Rotational interactions, effects

The authors of [315] applied linearly polarized synchrotron radiation (45-66 nm) for ionization, which corresponds to photon energy from 18.76 eV (threshold) + 0.7 eV up to 27 eV. The measured V values, as dependent on photon energy, changed correspondingly from 0.052 down to approximately half the value, which made it possible to determine the value of r within the range 0.4-0.7. Further improvement of the experiment and refinement of the theoretical description was carried out in [179]. Accounting for the hyperfine and spin-rotational interaction effect made it possible to refine the photoionization channel relation r, which yielded values of 0.2-0.4 for photon energies between threshold and 32 eV. 

One very effective approach for partitioning the molecular Hamiltonian so as to simplify vibration-rotation interaction effects involves the use of classical rotational sudden approximations. These are primarily applicable to high-velocity collisions, and they have been applied quite effectively to the Li" + CO2 system.In... 

A model which takes into account the spin-rotation interaction has been found to satisfactorily explain the 0 rotation band of PHg. The millimetre-wave spectra of HCP and DCP have been compared with those of HCN and DCN. A method of estimating frequencies of bands in this region due to processes such as pseudorotation has been suggested. This new approach involves calculation of the rovibronic energy levels from the effects of quantum-mechanical tunnelling. ... 

The first possibility is that the attractive potential associated with the solid surface leads to an increased gaseous molecular number density and molecular velocity. The resulting increase in both gas-gas and gas-wall collision frequencies increases the T1. The second possibility is that although the measurements were obtained at a temperature significantly above the critical temperature of the bulk CF4 gas, it is possible that gas molecules are adsorbed onto the surface of the silica. The surface relaxation is expected to be very slow compared with spin-rotation interactions in the gas phase. We can therefore account for the effect of adsorption by assuming that relaxation effectively stops while the gas molecules adhere to the wall, which will then act to increase the relaxation time by the fraction of molecules on the surface. Both models are in accord with a measurable increase in density above that of the bulk gas. 

Since these terms are proportional to tr, they increase with decreasing temperature.1 There are several line-width contributions, included in oc0, which do not depend on m,-. These include magnetic field inhomogeneity and the spin rotation interaction, the latter increasing with 1/tr and thus with increasing temperature. These and other line-width effects have been studied in some detail and are discussed elsewhere.13... 

Ab initio calculations on these conformers indicate that the anti geometry is 6.04 kcal/mol more stable than the syn291 Some of this energy difference is undoubtedly due to the eclipsing interaction of the hydrogens but this can not account for the total rotational barrier. Thus, the a—p+ interaction effect must be responsible for some major component of the rotational barrier. 

Recent microwave data for the potential interstellar molecule Sis is used together with high-level coupled-cluster calculations to extract an accurate equilibrium structure. Observed rotational constants for several isotopomers have been corrected for effects of vibration-rotation interaction subsequent least-squares refinements of structural parameters provide the equilibrium structure. This combined experimental-theoretical approach yields the following parameters for this C2v molecule re(SiSi) = 2.173 0.002A and 0e(SiSiSi) = 78.1 O.2 ... 

The purpose of this report is to demonstrate the ease with which highly accurate equilibrium structures can be determined by combining laboratory microwave data with the results of ab initio calculations. In this procedure, the effects of vibration-rotation interaction are calculated and removed from the observed rotational constants, Aq, Bq and Cq. The resulting values correspond to approximate rigid-rotor constants and and are thus inversely... 

Five isotopomers of Sia were studied in Ref (20), and are labeled as follows Si- Si- Si (I) Si- Si- Si (II) Si- Si- Si (III) Si- "Si- Si (IV) Si- Si- °Si (V). Rotational constants for each (both corrected and uncorrected for vibration-rotation interaction) can be found towards the bottom of Table I. Structures obtained by various refinement procedures are collected in Table II. Two distinct fitting procedures were used. In the first, the structures were refined against all three rotational constants A, B and C while only A and C were used in the second procedure. Since truly planar nuclear configurations have only two independent moments of inertia (A = / - 4 - 7. = 0), use of B (or C) involves a redundancy if the other is included. In practice, however, vibration-rotation effects spoil the exact proportionality between rotational constants and reciprocal moments of inertia and values of A calculated from effective moments of inertia determined from the Aq, Bq and Co constants do not vanish. Hence refining effective (ro) structures against all three is not without merit. Ao is called the inertial defect and amounts to ca. 0.4 amu for all five isotopomers. After correcting by the calculated vibration-rotation interactions, the inertial defect is reduced by an order of magnitude in all cases. 

In a previous study of cyclic SiCs, a residual inertial defect of only slightly smaller magnitude was found, despite the fact that an extremely high level of calculation (surpassing that in the present study) was used to determine the vibration-rotation interaction contributions to the rotational constants. This was subsequently traced to the so-called electronic contribution, which arises from a breakdown of the assumption that the atoms can be treated as point masses at the nuclear positions. Corrections for this somewhat exotic effect were carried out in that work and reduced the inertial defect from about 0.20 to less than 0.003 amu A. However, the associated change in the rotational constants had an entirely negligible effect on the inferred structural parameters. Hence, this issue is not considered further in this work. 

This phenomenon of antiparamagnetic paramagnetic terms clearly needs a name and is called here the Cornwell effect (ideally the Cornwell-Santry effect). Positive contributions to op (which may or may not be positive overall) are expected in heteronuclear diatomics if they have a IT state this excludes, e.g., HF, InF, and TIF. In homonuclear diatomics, the IT -> a excitation is symmetry-forbidden. The possibility has been mentioned for XeF (34), although, from the chemical shift and calculated values of aa, the resultant Op ( F) is negative in XeFg and KrFj (cf. Fig. 7). Another candidate is FC DH, from the evidence of the fluorine chemical shift and spin-rotation interaction (96). According to this interpretation there should be a substantial upheld shift of the... 

