Vibration

Basic:

• fundamental band: the vibration from the vibrational ground state to the vibrational first excited state
• overtone band: the vibration from the vibrational ground state to the high-order (> 1) excited vibrational states
• combination band: the superposition of two fundamental bands. The combination band is forbidden by harmonic oscillator selection rules.
• hot band: the transition between two excited vibrational states
• resonance: a resonance occurs when the energy of the normal modes or the sum of modes are close to one another in energy.
• Harmonic approximation will overestimate the energies of the fundamentals due to the neglect of anharmonicity.
• floppy molecule: the structure is not at all rigid, but rather constantly changing. It is also called fluctuating and fuxional. The bond connectivity has not been modified during the dynamical changes.
• CH$_5^+$: 2005-Science-Dominik Marx
• Various cis/trans conformations by thermally driven isomerization transitions
• Methyl groups can easily undergo internal rotations
• VPT2 needs 6N-11 Hessian calculations for a nonlinear system where 2*(3N-6)+1 = 6N-12+1 = 6N-11. The 6N-11 comes about due to the use of a two-sided finite difference approach to find the derivatives of the force constants with respect to displacements along each of the normal modes, plus one calculation for the unperturbed geometry.
• IR of molecular systems with increasing size and in different environments.

MISC

• For medium size PAHs, the addition of D3 has minor effects on band positions and intensities. There might be divergences for some vibrational peaks.
• SPECTRO program not available online: Gaw, J. F.; Willets, A.; Green, W. H.; Handy, N. C. in Advances in Molecular Vibrations and Collision Dynamics; Bowman, J. M.; Ratner, M. A., Eds.; JAI Press, Inc.: Greenwich, CT, 1991; pp 170– 185.
• IR from AIMD intrinsically contains some anharmonic effects. However, other anharmonic effects like mode coupling leading to combination bands and Fermi resonances are still not included because the nuclear motion is treated classically.