Theoretical grounds

The classical theory of kinetic isotope effect (Kill) treats the vibrational ground state quantum-mechanically and motion across the top of the barrier classically. The theory asserts that KIF arises from the larger quantum zero-point energy of the larger isotope and 

In the framework of Marcus theory (Marcus, 1968), the difference between Gibbs energy activation for hydrogen and deuterium transfer is given by the equation 

Application of Marcus rate theory to proton transfer in enzyme-catalyzed reactions was discussed by Kresge and Silverman, 1999. Relationships of log KIE and kinetics of the enzyme catalysis (kcat) and parameters of the reaction driving force were found to be in agreement with the Marcus model. 

The first theory of hydrogen transfer wich takes into account the nuclear tunneling was developed by Levich et al., (1970). The authors calculated the transfer probability, Wif, using the general formula of the perturbation theory  

The effect of isotopes substitution on fast nuclear vibrations and, therefore, nuclear tunneling and KIE can be derived from Marcus-Jortner Eq. 2.17. As seen from Eq. 2.17, both energy activation and preexponential factors are dependent on the vibration frequency. 

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Kolos W and Wolniewicz L 1968 Improved theoretical ground-state energy of the hydrogen molecule J. Chem. Phys. 49 404-10... 

Although the left to right reaction is exothermic, hence giving a better equilibrium yield of sulphur trioxide at low temperatures, the reaction is carried out industrially at about 670-720 K. Furthermore, a better yield would be obtained at high pressure, but extra cost of plant does not apparently justify this. Thus the conditions are based on economic rather than theoretical grounds (cf Haber process). 

Element 103, lawrencium, completes the actinides. Following this series, the transition elements should continue with the filling of the 6d orbitals. There is evidence for an element 104 (eka-hafnium) it is believed to form a chloride MCl4, similar to that of hafnium. Less positive evidence exists for elements 105 and 106 attempts (so far unsuccessful) have been made to synthesise element 114 (eka-lead). because on theoretical grounds the nucleus of this elemeni may be stable to decay by spontaneous fusion (as indeed is lead). Super-... 

An alternative chain-terminating decomposition of the tetroxide, known as the Russell mechanism (29), can occur when there is at least one hydrogen atom in an alpha position the products are a ketone, an alcohol and oxygen (eq. 15). This mechanism is troubling on theoretical grounds (1). Questions about its vaUdity remain (30), but it has received some recent support (31). 

The value of 9 can be estimated on purely theoretical grounds from estimates of the adsorption of surfactant which, in turn, can be estimated from the Gibbs adsorption equation relating adsorption to surface-tension lowering. 

The basicity of pyrazole and its relation with imidazole basicity (due both to enthalpy and entropy changes (77MI40403)) have been discussed on theoretical grounds (Section 4.04.1.2.1). The pK values of 90 pyrazoles have been determined by Gonzalez et al. (68BSF707,68BSF5009) and it is essentially his work that will be discussed below. A selection of pK values are shown in Table 28. The pK values for some other pyrazoles have been measured in connection with nitration studies (Section 4.04.2.1.4(ii)) (71JCS(B)2365). 

Main tasks on theoretical grounds and development of methodology for chemical analyses of ecological state of surface waterbodies under regulation of heavy metal ions discharges in the bodies. It is necessary to ... 

X-ray structural studies have played a major role in transforming chemistry from a descriptive science at the beginning of the twentieth century to one in which the properties of novel compounds can be predicted on theoretical grounds. When W.L. Bragg solved the very first crystal structure, that of rock salt, NaCl, the results completely changed prevalent concepts of bonding forces in ionic compounds. 

Herein, we summarize some of the basic electronic and structural properties expected of these nanotubes from theoretical grounds. First we will discuss the basic structures of the nanotubes, define the nomencla-... 

It is of interest that the reversible migration of hydrogen between positions 1 and 2 of thi.s sj stem corre.spond to a 1,5-sigmatropie shift, a proee.s.s predicted to be favorable on theoretical grounds [R. R. Woodward and R. Hoffmann, J. Am. Ghem. Soc. 87, 2511 (1965)] and known to occur with exceptional facility (R. B. Woodward in Aromaticity, Spec. Publ. No. 21, p. 217. The Chemical Society, London, 1967). 

On both experimental and theoretical grounds there is little doubt of the importance of polarizability as a major factor in determining the commonly encountered, though variable, high RS /RO ratios. Were thermodynamic carbon affinities mainly responsible for the usual reactivity order RS > RO, the peculiar behavior of chloroquinolines would be very difficult to understand. There is some indication, however, that carbon affinities roughly parallel basicities (hydrogen affinities), In the latter case, lower RS /RO ratios could be explained in terms of the intermediate complex mechanism, ... 

The book commences with a general introduction outlining the basic concepts. This is followed by a chapter on radical reactions that is intended to lay the theoretical ground-work for the succeeding chapters on initiation, propagation, and termination. Because of its importance, radical copolymerization is treated in a separate chapter. We then consider some of the implications of these chapters by... 

Berthelot and Jungfleisch considered, from their experimental results, that for any given trio of substances, k depended on the temperature, and on the concentration of the shared substance. It was shown, however, on theoretical grounds, by Aulich, and Nernst, that, provided the solute does not alter its molecular state in passing from one solvent to another, k should be independent of concentration, but will depend on the temperature. 

It has been known since the beginning of recorded history that not all liquids are completely miscible with one another. But only in recent times have we learned that gases may also, under suitable conditions, exhibit limited miscibility. The possible existence of two gaseous phases at equilibrium was predicted on theoretical grounds by van der Waals as early as 1894, and again by Onnes and Keesom in 1907 (see R8). Experimental verification, however, was not obtained until about forty years later, primarily by Krich-evsky, Tsiklis, and their co-workers in Russia (see Gl, SI), by Lindroos and Dodge at Yale (L5), and, more recently, by de Swaan Arons and Diepen at Delft (D3). 

First of all, it may be interesting that this type of structure is not referred to in the collections of structures mentioned by Sorriso (1978) and by Ershov et al. (1981) It is related, however, to the structure proposed for diazonium ions by Glaser et al. (1992b) on theoretical grounds (4.2). 

Instructions for the behaviour of every cell in the bodies of worms, flies and humans will soon reside in public databases for all to read. A complete set of these instructions, packaged as chromosomes, is inherited by most cells in our body. Because of this, many if not most somatic nuclei in mammals are totipotent that is, they are capable of programming all of mammalian development when injected into enucleated eggs (Wilmut et al 1997). Dolly s creation had dramatic practical consequences but its feasibility was never improbable on theoretical grounds. How cells inherit two complete packages of the genome at each cell division is one of the most fundamental questions in biology (Fig. la). 

Marchiano and Arvia (M3) also measured mass transfer by thermal and diffusional free convection at a vertical plate. They derived on theoretical grounds a combined Grashof number as follows ... 

That is, the removal of spherical particles from a flat surface is determined by the magnitude of the wall shear stress, x0. Visser (1) also claims that since the removal mechanism is unknown, it is not possible to relate the Fh (tangential force) to the Fa (adhesive force) on theoretical grounds. Therefore, he assumes that the tangential force required for particle release is proportional to the adhesive force. 

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