Mathematical optimization in the determination of the dissociation constants of a tribasic organic acid by 13C NMR spectroscopy

The calculation of dissociation constants from the chemical shifts of (13)C NMR spectra leads to a complicated non-linear equation. Two different mathematical methods for solution of this equation have been chosen--an iterative step method and a matrix pseudo-inversion method. When the iteration method is used the initial guesses for the parameters, the initial value of the step size and the escalation of the iteration must be optimized. For comparison the matrix pseudo-inversion method was used because it gives a unique result. With the optimized step method the results were as accurate or even better than those obtained with the matrix method. Although it takes time to optimize the system, the step method is the more suitable method of solving the problem. The matrix inversion can be done only with a computer with 13 significant digits and exponent capacity larger than +/- 38.     

High-pressure phase equilibrium for the binary systems of {carbon dioxide (1) + dimethyl carbonate (2)} and {carbon dioxide (1) + diethyl carbonate (2)} at temperatures of 273 K, 283 K,and 293 K

Phase equilibrium data for the binary systems {carbon dioxide (CO₂) + dimethyl carbonate (DMC)} and {carbon dioxide (CO₂) + diethyl carbonate (DEC)} were measured at temperatures of 273 K, 283 K and 293 K in the pressure range of 0.5 MPa to 4.0 MPa. The measurements were carried out in a cylindrical autoclave with a moveable piston and an observation window. The experimental data were correlated with the Peng–Robison (PR) equation of state (EOS) and the Peng–Robinson–Stryjek–Vera (PRSV) equation of state with van der Waals-1 or Panagiotopoulos–Reid mixing rules. The correlations produced reasonable values for the interaction parameters. The comparisons between calculation results and experimental data indicate that the PRSV equation of state coupled with the Panagiotopoulos–Reid mixing rule produced the better correlated results.     

Iterative Least-Squares Lineshape Fitting of 1H-decoupled 13C-DNMR.Spectra

Iterative least-squares lineshape fitting of ¹H-decoupled ¹³C-DNMR. spectra is advantageously used for the investigation of symmetrical or asymmetrical intramolecular (two-structure) exchange processes. The least-squares procedure adopted allows the following parameters to be either optimized by computer or kept constant (according to experimental conditions): the nuclei populations (taking into account line intensity effects resulting from differences in spin-lattice relaxation times and/or Overhauser enhancements), the corresponding chemical shifts and natural linewidths (characterizing the sites undergoing exchange), the fractional population of one structure (in the case of asymmetrical exchange), one of the chemical rates, the base-line position, and the base-line tilt. The relative sensitivity of the lineshape with respect to the fitted parameters as well as the importance of correlations among these parameters have been investigated and tested with examples. The reliability of the kinetic parameters as obtained by the iterative least-squares lineshape fitting procedure is discussed.     

Surface properties of some carotenoids spread in monolayers at the air/water interface. Experimental and computational approach

The surface pressure versus molecular area isotherms of some carotenoids: β,β-carotene-4-one (echinenone, ECH), β,β-carotene-4,4′-dione (canthaxanthin, CAN) and 4,4′-diapo-ω,ω-carotene-4,4′-dial (APO), spread at the air/water interface, are reported. A van der Waals type state equation is used to describe the high molecular area portions of the compression isotherms and interaction parameters within monolayers are derived. Quantum chemical semi-empirical SCF MO calculations (AM1 and PM3) are performed for the optimized geometries of molecules and dipole moments are calculated. Similar theoretical magnitudes are obtained by both methods. Surface properties, like collapse pressure, surface compressional modulus and interaction parameters are discussed in terms of dipole-dipole interactions, and correlations with the calculated quantities for the carotenoid molecules are analyzed. The orientation of the different carotenoid molecules in the monolayer is discussed.     

Conformation analysis of carotenoids in the purple bacterium Rhodobium marinum based on NMR spectroscopy and AM1 calculation

Five carotenoids existing in the purple bacterium of Rhodobium marinum, lycopene, anhydrorhodovibrin, spirilloxanthin, rhodopin, and rhodovibrin, were isolated and purified. Their configurations in the chromophore region and conformations of the terminal part were determined by 1D, 2D 1H and 13C NMR spectroscopy. The semiempirical quantum chemical calculation AM1 was subsequently performed using the rough 3-D structures established by NOE correlations as an initial input. The final optimized structures are coincident with 1H-1H NOE correlations and match with the X-ray crystallographic data of carotenoids. The calculation results show that chemically symmetrical carotenoids have a Ci point group. The Ci point group of molecules was destroyed by asymmetrical terminal part although the polyene chain still keeps it roughly. The polyene region of investigated carotenoids are in all-trans with slightly twisted in-plane and slight out-plane forming s-shape carbon backbone due to the spatial interaction of the methyl groups. Terminal parts, on the other hand, have several stable conformers due to the freely rotatable single bonds, but they prefer to take extended conformations.     

