Molecular structure extracted from residual dipolar couplings: diphenylmethane dissolved in a nematic liquid crystal

This paper describes an analysis of 1H-1H residual dipolar couplings (RDCs) in diphenylmethane (DPM) dissolved in a nematic liquid crystal, reported by Celebre et al. [J. Chem. Phys. 118, 6417 (2003)]. In that article, the conformational distribution function for DPM was extracted from the RDCs, using the additive potential (AP) model which is based on the molecular-field theory. The AP approach is a powerful, and frequently used, tool for analysis of the nuclear-magnetic-resonance (NMR) parameters in liquid crystals. It requires, however, a priori knowledge of the functional form of the torsional potential, which may even for a simple molecule, such as DPM, be complicated to determine. Here, we analyze the same set of the RDCs using our APME procedure, which is a hybrid model based on the AP approach and maximum entropy (ME) theory. The APME procedure does not require any assumptions about the functional form of the torsional potential and, in contrast with the ME method, is applicable to weakly ordered systems. In the investigation reported in the present study, the results from the APME analysis are in good agreement with the AP interpretation, whereas the ME approach essentially fails in the extraction of the conformational distribution function for DPM.     

The structure of substituted biphenyls as studied by proton NMR in nematic solvents. Single conformation model versus maximum entropy analysis

Published [11,12] proton nuclear magnetic resonance data for two substituted biphenyl molecules dissolved in nematic solvents are analysed in terms of the single conformation model and compared with the results of the maximum entropy analysis of [11]. It is shown that (i) this model, in which the number of adjustable parameters is less than the number of data, can describe very well the data for both molecules and (ii) the results of the maximum entropy analysis provide global support for this model. It is argued that the ultimate support of the single conformation model would be that introduction of a sufficiently large number of additional data in the maximum entropy analysis leads to a distribution for the dihedral angle between the two phenyl rings with two symmetrical very sharp peaks.     

The structure of substituted biphenyls as studied by proton NMR in nematic solvents. Single conformation model versus maximum entropy analysis

Abstract

Published [11,12] proton nuclear magnetic resonance data for two substituted biphenyl molecules dissolved in nematic solvents are analysed in terms of the single conformation model and compared with the results of the maximum entropy analysis of [11]. It is shown that (i) this model, in which the number of adjustable parameters is less than the number of data, can describe very well the data for both molecules and (ii) the results of the maximum entropy analysis provide global support for this model. It is argued that the ultimate support of the single conformation model would be that introduction of a sufficiently large number of additional data in the maximum entropy analysis leads to a distribution for the dihedral angle between the two phenyl rings with two symmetrical very sharp peaks.     

Solvent excess entropy at the electrode—solution interface

A model for water molecules in the double layer based upon information from gas-phase adsorption measurements has been used to calculate the configurational entropy of water in the double layer as a function of electric charge. The calculations agree well experimentally both in respect to dependence on charge and particularly in the position of the maximum entropy. The model can also be made consistent with the rest of the solvent excess entropy. The consistency between model and experiment favours models of capacitance humps which are not dependent upon water molecule orientation.     

基于液态合金短程序的混合构型熵新模型

基于液态合金化学短程序与拓扑短程序发展了一个新的混合构型熵计算模型, 从这个模型可以导出用来描述等原子直径随机混合物的理想混合熵. 通过将该模型应用于一些理想的和真实的液态二元合金, 可以看到化学短程序减小了混合构型熵, 而原子尺寸差异的影响则较为复杂. 当大原子进入小原子基体时, 混合构型熵增大; 而当小原子进入大原子基体时, 混合构型熵减小. 在这些合金中, 共晶成分处并没有出现混合构型熵极大值.     

