Molecular fractionation theory

O Neil JR (1986) Theoretical and experimental aspects of isotopic fractionation. Rev Mineral 16 1-40 Oi T (2000) Calculations of reduced partition function ratios of monomeric and dimeric boric acids and borates by the ab initio molecular orbital theory. J Nuclear Sci Tech 37 166-172 Oi T, Nomura M, Musashi M, Ossaka T, Okamoto M, Kakihana H (1989) Boron isotopic composition of some boron minerals. Geochim Cosmochim Acta 53 3189-3195 Oi T, Yanase S (2001) Calculations of reduced partition function ratios of hydrated monoborate anion by the ab initio molecular orbital theory. J Nuclear Sci Tech 38 429-432 Paneth P (2003) Chlorine kinetic isotope effects on enzymatic dehalogenations. Accounts Chem Res 36 120-126... 

Hard and soft acid and base theory gives access to an early part of the slope in a reaction profile like that in Fig. 3.3, just as perturbation molecular orbital theory does. Using the definitions of absolute electronegativity and absolute hardness derived in Equations 3.5 and 3.6, the (fractional) number of electrons AN transferred is given by Equation 3.14. 

In theoretical chemistry, simple molecular orbital theory (Hiickel and semi-em-pirical Wolfsberg-Helmholz) was just being applied to metal complexes such as the vanadyl ion and mononuclear metal carbonyls when Inorganic Chemistry started, but none of the power, sophistication, and ease of use of today s density functional theory (DFT) existed. Today, DFT calculations are found in a large fraction of our submissions, often when the paper is predominantly experimental in nature. 

The molecular-statistical theory of polymer solutions in confined media was also applied to the conventional chromatographic theory of gradient elution [ 163]. This approach leads to the prediction of the special mode of interactive polymer chromatography gradient elution at critical point of adsorption. It was demonstrated theoretically and experimentally that under appropriate conditions elution of each compositionally homogeneous fraction of copolymer occurs at the critical mobile phase composition. This critical mobile phase composition depends only on the local structure of the copolymer chain and is independent of its molecular weight. As a consequence, gradient elution produces the chemical com-... 

Coulson (1939) contributed still another paper in which the notion of fractional bond orders was introduced for the first time in the context of molecular orbital theory. Fractional bond orders formalized the notion entertained by many chemists for a long time that in many substances, of which benzene is the paradigmatic example, bonds appear to have an intermediate character between single and double bonds. Hiickel was the first to introduce the distinction between a- and w-electrons in benzene, and it was in the framework of valence bond theory that the first definition... 

This chapter presents first some fundamental aspects of nucleation, and second the general Avrami equation, which is frequently used to describe overall crystallization. The growth theories of Lauritzen and Hoffman and Sadler and Gilmer are discussed in sections 8.4.2 and 8.4.3. Molecular fractionation and orientation-induced crystallization are dealt with in sections 8.5 and 8.6. 

The Fukui function is motivated by the following consideration if a fraction of an electron 5 is transferred to an N electron molecule, it wiU tend to distribute so as to minimize the energy of the resulting A + 8 electron syston. The resulting change in electron density (dp(r)/SNX y defined in Equation 14.28 is the nuleophilic Fukui function. In analogy, the (5p(r)/5A) .) defined in Equation 14.29 is the electrophilic Fukui function. In this work, we use 8 values of 0.1 and -0.1 electrons. It is notable that there are similarities between the interpretation of the Fukui functions and the frontier molecular orbital theory proposed by Fukui. °... 

Mention was made in Section XVIII-2E of programmed desorption this technique gives specific information about both the adsorption and the desorption of specific molecular states, at least when applied to single-crystal surfaces. The kinetic theory involved is essentially that used in Section XVI-3A. It will be recalled that the adsorption rate was there taken to be simply the rate at which molecules from the gas phase would strike a site area times the fraction of unoccupied sites. If the adsorption is activated, the fraction of molecules hitting and sticking that can proceed to a chemisorbed state is given by exp(-E /RT). The adsorption rate constant of Eq. XVII-13 becomes... 

In contrast molecular interaction kinetic studies can explain and predict changes that are brought about by modifying the composition of either or both phases and, thus, could be used to optimize separations from basic retention data. Interaction kinetics can also take into account molecular association, either between components or with themselves, and contained in one or both the phases. Nevertheless, to use volume fraction data to predict retention, values for the distribution coefficients of each solute between the pure phases themselves are required. At this time, the interaction kinetic theory is as useless as thermodynamics for predicting specific distribution coefficients and absolute values for retention. Nevertheless, it does provide a rational basis on which to explain the effect of mixed solvents on solute retention. 

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