Liquid–liquid equilibria of copolymer mixtures based on an equation of state

Liquid–liquid equilibria of copolymer mixtures were studied by an equation of state (EoS) for chain-like fluids. The equation consists of a reference term for hetero-nuclear hard-sphere chain fluids developed by Hu et al. where the next-to-nearest-neighbor correlations have been taken into account; and a perturbation term from Alder et al.’s square-well attractive potential. The segment parameters, including number of segments, segment diameter and interaction energy between segments, are obtained by fitting pVT data of pure homopolymer. For the case of different species in the same copolymer, the interaction parameters for unlike segment pairs are obtained by fitting pVT data of pure copolymer. For the interaction between segment of homopolymer and different species in copolymer, the parameters are treated as adjustable by fitting liquid–liquid equilibria data. In the latter case, the difference between different species in a copolymer is simply neglected as an approximation. Therefore, in general, only one pair of adjustable interaction parameter is determined from LLE data. To model miscibility maps of copolymer mixtures having two or three kinds of species, the interaction parameters are obtained from the boundary between miscible and immiscible regions. The EoS used in this work can correlate phase behavior including coexistence curves, miscibility windows and miscibility maps.     

Fermi interaction between the nu1 and the nu2+4 nu(s) bands of Ar...DN2(+)

Two rotationally fully resolved vibrational bands have been assigned unambiguously to the linear deuteron bound Ar...DN(2) (+) complex by using ground state combination differences. The ionic complex is formed in a supersonic planar plasma expansion optimized and controlled by a mass spectrometer and is detected in direct absorption using tunable diode lasers and applying production modulation spectroscopy. The band origins are located at 2436.272 cm(-1) and at 2435.932 cm(-1) and correspond to the nu(1) band (NN stretch) and to the nu(2)+4 nu(s) combination band (DN and intermolecular stretch), respectively. The two bands overlap strongly and the large intensity of the combination band is explained in terms of a Fermi interaction. This interaction perturbs the observed transitions, particularly for low J values. Least-squares fitting yields values for the Fermi interaction parameters of F(0)=0.332 cm(-1) and F(J)=-0.001 46 cm(-1) and results in accurate rotational constants. These are discussed both from an experimental and a theoretical point of view.     

Modification of the predictive capability of the PRSV-2 equation of state for critical volumes of binary mixtures

The predictive capability of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state for critical properties of binary mixtures showing continuous critical lines has been investigated. The procedure adopted by Heidemann and Khalil and discussed by Abu-Eishah et al., in a previous paper, has been followed. The effect of using the pure-component parameters of the PRSV-2 equation of state (κ₁, κ₂ and κ₃), new values of κ₁, revised values of κ₁, or giving zero values for these parameters have been investigated. The effect of using zero values or optimized values for the binary interaction parameter on the PRSV-2 predictive capability of critical properties have also been investigated. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperature and pressure for the 20 nonpolar and 18 polar systems studied here agree well with experimental data, and are always better than those predicted by the group-contribution method. A correction has been introduced here to the critical volume predicted by PRSV-2 equation of state that makes the average deviations between the predicted and experimental values very close to or even better than those predicted by the group-contribution method.     

Uniqueness of the iterative solution of the optimized effective potential equation

The optimized effective potential (OEP) equation can be used in a numerically efficient self-consistent form to solve for the density functional exchange and correlation potentials, as shown in a recent paper of Kummel and Perdew [Phys. Rev. Lett. 90, 43004 (2003)]. The uniqueness of an iterative solution of the OEP equation has not yet been adequately addressed. In this paper, it is shown that no nonconstant multiplicative potentials that can contaminate an iterative solution of the OEP equation exist and, hence, that formally the exact exchange-correlation potential determined form of the OEP equation is unique to within a constant.     