Pure component spectral reconstruction from mixture data using SVD, global entropy minimization, and simulated annealing. Numerical investigations of admissible objective functions using a synthetic 7-species data set

A combination of singular value decomposition, entropy minimization, and simulated annealing was applied to a synthetic 7-species spectroscopic data set with added white noise. The pure spectra were highly overlapping. Global minima for selected objective functions were obtained for the transformation of the first seven right singular vectors. Simple Shannon type entropy functions were used in the objective functions and realistic physical constraints were imposed in the penalties. It was found that good first approximations for the pure component spectra could be obtained without the use of any a priori information. The present method out performed the two widely used routines, namely Simplisma and OPA-ALS, as well as IPCA. These results indicate that a combination of SVD, entropy minimization, and simulated annealing is a potentially powerful tool for spectral reconstructions from large real experimental systems.     

Characterizing multiple molecular States in single-molecule multiparameter fluorescence detection by probability distribution analysis

Probability distribution analysis (PDA) [M. Antonik et al., J. Phys. Chem. B 2006, 110, 6970] allows one to quantitatively analyze single-molecule (SM) data obtained in Forster resonance energy transfer (FRET) or fluorescence polarization experiments. By taking explicitly background and shot noise contributions into account, PDA accurately predicts the shape of one-dimensional histograms of various parameters, such as FRET efficiency or fluorescence anisotropy. In order to describe complex experimental SM-FRET or polarization data obtained for systems consisting of multiple non-interconverting fluorescent states, several extensions to the PDA theory are presented. Effects of brightness variations and multiple-molecule events are considered independently of the detection volume parameters by using only the overall experimental signal intensity distribution. The extended PDA theory can now be applied to analyze any mixture, by using any a priori model or a model-free deconvolution approach based on the maximum entropy method (MEM). The accuracy of the analysis and the number of free parameters are limited only by data quality. Correction of the PDA model function for the presence of multiple-molecule events allows one to measure at high SM concentrations to avoid artifacts due to a very long measurement time. Tools such as MEM and combined mean donor fluorescence lifetime analysis have been developed to distinguish whether extra broadening of PDA histograms could be attributed to structural heterogeneities or dye artifacts. In this way, an ultimate resolution in FRET experiments in the range of a few Angstrom is achieved which allows for molecular Angstrom optics distinguishing between a set of fixed distances and a distribution of distances. The extended theory is verified by analyzing simulations and experimental data.     

Photosynthetic models with maximum entropy production in irreversible charge transfer steps

Steady-state bacterial photosynthesis is modelled as cyclic chemical reaction and is examined with respect to overall efficiency, power transfer efficiency, and entropy production. A nonlinear flux–force relationship is assumed. The simplest two-state kinetic model bears complete analogy with the performance of an ideal (zero ohmic resistance of the P–N junction) solar cell. In both cases power transfer to external load is much higher than the 50% allowed by the impedance matching theorem for the linear flux–force relationship. When maximum entropy production is required in the transition with a load, one obtains high optimal photochemical yield of 97% and power transfer efficiency of 91%. In more complex photosynthetic models, entropy production is maximized in all irreversible electron/proton (non-slip) transitions in an iterative procedure. The resulting steady-state is stable with respect to an extremely wide range of initial values for forward rate constants. Optimal proton current increases proportionally to light intensity and decreases with an increase in the proton-motive force (the backpressure effect). Optimal affinity transfer efficiency is very high and nearly perfectly constant for different light absorption rates and for different electrochemical proton gradients. Optimal overall efficiency (of solar into proton-motive power) ranges from 10% (bacteriorhodopsin) to 19% (chlorophyll-based bacterial photosynthesis). Optimal time constants in a photocycle span a wide range from nanoseconds to milliseconds, just as corresponding experimental constants do. We conclude that photosynthetic proton pumps operate close to the maximum entropy production mode, connecting biological to thermodynamic evolution in a coupled self-amplifying process.     

