Statistical theory of endothermic reactions

The rate of unimolecular decomposition of an excited molecule is calculated from the statistical theory based on conservation of the total energy and total momentum. The limits of applicability of the quasiequilibrium theory are examined. Distribution functions are calculated for the dissociation products from photon capture and electron impact.     

Statistical mechanical theory of local compositions

The concept of local composition has received much attention during the past few years, much of which has been devoted to justifying the empirical model proposed by Wilson in 1964. In this report the concept of local composition is defined on statiscal mechanical grounds and expressions relating these compositions to thermodynamic properties of equilibrium fluid mixtures are derived. In particular, different local composition approximations are presented and new approximations based on molecular theories of mixtures are derived. Sets of mixing rules consistent with these different local composition approximations result, some of which are density and temperature dependent. Also, relations for partial molar properties in terms of local compositions are derived from the Kirkwood-Buff solution theory. Finally the radius of the sphere of influence of local compositions is formulated on statistical mechanical grounds.     

Statistical mechanical theory of liquid entropy

The multiparticle correlation expansion for the entropy of a classical monatomic liquid is presented. This entropy expresses the physical picture in which there is no free particle motion, but, rather, each atom moves within a cage formed by its neighbors. The liquid expansion, including only pair correlations, gives an excellent account of the experimental entropy of most liquid metals, of liquid argon, and of the hard-sphere liquid. The pair correlation entropy is well approximated by a universal function of temperature. Higher-order correlation entropy, due to n-particle irreducible correlations for n ≥ 3, is significant in only a few liquid metals, and its occurrence suggests the presence of n-body forces. When the liquid theory is applied to the study of melting, we discover the important classification of normal and anomalous melting, according to whether there is not or is a significant change in the electronic structure upon melting, and we discover the universal disordering entropy for melting of a monatomic crystal. Interesting directions for future research are extension to include orientational correlations of molecules, theoretical calculation of the entropy of water, application to the entropy of the amorphous state, and correlational entropy of compressed argon. We clarify the relation among different entropy expansions in the recent literature. © 1994 John Wiley & Sons, Inc.     

Statistical theory of exothermic ion-molecule reactions

A statistical theory is presented for ion-molecule reactions of the type A₂+A⁺ ₂A⁺ ₃+A, with allowance for conservation of the total energy and of the angular momentum of the composite system A⁺ ₄. The conservation of the momentum greatly reduces the phase volume of the initial reaction channel; the probability of decomposition in the forward direction is less than one even for exothermic reactions. A reaction of this type is considered for hydrogen, for which the statistical theory gives a qualitative explanation of the observed relation of reaction cross-section to vibrational quantum number for H⁺ ₂.     

Landmarks in the theory of mass spectra

Statistical theories of mass spectra are based on two assumptions. The first one, which postulates efficient phase space sampling, is substantiated by various experimentation and is now theoretically much better understood. The efficiency of phase space sampling can be estimated and is found to be quite good. Much effort remains to be done concerning the second assumption. A new impetus should be given to the concept of transition state. A better understanding of the role played by the conservation of angular momentum, the exact significance of transition state switching, and the incorporation of quantum effects are set as goals for the future.     

Statistical models in the polarization radiation theory

The survey is devoted to general results for polarization free–free and free–bound radiative transitions in collisions of charged particles with heavy atoms and ions following from statistical atomic models. The atomic plasma model results for dynamic atomic polarizabilities are presented. Polarization Bremsstrahlung in collisions of fast and moderate energy electrons with Thomas–Fermi atoms is analyzed in details. A new polarization electron-heavy ions recombination channel is considered and compared with known radiative recombination channel. It is shown that recombination channels can be compared or even dominates over standards static radiation channels. Polarization radiation of fast multicharged ions in condensed media is also under consideration.     

Statistical analysis of intensity fluctuations in single molecule SERS spectra

We have investigated the fluctuations of the intensity and the line intermittency in the surface enhanced Raman spectra of a single iron-protoporphyrin IX molecule. A statistical analysis has revealed a high correlation between the intensity of each frequency couple in the spectrum. Removal of the continuum background has led to a suppression of the correlation at those frequencies where no Raman lines are present. Conversely, we have observed the persistence of a strong correlation at the intensities corresponding to the vibrational modes of the molecule. Further evidence of correlation between the intensities and the background signal indicates that the background is involved in the enhancement mechanism. Moreover, analysis of the Raman line intermittency reveals a random activation of the different molecular vibrational modes. These results can be generally put into relationship to the presence of two different contributions to the intensity fluctuations: one, strictly related to the continuum background, and affecting the whole spectrum, and another one which selectively acts on the various vibrational modes of the molecule.     

