On a unified treatment of kinetics and diffusion,and a connection to a nonlocal boltzmann equation

Fick's law of diffusion has been generalized to include kinetic processes, the transport term of the Boltzmann equation, and nonlocal interaction processes. It is shown that the collision interaction term can be obtained by the introduction of a quantum stochastic potential equation. Some approximations of a nonlocal Boltzmann equation can be solved exactly. The solutions can be applied to problems of molecular pattern in biology.     

Solutions to the Quantum QSPR problem in molecular spaces

The molecular quantum similarity framework is used to present a new set of Quantum Quantitative Structure– Properties Relationship (QQSPR) procedures. The theoretical basis consists of the so-called fundamental QQSPR equation, deducible from quantum mechanical first principles, associated with the quantum mechanical expectation values computation. Approximate solutions of the fundamental QQSPR equation within direct and reciprocal spaces, containing molecular density functions, are studied in a common framework. Contribution to the Serafín Fraga Memorial Issue. This paper is dedicated to Serafín Fraga and Xavier Gironès, in memoriam. They have formed part of my life as a scientist: I had been an apprentice with the first and I tried to be a teacher with the second. I learned from both, though. They will be like stars in my mind, until we can walk together the endless path of nothingness.     

Kinetic Modeling and Parameter Estimation in a Tower Bioreactor for Bioethanol Production

In this work, a systematic method to support the building of bioprocess models through the use of different optimization techniques is presented. The method was applied to a tower bioreactor for bioethanol production with immobilized cells of Saccharomyces cerevisiae. Specifically, a step-by-step procedure to the estimation problem is proposed. As the first step, the potential of global searching of real-coded genetic algorithm (RGA) was applied for simultaneous estimation of the parameters. Subsequently, the most significant parameters were identified using the Placket–Burman (PB) design. Finally, the quasi-Newton algorithm (QN) was used for optimization of the most significant parameters, near the global optimum region, as the initial values were already determined by the RGA global-searching algorithm. The results have shown that the performance of the estimation procedure applied in a deterministic detailed model to describe the experimental data is improved using the proposed method (RGA–PB–QN) in comparison with a model whose parameters were only optimized by RGA.     

Microcalorimetric determination of effect of the antioxidant (Quercetin) on polymer/surfactant interactions

Isothermal titration calorimetry (ITC) and batch calorimetry techniques have been used to evaluate the effect of added antioxidant (Quercetin, QN) on the binding between a polymer/surfactant complex, namely the sodium salt of polystyrene sulfonate (PSS) and typical anionic surfactant sodium dodecylsulfate (SDS). An indirect isotherm approximation method and the Satake–Yang model have been used to evaluate the binding parameter (Ku), adsorption cooperativity (u), and the Gibbs free energy of cooperative and non-cooperative binding (ΔG _C and ΔG _N) from the ITC data. The enthalpy of dissolution of QN into various PSS/water and PSS/SDS/water solutions has been evaluated from batch calorimetry to study the energetics of the polymer/surfactant binding in the presence of QN.     

Temperature-time duality exemplified by Ising magnets and quantum-chemical many electron theory

In this work, we first present a detailed analysis of temperature-time duality in the 3D Ising model, by inspecting the resemblance between the density operator in quantum statistical mechanics and the evolution operator in quantum field theory, with the mapping β = (k _B T)⁻¹ → it. We point out that in systems like the 3D Ising model, for the nontrivial topological contributions, the time necessary for the time averaging must be infinite, being comparable with or even much larger than the time of measurement of the physical quantity of interest. The time averaging is equivalent to the temperature averaging. The phase transitions in the parametric plane (β, it) are discussed, and a singularity (a second-order phase transition) is found to occur at the critical time t _c , corresponding to the critical point β _c (i.e, T _c ). It is necessary to use the 4-fold integral form for the partition function for the 3D Ising model. The time is needed to construct the (3 + 1)D framework for the quaternionic sequence of Jordan algebras, in order to employ the Jordan-von Neumann-Wigner procedure. We then turn to discuss quite briefly temperature-time duality in quantum-chemical many-electron theory. We find that one can use the known one-dimensional differential equation for the Slater sum S(x, β) to write a corresponding form for the diagonal element of the Feynman propagator, again with the mapping β → it.     