Thermodynamics of mixtures containing linear monocarboxylic acids II. Binary systems showing cross-association between components: DISQUAC characterization of linear monocarboxylic acid + 1-alkanol,or + linear monocarboxylic acid mixtures

Binary mixtures containing compounds which show cross-association between them are investigated in terms of DISQUAC: namely, systems with two linear monocarboxylic acids, or with one acid and one 1-alkanol. In the former, the interactions between the COOH groups of the acids are represented by dispersive parameters only. Binary systems involving two 1-alkanols behave similarly. In the linear monocarboxylic acids + 1-alkanol mixtures, the COOH/OH interactions are represented by structure-dependent dispersive and quasichemical parameters. It is shown that those solutions with methanol and ethanol do not fit into the general scheme followed by the higher members of each homologous series considered here. A similar behaviour is found when mixtures containing methanol and benzene or CCl₄ are compared with those involving higher alkanols in the frameworks of DISQUAC or of the Barker's theory.Vapor-liquid equilibria, VLE, and excess enthalpy, H^E, data are consistently described by DISQUAC. Discrepancies are analysed.The UNIQUAC association model or an equation of state (Carnahan-Starling) with the association built in have been applied in the literature as pure correlations of the experimental data for acids + 1-alkanols systems. Their results are compared with those reported in this work by DISQUAC.     

PSRK group contribution equation of state: comprehensive revision and extension IV,including critical constants and α-function parameters for 1000 components

As a part of an ongoing process, the predictive Soave–Redlich–Kwong (PSRK) group contribution equation of state was extended by the introduction of additional structural groups (F₂, Cl₂, Br₂, HCN, NO₂, CF₄, O₃ and ClNO) and fitting of the corresponding group interaction parameters. Interaction parameters between already existing main groups were also optimized to the growing literature data base. Overall, 75 new parameter sets are given herein, and typical results are presented for various systems. For the sake of completeness, not only the group new interaction parameters but all available PSRK/UNIFAC interaction parameter sets (more than 900) are given as supplementary material. Moreover, the required pure component properties (critical properties, acentric factors, and Mathias–Copeman constants) were revised and are also included for about 1000 components.     

First‐Principles Prediction of Nucleophilicity Parameters for π Nucleophiles: Implications for Mechanistic Origin of Mayr’s Equation

Quantitative nucleophilicity scales are fundamental to organic chemistry and are usually constructed on the basis of Mayr’s equation [log k=s(N+E)] by using benzhydrylium ions as reference electrophiles. Here an ab initio protocol was developed for the first time to predict the nucleophilicity parameters N of various π nucleophiles in CH₂Cl₂ through transition‐state calculations. The optimized theoretical model (BH&HLYP/6‐311++G(3df,2p)//B3LYP/6‐311+G(d,p)/PCM/UAHF) could predict the N values of structurally unrelated π nucleophiles within a precision of ca. 1.14 units and therefore may find applications for the prediction of nucleophilicity of compounds that are not readily amenable to experimental characterization. The success in predicting N parameters from first principles also allowed us to analyze in depth the electrostatic, steric, and solvation energies involved in electrophile–nucleophile reactions. We found that solvation does not play an important role in the validity of Mayr’s equation. On the other hand, the correlations of the E, N, and log k values with the energies of the frontier molecular orbitals indicated that electrostatic/charge‐transfer interactions play vital roles in Mayr’s equation. Surprising correlations observed between the electrophile–nucleophile C? C distances in the transition state, the activation energy barriers, and the E and N parameters indicate the importance of steric interactions in Mayr’s equation. A method is then proposed to separate the attraction and repulsion energies in the nucleophile–electrophile interaction. It was found that the attraction energy correlated with N+E, whereas the repulsion energy correlated to the s parameter.     

Densities and viscosities for binary mixtures of phenetole with 1-pentanol, 1-hexanol, 1-heptanol, 1-octanol, 1-nonanol,and 1-decanol at different temperatures

Density (ρ) and viscosity (η) values of the binary mixtures of phenetole+1-pentanol, + 1-hexanol, + 1-heptanol, + 1-octanol, + 1-nonanol, and + 1-decanol over the entire range of mole fraction at 293.15, 298.15, 308.15, and 318.15 K have been measured at atmospheric pressure. The excess molar volume (V^E), viscosity deviations (Δη), and excess Gibbs energy of activation (G*^E) have been calculated from the experimental measurements. These results were fitted to Redlich and Kister polynomial equation to estimate the binary interaction parameters. The viscosity data were correlated with equations of Grunberg and Nissan, Hind et al., Frenkel, and McAllister. While the excess molar volumes of phenetole+1-pentanol, + 1-hexanol are positive, the remaining binary mixtures are negative. The viscosity deviations and excess Gibbs energy of activation are negative for all investigated systems. As the chain length of 1-alkanols increases, both viscosity deviations and excess molar volume values decrease while excess Gibbs energy of activation value increase. The temperature has no effect on excess molar volume, slight effect on excess Gibbs energy of activation, and significant effect on viscosity deviations. The calculated functions have been used to explain the intermolecular interaction between the mixing components.     

