowledge of the adsorption processes of nonelectrolytes from liquid solution on solid materials involves the study of their kinetic and equilibrium aspects as well as the understanding of their thermodynamic functions. However, in most published papers adsorption isotherms are analyzed by using the Giles classification and other proposed equations which are either empirical or based on kinetic or thermodynamic criteria. Our opinion is that both the kinetic and the equilibrium studies must be complementary and that, in general, equations describing the adsorption isotherms come from the kinetic laws governing the different partial processes which determine the global process. These kinetic laws may be derived from single models. In this paper a single model is proposed, which makes it possible to establish a kinetic law satisfactorily fitting a great number of C (concentration) vs t (time) isotherms. This model has been applied to study the adsorption process of prednisolone by six carbonaceous materials from ethanol solution, the specific adsorption rate, and the activation thermodynamic functions being calculated. The results obtained have also been used to analyze the influence of the intraparticle diffusion on the kinetics of the process.     

Is it possible to predict the average surface hydrophobicity of a protein using only its amino acid composition?

Hydrophobicity is one of the most important physicochemical properties of proteins. Moreover, it plays a fundamental role in hydrophobic interaction chromatography, a separation technique that, at present time, is used in most industrial processes for protein purification as well as in laboratory scale applications. Although there are many ways of assessing the hydrophobicity value of a protein, recently, it has been shown that the average surface hydrophobicity (ASH) is an important tool in the area of protein separation and purification particularly in protein chromatography. The ASH is calculated based on the hydrophobic characteristics of each class of amino acid present on the protein surface. The hydrophobic characteristics of the amino acids are determined by a scale of aminoacidic hydrophobicity. In this work, the scales of Cowan-Whittaker and Berggren were studied. However, to calculate the ASH, it is necessary to have the three-dimensional protein structure. Frequently this data does not exist, and the only information available is the amino acid sequence. In these cases it would be desirable to estimate the ASH based only on properties extracted from the protein sequence. It was found that it is possible to predict the ASH from a protein to an acceptable level for many practical applications (correlation coefficient > 0.8) using only the aminoacidic composition. Two predictive tools were built: one based on a simple linear model and the other on a neural network. Both tools were constructed starting from the analysis of a set of 1982 non-redundant proteins. The linear model was able to predict the ASH for an independent subset with a correlation coefficient of 0.769 for the case of Cowan-Whittaker and 0.803 for the case of Berggren. On the other hand, the neural model improved the results shown by the linear model obtaining correlation coefficients of 0.831 and 0.836, respectively. The neural model was somewhat more robust than the linear model particularly as it gave similar correlation coefficients for both hydrophobicity scales tested, moreover, the observed variabilities did not overcome 6.1% of the mean square error. Finally, we tested our models in a set of nine proteins with known retention time in hydrophobic interaction chromatography. We found that both models can predict this retention time with correlation coefficients only slightly inferior (11.5% and 5.5% for the linear and the neural network models, respectively) than models that use the information about the three-dimensional structure of proteins.     

Construction and Evaluation of Merged Pharmacophore Based on Peroxisome Proliferator Receptor-Alpha Agonists

Pharmacophore is a commonly used method for molecular simulation, including ligand-based pharmacophore (LBP) and structure-based pharmacophore (SBP). LBP can be utilized to identify active compounds usual with lower accuracy, and SBP is able to use for distinguishing active compounds from inactive compounds with frequently higher missing rates. Merged pharmacophore (MP) is presented to integrate advantages and avoid shortcomings of LBP and SBP. In this work, LBP and SBP models were constructed for the study of peroxisome proliferator receptor-alpha (PPARα) agonists. According to the comparison of the two types of pharmacophore models, mainly and secondarily pharmacological features were identified. The weight and tolerance values of these pharmacological features were adjusted to construct MP models by single-factor explorations and orthogonal experimental design based on SBP model. Then, the reliability and screening efficiency of the best MP model were validated by three databases. The best MP model was utilized to compute PPARα activity of compounds from traditional Chinese medicine. The screening efficiency of MP model outperformed individual LBP or SBP model for PPARα agonists, and was similar to combinatorial screening of LBP and SBP. However, MP model might have an advantage over the combination of LBP and SBP in evaluating the activity of compounds and avoiding the inconsistent prediction of LBP and SBP, which would be beneficial to guide drug design and optimization.     