Are the critical exponents for Anderson localization due to disorder well understood?

Semiclassical theory has been used, with some success, to discuss Anderson localization due to disorder. Our attention is focused on the quantum–chemical network model via a Boltzmann–like equation, and García-García’s semiclassical approach, contacted with early work of Care and March on compensated semiconductor. This work is related with the recent semiclassical treatment on the effect of disorder on the nature of electron states in the quantum–chemical network model.     

Variational justification of the dimensional-scaling method in chemical physics: the H-atom

The dimensional scaling (D-scaling) method first originated from quantum chromodynamics by using the spatial dimension D as an order parameter. It later has found many useful applications in chemical physics and other fields. It enables, e.g., the calculation of the energies of the Schr?dinger equation with Coulomb potentials without having to solve the partial differential equation (PDE). This is done by imbedding the PDE in a D-dimensional space and by letting D tend to infinity. One can avoid the partial derivatives and then solve instead a reduced-order finite dimensional minimization problem. Nevertheless, mathematical proofs for the D-scaling method remain to be rigorously established. In this paper, we will establish this by examining the D-scaling procedures from the variational point of view. We show how the ground state energy of the hydrogen atom model can be calculated by justifying the singular perturbation procedures. In the process, we see in a more clear and mathematical way confirming (Herschbach J Chem Phys 85:838, 1986 Sect. II.A) how the D-dimensional electron wave function “condenses into a particle,” the Dirac delta function, located at the unit Bohr radius.     

Characterizing and modeling the tensile deformation of polyethylene: The temperature and crystallinity dependences

For various polyethylenes at ambient and elevated temperatures, tensile deformation was characterized by measurements of true stress-true strain curves at constant strain rates, the determination of the elastic and plastic part of strains, and registrations of the stress relaxation at fixed strains. Some peculiar features show up: (i) The yield point is associated with a drop in the stiffness rather than an onset of plastic flow. (ii) The elasticity reaches a plateau at a temperature and crystallinity invariant critical strain (ɛ _H ≈ 0.6). (iii) Moduli as derived from the stretching curve can be strongly modified by viscous forces. A recently introduced model treats the stress as arising from three contributions, rubberlike forces originating from the stretched network of entangled amorphous chains, forces transmitted by the skeleton of crystallites, and viscous forces described by Eyring’s equation. Adjustment of the measured data to the model provides a decomposition of the stress in the three parts and thus allows an analysis of the effects of temperature and crystallinity. Published in Russian in Vysokomolekulyarnye Soedineniya, Ser. A, 2008, Vol. 50, No. 5, pp. 760–772. This article was submitted by the authors in English.     

A New Flow Instrument for Conductance Measurements at Elevated Temperatures and Pressures: Measurements on NaCl(aq) to 458 K and 1.4 MPa

A new flow electrical conductance instrument was constructed and tested on dilute NaCl solutions up to 458 K, and on more concentrated solutions (maximum 0.436 mol⋅kg⁻¹) at 373 K. The results of the new instrument agreed with those of previous authors within the estimated experimental errors. The model of Bernard et al. (J. Phys. Chem. 96, 3833–3840 (1992), MSA) was found to represent the high-temperature results without introducing an ion-pairing equilibrium constant. The Fuoss–Hsia conductance equation as given by Fernandez-Prini was found to represent the dilute concentrations with Λ° (NaCl) as the only adjustable parameter. It was found that Λ° (NaCl) could be expressed as a function of solvent viscosity and density by using three parameters found by regression of literature results between 278.15 and 523 K. This equation along with the FHFP theory permits the equivalent conductivity of dilute sodium chloride solutions to be calculated within the accuracy of the existing experimental measurements.     

