Asymmetric anharmonic oscillator

FIGURE 2 Potential energy as a function of displacement for an asymmetric anharmonic oscillator potential. 

Fig. 7.11. The ground-state vibrational wave funetion of the anharmonic oscillator (of potential energy V2) is asymmetric and shifted towards positive values of the displacement when compared to the wave function for the harmonic oscillator with the same force constant (the potential energy Vi).

For the reflection symmetric two-level electron-phonon models with linear coupling to one phonon mode (exciton, dimer) Shore et al. [4] introduced variational wave function in a form of linear combination of the harmonic oscillator wave functions related with two levels. Two asymmetric minima of elfective polaron potential turn coupled by a variational parameter (VP) respecting its anharmonism by assuming two-center variational phonon wave function. This approach was shown to yield the lowest ground state energy for the two-level models [4,5]. 

Most of the symbols in (5-26) are the same as those in expression (5-22) for the dissociation rate coefficient in a one-temperature approximation. Additionally, d = Aty/XasUl is a vibrational quantum number corresponding to the transition to quasi continuum along the asymmetric mode (5-24) f E) is the vibrational energy-dependent ratio of rate coefficients of VT and W relaxation (see Fig. 5-12) y = is the logarithmic sensitivity of the VTAA relaxation ratio to vibrational energy accumulated on the asymmetric mode (see Fig. 5-12) and Xm is the effective CO2 oscillation anharmonicity in quasi continuum (for... 

---