Note on Monte Carlo methods without necessary detailed balance

Simple criteria for convergence of Monte Carlo algorithms not necessarily requiring detailed balance for any specified transition probability are derived and it is shown that it is possible to view the algorithm as a superimposition of a Brownian motion on configurational space coupled to the transition probabilities. As such, the error contributions due to a particular Monte Carlo algorithm and the integration limits in configuration space must be distinguished from those due to the nonuniform sampling of the Brownian motion, and criteria related to the number of steps required to distinguish these errors are provided for the simplest cases involving one dimension and symmetrical probability distributions.     

The form of the rate constant for elementary reactions at equilibrium from MD: framework and proposals for thermokinetics

The rates of formation and concentration distributions of a dimer reaction showing hysteresis behavior are examined in an ab initio chemical reaction designed as elementary and where the hysteresis structure precludes the formation of transition states (TS) with pre-equilibrium and internal sub-reactions. It was discovered that the the reactivity coefficients, defined as a measure of departure from the zero density rate constant for the forward and backward steps had a ratio that was equal to the activity coefficient ratio for the product and reactant species. This surprising result, never formally incorporated in elementary rate expressions over approximately one and a half centuries of quantitative chemical kinetics measurement and calculation is accepted axiomatically and leads to an outline of a theory for the form of the rate constant, in any one given substrate—here the vacuum state. A major deduction is that the long-standing definition of the rate constant for elementary reactions is not complete and is nonlinear, where previous works almost always implicitly refer to the zero density limit for strictly irreducible elementary reactions without any attending concatenation of side-reactions. This is shown directly from MD simulation, where for specially designed elementary reactions without any transition states, density dependence of reactants and products always feature, in contrast to current practice of writing rate equations. It is argued that the rate constant expression without reactant and product dependence is due to historical conventions used for strictly elementary reactions. From the above observations, a theory is developed with the aid of some proven elementary theorems in thermodynamics, and expressions under different state conditions are derived whereby a feasible experimental and computational method for determining the activity coefficients from the rate constants may be obtained under various approximations and conditions. Elementary relations for subspecies equilibria and its relation to the bulk activity coefficient are discussed. From one choice of reaction conditions, estimates of activity coefficients are given which are in at least semi-quantitative agreement with the data for non-reacting Lennard-Jones (LJ) particles for the atomic component. The theory developed is applied to ionic reactions where the standard Brönsted-Bjerrum rate equation and exceptions to this are rationalized.     

Conformational characteristics of single flexible polyelectrolyte chain

The behaviour of a flexible anionic chain of 150 univalent and negatively charged beads connected by a harmonic-like potential with each other in the presence of an equal number of positive and free counterions, is studied in molecular dynamics simulations with Langevin thermostat in a wide range of temperatures. Simulations were carried out for several values of the bending parameter, corresponding to fully flexible polyion, moderately and strongly stiff polyion as well as for the case when bend conformation is preferable to the straight one. We have found that in all cases three regimes can be distinguished, which can be characterized as “random coil”, observed at high temperatures; “extended conformation” observed at moderate temperatures (of the order of 1 in reduced units), and compact “globular conformation” attained at low temperatures. While the transition between high-temperature random and extended conformations is gradual, the transition from the extended coil to the globular state, taking place at a temperature of about 0.2 in reduced units, is of abrupt character resembling a phase transition.     

An Energy Interconversion Principle Applied in Reaction dynamics for the determination of equilibrium standard states

Chemical and other reaction theories involving thermodynamical equilibrium states utilize statistical mechanical equilibrium density distributions. Here, a definition of heat-work transformation termed thermo-mechanical coherence is first made, and it is conjectured that most molecular bonds have the above heat-work transformation property, which models a chemical bond as a “centrifugal heat engine”, where the internal energy state need not correspond to any of the standard equilibrium densities. Expressions are derived for the standard Gibbs free energy, enthalpy, and entropy where the bond coordinates need not conform to a non-degenerate Boltzmann state, since bond breakdown and formation are processes that have direction, whereas equilibrium distributions are derived when the Hamiltonian is of fixed form, which is not the case for chemical reactions using localized Hamiltonians. The empirically determined Gibbs free energy from a known molecular dynamics simulation of a dimer reaction , accords rather well with the theoretical estimate. A relation connecting the rate of reaction with the equilibrium constant and other kinetic parameters is derived and could place the commonly observed linear relationship between the logarithms of the rate constant and equilibrium constant on a firmer theoretical footing. These relationships could include analogues of the Hammett correlations used extensively in physical organic chemistry, as well as others which are temperature dependent. One prediction of the principles developed here is that the equilibrium standard reaction free energy is more dependent on the height of the intermolecular potential than its depth, so that the sign of the ΔG ^θ can change for varying barrier height with fixed well depth, which may appear counter-intuitive. All the above developments can be tested directly in simulations and therefore provides a fertile ground for further research with significant implications on how standard states are determined in relation to the direction of chemical reaction.This work treats the molecular bond using standard thermodynamics as if it were a system, and it is anticipated that with the advent of single-molecule science and experiment, that might be one direction in which molecular statistical thermodynamics would develop.     

