Isotopes molecules

For mote complete discussion of isotope effects, see W H. Saunders, in Investigation cf Rates and Mechanisms of Reactions, E. S. Lewis, ed.. Techniques of Chemistry, 3rd ed., 4)1. VI, Part 1, John Wiley Sons, New York, 1974, pp. 211-255 L. Melander and W. H. Saunders, Jr., Reaction Rates of Isotopic Molecules, John Wiley Sons, New bik, 1980 W. H. Saunders, in Investigation of Rates and Mechanisms of Reactions, C. F. Bemasconi, ed.. Techniques of Chemistry, 4th ed., Vol. VI, Part 1, John Wiley Sons, New feik, 1986, Chapter VUI. 

L. Melander and W. H. Saunders, Reaction Rates of Isotopic Molecules, Wiley, New York, 1980, 331 pp. 

In the Bom-Oppenheimer picture the nuclei move on a potential energy surface (PES) which is a solution to the electronic Schrodinger equation. The PES is independent of the nuclear masses (i.e. it is the same for isotopic molecules), this is not the case when working in the adiabatic approximation since the diagonal correction (and mass polarization) depends on the nuclear masses. Solution of (3.16) for the nuclear wave function leads to energy levels for molecular vibrations (Section 13.1) and rotations, which in turn are the fundamentals for many forms of spectroscopy, such as IR, Raman, microwave etc. 

Isotopic molecules will have force fields which are identical to a high degree of accuracy. The vibrational amplitudes, on the other hand, will be mass-dependent, which means that the steric requirements of isotopic molecules will be slightly different. For this reason it is to be expected quite generally that isotopic molecules will respond differently to the change in steric conditions imposed by a chemical reaction, and hence that their reaction rates will differ somewhat. 

State-of-the-art TOF-SIMS instruments feature surface sensitivities well below one ppm of a mono layer, mass resolutions well above 10,000, mass accuracies in the ppm range, and lateral and depth resolutions below 100 nm and 1 nm, respectively. They can be applied to a wide variety of materials, all kinds of sample geometries, and to both conductors and insulators without requiring any sample preparation or pretreatment. TOF-SIMS combines high lateral and depth resolution with the extreme sensitivity and variety of information supplied by mass spectrometry (all elements, isotopes, molecules). This combination makes TOF-SIMS a unique technique for surface and thin film analysis, supplying information which is inaccessible by any other surface analytical technique, for example EDX, AES, or XPS. 

The equilibrium bond lengths and bond angles can be seen to differ little between the different isotopic molecules. Such a finding agrees with the predictions of the Bom-Oppenheimer approximation, that the electronic structure of a molecule is independent of the mass of its nuclei, it being the electronic structure of a molecule alone which determines the geometry. 

The Relative Reaction Velocities of Isotopic Molecules. J. chem. Physics... 

Since the discovery of the deuterium isotope in 1931 [44], chemists have long recognized that kinetic deuterium isotope effects could be employed as an indicator for reaction mechanism. However, the development of a mechanism is predicated upon analysis of the kinetic isotope effect within the context of a theoretical model. Thus, it was in 1946 that Bigeleisen advanced a theory for the relative reaction velocities of isotopic molecules that was based on the theory of absolute rate —that is, transition state theory as formulated by Eyring as well as Evans and Polanyi in 1935 [44,45]. The rate expression for reaction is given by... 

Melander, L. and Saunders, W. H., Jr. (1980c). In Reaction Rates of Isotopic Molecules Wiley-Interscience, New York, pp. 197-199 Melander, L. and Saunders, W. H., Jr. (1980d). In Reaction Rates of Isotopic Molecules. Wiley-Interscience, New York, p. 209... 

Melander, L. and Saunders, W. H., Jr. (1980e). In Reaction Rates of Isotopic Molecules. 

Bigeleisen, J. and Ishida, T. Application of finite orthogonal polynomials to the thermal functions of harmonic oscillators. I. Reduced partition function of isotopic molecules, J. Chem. Phys. 48, 1311 (1968). Ishida, T., Spindel, W. and Bigeleisen, J. Theoretical analysis of chemical isotope fractionation by orthogonal polynomial methods, in Spindel, W., ed. Isotope Effects on Chemical Processes. Adv. Chem. Ser. 89, 192 (1969). 

Bigeleisen J (1949) The relative velocities of isotopic molecules. J Chem Phys 17 675-678 Bigeleisen J (1955) Statistical mechanics of isotopic systems with small quantum corrections. I. General considerations and the rule of the geometric mean. J Chem Phys 23 2264-2267 Bigeleisen J (1998) Second-order correction to the Bigeleisen-Mayer equation due to the nuclear field shift. Proc National Acad Sci 95 4808-4809... 

Teller-Redllch rule phys chem For two isotopic molecules, the product of the frequency ratio values of all vibrations of a given symmetry type depends only on the geometrical structure of the molecule and the masses of the atoms, and not on the potential constants. tel-or red-lik, rul ... 

Based on equation 11.41, the difference between the Helmholtz free energies of formation of two isotopic molecules with respect to their gaseous atoms depends on the shift of vibrational frequencies between heavy and light isotope-bearing compounds—i.e., according to Bigeleisen and Mayer (1947),... 

Bigeleisen J. (1949). The relative reaction velocities of isotopic molecules. J. Chem. Phys., 17 675-678. 

Kinetic processes that depend primarily on differences in reaction rates of isotopic molecules... 

The temperature ranges in which these simple behaviours are approximated depend on the vibrational frequencies of the molecules involved in the reaction. For the calculation of a partition function ratio for a pair of isotopic molecules, the vibrational frequencies of each molecule must be known. When solid materials are considered, the evaluation of partition function ratios becomes even more complicated, because it is necessary to consider not only the independent internal vibrations of each molecule, but also the lattice vibrations. 

Ordinary diffusion can cause significant isotope fractionations. In general, light isotopes are more mobile and hence diffusion can lead to a separation of light from heavy isotopes. For gases, the ratio of diffusion coefficients is equivalent to the inverse square root of their masses. Consider the isotopic molecules of carbon in CO2 with masses and C 0 0 having molecular weights of 44 and 45. 

Melander L, Saunders WH (1980) Reaction rates of isotopic molecules. WUey and Sons, New York Mengel K, Hoefs J (1990) Li - 8 0 - Si02 systematics in volcanic rocks and mafic lower crustal xenoliths. Earth Planet Sd Lett 101 42-53... 

Since potential energy surfaces of isotopic molecules are nearly identical, equilibrium isotope effects can only arise from the effect of isotopic mass on the nuclear motions of the reactants and products. Thus the ratio can be expressed in terms of partition functions for nuclear... 

L. Melander, W.H. Saunders Jr., Reaction Rates of Isotopic Molecules, (Robert E. Krieger Publ. Co.) Malabar, Florida (1987). 

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