Overtone transition

With broad-band pulses, pumping and probing processes become more complicated. With a broad-bandwidth pulse it is easy to drive fundamental and overtone transitions simultaneously, generating a complicated population distribution which depends on details of pulse stmcture [75], Broad-band probe pulses may be unable to distinguish between fundamental and overtone transitions. For example in IR-Raman experiments with broad-band probe pulses, excitation of the first overtone of a transition appears as a fundamental excitation with twice the intensity, and excitation of a combination band Q -t or appears as excitation of the two fundamentals 1761. 

If the vibrational funetions are deseribed within the harmonie oseillator approximation, it ean be shown that the integrals vanish unless vf = vi +1, vi -1 (and that these integrals are proportional to (vi +1)E2 and (vi)i/2 the respeetive eases). Even when Xvf and Xvi are rather non-harmonie, it turns out that sueh Av = 1 transitions have the largest integrals and therefore the highest infrared intensities. For these reasons, transitions that eorrespond to Av = 1 are ealled "fundamental" those with Av = 2 are ealled "first overtone" transitions. 

One effect of mechanical anharmonicity is to modify the Au = t infrared and Raman selection rule to Au = 1, 2, 3,. .., but the overtone transitions with Au = 2, 3,... are usually weak compared with those with Au = t. Since electrical anharmonicity also has this effect both types of anharmonicity may contribute to overtone intensities. 

In Section 6.1.3 it was noted that vibrational overtone transitions, whether observed by infrared or Raman spectroscopy, are very weak. They become even weaker as the vibrational quantum number increases. The high sensitivity of CRDS makes it an ideal technique for attempting to observe such transitions. 

Fig. 1. Model Spectra re-binned to CRIRES Resolution To demonstrate the potential for precise isotopic abundance determination two representative sample absorption spectra, normalized to unity, are shown. They result from a radiative transfer calculation using a hydrostatic MARCS model atmosphere for 3400 K. MARCS stands for Model Atmosphere in a Radiative Convective Scheme the methodology is described in detail e.g. in [1] and references therein. The models are calculated with a spectral bin size corresponding to a Doppler velocity of 1 They are re-binned to the nominal CRIRES resolution (3 p), which even for the slowest rotators is sufficient to resolve absorption lines. The spectral range covers ss of the CRIRES detector-array and has been centered at the band-head of a 29 Si16 O overtone transition at 4029 nm. In both spectra the band-head is clearly visible between the forest of well-separated low- and high-j transitions of the common isotope. The lower spectrum is based on the telluric ratio of the isotopes 28Si/29Si/30Si (92.23 4.67 3.10) whereas the upper spectrum, offset by 0.4 in y-direction, has been calculated for a ratio of 96.00 2.00 2.00.

In a case where the transition of an energy state is from 0 to 1 in any one of the vibrational states (vi,v2,v3,. ..), the transition is considered as fundamental and is allowed by selection rules. When a transition is from the ground state to v — 2,3,. .., and all others are zero, it is known as an overtone. Transitions from the ground state to a state for which Vj = 1 and vj = 1 simultaneously are known as combination bands. Other combinations, such as v — 1, Vj = 1, v = 1, or v, — 2, v7 — 1, etc., are also possible. In the strictest form, overtones and combinations are not allowed, however they do appear (weaker than fundamentals) due to anharmonicity or Fermi resonance. 

On the other hand, one must recognize that quantal interference oscillations may result in transition probabilities that oscillate around the simple classical-like scaling laws (Levine and Wulfman, 1979). Figure 2.4 is an illustration of such a phenomenon for the overtone transitions in HF. 

Benjamin, I., Cooper, I. L., and Levine, R. D. (1987), Dipole Operator and Vibrational Overtone Transitions in Diatomic Molecules Via an Algebraic Approach, Chem. Phys. Lett. 139, 285. 

However, an overtone transition in an anharmonic well involving An = 2 has an energy of... 

When exposed to electromagnetic radiation of the appropriate energy, typically in the infrared, a molecule can interact with the radiation and absorb it, exciting the molecule into the next higher vibrational energy level. For the ideal harmonic oscillator, the selection rules are Av = +1 that is, the vibrational energy can only change by one quantum at a time. However, for anharmonic oscillators, weaker overtone transitions due to Av = +2, + 3, etc. may also be observed because of their nonideal behavior. For polyatomic molecules with more than one fundamental vibration, e.g., as seen in Fig. 3.1a for the water molecule, both overtones and... 

An additional point that should be considered is that in the harmonic oscillator approximation, the selection mle for transitions between vibrational states is Ay = 1, where v is the vibrational quantum number and Ay > 1, that is, overtone transitions, which involve a larger vibrational quantum number change, are forbidden in this approximation. However, in real molecules, this rule is slightly relaxed due to the effect of anharmonicity of the oscillator wavefunction (mechanical anharmonicity) and/or the nonlinearity of the dipole moment function (electrical anharmonicity) [55], affording excitation of vibrational states with Ay > 1. However, the absorption cross sections for overtone transitions are considerably smaller than for Ay = 1 transitions and sharply decrease with increasing change in Av. 

A rule of thumb for hydride stretches [56, 57] is that the intensities of the vibrational overtone and combination transitions decrease, approximately, as IQ-Ay jjjg drop-off in intensity for the first few quanta of excitation may be even steeper, by another factor of 10. This implies that, in a specific spectral interval, the strongest vibrational transitions from the vibrationless ground state level correspond to the transition with the smallest Av and the greatest anharmonicity. However, as shown later, even these small absorption cross sections of vibrational overtone transitions can be sufficient for overtone preexcitation. 

It is also possible that the unimolecular reaction takes place with the molecule in the electronic ground state, but it requires very intense fields to generate so-called multiphoton or direct overtone transitions that is, transitions from the vibrational ground state of the type 0 —> n, where n > 1. The opening of the cyclo-butene ring to form butadiene is an example of a unimolecular reaction induced by direct overtone excitation ... 

The dominant term for vibrational transitions is, of course, the second, which gives the primary selection rule for a harmonic oscillator of Ac = 1. The overtone transitions Av = 2, 3, etc., are very much weaker because of the rapid convergence of (6.325). 

Recent advances in solid-state laser systems offer several potential improvements. In particular, tunable optical parametric amplifiers provide tunable pulses with excellent synchronization and beam quality. However, most reported systems produce pulses of <100 fs. Pulses this short are not needed to measure vibrational dephasing in most systems, and they unnecessarily exacerbate the problems of self-focusing and excitation of overtone transitions. A solid-state system optimized for longer pulses has... 

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