Multiscale theory of collective and quasiparticle modes in quantum nanosystems

A quantum nanosystem (such as a quantum dot, nanowire, superconducting nanoparticle, or superfluid nanodroplet) involves widely separated characteristic lengths. These lengths range from the average nearest-neighbor distance between the constituent fermions or bosons, or the lattice spacing for a conducting metal, to the overall size of the quantum nanosystem (QN). This suggests the wave function has related distinct dependencies on the positions of the constituent fermions and bosons. We show how the separation of scales can be used to generate a multiscale perturbation scheme for solving the wave equation. Results for electrons or other fermions show that, to lowest order, the wave function factorizes into an antisymmetric (fermion) part and a symmetric (bosonlike) part. The former manifests the short-range/exclusion-principle behavior, while the latter corresponds to collective behaviors, such as plasmons, which have a boson character. When the constituents are bosons, multiscale analysis shows that, to lowest order, the wave function can also factorize into short- and long-scale parts. However, to ensure that the product wave function has overall symmetric particle label exchange behavior, there could, in principle, be states of the boson nanosystem where both the short- and long-scale factors are either boson- or fermionlike; the latter "dual fermion" states are, due to their exclusion-principle-like character, of high energy (i.e., single particle states cannot be multiply occupied). The multiscale perturbation analysis is used to argue for the existence of a coarse-grained wave equation for bosonlike collective behaviors. Quasiparticles, with effective mass and interactions, emerge naturally as consequences of the long-scale dynamics of the constituent particles. The multiscale framework holds promise for facilitating QN computer simulations and novel approximation schemes.     

Characterization of PDZ domain–peptide interactions using an integrated protocol of QM/MM,PB/SA,and CFEA analyses

Protein–protein interactions, particularly weak and transient ones, are often mediated by peptide recognition domains. Characterizing the interaction interface of domain–peptide complexes and analyzing binding specificity for modular domains are critical for deciphering protein–protein interaction networks. In this article, we report the successful use of an integrated computational protocol to dissect the energetic profile and structural basis of peptide binding to third PDZ domain (PDZ3) from the PSD-95 protein. This protocol employs rigorous quantum mechanics/molecular mechanics (QM/MM), semi-empirical Poisson–Boltzmann/surface area (PB/SA), and empirical conformational free energy analysis (CFEA) to quantitatively describe and decompose systematic energy changes arising from, respectively, noncovalent interaction, desolvation effect, and conformational entropy loss associated with the formation of 30 affinity-known PDZ3–peptide complexes. We show that the QM/MM-, PB/SA-, and CFEA-derived energy components can work together fairly well in reproducing experimentally measured affinity after a linearly weighting treatment, albeit they are not compatible with each other directly. We also demonstrate that: (1) noncovalent interaction and desolvation effect donate, respectively, stability and specificity to complex architecture, while entropy loss contributes modestly to binding; (2) P₀ and P₋₂ of peptide ligand are the most important positions for determining both the stability and specificity of the PDZ3–peptide complex, P₋₁ and P₋₃ can confer substantial stability (but not specificity) for the complex, and N-terminal P₋₄ and P₋₅ have only a very limited effect on binding.     

Achieving fast convergence of ab initio free energy perturbation calculations with the adaptive force-matching method

This paper studies the possibility of improving the convergence of ab initio free energy perturbation (FEP) calculations by developing customized force fields with the adaptive force-matching (AFM) method. The ab initio FEP method relies on a molecular mechanics (MM) potential to sample configuration space. If the Boltzmann weight of the MM sampling is close to that of the ab initio method, the efficiency of ab initio FEP will be optimal. The difference in the Boltzmann weights can be quantified by the relative energy difference distribution (REDD). The force field developed through AFM significantly improves the REDD when compared with standard MM models, thus improving the convergence of the ab initio FEP calculation. The static dielectric constant ε_s of ice-Ih was studied with PW-91 through ab initio FEP. With a customized force field developed through AFM, we were able to converge ε_s to 80 ± 4 with 3,600 configurations. A similar ab initio FEP calculation with the TIP4P model would require 220 times more configurations to achieve the same accuracy. Our study indicates that the PW-91 functional underestimates ice-Ih ε_s by about 20%.     