Equivalence of the microscopic and macroscopic models of chromatography: stochastic-dispersive versus lumped kinetic model

The microscopic model of chromatography is a stochastic model that consists of two fundamental processes: (i) the random migration of the molecules in the mobile phase, and (ii) the random adsorption-desorption of molecules on the stationary phase contained in a chromatographic column. The diffusion and drift of the molecules in the mobile phase is described with a simple one-dimensional random walk. The adsorption-desorption process is modeled by a Poisson process that assumes exponential sojourn times of the molecules in both the mobile and the stationary phases. The microscopic, or molecular model of chromatography studied here turns out to be identical to the macroscopic lumped kinetic model of chromatography, whose solution is well known in chromatography. A complete equivalence of the two models is established via the identical expressions they provide for the band profiles.     

Al(H2O)63+水交换反应溶剂效应的量子化学团簇模型-密度泛函理论方法研究

在气相模型、极化连续模型、超分子模型和超分子-极化连续模型的基础上,采用量子化学团簇模型密度泛函理论方法,在B3LYP/6-311+G(d,p)基组水平下系统地开展了以下研究:优化得到Al(H2O)63+水交换反应的反应物、过渡态和产物构型,采用MP2方法在相同基组水平下计算得到相应的单点能,考虑零点振动能、热力学校正项和熵等参数的影响,计算得到Al(H2O)63+水交换反应的Gibbs自由能变和反应速率常数kex.计算结果表明:GP-SM//MP2-PCM和GP-SM-PCM//MP2-PCM模型得到的kex相近,并且与文献值相符,说明GP-SM//MP2-PCM模型可以充分考虑真实溶剂效应和主体溶剂效应,适用于Al(H3O)63+体系水交换反应的模拟.     

Theoretical Aspects of Hydrolysis of Peptide Bonds by Zinc Metalloenzymes

Activation and reaction energies for four model systems capturing the essential physicochemical features of the hydrolysis of the peptide bond have been calculated at various level of theory, including the presumably accurate CCSD(T) calculations. The models studied covered a part of the spectrum encountered in biological systems: the hydrolysis in the absence of metal ions (represented by formamide and Ala–Ala) and the hydrolysis in the presence of one and two zinc(II) ions, mimicking the active sites of mono‐ and dizinc metallopeptidases, respectively (by using thermolysin and glutamate carboxypeptidase II as the model catalytic systems and formamide as the model substrate). The results obtained using CCSD(T)/def2‐TZVP and CCSD(T)/aug‐cc‐pVTZ calculations were used as the benchmark values to which the set of cheaper methods, such as (RI‐)DFT, (RI‐)MP2, and SCS‐MP2, were referenced. It was shown that deviations of 3–5 kcal mol^?1 (translating to 2–3 orders in reaction constants) with respect to the reference CCSD(T) barriers are frequently encountered for many correlated methods and most of studied DFT functionals. It has been concluded that from the set of wave‐function methods, both MP2 and SCS‐MP2 methods can be recommended for smaller models (measured by the mean absolute deviation of the activation barriers over the four systems studied), whereas among the popular DFT functionals, B3LYP and especially M06‐2X are likely to be reasonable choices for calculating the activation barriers of zinc metallopeptidases. Finally, with the model of glutamate carboxypeptidase II, issues related to the convergence of the calculated barriers with the size of the model system used as the representative of the enzyme active site were addressed. The intricacies related to system truncation are demonstrated, and suggest that the correlated wave‐function methods may suffer from problems, such as intramolecular BSSE, which make their usage for the larger system questionable. Altogether, the presented data should contribute to efforts to understand enzymatic catalysis more deeply and to gain control of the accuracy and deficiencies of the available theoretical methods and computational approaches.     

