Perturbation, chiral

Fettes N., Meissner U. G., Steininger S. Pion-nucleon scattering in chiral perturbation theory (I) Isospin-symmetric case. Nucl. Phys.A 640, 199-234 (1998)... 

Recently the density dependence of the symmetry energy has been computed in chiral perturbation effective field theory, described by pions plus one cutoff parameter, A, to simulate the short distance behavior [23]. The nuclear matter calculations have been performed up to three-loop order the density dependence comes from the replacement of the free nucleon propagator by the in-medium one, specified by the Fermi momentum ItF... 

The Cotton effects may be classified into three types168 those arising from chirally perturbed local achiral chromophores (ketones, /i.y-unsaturated ketones, double bonds, benzoates, aromatic compounds) those arising from inherently achiral chromophores, such as conjugated dienes or a,/3-unsaturated ketones those arising from interaction of the various electric transition moments when two or more chromophores which are chirally disposed are positioned nearby in space, intra- or intermolecularly (exciton chirality method)169. 

In Section 3.4.6 it was noted that chiral mesophases behave as chiral perturbation moieties for achiral molecules inserted to the mesophases. Here, only relations between the observed signs in LCICD and the pitch-dependent CD in liquid crystalline systems, and the helical sense of the liquid crystalline phases are described. 

We want now to see how this state of affairs is affected by the chiral perturbation of our reaction-diffusion equations [term in M in equation (29)]. To this end we follow the lines of imperfection theory (Section II.C) and expand the variables and parameters in series around X = X,. We also set the frequency fl of the solution to be identical to the external frequency w, and assume that o> is close to the linearized intrinsic frequency, ft, in the absence of the field ... 

Fig. 4.78 Majority rules principle as model for chirality amplification in (intermolecular) polymerisation of (unsymmetrically substituted) monomeric ethenes to form polymers, which can also convey the concept of (intramolecular) transmission of chiral perturbations [e.g. emanating from a stereogenic centre) in dendritic molecules The perturbation introduced into a system having a prior order (dance group a) in the form of an ex-...

The origin of the various additive effects is still unknown. However, taking into account the wide variety of chiral additives that cause effects with considerable sensitivity, it can be assumed that unspecific rather than specific interactions between the additives and species involved in the reaction mechanism of the Soai reaction take place. These may cause small but directed chiral perturbations where advantage is taken of the extraordinarily strong autocatalytic amplification capacity of the system. As already demonstrated by Singleton and Vo [36], these perturbations can be extremely small without losing its enantiomeric direction. In fact, as we describe later, the assumption of interactions between these chiral additives and the Soai reaction product itself, i.e., the autocatalytic species, could provide a tentative explanation for such effects. 

Supramolecular architectures are highly sensitive to chiral perturbations in general, and in systems that form liquid crystals in particular. Small amounts of enantiopure guest molecule added to a nematic host can induce a transition to a cholesteric phase, and the helical organization in the mesoscopic system is very sensitive to the structure of the guest molecule. Chiral amplification was successfully achieved in such liquid crystals, using CPL as the chiral trigger for the phase transition [183]. 

The C-17 side-chain of corticosteroids does not contain a chromophoric group suitable for spectrophotometric measurement, nor does oxidation of the chain lead directly to spectrophotometrically active derivatives. However, the 20-keto group of the 17 a-ketol side-chain, as a chirally perturbed chromophoric group, has an optically active absorbance band in the interval 270-300 nm that is characteristic of the n-7T electronic transition for saturated ketones. An intense positive Cotton effect is observed in the CD spectra see the CD spectra for hydrocortisone and cortisone in Figures 8 and 9. 

Obtaining high asymmetric induction therefore requires the placement of every reactant molecule next to a chiral inductor molecule (type B situation) i.e., enhancement of the ratio of type B cages to the sum of types A and C. In the chiral auxiliary method (CAM) the chiral perturber is connected to the reactant via a covalent bond [186,187,197-205]. In this... 

