Coupled-oscillator contribution

The first term in eq. [21] is the contribution of the intrinsic rotational strengths if oscillators a and/or b are themselves chiral. The second term is the coupled oscillator contribution due to the intrinsic moments and the third term is the coupled oscillator contribution due to the geometric arrangement of the two electric dipole oscillators. The latter two contributions give rise to a conservative bisignate couplet in the observed spectrum, if the coupled modes are sufficiently separated in frequency such that the positive and negative contributions do not cancel. 

Contributions of Aromatic Side Chains to the Far UV CD of Proteins. Numerous theoretical studies of the effects of aromatic groups on both the far and near UV CD spectra of proteins have been conducted by Hooker and co-workers [143-154], While the calculations on larger proteins were limited in scope, they do provide the only comprehensive attempt to include these chromophores into CD calculations (see below). Other researchers have attempted coupled-oscillator calculations on proteins such as insulin [155, 156], to assess the effects of tertiary structure on near UV CD spectra. More recent work by Woody and co-workers expanded the matrix method to include more elaborate descriptions of... 

Figure 5. A typical 2D-IR real part of the rephasing spectrum for a pair of coupled oscillators. Shown at the bottom is the projection of this spectrum onto the to, axis obtained by summing contributions from all values of co at a particular C0(.

More testing of these approaches is certainly required before any final pronouncements on their worth can be made. One important contribution to assessing the ideas was that of Sewell et al. (53). For a system of coupled oscillators, they showed that the constraints of Miller et al. and Bowman et al. (45,46) may induce physically undesirable effects. In particular, they gave an example of a trajectory in the quasiperiodic regime being transformed into a chaotic one by the action of the constraints. 

The problem just set forth can be approached in at least three different ways. The first of these is somewhat ad hoc, although it does lead to essentially correct conclusions. It begins by allowing the quite arbitrary insertion of the damping factor Fj into as in (63). One may then show that this introduces no apparent inconsistencies if the theory as developed by Rosenfeld be preserved in toto. In fact the consequence in many instances is to recover familiar expressions intact. One may then use a stratagem originally employed by Kuhn and Braun in connection with a classical coupled oscillator model to sum the contributions of the narrow lines. The use of this device in association with Rosenfeld theory effects, in essence, a translation of their results into quantum mechanical language. 

From private conversations with E. U. Condon, the writer learned that a good part of the motivation for developing the one-electron model was a desire to dispel the then popular misconception that coupled oscillators were the sine qua non of optical activity. In this effort Condon, Altar, and E5Ting were patently successful. But for the present author, their most important contribution lay in showing that perturbation methods provide a neat and incisive way... 

Grishina, I.B., Woody, R.W. Contributions of tryptophan side chains to the circular dichroism of globular proteins exciton couplets and coupled oscillators. Faraday Discuss. 99, 245-267 (1994)... 

In this case the higher frequency (more intense) mode corresponds to the in-phase vibration and the out-of-phase vibration to the lower (less intense) mode. The reason for the reversal of the usual mechanics for these coupled oscillators has been suggested by Colthup. It is proposed that an additional interaction constant is required because of the heavy contributions of the dipolar resonance forms II and III. These forms enhance the single-bond character in the out-of-phase mode and thereby drop that mode below the in-phase stretch, which depends more heavily on contributions from form I and has more double-bond character. 

The components connected between the emitter-follower and the currentsensing filter capacitor can be thought of as a resistor divider. An additional 0.17 V needs to appear at pin 7 (through a 1K resistor) so the amount of current that must be contributed to that node is 0.17 V/1K which is 170 pA. The capacitive coupling of the PNP to pin 7 essentially centers the oscillator waveform upon the current ramp. So,... 

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