Proton motion and proton transfer in the formamidine-formic acid complex: an Ab initio projector augmented wave molecular dynamics study

An ab initio molecular dynamics study performed with the projector augmented wave method (PAW) on proton motion and (double) proton transfer in the formamidine-formic acid complex is reported. The PAW trajectories were calculated with a time interval of 0.12 fs, for a total evolution time period of 36ps, and for temperatures in the range 500-600 K. All proton-transfer processes start with a proton transition at the O-H...N group, and are followed by a second proton transition, either at the same group ("single crossing-recrossing transitions") or at the other group, namely the N-H...O group ("double proton transfers"). According to the delay between the two transitions (more or less than 15 fs), one may distinguish between "concerted" (42%) or "successive" (16%) single crossing-recrossing transitions, and between "simultaneous" (7%) or "successive" (35%) double proton transfers. Successive processes take place via a zwitterionic intermediate, which remains stable for up to approximately 120 fs ("ionic regions"). The findings are in excellent agreement with the results of ab initio (HF, MP2) and density functional theory (DFT; B3LYP, B3P86) calculations, according to which the zwitterionic intermediate that results from the first proton transition is a true local minimum. Furthermore, it is shown that the optimized geometries of stationary points (ground state, transition state, and zwitterion) comply well with corresponding average data obtained from the PAW trajectories for normal periods, crossover points, and ionic regions.     

Effect of model potential of adsorptive bond on the thermodynamic properties of adsorbed CO molecules on Ni(111) surface

The effect of anharmonicity on the adsorption of CO molecules on the Ni(111) surface has been investigated. The DFT calculations are used to obtain the effective adsorption potential of the CO molecule on the Ni(111) surface. First, using an appropriate slab model, the geometry of adsorption system corresponding to hcp, fcc, bridge, and on-top sites with p(2 x 2) arrangement and coverage of 0.25 ML is optimized by the DFT calculations using a plane wave basis set and ultrasoft pseudopotentials; this gives the hcp site as the most stable site with De = 185 kJ/mol, for which the equilibrium distance of CO from the surface and C-O bond length on the surface are found to be 1.31 and 1.192 A, respectively. Then, the potential function of adsorption versus adsorptive bond distance was plotted, which is significantly different from that of a harmonic oscillator, i.e., the anharmonicity for the adsorptive bond is significant. Also the harmonic and anharmonic shifts of vibrational frequencies of adsorptive and C-O bonds are calculated to be -22.6 and 7.8 cm(-1), respectively. Hence, two potential models are selected for which their Schr?dinger equations are solved analytically, namely the hard repulsion-soft attraction (HS) and Morse potential (MP) models. The adsorption isotherms, internal energy, isochoric heat capacity, and entropy of adsorbed CO molecules have been calculated for the mentioned model potentials and compared with those of the harmonic oscillator (H). As a result, the adsorption isotherms are not considerably sensitive to the model potential. The anharmonicity of CO-Ni bond, which is included in HS and MP models, gives an average deviation in pressure as much as 1.4% for HS and 5.8% for MP, compared to 6.1% for the H model. However, isochoric heat capacity and entropy depend on the model potential significantly, and the differences may be as high as 69% and 55% for isochoric heat capacity and entropy, respectively.     

Development of a resolution metric for comprehensive two-dimensional chromatography