The contribution of the hadronic l-l scattering effect (32) is relatively small but is potentially a source of serious problem because it is difficult to express in terms of experimentally accessible observables it must be evaluated by theoretical consideration. It has been estimated by two groups, within the framework of chiral perturbation theory and the 1 /Nc expansion [64,65], Recently the theory dependence of these calculations has been reduced [31] by improving a part of the calculation incorporating the measurements of the P77 form factors [66], where P stands for 7r°, 77, and rj. The value quoted in (32) is the result of this work. Evaluation of these effects in lattice QCD will be particularly timely and interesting. 

These parameters can be evaluated using effective Lagrangian and Chiral Perturbation Theory [18,19,20,21,22] which is mathematically equivalent to QCD [19,21]. At present time, the value ao — a2 has been determined within 2% [23], The QCD Lagrangian and effective Lagrangians are determined by Lorentz invariance, P and C-invariance and by the chiral symmetry. For this reason, the measurement of do — < 21 provides an opportunity to check our understanding of the chiral symmetry breaking of QCD. 

The pion-nucleon interaction has been subject both to experimental and theoretical studies since the very beginning of the development of particle physics. On the theoretical side the description of the pion-nucleon system with QCD is considered to be a fundamental issue in the development of this theory. The understanding of strong interaction in the confinement regime has advanced recently, as chiral perturbation theory was developed to perform calculations at low energies [1,2]. 

Its extension to heavy baryon chiral perturbation theory (HBCHPT) [3] allows to calculate many of the experimentally accessible processes in the meson nucleon sector. The check of the soundness of this approach requires high precision experiments. This resembles the situation in the development of QED during the last 50 years, where the measurement of the Lamb shift contributed much to the development of QED. In a comparable way the measurement of strong interaction shift and width in pionic hydrogen may be a key experiment in strong interaction physics at low energies. 

Chiral-response sector maps computed from first principles to describe chiral perturbations of nonchiral chromophores are a tool proposed recently [136, 155, 170] to study CD and OR. The computation of such sector maps has been inspired by the sector rules for ketones that are well known to chemists... 

On the lowest level the carbonyl chromophore is viewed as the prototype of an inherently symmetric, but chirally perturbed chromophore This means that in a chiral ketone the particular carbonyl chromophore retains (largely) its (achiral) symmetry and optical activity will be induced by the chiral environment (i.e. the chiral arrangement of other groups in the whole molecule). In terms of perturbation theory this can be expressed by the statement that in zeroth order the chromophore is achiral and chirality is induced by perturbations in first (or higher) order. On the other hand, if, for a given electronic excitation, optical activity exists in zeroth order (without perturbation by the chiral field of the remaining groups of the molecule not directly involved in the electronic transition) the chromophore is termed inherently chiral ... 

On the lowest level, using symmetry and nodal properties of the MOs of H2C=0 as a representative of the inherently symmetric carbonyl chromophore, an octant rule can be derived for the influence of a (static) perturber of the (n, n ) excitation The geometrical symmetry (C2v) of the H2C=0 unit with the two symmetry planes, yz and xz, leads to a quadrant rule. If the orbitals involved in the (n, n ) excitation of ketones are described as " = 2p and n = N 2p — 2pJ) (N being a normalization constant), the nodal plane (xy) of the virtual orbital generates the octant diagram for the contributions of substituents of chirally perturbed compounds (Figure 10). 

For 152-154 octant projections predict that static chiral perturbers will contribute (according to the octant rule) only little to the overall Therefore, it was... 

In deciding whether analytes are CD-active, it is not always a simple matter to inspect a molecular formula and be certain that the chromophore and the chiral center are mutually located in a manner that produces activity. Even if the molecular structure suggests that a chirally perturbed chromophore is present, the substance might only be available as an achiral racemic mixture and therefore is not detected by CD. 

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