Vibrational isotopic species

Over the next few years, both the mid-infrared and the far-infrared spectra for Ar-HF and Ar-HCl were extended to numerous other bands and to other isotopic species (most importantly those containing deuterium). In 1992, Hutson [18, 39] combined all the available spectroscopic data to produce definitive potential energy surfaces that included both the angle dependence and the dependence on the HF/HCl monomer vibrational quantum number v... 

Figure 6-19. Bond dissociation curve showing the different zero-point vibrational energies of isotopic species R-H and R-D.

For a molecular ion with charge number Q a transformation between isotopic variants becomes complicated in that the g factors are related directly to the electric dipolar moment and irreducible quantities for only one particular isotopic variant taken as standard for this species these factors become partitioned into contributions for atomic centres A and B separately. For another isotopic variant the same parameters independent of mass are still applicable, but an extra term must be taken into account to obtain the g factor and electric dipolar moment of that variant [19]. The effective atomic mass of each isotopic variant other than that taken as standard includes another term [19]. In this way the relations between rotational and vibrational g factors and and its derivative, equations (9) and (10), are maintained as for neutral molecules. Apart from the qualification mentioned below, each of these formulae applies individually to each particular isotopic variant, but, because the electric dipolar moment, referred to the centre of molecular mass of each variant, varies from one cationic variant to another because the dipolar moment depends upon the origin of coordinates, the coefficients in the radial function apply rigorously to only the standard isotopic species for any isotopic variant the extra term is required to yield the correct value of either g factor from the value for that standard species [19]. 

Photolysis of H3NBH3 with 121.5 nm radiation yields imidoborane, HBNH, which has been of theoretical interest Spectral shifts observed for several isotopic species containing °B, N, and D show clearly that the spectrum is due to HNBH which is isoelectronic with HBO, HCN and HCCH. From the spectrum of the isolated species two of the and one of the tr-type vibration frequencies for a linear molecule have been obtained. The location of the missing S (B-H stretch) frequency has been calculated. A comparison of observed and calculated frequencies for HBNH is given in Table 7. Another isolated product observed in these experiments is identified as HNB. This radical may be generated by photodissociation of HNBH subsequent to its formation. In this respect the photolysis mechanism would be similar to the formation of C2H from acetylene. 

Within the harmonic approximation the choice of a system of internal coordinates is irrelevant provided they are independent and that a complete potential function is considered ). For example, the vibrations of HjO can be analysed in terms of valence coordinates (r, >2, or interatomic coordinates (r, r, 3) and any difference in the accuracy to which observed energy levels are fitted (considering all the isotopic species H2O, HDO and D2O) will be due to the neglect of anharmonic terms. If one makes the approximation of a diagonal force field so that one is comparing the two potentials... 

In calculating the moment of inertia, Ie = fiR 2, one customarily evaluates ja from the masses of the neutral atoms, considering this mass to be concentrated at the nucleus.1 Of course, this is an approximation, but it is a very good one, since electrons are so light. The atomic masses ma and mb in (4.5) cannot usually be gotten from tables of atomic weights, since most elements are mixtures of different isotopes. Each isotopic species has its own vibration-rotation levels. Masses for some common isotopes are given in the Appendix. 

Hammaker et al (34) deduced approximate expressions for the frequencies of the two infrared active modes of the system composed of a central adsorbed molecule of one isotopic species coupled to an environment of the other species. In one mode the labelled molecule vibrates in phase with its neighbours giving a frequency tojj higher than the frequency of the other mode where the motion is 180° out of phase. The two frequencies are related to wJ (the frequency of the 2-D lattice in the absence of the labelled molecule) and u>2 (the frequency of the labelled molecule in the absence of surrounding molecules, i.e. a labelled single-ton) by... 

A secondary motive is our general desire to verify and extend our understanding of vibration-rotation interactions in molecular spectra, and particularly to interpret data on different isotopic species in a consistent manner. Consider, for example, a constants (which measure the dependence of the rotational constant B on the vibrational quantum numbers vr) determined experimentally for several isotopic species of the same molecule. It is clear that these constants are not all independent, since they are related to the potential function which is common to all isotopic species. However, the consistency of the data and of our theoretical formulae can only be tested through a complete anharmonic force field calculation (there are at this time no known relationships between the a values analogous to the Teller-Redlich product rule). Similar comments apply to many other vibration-rotation interaction constants. 

Often the original structure determination will have involved some uncorrected vibrational averaging effects it may be an r0 or an r, structure.28 However, once /2, or some approximation to /3, has been determined it is possible to correct r to re and obtain an improved equilibrium structure (in most cases this correction can be made directly from the cubic anharmonic calculation, but in some cases the calculation will allow unobserved a. values to be determined, perhaps for other isotopic species, etc.). Similarly, it is often true that the harmonic field /2 is calculated from the observed fundamentals (the v values) rather than the harmonic vibration wavenumbers (the to values), for want of information on the corrections. However, once /4, or some approximation to/4, has been determined, it may be used to calculate a complete set of x values and hence to calculate all the corrections to obtain the co values. Thus the calculation of re and may be improved from a knowledge of /3 and /4. 

It should be noted that the rotational spectroscopy of CO confined to a single vibrational level, usually the ground v = 0 level, provides only a limited amount of information about molecular structure. In the field of vibration-rotation spectroscopy, however, CO has been studied extensively and particular attention paid to the variation of the rotational and centrifugal distortion constants with vibrational quantum number. Vibrational transitions involving v up to 37 have been studied with high accuracy [78, 79, 80], and the measurements extended to other isotopic species [81] to test the conventional isotopic relationships. CO is, however, an extremely important and widespread molecule in the interstellar medium. CO distribution maps are now commonplace and with the advent of far-inffared telescopes, it is also an important... 

The situation when the gas is isotopically scrambled, however, is very different and indeed the experimentally observed measured quantity is also very different. When the gas is isotopically scrambled, one does not measure these specific ratios of rate constants. Instead, a statistical steady-state, such as Q -F OO QOO QO + O and in the above example O + QQ OQQ OQ + Q, exists at all energies, and now the energy distribution of the vibrationally excited intermediates is that which is dictated by the steady-state equations for the above reactions, and not by that of a vibrationally hot intermediate formed solely via one channel. Under such conditions all energies of the intermediate are statistically accessible, if not from one side of the reaction intermediate then from the other. Phrased differently, the isotopic composition of the collisionally stabilized product Q3 or QO2 or will typically differ from that of the vibrationally excited species Q or QO2, since the intrinsic lifetime of the latter is isotope-dependent, as discussed in [15]. The usual RRKM-type pressure-dependent rate expression and conventional isotope effect results, modified by the nonstatistical effect discussed earlier [15]. 

Table 4.3-3 Infrared fundamental vibration wavenumbers of different isotopic species of CO (Rothman et al., 1987)...

In the gase phase, the infrared bands are broad (50 cm ), due to the rotational structure, overlapping vibrations, and hot transitions. In the solid state, the rotational motions are quenched, but due to intermolecular (hydrogen bond) and correlation field interactions, the band positions are shifted and the bands are even broader. The infrared absorptions of matrix-isolated molecules are close to the gas-phase frequencies and exhibit a sharp line-like character (half-widths 0.1 to 2 cm ). Hence the spectra of matrix-isolated molecules are less complicated, and, in comparison to gas phase or solid state spectra, the sensitivity and selectivity of detection increase by a factor of about 10 to 100. Closely spaced vibrations attributed to mixtures of similar molecules, such as conformers, rotamers, molecular complexes, or isotopic species, e.g., H C104 and H CI04, are easily distinguished. 

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