Analysis of the transition from normal modes to local modes in a system of two harmonically coupled Morse oscillators

Theoretical and experimental studies for the interpretation of vibrational circular dichroism spectra in the CH-stretching overtone region

“…60 All curves are regular and thus multiperiodic. [60][61][62][63] Three families of curves are topologically distinguished in Figure 5, the extent of each being different in going from ⌬v = 1 to ⌬v = 4. The first family is composed of deformed ellipses centered around a fixed point at l 2 = l 20 and p 2 > 0: we call this family normal modes comprising purely symmetric normal modes close to the fixed point and deformed symmetric normal modes with large antisymmetric contributions, the latter being those curves crossing the line p 2 = 0.…”

“…The first family is composed of deformed ellipses centered around a fixed point at l 2 = l 20 and p 2 > 0: we call this family normal modes comprising purely symmetric normal modes close to the fixed point and deformed symmetric normal modes with large antisymmetric contributions, the latter being those curves crossing the line p 2 = 0. 63,64 The second and third families are the inner and outer circles, respectively, both centered approximately at l 2 = l 20 and p 2 = 0: we call both of them local modes. The general aspect of Figure 5 is determined by the harmonic interaction force constant K between C 1 H 1 and C 2 H 2 being positive.…”

“…The general aspect of Figure 5 is determined by the harmonic interaction force constant K between C 1 H 1 and C 2 H 2 being positive. 63 The torsion is seen to have no appreciable influence, due to the smallness of its interaction with the CH-stretchings, represented by the kinetic terms of Eq. [16Ј].…”

“…Approximately, low values for 1 correspond to small ⌬E values of the two stretchings energies and thus to banana-shaped normal modes curves of increasing area; high values of 1 to higher ⌬E values and thus to local modes, close to v being assigned wholly to one bond. 63 . For this reason, we report in Figure 7 the Fourier crossspectra 64 of an almost pure symmetric normal mode A, of a more perturbed normal mode B, and of a local mode C, respectively, for (3R)-methylcyclopentanone (see Figure 6), the torsional excitation being at ZPE, with the McKeanWatt effect of Eq.…”

Bifurcation Analysis of Higherm:nResonance Spectroscopic Hamiltonian†

“…The resonances that we focus on are those that are most important in the dynamics of the normal modes in the system of two kinetically coupled Morse oscillators. [12][13][14][15][16][17][18][34][35][36][37][38][39][40][41][42][43] Because of the symmetry of the system, n is limited to even numbers. These resonances are not limited to the coupled Morse system and may occur in general molecular spectroscopic systems.…”