Focus on the Clausius Inequalities as a consequence of modeling thermodynamic systems as a series of open Carnot cycles

Various results in thermodynamics developed recently are brought into focus by further refinement to set in less ambiguous form topics connected to irreversibility and the so called “Clausius Inequality”. This singular “Clausius Inequality” for both closed and open systems was traditionally deduced from the Riemann “integration” of closed Carnot cycle loops for irreversible transitions. Evidently topological problems might be expected to arise concerning boundary conditions when “open” and “closed” systems exists simultaneously in such a scheme. It has hitherto been assumed that in this scheme, only one central Clausius Inequality can exist coupling all processes. Based on a new recent development of open system Carnot cycles, it is shown that other analogous inequalities can be derived, due to the presence of another fundamental entropy state function derived in the recent development, implying non-singularity. Their properties are such as to indicate that no new non-equilibrium entropy can arise from the inequalities as has been proposed over the decades. It is shown that a sequence of points along a non-equilibrium state space must have excess variables augmenting those for the equilibrium situation, which demonstrates that the often used Principle of Local Equilibrium (PLE) is only an approximation, implying that far-from-equilibrium theories should be developed ab initio from irreversible dynamical laws rather than from PLE. Examples presented from actual computations for both systems in equilibrium and non-equilibrium appears to support this deduction. Large scale and extensive thermodynamical theories have been created based on the assumption of a single Clausius-like inequality, such as those stemming from the very influential and extensive Truesdale school, and so such pervasive developments are also open to question.     

The use of high-throughput synthesis and purification in the preparation of a directed library of adrenergic agents

A library of potential agonists and antagonists for adrenergic receptors was prepared using high-throughput solution-phase parallel synthesis. Traditional solution-phase reductive amination reactions followed by rapid purification by ion exchange chromatography yielded products with near-analytical purity. An array of ketones and amines, arranged in an 8 × 12 matrix, were combined to form 96 individual compounds. This revised version was published online in August 2006 with corrections to the Cover Date.     

Reflections on the conformation, topology and thermodynamics of a polyelectrolyte chain in the presence of counterions with plausible applications

The simulation results from a basic polyelectrolyte chain consisting of an anionic string of 150 univalent negatively charged particles connected under various harmonic-like potential interactions with each other in the presence of a similar number of positive and free counter ions found in Jesudason et al. (EPJE $30$ 30 :341–350, 2009) forms the focal point for further discussion on chain models based on a survey of more recent developments in general polyelectrolyte theory. The topics discussed include persistence length definition, forcefields and methods of controlling simulation parameters, and thermodynamics. The data for the basic system was derived for the temperature range $0.1$ 0.1 – $10.0$ 10.0 in reduced units (corresponding to $\xi =10\text{-- }0.1$ ξ = 10 -- 0.1 ); the augmented data involves a $360$ 360 monomer chain. The data include the total and Coulombic energies, radial distribution functions, radii of gyration, end-to-end distances and snapshots of the system which are all discussed anew. Polyelectrolyte systems have been overwhelmingly associated with biophysical interpretations, but here it is suggested that these detailed studies and the consequent theoretical formulations could be extended further afield; non-biological ionic liquid systems with catalytic and energy storage applications are some of many other possibilities. However, the approach used by MD simulations to validate ionic liquid systems as carriers of molecules with catalytic moieties often refer to CPMD and DFT quantum methods, which is not the current norm as judged by the literature in especially coarse grained polyelectrolyte MD. The quantum approach could also be used for more detailed analysis of biophysical systems where one trend seems to be that the incorporation of details in simulations accounts for phenomena not explicable in coarser grained MD, for instance if conventional atomic ionic charges are assigned to all atom modeling. This is illustrated by a linear chain modeling a DNA polymer using different charge and size assignments for the same linear charge density. The trends are such that it might be expected that some form of routine standardization of force fields in the spirit of the Jorgensen OPLS-AA method that incorporates quantum calculations specific to a system will be implemented as a routine as refinements are seen to lead to more comprehensive rationalization.     

I. Numerical nonlinear analysis: differential methods and optimization applied to chemical reaction rate determination

The primary emphasis of this work on kinetics is to illustrate the a posteriori approach to applied nonlinear analysis, where focus on data may also lead to novel outcomes, as may also be the case with the current a priori tendencies of applied analysis, which relies on axioms or constructs concerning the nature of the observable. Here, methods for the determination of chemical rate constants are developed and discussed utilizing nonlinear analysis which does not require exact knowledge of initial reactant concentrations. These methods are compared with those derived from standard methodology for known chemical reactions studied by eminent kineticists and in one case with a reaction whose initial reactant concentration was in doubt. These gradient methods are shown to be consistent with the standard methods on average, and could readily serve as alternatives for standard conditions and can be used for studies where there are limits or unknowns in the initial conditions, such as in the burgeoning fields of astrophysics and astrochemistry, forensics, archeology and biology where the standard methods are not applicable. All four reactions studied exhibited semi-sinusoidal-like change with reactant concentration change which standard integral methods have not highlighted, and which seems to constitute the observation of a new effect. Reasons based on two mechanisms are given for this observation, and experiments are suggested that can discriminate between these two factors. Although first and second order reactions were investigated here, the method applies to arbitrary fractional orders by polynomial expansion of the rate decay curves where closed form integrated expressions do not exist at present. Integral methods for the above will be investigated next.     

Prediction of viscosities and COSMO-RS analyses in binary mixtures of N,N-dimethylformamide with acetone

Experimental viscosities, η, for pure N,N-dimethylformamide (DMF) and acetone (ACT) and their binary mixtures are measured over the whole composition range as a function of temperature between 298.15 and 313.15 K. The deviations in viscosity, ?η, Gibbs free energy of activation ?G, entropies ?S*, enthalpies ?H of activation of viscous flow have been calculated. The determination of excess molar volumes, Vη^E, was calculated from the experimental viscosities for the binary mixtures. The conductor-like screening model is applied to interpret the intermolecular forces. The σ-profile is computed for the N,N-DMF and ACT with conductor-like screening model for real solvents. The experimental results were found to be in good agreement with the theoretical predictions. Moreover, viscosity data were calculated from the theoretical equations of Grunberg and Nissan, Hind et al. and Wilke for the entire systems. All results obtained were averaged experimentally and theoretically in terms of average deviations.