Isotope effects isotopologues

A key feature of the competitive isotope fractionation measurements is the use of natural abundance O2. Isotope effects are, therefore, determined for the reactions of the most abundant isotopologues 160-160 and 180-160. It is the intermolecular competition of these species that is reflected in the isotope effect. Aside from the obvious advantage of not requiring costly enriched materials, the competitive measurements also avoid the error that could arise from small leaks in the vacuum manifold and dilution due to ambient air. 

The reduced isotopic partition functions are computed from the vibrational frequencies of the heavy and light isotopologues within the reactant and product states. The ZPE and EXC terms describe the isotope effects emanating from the quantized vibrational energy levels of these states, whereas the MMI represents the isotope effect that derives from translational and rotational modes.27 The formulas for... 

Calculations of 180 EIEs upon reactions of natural abundance O2 require the normal mode stretching frequencies for the 160—160 and 180—160 isotopologues (16 16j/ and 18 16, ). These values can often be obtained directly from the literature or estimated from known force constants. DFT calculations can be used to obtain full sets of vibrational frequencies for complex molecules. Such calculations are actually needed to satisfy the requirements of the Redlich-Teller product rule. In the event that the full set of frequencies is not employed, the oxygen isotope effects upon the partition functions change and are redistributed in a manner that does not produce a physically reasonable result. 

Some of these ideas were recently used to calculate the isotope effect for the photodissociation of N2O and O3 by Liang et al. [15]. They predict the isotope effect based on a numerical analysis in which they describe the Abs. XS divided by E (where E is the photon energy, see below) as the product of a Gaussian and a numerical Y function assumed to be the same for all isotopologues. The isotope effect is taken into account in the 3 parameters of the Gaussian wavefunction and then reported on the Abs. XS of each isotopologue. From this the related fractionation constant can be determined. 

When applied to isotope effects, the main weakness of the reflection method is the assumption that the transition dipole moment is constant for all isotopologues. This weakness remains in the improved model presented below. Only ab initio calculations are able to go beyond this approximation. However, the dependence of the transition dipole moment along the nuclear coordinates can be introduced (numerically or analytically) in the model below, even if a less compact analytic form is expected. This paper is organized as follows in Section 2 the "standard" reflection model is improved by taking into account the curvature of the upper state potential (in addition to its slope). In Section 3, the quantum character of the final state is taken into account by replacing the Dirac function by an Airy function. In Section 4 the model is applied to the CI2 molecule. In Section 5 the model is adapted and applied to the O3, SO2 and CO2 triatomic molecules. Conclusions and perspectives are presented in Section 6. 

It is seen that DCDO is photolysed the most slowly in natural simlight, followed by HCDO, and the and isotopologues. Symmetry and the roaming atom pathway are likely to play a role in these isotope effects. Further evidence for this appears in the channel-specific photolysis rates, which show that HCDO... 

Isotope effects like the above, involving a direct or indirect comparison of the rates of reaction of iso-TOPOLOGUEs, are called intermolecular, in contrast to intramolecular isotope effects, in which a single substrate reacts to produce a nonstatistical distribution of isotopologue product molecules. 

The natural abundances of the stable isotopes given in Table 6.3 are global average values, whereas the actual exact values are subjected to small local and temporal variations, due to the slightly different behaviour of isotopologue molecules (by lUPAC definition a molecular entity that differs only in isotope composition, means number of isotopic substitutions in contrast, isotopomer [ isotopic isomer ] molecules are isomers, having the same number of each isotopic atom but in different positions) in the course of chemical reactions or physical processes ([8], kinetic and thermodynamic isotope effects, respectively, see below). The corresponding shifts are so small that they caimot be indicated in the atom-% scale therefore they are expressed in 5-values, differences of the isotope ratio R, e.g., ([ C]/[ C]) of the sample and an international standard relative to this international standard ... 

Isotopic molecules — or isotopologues — mean molecules of the same compound that only differ in isotopic composition. Related terms such as isotopomers are explained in O Sect. 15.1 of Chap. 15, Vol. 2, on Isotope Effects, a topic closely associated with isotope... 

We have seen that the effect of a full or partial deuteration of the cation not only leads to line shifts but also significantly changes the intensities and modifies the assignment of the infrared signatures of the different isotopologues. This is due to the soft, anharmonic, and coupled potential of the Zundel cation, where the dynamics and spectroscopy are strongly dominated by Fermi resonances between various coupled zeroth-order vibrations. The discussed quantum dynamical calculations represent an important milestone in our understanding of the spectroscopy and dynamics of protonated water clusters and on their dramatic isotope effects [41], and could only be achieved after a full-dimensional quantum dynamical treatment of the clusters. 

VendreU O, Gatti F, Meyer H-D (2009) Full dimensional (15D) quantum-dynamical simulation ofthe protonated water dimer IV isotope effects in the infrared spectraof D(D20), H(D20) andD(H20) isotopologues. J Chem Phys 131 034308... 

Different from the correction for differences of the number of carbon atoms between individual species of a lipid class, correction for another isotope effect on quantification due to the double-bond overlapping effects (see below) has to be performed for those utilizing unit-resolution mass spectrometers. For those who utilize high-resolution mass spectrometers for quantification, another approach to extract ion peak intensity from a partially overlapped ion peak can be consulted as described [33]. Herein, the double-bond overlapping effect refers to the overlap or partial overlap between the two atom-containing isotopologue of a species M (i.e., M-i-2 isotopologue) and the ion of a species with one less double bond than M. 

For these reasons, the experimental determination of fhe Absorption Cross Sections of polyatomic molecules will not be supplanted for a long time by theoretical calculations. This is also true when the Cross Sections of various isotopologues need to be compared but, then, some significant progress can be predicted, mostly because, within the Born-Oppenheimer approximation, the same PESs are involved for the various isotopologues. So, differential effects due to various isotope substitutions in triatomic molecules seem easier to characterize than the differences between various molecules. 

Several approaches have been used to calculate the effect of isotopic substitution on the absorption cross section of N2O. The zero point energy (ZPE) model [83] as described in Section 4, 2D and 3D wavepacket dynamics [110,118], a semi-empirical model [85,86] and an extended reflection principle model [84] have been used to explain the differences in the absorption that stem from isotopic substitution. In the following the emphasis lies on the enhanced understanding of the isotopic differences in the photodissociation reactions, which arises from employing wavepacket propagation calculations for the various isotopologues. 

Ultraviolet photolysis of carbon monoxide occurs through absorption in narrow lines, corresponding to specific rotational and vibrational levels of several electronic transitions. The absorption wavelengths are isotope-dependent due to the effect of isotopic mass on the vibrational and rotational energies. As a consequence, the absorption lines due to C 0, the most abundant isotopologue, do not overlap those due to C O and Because of the... 

In addition, the rotational spectra of ten different isotopologues (one parent, one three and five deuterated species) for the two most stable conformers of alanine were detected. The extensive isotopic data were analyzed to derive the substitution [106, 107] and effective stmctures for both I and Ila conformers. Unlike glycine, the amino acid skeleton in alanine is non-planar. Deuteration at the amino and... 

In order to fit vibration-rotation spectra of several isotopologues of diatomic molecules to the effective Hamiltonian, Eq. (6.90), one normally partitions the corrections to the reduced masses, i.e. the g factor radial functions gj R) and gv R), into two isotopically independent terms that are associated with one or the other nucleus... 

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