anharmonicity

If the anharmonicity is large then other numerical techniques have to be used.

It is a measure of the anharmonicity of the system.

However, when anharmonicity is taken into account, the transitions are weakly allowed.

Higher order anharmonicity terms can be accounted by using perturbative methods.

This trend matches the anharmonicity found in real molecules.

The difference is not exact because there is anharmonicity in both vibrations.

We shall meet other consequences of anharmonicity later.

Due to the anharmonicity within the crystal potential, the phonons in the system are known to scatter.

There is also the problem of anharmonicity.

However, when the vibrational amplitudes are large, for example at high temperatures, anharmonicity becomes important.

In classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator.

The magnitude of the observed shift is correlated to the degree of anharmonicity in the corresponding normal modes.

These three terms alone give rise to the Jaynes-Cummings ladder of dressed states, and the associated anharmonicity in the energy spectrum.

He investigated in particular the effect of hydrogen bonding on the anharmonicity of molecular vibrations.

Their appearance is connected with anharmonicity, which leads to a breakdown of the selection rules derived assuming simple harmonic motion.

The spacing between adjacent vibrational lines decreases with increasing quantum number because of anharmonicity in the vibration.

However, optical phonons have a short life-time (they split into two due to anharmonicity) and therefore they add some important complications.

Combination bands typically have weak spectral intensities, but can become quite intense in cases where the anharmonicity of the vibrational potential is large.

The anharmonicity of a vibration can be read from the spectra as the distance between the diagonal peak and the overtone peak.

If anharmonicity is to be taken into account, terms in higher powers of J should be added to the expressions for the energy levels and line positions.

In real oscillators the effect of anharmonicity is to change (usually to reduce) the frequency of an overtone or combination [see Section 5.2.3].

It also accounts for the anharmonicity of real bonds and the non-zero transition probability for overtone and combination bands.

Because anharmonicity decreases the spacing between adjacent vibrational levels, hot bands exhibit red shifts (appear at lower frequencies) than the corresponding fundamental transitions.

Anharmonicity also modifies the profile of the resonance curve, leading to interesting phenomena such as the foldover effect and superharmonic resonance.

An example of the effects of anharmonicity is the thermal expansion of solids, which is usually studied within the quasi-harmonic approximation.