Statistical theory of multiple-site linear wall-adsorption capillary Chromatography

Based on the mass-balance principle, a particular diffusion equation to describe the movement of solute molecules in the stagnant layer of multiple-site solid surfaces is constructed. From the equation, the moments of residence time in a step on multiple-site surfaces are derived. Similarly, the moments in a step in the mobile phase are also derived from a diffusion-drift equation. According to the probability theory, there exists a general relationship between the moments of an elution curve and the moments in a step. Through this relationship, the expressions of the elution-curve moments are derived from the step moments. In this paper, the details related to multiple-site linear wall-adsorption capillary chromatography are described and added in the equations to determine the step moments. The resultant expressions of the elution-curve moments involve various factors, such as adsorption–desorption rate constants, equilibrium constants, axial and radial dispersions in the mobile phase. Afterwards, the moment expressions are used to analyze the peak tailing. The results show that a small quantity of sites with a slow desorption rate will lead to a large peak asymmetry.     

Statistical rate theory and kinetic energy-resolved ion chemistry: theory and applications

Ion chemistry, first discovered 100 years ago, has profitably been coupled with statistical rate theories, developed about 80 years ago and refined since. In this overview, the application of statistical rate theory to the analysis of kinetic-energy-dependent collision-induced dissociation (CID) reactions is reviewed. This procedure accounts for and quantifies the kinetic shifts that are observed as systems increase in size. The statistical approach developed allows straightforward extension to systems undergoing competitive or sequential dissociations. Such methods can also be applied to the reverse of the CID process, association reactions, as well as to quantitative analysis of ligand exchange processes. Examples of each of these types of reactions are provided and the literature surveyed for successful applications of this statistical approach to provide quantitative thermochemical information. Such applications include metal-ligand complexes, metal clusters, proton-bound complexes, organic intermediates, biological systems, saturated organometallic complexes, and hydrated and solvated species.     

Statistical mechanical theory for steady state systems. VII. Nonlinear theory

The second entropy theory for nonequilibrium thermodynamics is extended to the nonlinear regime and to systems of mixed parity (even and odd functions of molecular velocities). The steady state phase space probability density is given for systems of mixed parity. The nonlinear transport matrix is obtained and it is shown to yield the analog of the linear Onsager-Casimir reciprocal relations. Its asymmetric part contributes to the flux and to the production of second entropy. The nonlinear transport matrix is not simply expressible as a Green-Kubo fluctuation equilibrium time correlation function. However, here the first nonlinear correction to the transport coefficient is given explicitly as a type of the Green-Kubo equilibrium time correlation function. The theory is illustrated by application to chemical kinetics.     

Statistical evaluation of electrospray tandem mass spectra for optimized peptide fragmentation

Liquid chromatography-tandem mass spectrometry (LC-MS/MS) has become the method of choice for the analysis of complex peptide mixtures. It combines the separation power of nanoflow LC with highly specific sequence analysis, allowing automated peptide sequencing with high resolution and throughput. For peptide fragmentation, the current experimental setup uses predefined parameters based on the mass-to-charge ratio of the individual precursor. Suitable parameters are typically established by empirical evaluation of fragment spectra of individual peptides used as standards. As a result, nonoptimal fragment spectra are obtained if peptides show fragmentation behavior different from these standards, which often result in the loss of sequence-specific fragment ion information. Here we describe a statistical approach for the systematic evaluation of the quality of individual peptide fragment spectra based on the calculation of their arithmetic mean and standard deviation. The method utilizes the dependence of these parameters on the difference in electric potential across the collision cell to determine the value that results in maximum information content. We show that the method is applicable to fragment spectra generated from a variety of multiply-charged tryptic peptides, over a wide concentration range, and on different types of mass analyzers. We also show how this novel approach can be used to define optimized collision energy settings over a wide mass-to-charge range.     

Statistical Rice-Ramsperger-Kassel-Marcus quasiequilibrium theory calculations in mass spectrometry

The statistical theory [Rice-Ramsperger-Kassel-Marcus quasiequilibrium theory (RRKM/QET)] for calculating dissociation rate constants is explained and its implementation is outlined with sample computer programs. The energy deposition involved in various types of ionization processes is discussed and related to the appearance of the mass spectrum. The RRKM/QET calculations are used to explain the kinetic shift and its effect on the observed onset for fragmentations in the halobenzene ions. Direct dissociation versus rearrangement reactions are discussed in terms of the dissociation rates and the observation of metastable ions. Finally, it is shown how an average rate constant can be obtained from metastable peak intensities as a function of the ion extraction voltage in a conventional mass spectrometer.