Ionic melts with waterlike anomalies: thermodynamic properties of liquid BeF2

Thermodynamic properties of liquid beryllium difluoride (BeF(2)) are studied using canonical ensemble molecular dynamics simulations of the transferable rigid ion model potential. The negative slope of the locus of points of maximum density in the temperature-pressure plane is mapped out. The excess entropy, computed within the pair correlation approximation, is found to show an anomalous increase with isothermal compression at low temperatures which will lead to diffusional as well as structural anomalies resembling those in water. The anomalous behavior of the entropy is largely connected with the behavior of the Be-F pair correlation function. The internal energy shows a T(35) temperature dependence. The pair correlation entropy shows a T(-25) temperature dependence only at high densities and temperatures. The correlation plots between internal energy and the pair correlation entropy for isothermal compression show the characteristic features expected of network-forming liquids with waterlike anomalies. The tagged particle potential energy distributions are shown to have a multimodal form at low temperatures and densities similar to those seen in other liquids with three-dimensional tetrahedral networks, such as water and silica.     

Encoding of stoichiometric constraints in the composition depth profile reconstruction from angle resolved X‐ray photoelectron spectroscopy data

The inversion of angle resolved XPS data is a difficult problem, due to mathematical complexity of accurate model of electron transport, sensitivity to noise and small number of measured points limiting the depth resolution and the accuracy of the calculated depth profiles. Extended maximum entropy model for the calculation of apparent compositions (measured intensity ratios) is presented which allows to encode linear relationship between element concentrations. These can be used to calculate a solution with additional stoichiometric relationships and analyze, simultaneously, signals from several synthetic peak components. The synthetic peak components used in the model can represent various core level energy shifts, which are otherwise difficult to determine unambiguously from the measured signal. Element concentrations linked with stoichiometric relationships are used to identify compound materials with known density and inelastic scattering properties. The new model, thus allows self‐consistent recovery of depth profiles using maximum entropy method without the assumption of homogeneous density. The improved accuracy of the recovered depth profiles is demonstrated on the analysis of HfON/SiON overlayers. Various artefacts in the depth profiles obtained with standard maximum entropy model, which assumes constants density are identified. Copyright © 2011 John Wiley & Sons, Ltd.     

Approximate density matrices and Husimi functions using the maximum entropy formulation with constraints

The entropy of an electronic system is defined in terms of the Husimi function, a nonnegative distribution function in phase space. The Husimi function is calculated by maximizing the entropy subject to the constraints that the Husimi function give a Gaussian convolution of the desity when integrating over the momentum coordinates and that its second moment with respect to momentum give a sum of Gaussian convolutions of the density and the kinetic energy density. The result is compared with the Wigner function. Equations are given for calculating the density matrix from the Husimi function. The resulting equation for the exchange energy requires a difficult numerical integration. An alternate method is used to obtain the density matrix from an approximate partially collapsed Husimi matrix that gives the maximum entropy Husimi function as its diagonal. The results are exact for the harmonic oscillator ground state. Exchange energies calculated for H and the He isoelectronic series through C⁺⁴ show slight improvements over those calculated using a maximum entropy Wigner function.     

Pair-correlation entropy of hydrophobic hydration: decomposition into translational and orientational contributions and analysis of solute-size effects

We develop an efficient method to evaluate the translational and orientational contributions to the solute-water pair-correlation entropy that is a major component of the hydration entropy. A water molecule is modeled as a hard sphere of diameter dS=0.28 nm in which a point dipole and a point quadrupole of tetrahedral symmetry are embedded. A hard sphere of diameter dM, a hydrophobic solute, is immersed at infinite dilution in the model water. The pair-correlation entropy is decomposed into the translational and orientational contributions in an analytical manner using the angle-dependent Ornstein-Zernike integral equation theory. The two contributions are calculated for solutes with a variety of sizes (0.6相似文献   

Transport in nanoporous zeolites: relationships between sorbate size, entropy, and diffusivity