A reliable new three-dimensional potential energy surface for H(2)-Kr

An improved three-dimensional potential energy surface for the H(2)-Kr system is determined from a direct fit of new infrared spectroscopic data for H(2)-Kr and D(2)-Kr to a potential energy function form based on the exchange-Coulomb model for the intermolecular interaction energy. These fits require repetitive, highly accurate simulations of the observed spectra, and both the strength of the potential energy anisotropy and the accuracy of the new data make the "secular equation perturbation theory" method used in previous analyses of H(2)-(rare gas) spectra inadequate for the present work. To address this problem, an extended version of the "iterative secular equation" method was developed which implements direct Hellmann-Feynman theorem calculation of the partial derivatives of eigenvalues with respect to parameters of the Hamiltonian which are required for the fits.     

Structure-property relationships of polyselenoethers [-(CH2)ySe-]x (y=1, 2, and 3) and related polyethers and polysulfides

Conformational characteristics, solution (melt) properties, and thermal properties of polyselenoethers [-(CH2)ySe-]x ( y=1, 2, and 3) have been revealed by the rotational isomeric state analysis of ab initio molecular orbital calculations and (1)H and (13)C NMR experiments for monomeric model compounds and compared with those of typical polyethers and polysulfides. The comparative results are summarized here as correlations in conformation among model compounds and unperturbed and crystalline states of the polymers, and thermal properties of the polymer crystals are discussed in terms of intramolecular and intermolecular interactions. By ab initio molecular orbital calculations under periodic boundary conditions, helical structures of poly(methylene oxide), poly(methylene sulfide), and poly(methylene selenide), and the crystal structure of poly(ethylene selenide) have been optimized, and their electronic structures have been predicted. A systematic methodology to predict and characterize up to higher-order structures and various physical properties of polymers incorporated in different phases has been attempted to be developed.     

Vapor–liquid equilibrium in the system ethane + ethylene glycol

The solubility of ethane in ethylene glycol (EG) has been determined at temperatures in the range 298–398 K at pressures up to 20 MPa. The experimental results were correlated by the Peng–Robinson equation of state, and interaction parameters have been obtained for this system. The parameters in the Krichevsky–Ilinskaya equation were calculated from these interaction parameters.     

A block variational procedure for the iterative diagonalization of non-Hermitian random-phase approximation matrices

We present a technique for the iterative diagonalization of random-phase approximation (RPA) matrices, which are encountered in the framework of time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation. The non-Hermitian character of these matrices does not permit a straightforward application of standard iterative techniques used, i.e., for the diagonalization of ground state Hamiltonians. We first introduce a new block variational principle for RPA matrices. We then develop an algorithm for the simultaneous calculation of multiple eigenvalues and eigenvectors, with convergence and stability properties similar to techniques used to iteratively diagonalize Hermitian matrices. The algorithm is validated for simple systems (Na(2) and Na(4)) and then used to compute multiple low-lying TDDFT excitation energies of the benzene molecule.     

A direct,restricted-step,second-order MC SCF program for large scale ab initio calculations

A general purpose MC SCF program with a direct, fully second-order and step-restricted algorithm is presented. The direct character refers to the solution of an MC SCF eigenvalue equation by means of successive linear transformations where the norm-extended hessian matrix is multiplied onto a trial vector without explicitly constructing the hessian. This allows for applications to large wavefunctions. In the iterative solution of the eigenvalue equation a norm-extended optimization algorithm is utilized in which the number of negative eigenvalues of the hessian is monitored. The step control is based on the trust region concept and is accomplished by means of a simple modification of the Davidson—Liu simultaneous expansion method for iterative calculation of an eigenvector. Convergence to the lowest state of a symmetry is thereby guaranteed, and test calculations also show reliable convergence for excited states. We outline the theory and describe in detail an efficient implementation, illustrated with sample calculations.     

Equation of state for mercury: revisited

An analytical equation of state by Song and Mason is developed to calculate the PVT properties of mercury. The equation of state is based on the statistical-mechanical perturbation theory of hard convex bodies and can be written as a fifth-order polynomial in the density. There exists three temperature-dependent parameters in the equation of state; the second virial coefficient, an effective molecular volume, and a scaling factor for the average contact pair distribution function of hard convex bodies. The temperature-dependant parameters have been calculated using corresponding-states correlations based on the surface tension and the liquid density at the normal boiling point. Employing the present equation of state, we have calculated the PVT properties of mercury over a wide range of temperatures and pressures. The average absolute deviation for the calculated density of mercury in the saturation and compressed states is 1.09%.