Remote perturber

The very few residual Na+ ions would cause a remote perturbation of the acid sites structure by modifying significantly the TOT bond angles26. 

The R- or w-dependence of second-order constants (o,p,q, 7, etc.) is more important than that of the off-diagonal perturbation parameters themselves (as determined from a direct fit to perturbed levels) because, in their definitions as sums over the interactions with energetically remote levels [Eqs. (5.5.1a) - (5.5.3a)], the off-diagonal matrix elements are taken between nondegenerate vibrational levels. Thus the ii-centroid, R vi, will vary with v and v and will not be equal to Rc- Since a+ and b are not independent of RuV and RvVi is not independent of v at fixed v, it is not permissible to remove the electronic factor from the summation over remote perturbers. Furthermore, the denominator of each term in the perturbation summation depends on an energy difference. This can cause a strong v, J-dependence of the second-order constants, especially when the vibrational levels of the state under consideration are near the energy... 

Forbidden Transitions Intensity Borrowing by Mixing with a Remote Perturber 406... 

The phrase remote perturber is intended to imply that... 

The assumptions required to obtain Eqs. (6.4.9) and (6.4.10) are more drastic than those for Eqs. (6.4.5) and (6.4.6), but their failure can often be absorbed into a strongly f -centroid dependent effective p2 parameter. Note that Eq. (6.4.9) contains the intuitive Franck-Condon factors but the Honl-London factors are those appropriate to the Q-value of the remote perturber. 

When one remote perturber, j), dominates the radiative lifetime of state z), where the j —> X transition is allowed, the lifetime of the t) state, Tj, can be easily estimated using experimental data, by the formula ... 

An effective Hamiltonian is profoundly different from an exact Hamiltonian. This is a reason for imperfect communication between experimentalists and ab initio theorists. The two communities use the same symbols and language to refer to often quite different molecular properties. The main difference between effective and exact Hamiltonians is that the molecule gives experimentalists an empirical basis set that has been prediagonalized implicitly to account for the infinite number of remote perturbers . This is the Van Vleck or contact transformation, but it is performed by the molecule, not by a graduate student. The basis set is truncated and the dynamics occurs in a reduced-dimension state space. 

Natural circular dichroism (optical activity). Although circular dichroism spectra are most difficult to interpret in terms of electronic structure and stereochemistry, they are so very sensitive to perturbations from the environment that they have provided useful ways of detecting changes in biopolymers and in complexes particularly those remote from the first co-ordination sphere of metal complexes, that are not readily apparent in the absorption spectrum (22). It is useful to distinguish between two origins of the rotational strength of absorption bands. 

Equation (3.40) tells us that the symmetry adaptation (3.39) from LMOs to CMOs is purely decorative, with no energetic consequence. As physical intuition suggests, we are perfectly justified in describing the Hearth—Hmooh system in terms of localized atom-like functions, each weakly perturbed by its remote twin, rather than as a completely delocalized MO of symmetry-adapted form. 

Abstract For the case of small matter effects V perturbation theory using e = 2V E/ Am2 as the expansion parameter. We derive simple and physically transparent formulas for the oscillation probabilities in the lowest order in e which are valid for an arbitrary density profile. They can be applied for the solar and supernova neutrinos propagating in matter of the Earth. Using these formulas we study features of averaging of the oscillation effects over the neutrino energy. Sensitivity of these effects to remote (from a detector), d > PE/AE, structures of the density profile is suppressed. 

In a completely different interpretation Zefirov (242) proposed a new concept of frontier-orbital mixing (243) to explain how conformational and electronic effects in monosubstituted cyclohexanes are transmitted to remote 8-carbon atoms (Scheme 36). The orbitals at C(l) and C(4) in 112 are considered to be equatorial (242). A perturbation at C(l) (H is replaced by X) produces an electron-density shift from H(4) toward C(4) (242), which is associated with an upheld shift of the latter s signal. Although this approach appears to be quite crude and does not account for axial substituents, it deserves fiirther attention. 

These results have been interpreted in terms of HOMO-LUMO interactions. As a result of the orbital perturbation, the interaction of the HOMO of the cyclohexene double bond with the LUMO of the developing cation may become effective. At the first stage of this interaction, an overlap of the LUMO of the cyclobutyl cation with the p lobe of the double bond located close to the cation center is probably important. However, when the reaction progresses, the interaction with the p lobe on the remote carbon atom has been assumed to increase significantly. 

Remote steric effects have also been noted to play an unanticipated role in the sense of asymmetric induction. This is apparent from related condensations carried out on aldehydes 106 (26) and 107 (eqs. [76]-[78]) (26,92). Other examples illustrating the influence of remote structural perturbations on the carbonyl addition process have been observed in these laboratories. The addition of the lithio benzoxazole 110 to aldehyde 108 proceeded with good Cram diastereoface selection (95a), whereas the same nucleophilic addition to aldehyde 109 was stereorandom (95b). 

As reported by Olmez and Gordon (University of Maryland), the concentration pattern of rare earth elements on fine airborne particles (less than 2.5 micrometers in diameter) is distorted from the crustal abundance pattern in areas influenced by emissions from oil-fired plants and refineries. The ratio of lanthanum (La) to samarium (Sm) is often greater than 20 (crustal ratio is less than 6). The unusual pattern apparently results from tlie distribution of rare earths in zeolite catalysts used in refining oil. Oil industry emissions have been found to perturb the rare earth pattern even in very remote locations, such as the Mauna Loa Observatory in Hawaii. 

In cases of extensive branching, as for the alkylbenzenesulfonates, the CnH2n+2 1°33 series is significantly perturbed compared to the straight chain alkyl sulfates, but it is sufficiently abundant to show perturbations in the loss pattern. These perturbations may be interpretable for identifying branch points. N-Acylated amino acids also show a suppressed remote charge site loss series because the preferred fragmentations are the decarboxylation of the parent anion and formation of the carboxylate anion of the amino acid (8). 

---