A new resolution metric for two-dimensional chromatography is proposed and tested. This resolution measurement is based on the concept of the (one-dimensional) valley-to-peak ratio, which has been adapted and modified for two-dimensional chromatography. Two questions are considered related to the computation of the resolution of a given (two-dimensional) peak. First, the concept of peak neighbourhood is revised, since it changes drastically from one- to two-dimensional chromatography. In a chromatogram resulting from a two-dimensional analysis, one peak may be surrounded by more than two neighbouring peaks. However, the neighbouring peaks can be remote from the peak or some interfering peaks may be in between. In these cases, it is not meaningful to compute the resolution between them. A method is proposed to determine whether a resolution measurement between two two-dimensional peaks is reasonable. Second, a measurement of the valley-to-peak ratio in two-dimensional chromatography is proposed. The measurement is based on the concept of the saddle point (which is defined for two-dimensional surface plots). A study of the correlation of the valley-to-peak ratio with the error obtained for quantification is presented. The new metric can be used as an estimator of the quantification errors. Also, valley-to-peak ratios can be calculated for one or more target peak(s) to estimate the separation quality of the entire chromatogram. This makes the proposed measurement suitable for optimisation purposes. Although the algorithm was developed for GC x GC, preliminary studies suggested that its application to other two-dimensional separation methods (e.g. LC x LC) should only require minor modification (if any).     

Mid-IR spectra of different conformers of phenylalanine in the gas phase

The experimental mid- and far-IR spectra of six conformers of phenylalanine in the gas phase are presented. The experimental spectra are compared to spectra calculated at the B3LYP and at the MP2 level. The differences between B3LYP and MP2 IR spectra are found to be small. The agreement between experiment and theory is generally found to be very good, however strong discrepancies exist when -NH2 out-of-plane vibrations are involved. The relative energies of the minima as well as of some transition states connecting the minima are explored at the CCSD(T) level. Most transition states are found to be less than 2000 cm(-1) above the lowest energy structure. A simple model to describe the observed conformer abundances based on quasi-equilibria near the barriers is presented and it appears to describe the experimental observation reasonably well. In addition, the vibrations of one of the conformers are investigated using the correlation-corrected vibrational self-consistent field method.     

Potential energy surfaces for small alcohol dimers I: methanol and ethanol

Potential energy landscapes for homogeneous dimers of methanol and ethanol were calculated using counterpoise (CP) corrected energies at the MP26-311+G(2df,2pd) level. The landscapes were sampled at approximately 15 dimer separation distances for different relative monomer geometries, or routes, given in terms of a relative monomer yaw, pitch, and roll and the spherical angles between the monomer centers (taken as the C atom attached to the O). The 19 different routes studied for methanol and the 22 routes examined for ethanol include 607 CP corrected energies. Both landscapes can be adequately represented by site-site, pairwise-additive models, suitable for use in molecular simulations. A modified Morse potential is used for the individual pair interactions either with or without point charges to represent the monomer charge distribution. A slightly better representation of the methanol landscape is obtained using point charges, while the potential energy landscape of ethanol is slightly better without point charges. This latter representation may be computationally advantageous for molecular simulations because it avoids difficulties associated with long-range effects of point-charge-type models.     

Predicting the behaviour of polydisperse polymers in liquid chromatography under isocratic and gradient conditions

In this paper we describe how the existing theories to describe retention and peak width in isocratic and gradient-elution liquid chromatography can be expanded to describe the retention behaviour of natural and synthetic repetitive polymers, which feature distributions of molecules with different masses (and often different structures) rather than unambiguous molecular formulas. For polydisperse samples, it is vital that the model accommodates (isocratic) elution of sample components before the onset of a gradient, elution during the gradient, and elution after the completion of the gradient. The expanded models can readily be implemented in standard spreadsheet software, such as Excel. We have created such spreadsheets based on the conventional model for retention in reversed-phase liquid chromatography (RPLC) and on two different models for retention in normal-phase liquid chromatography. The implementation allows an easy visualization of the theoretical concept. Up to three different polymeric series can be entered, with a total of up to 100 peaks being computed and displayed in isocratic or gradient-elution chromatograms. Also visualized are "retention models" (diagrams of isocratic retention vs. composition) and "calibration curves" (retention or elution composition vs. molecular mass or degree of polymerization). The coefficients in the isocratic retention model may be correlated, as has often been observed in RPLC. It is shown that under certain conditions such a correlation corresponds to the existence of so-called critical (isocratic) conditions, at which all the members of a given polymeric series (same composition and end groups, different number of repeat units) show co-elution.