Molecular dynamics simulations have been performed on monatomic sorbates confined within zeolite NaY to obtain the dependence of entropy and self-diffusivity on the sorbate diameter. Previously, molecular dynamics simulations by Santikary and Yashonath [J. Phys. Chem. 98, 6368 (1994)], theoretical analysis by Derouane et al. [J. Catal. 110, 58 (1988)] as well as experiments by Kemball [Adv. Catal. 2, 233 (1950)] found that certain sorbates in certain adsorbents exhibit unusually high self-diffusivity. Experiments showed that the loss of entropy for certain sorbates in specific adsorbents was minimum. Kemball suggested that such sorbates will have high self-diffusivity in these adsorbents. Entropy of the adsorbed phase has been evaluated from the trajectory information by two alternative methods: two-phase and multiparticle expansion. The results show that anomalous maximum in entropy is also seen as a function of the sorbate diameter. Further, the experimental observation of Kemball that minimum loss of entropy is associated with maximum in self-diffusivity is found to be true for the system studied here. A suitably scaled dimensionless self-diffusivity shows an exponential dependence on the excess entropy of the adsorbed phase, analogous to excess entropy scaling rules seen in many bulk and confined fluids. The two trajectory-based estimators for the entropy show good semiquantitative agreement and provide some interesting microscopic insights into entropy changes associated with confinement.     

Resolution enhancement in electron spin-echo spectroscopy by means of the maximum entropy method

The resolving power of electron spin-echo spectroscopy decreases as the available data segment becomes shorter. A dramatic restoration of the resolving power is achieved by applying maximum entropy spectral analysis. This is possible because the maximum entropy formalism is maximally non-committal with regard to unavailable data.     

Thermodynamic Properties and Molecular Dipole Moments of Antimony Compounds from Quantum Chemical Evaluations

By the PM3 method, standard values of entropy, heats and Gibbs energies of formation and dipole moments of the molecules have been computed for a series of inorganic and organic antimony compounds. Linear dependences P exper = bP theor (where P is any of the mentioned properties) have been stated, allowing a priori evaluation of thermodynamic characteristics and molecular dipole moments of Sb-containing substances. It has been concluded that triphenylstibinedichloride in benzene solution, as well as triphenylstibinehydroxychloride in dioxane medium, exist in the form of trigonal bipyramid with two axial chlorine and oxygen atoms.     

Optimizing hierarchical equations of motion for quantum dissipation and quantifying quantum bath effects on quantum transfer mechanisms

We present an optimized hierarchical equations of motion theory for quantum dissipation in multiple Brownian oscillators bath environment, followed by a mechanistic study on a model donor-bridge-acceptor system. We show that the optimal hierarchy construction, via the memory-frequency decomposition for any specified Brownian oscillators bath, is generally achievable through a universal pre-screening search. The algorithm goes by identifying the candidates for the best be just some selected Padé spectrum decomposition based schemes, together with a priori accuracy control criterions on the sole approximation, the white-noise residue ansatz, involved in the hierarchical construction. Beside the universal screening search, we also analytically identify the best for the case of Drude dissipation and that for the Brownian oscillators environment without strongly underdamped bath vibrations. For the mechanistic study, we quantify the quantum nature of bath influence and further address the issue of localization versus delocalization. Proposed are a reduced system entropy measure and a state-resolved constructive versus destructive interference measure. Their performances on quantifying the correlated system-environment coherence are exemplified in conjunction with the optimized hierarchical equations of motion evaluation of the model system dynamics, at some representing bath parameters and temperatures. Analysis also reveals the localization to delocalization transition as temperature decreases.     

Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics

Stochastic thermodynamics of chemical reaction systems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalytic oxidation of carbon monoxide on the surface of platinum crystal as an example. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the time-averaged entropy production P on the system size N in a parameter region close to the deterministic Hopf bifurcation (HB). In the large system size (weak noise) limit, we find that P ～ N(β) with β = 0 or 1, when the system is below or above the HB, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly, P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system parameter approaches the so-called CANARD point where the maximum disappears. This phenomenon could be qualitatively understood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.     

Interplay of host volume variations and internal distortions in the course of intercalation into disordered matrices

Based on a combination of the distortive lattice gas model and the maximum information entropy approach, the thermodynamics of insertion into disordered hosts is analyzed. It is found that the isotherm specificities can be explained as a cooperative interplay of the host volume expansion and the internal distortions, which tend to optimize the host structure inducing a local lowering of the insertion energetic cost. Behavior of amorphous LixWO3 films of different thicknesses is discussed in this context.