Aside from the question of the precise model by which relaxation times are interpreted there is the more practical problem of isolating that part of the relaxation specifically caused by diffusion. The contributions of exchange processes (see below), spin-rotation interaction (9), and spin diffusion (9) can be identified by temperature dependences different from that which is solely the result of the motionally modulated nuclear dipolar interaction as sketched above, and corrections can be made. The molecular rotation contributions to dipolar relaxation can be removed or corrected for by (a) isotopic substitution methods (19), (b) the fact that rotation is in some cases much faster than diffusion, and its relaxation effects are shifted to much lower temperatures (7, 20), and (c) doping with paramagnetic impurities as outlined above. The last method has been used in almost all cases reported thus far, more by default than by design, because commercial zeolites are thus doped by their method of preparation this... 

Energy near-resonance and favorable overlap of vibrational states are the dominant factors affecting the magnitudes of the charge-transfer cross sections in the AB + -AB systems. It was found188 that an adequate theoretical treatment of the H2+ -H2 system necessitated inclusion of the effects of vibration-rotation interaction in calculating vibrational overlaps from accurate vibrational wave functions. Charge-transfer cross sections were thus computed as a function of different vibrational and rotational levels of the incident-ion species. 

The application of surface-enhanced Raman spectroscopy (SERS) for monitoring redox and other processes at metal-solution interfaces is illustrated by means of some recent results obtained in our laboratory. The detection of adsorbed species present at outer- as well as inner-sphere reaction sites is noted. The influence of surface interaction effects on the SER spectra of adsorbed redox couples is discussed with a view towards utilizing the frequency-potential dependence of oxidation-state sensitive vibrational modes as a criterion of reactant-surface electronic coupling effects. Illustrative data are presented for Ru(NH3)63+/2+ adsorbed electrostatically to chloride-coated silver, and Fe(CN)63 /" bound to gold electrodes the latter couple appears to be valence delocalized under some conditions. The use of coupled SERS-rotating disk voltammetry measurements to examine the kinetics and mechanisms of irreversible and multistep electrochemical reactions is also discussed. Examples given are the outer- and inner-sphere one-electron reductions of Co(III) and Cr(III) complexes at silver, and the oxidation of carbon monoxide and iodide at gold electrodes. 

Temperature from Rotational and Vibrational Raman Scattering Effects of Vibrational-Rotational Interactions and Other Corrections... 

This would imply a very simple linear Zeeman effect but, as we show in chapter 8, additional terms describing the nuclear spin rotation interaction and the spin-spin interaction make the system much more interesting. The nuclear spin transitions are induced by an oscillating magnetic field applied perpendicular to the static magnetic field, the perturbation being represented, for example, by the term... 

The experimental evidence for such a contribution to the spin-rotation interaction in the effective Hamiltonian was somewhat elusive in the early days although there are now well documented cases of its involvement, for example for CH in its 4E state [21]. Equation (7.166) suggests one reason why this parameter is not as important in practice as might be expected. The last factor on the right-hand side of (7.166) is just the difference of the rotational constant operators for the upper and lower states. This causes a considerable degree of cancellation in a typical situation because the B value is not expected to vary markedly between the electronic states. 

By this stage, it will be apparent that even the sign of the spin-rotation parameter contains valuable information on the electronic structure of the molecule. To appreciate this point fully, let us consider a3 state which arises from a 2 electron configuration. The effective spin rotation interaction arises from second-order mixing with3 n states. Let us assume that there is only one such state which lies higher in energy so that the... 

We calculate the effects of the Hamiltonian (8.105) on these zeroth-order states using perturbation theory. This is exactly the same procedure as that which we used to construct the effective Hamiltonian in chapter 7. Our objective here is to formulate the terms in the effective Hamiltonian which describe the nuclear spin-rotation interaction and the susceptibility and chemical shift terms in the Zeeman Hamiltonian. We deal with them in much more detail at this point so that we can interpret the measurements on closed shell molecules by molecular beam magnetic resonance. The first-order corrections of the perturbation Hamiltonian are readily calculated to be... 

The rotational and Zeeman perturbation Hamiltonian (X) to the electronic eigenstates was given in equation (8.105). It did not, however, contain terms which describe the interaction effects arising from nuclear spin. These are of primary importance in molecular beam magnetic resonance studies, so we must now extend our treatment and, in particular, demonstrate the origin of the terms in the effective Hamiltonian already employed to analyse the spectra. Again the treatment will apply to any molecule, but we shall subsequently restrict attention to diatomic systems. 

The nuclear spin-rotation interaction becomes very simple for a diatomic molecule. The principal components of the tensor a for a polyatomic molecule were described in equation (8.163) this expression reveals that for a diatomic system the axial component (c/)zz is zero and, of course, the two perpendicular components are equal. The nuclear spin rotation interaction for a diatomic molecule is therefore described by a single parameter c/. The appropriate term in the effective Hamiltonian, first presented in equation (8.7), is... 

The most important terms in the effective hyperftne Hamiltonian are those which describe the nuclear quadrupole and nuclear spin-rotation interactions ... 

Finally in this part of the effective Hamiltonian, the spin rotation interaction takes the simple form... 

The final term in the effective Hamiltonian describes the nuclear spin-rotation interaction and its matrix elements are relatively straightforward ... 

There is a further term which should be included in the effective Hamiltonian, derived in chapter 7, describing the electron spin-nuclear rotation interaction. This may be written in the form... 

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