Isotope theoretical

Wolfsberg, M. Comments on selected topics in isotope theoretical chemistry. In Kohen, A. and Limbach, H. H., Eds. Isotope Effects in Chemistry and Biology, CRC Press/Taylor Francis, Boca Raton, FL (2006), Chapter 3, p. 89. 

Because of the occurrence of 13c, and 1 0, and because mass spectrometry sorts ions according to m/e values, the peak intensities at m/e 252-256 do not represent the true proportion of iron isotopes. Table II is an example of how the abundances of the diligand ions deviate from the abxmdeuices of iron isotopes. Theoretically, the abundances of the diligand species can be calculated from the abundances of iron isotopes (IJ ). Calculated values may be used as a reference for the accuracy of the experimental values. 

So far, elements heavier than 118 were not studied at the MO level. Some general aspects of their chemistry were considered on the basis of atomic DF and DS calculations and can be found in [20,49,50]. Due to the very strong relativistic effects, the chemistry of those elements will be much more different to anything known before. Experimental investigations are still a matter of a far future and are dependent on discoveries of longer-lived isotopes. Theoretically, accurate predictions of properties of specific compounds will be quite a challenging task. The evolution of the Periodic Table has lately been discussed by Seaborg [184]. 

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

Quantitative mass spectrometry, also used for pharmaceutical appHcations, involves the use of isotopicaHy labeled internal standards for method calibration and the calculation of percent recoveries (9). Maximum sensitivity is obtained when the mass spectrometer is set to monitor only a few ions, which are characteristic of the target compounds to be quantified, a procedure known as the selected ion monitoring mode (sim). When chlorinated species are to be detected, then two ions from the isotopic envelope can be monitored, and confirmation of the target compound can be based not only on the gc retention time and the mass, but on the ratio of the two ion abundances being close to the theoretically expected value. The spectrometer cycles through the ions in the shortest possible time. This avoids compromising the chromatographic resolution of the gc, because even after extraction the sample contains many compounds in addition to the analyte. To increase sensitivity, some methods use sample concentration techniques. 

From equation 60 one can obtain a theoretical power requirement of about 900 kWh/SWU for uranium isotope separation assuming a reasonable operating temperature. A comparison of this number with the specific power requirements of the United States (2433 kWh/SWU) or Eurodif plants (2538 kWh/SWU) indicates that real gaseous diffusion plants have an efficiency of about 37%. This represents not only the barrier efficiency, the value of which has not been reported, but also electrical distribution losses, motor and compressor efficiencies, and frictional losses in the process gas flow. 

Our present views on the electronic structure of atoms are based on a variety of experimental results and theoretical models which are fully discussed in many elementary texts. In summary, an atom comprises a central, massive, positively charged nucleus surrounded by a more tenuous envelope of negative electrons. The nucleus is composed of neutrons ( n) and protons ([p, i.e. H ) of approximately equal mass tightly bound by the force field of mesons. The number of protons (2) is called the atomic number and this, together with the number of neutrons (A ), gives the atomic mass number of the nuclide (A = N + Z). An element consists of atoms all of which have the same number of protons (2) and this number determines the position of the element in the periodic table (H. G. J. Moseley, 191.3). Isotopes of an element all have the same value of 2 but differ in the number of neutrons in their nuclei. The charge on the electron (e ) is equal in size but opposite in sign to that of the proton and the ratio of their masses is 1/1836.1527. 

The author concerns himself with a comparison between theoretical and experimental studies of simple molecules containing the C = N linkage. A large number of spectroscopic studies have been made for XCN molecules, and in the majority of cases many isotopic species have been studied. The experimental data is very accurate. An interesting feature of such molecules is that the C s N distances are equal to within experimental error, and one might expect that the quadrupole coupling constants would be similar. This is not the case, as shown in Table 16.4. 

The theoretical difficulties encountered in attempting to relate the isotope effect in iodination with the occurrence of base catalysis are also apparent in bromina-tion, for Vainshtein and Shilov224 have shown that the isotope effects ArH/ArD are 1.0 (Br+), 2.6 (Br2) and 1.0 (HOBr) whereas the corresponding reactivities of the electrophiles in the systems used are > 1400 1.0 0.0015. 

Most of the chemical reactions presented in this book have been studied in homogeneous solutions. This chapter presents a conceptual and theoretical framework for these processes. Some of the matters involve principles, such as diffusion-controlled rates and applications of TST to questions of solvent effects on reactivity. Others have practical components as well, especially those dealing with salt effects and kinetic isotope effects. 

Rare-Gas-Hydrogen Reactions. Ion-molecule reactions in the rare gas-hydrogen system are of great interest both theoretically and experimentally. The properties of the reactants and products are well known or may be calculated, and the properties of the intermediate three-body complex pose a tractable theoretical problem. Systematic studies of cross-section energy dependence and isotope effects in these systems have been undertaken by Friedman and co-workers (29, 47, 49, 67), by Koski and co-workers (2, 3), and by Giese and Maier (15, 16). 

The work of Melander and Carter (1964) on 2,2 -dibromo-4,4 -di-carboxybiphenyl-6,6 -d2 (1) has been referred to above in the introductory and theoretical sections, where it was pointed out that the availability of two detailed theoretical computations of the inversion barrier (Westheimer and Mayer, 1946, Westheimer, 1947 Hewlett, 1960) made this system especially attractive for the study of steric isotope efifects. Furthermore, in the preferred initial-state conformation the two bromines are probably in van der Waals contact (cf. Hampsoii and Weissberger, 1936 Bastiansen, 1950), and thus initial-state steric effects are unaffected by deuterium substitution in the 6 and 6 positions. The barrier calculations provided two different theoretical values for the non-bonded H Br distance in the transition state which, together with the corresponding H Br potential function, could be inserted in equation (10) to yield values for A AH. For... 

Thermodynamic energy terms (and equilibrium constants) may differ for compounds containing different isotopic species of an element. This effect is described in theoretical detail by Urey (1947), and applications to geochemistry are discussed by Broecker and Oversby (1971) and Faure (1977). A good example is the case of the vapor/liquid equilibrium for water. The vapor pressure of a lighter isotopic species, H2 0, is higher relative to that of heavier species, (or HD O), and others. 

In carbon, an uncertainty exists which arises because we have neither sufficient empirical data nor an accepted theoretical model to explain the quantitative relationships between dietary carbon isotope signals and those... 

Schwarcz, H.P. 1991 Some theoretical aspects of isotope paleodiet studies. Journal of Archaeological Science 18 261-275. 

Some fifty years ago, a classic theoretical paper (Urey 1947) proposed that the oxygen isotope ratio ( 0/ 0) in various minerals depends on two variables the local environmental temperature and the oxygen isotopic ratio in the environmental water. The proposal was verified experimentally in carbonates (Epstein et al. 1951, 1953 McCrea 1950) where the oxygen isotope ratio is dependent on the temperature of formation and the ratio in... 

The only (to the best of our knowledge) theoretical treatment of hydrogen transfer by tunnelling to explicitly recognise the role of protein dynamics, and relate this in turn to the observed kinetic isotope effect, was described by Bruno and Bialek. This approach has been termed vibration-ally enhanced ground state tunnelling theory. A key feature of this theory... 

However, it cannot be decided at present which processes (degree of seawater-rock interaction or mixing ratio of seawater, igneous water and meteoric water) are important for the generation of Kuroko ore fluids solely from the isotopic studies. But experimental and theoretical considerations on seawater-volcanic rocks interaction and origin of hydrothermal solution at midoceanic ridges suggest that Kuroko ore fluids can be produced dominantly by seawater-volcanic rock interaction. 

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