Molecular receptors for monosaccharides: di(pyridyl)naphthyridine and di(quinolyl)naphthyridine

The recognition capabilities of two molecular receptors 2,7-di(3′-pyridyl)-1,8-naphthyridine (DPN) and 2,7-di(3′-quinolyl)-1,8-naphthyridine (DQN) toward monosaccharides in chloroform were evaluated. Both DPN and DQN possess a naphthyridine core moiety, in which two pyridinic nitrogen atoms serve as the proton acceptors. Attached to the C2 and C7 positions of naphthyridine are two identical arms, each of which consists of pyridine (DPN) or quinoline (DQN) moiety that also acts as the proton acceptor. The arrangement of hydroxyl groups in monosaccharides offers the proton donors complementary to the proton acceptors of DPN (or DQN) to form a quadruply hydrogen bonds complex. The binding processes were studied by UV-vis, fluorescence and ¹H NMR spectrophotometric titrations as well as electrospray ionization mass spectroscopy. The binding strength between DPN (or DQN) and examined monosaccharides was comparable to that for many other hydrogen-bonding host molecules previously reported.     

Exploring the quantum mechanical/molecular mechanical replica path method: a pathway optimization of the chorismate to prephenate Claisen rearrangement catalyzed by chorismate mutase

 A replica path method has been developed and extended for use in complex systems involving hybrid quantum/classical (quantum mechanical/molecular mechanical) coupled potentials. This method involves the definition of a reaction path via replication of a set of macromolecular atoms. An “important” subset of these replicated atoms is restrained with a penalty function based on weighted root-mean-square rotation/translation best-fit distances between adjacent (i±1) and next adjacent (i±2) pathway steps. An independent subset of the replicated atoms may be treated quantum mechanically using the computational engine Gamess-UK. This treatment can be performed in a highly parallel manner in which many dozens of processors can be efficiently employed. Computed forces may be projected onto a reference pathway and integrated to yield a potential of mean force (PMF). This PMF, which does not suffer from large errors associated with calculated potential-energy differences, is extremely advantageous. As an example, the QM/MM replica path method is applied to the study of the Claisen rearrangement of chorismate to prephenate which is catalyzed by the Bacillus subtilis isolated, chorismate mutase. Results of the QM/MM pathway minimizations yielded an activation enthalpy ΔH ^†† of 14.9 kcal/mol and a reaction enthalpy of −19.5 kcal/mol at the B3LYP/6-31G(d) level of theory. The resultant pathway was compared and contrasted with one obtained using a forced transition approach based on a reaction coordinate constrained repeated walk procedure (ΔH ^†† =20.1 kcal/mol, ΔH _rxn = −20.1 kcal/mol, RHF/4-31G). The optimized replica path results compare favorably to the experimental activation enthalpy of 12.7±0.4 kcal/mol. Received: 16 December 2001 / Accepted: 6 September 2002 / Published online: 8 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 22nd National Meeting of the American Chemical Society, 2001. Correspondence to: H.L. Woodcock e-mail: hlwood@ccqc.uga.edu Acknowledgements. The authors thank Eric Billings, Xiongwu Wu, and Stephen Bogusz for helpful discussions and related work. The authors also show grateful appreciation to The National Institutes of Health and The National Science Foundation for support of the current research.     

Theoretical study of vitamin properties from combined QM-MM methods: Comparison of chemical shifts and energy

The combination of quantum mechanics (QM) and molecular mechanics (MM) methods has become an alternative tool for many applications for which pure QM and MM are not suitable. The QM-MM method has been used for different types of problems, for example, structural biology, surface phenomena, and the liquid phase. In this paper, we have implemented these methods for vitamins, an important kind of biological molecule, and then compared results. The calculations were done by the full ab initio method (HF/3–21 g and HF/6–31 g) and QM-MM (ONIOM) method with HF(3–21 g)/AM1/UFF; then, we found that the geometry obtained by the QM-MM method is very accurate and this rapid method can be used in place of time consuming ab initio methods for large molecules. A comparison of energy values in the QM-MM and QM methods is given. We compare chemical shifts and conclude that the QM-MM method is a perturbed full QM method. The text was submitted by the authors in English.     

The importance of electron-molecule interactions in free-free continuum emission for microwave discharge CVD

Optical emission spectroscopic (OES) measurements are acquired by collecting absolute line and continuum emission from a hydrogen/methane plasma (300 sccm H₂, 3 sccm CH₄, 40–70 torr, 1600–3200 W) used for diamond deposition. The experimental results are used in tandem with numerical modeling to infer plasma parameters of interest. Numerical solutions for a microwave chemical vapor deposition (CVD) reactor are generated by coupling solutions of the Boltzmann equation and the electron energy equation to a collisional-radiative model (CRM). Results indicate that the electron-neutral free-free emission, which depends strongly on neutral density, electron density, and electron temperature, is the dominant source of continuum emission. All numerical solutions are found to be inconsistent with the experimentally measured continuum emission. A meaningful interpretation, however, is possible if the electron-H₂ cross-section, used for calculating electron-neutral free-free continuum emission, is increased by between 4 and 20 above the momentum cross-section value. We believe that such an increase is justified because of enhanced energy exchange in electron-molecule interactions.     

The charge ratio between O and N on amide bonds: a new approach to the mobile proton model

The influence of charge distribution on the cleavage of the peptides was investigated by fragmentation efficiency curves and quantum chemical calculations in order to clarify the fragmentation mechanism in this paper. The peptide Arg-Gly-Asp-Cys (RGDC) was oxidized to change the charge distribution, but its main sequence was retained. Under this study, it was illustrated that the fragmentation of the peptide RGDC became easier with each addition of an O atom to the Cys hydrosulfide group and the relative charge ratios between O and N (QO/QN) in the amide bonds had much to do with the cleavage of the peptide RGDC. For each amide bond, the situations coincided with overall conclusion: the increase of the QO/QN values results in a higher fragmentation efficiency and vice versa. The methods which combined fragmentation efficiency curves with the charge distribution of peptides provided a way to refine the mobile proton model for peptide fragmentation and to probe the discrepant fragmentation of peptides in peptide/protein identification.     

The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives

 Hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials are becoming increasingly important for studying condensed-phase systems but one of the outstanding problems in the field has been how to treat covalent bonds between atoms of the QM and MM regions. Recently, we presented a generalized hybrid orbital (GHO) method that was designed to tackle this problem for hybrid potentials using semiempirical QM methods [Gao et al. (1998) J Phys Chem A 102: 4714–4721]. We tested the method on some small molecules and showed that it performed well when compared to the purely QM or MM potentials. In this article, we describe the formalism for the determination of the GHO energy derivatives and then present the results of more tests aimed at validating the model. These tests, involving the calculation of the proton affinities of some model compounds and a molecular dynamics simulation of a protein, indicate that the GHO method will prove useful for the application of hybrid potentials to solution-phase macromolecular systems. Received: 4 October 1999 / Accepted: 18 December 1999 / Published online: 5 June 2000     

Influence of a reaction medium on the oxidation of aromatic nitrogen-containing compounds by peroxyacids

The influence of different solvents on the oxidation reaction rate of pyridine (Py), quinoline (QN), acridine (AN), α-oxyquinoline (OQN) and α-picolinic acid (APA) by peroxydecanoic acid (PDA) was studied. It was found that the oxidation rate grows in the series Py < QN < AN, and the rate of the oxidation reaction of compounds containing a substituent in the α position from a reactive center is significantly lower than for unsubstituted analogues. The effective energies of activation of the oxidation reaction were found. It was shown that in the first stage, the reaction mechanism includes the rapid formation of an intermediate complex nitrogen-containing compound, peroxyacid, which forms products upon decomposing in the second stage. A kinetic equation that describes the studied process is offered. The constants of equilibrium of the intermediate complex formation (K _eq) and its decomposition constant (k ₂) in acetone and benzene were calculated. It was shown that the nature of the solvent influences the numerical values of both K _p and k ₂. It was established that introduction of acetic acid (which is able to form compounds with Py) into the reaction medium slows the rate of the oxidation process drastically. Correlation equations linking the polarity, polarizability, electrophilicity, and basicity of solvents with the constant of the PDA oxidation reaction rate for Py were found. It was concluded that the basicity and polarity of the solvent have a decisive influence on the oxidation reaction rate, while the polarizability and electrophilicity of the reaction medium do not influence the oxidation reaction rate.