Anharmonic spectra

Keywords Anharmonic spectra Chemical dynamics DFT-based dynamics Gas phase fragmentation IR-MPD IR-PD RRKM Vibrational spectroscopy... 

In this chapter, our goal is to present theoretical methods applied to gas phase vibrational spectroscopy. This is reviewed in Sect. 3 where we present harmonic and anharmonic spectra calculations, with special emphasis on dynamical approaches to anharmonic spectroscopy. In particular, we present the many reasons and advantages of dynamical anharmonic theoretical spectroscopy over harmonic/ anharmonic non-dynamical methods in Sect. 3.1. Illustrations taken from our work on dynamical theoretical spectroscopy are then presented in Sects. 4-6 in relation to action spectroscopy experiments. All examples presented here are conducted either in relation to finite temperature IR-MPD and IR-PD experiments, or to cold IR-MPD experiments. Beyond the conformational dynamics provided by the finite temperature trajectories, the chosen examples illustrate how the dynamical spectra manage to capture vibrational anharmonicities of different origins, of different strengths, in various domains of the vibrations from 100 to 4,000 cm and on various molecular systems. Other comprehensive reviews on theoretical anharmonic spectroscopy can be found in [7-9]. 

Thus far we have discussed the direct mechanism of dissipation, when the reaction coordinate is coupled directly to the continuous spectrum of the bath degrees of freedom. For chemical reactions this situation is rather rare, since low-frequency acoustic phonon modes have much larger wavelengths than the size of the reaction complex, and so they cannot cause a considerable relative displacement of the reactants. The direct mechanism may play an essential role in long-distance electron transfer in dielectric media, when the reorganization energy is created by displacement of equilibrium positions of low-frequency polarization phonons. Another cause of friction may be anharmonicity of solids which leads to multiphonon processes. In particular, the Raman processes may provide small energy losses. 

Raman spectra of S2 in its triplet ground state have been recorded both in sulfur vapor and after matrix isolation using various noble gases. The stretching mode was observed at 715 cm in the gas phase [46], and at 716 cm in an argon matrix [71]. From UV absorption and fluorescence spectra of sulfur vapor the harmonic fundamental mode of the S2 ground state was derived as t e = 726 cm . The value corrected for anharmonicity is 720 cm [26, 27]. Earlier reports on the infrared absorption spectrum of 2 in matrix isolated sulfur vapor [72] are in error the observed bands at 660, 668 and 680 cm are due to S4 [17] and other species [73]. 

The approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

Figure 13. Photodissociation spectrum of V (OCO), with assignments. Insets and their assignments show the photodissociation spectrum of molecules excited with one quanmm of OCO antisymmetric stretch, v" at 2390.9 cm . These intensities have been multiplied by a factor of 2. The shifts show that Vj (excited state) lies 24 cm below v ( (ground state), and that there is a small amount of vibrational cross-anharmonicity. The box shows a hot band at 15,591 cm that is shifted by 210 cm from the origin peak and is assigned to the V" -OCO stretch in the ground state.

A complete analysis of the vibrational spectrum had to wait until we were able to prepare T-36 via the photoisomerization of S-2. Even if an anharmonic approximation was taken in account in the calculation (UMP2/6-31G ) the IR spectrum was still in poor agreement with the observed spectrum.64 But one thing was clear formula T-36 does not represent the real structure of propargylene, since no IR band in the expected region for the C,C triple bond vibration of an acetylene was found, but a C,C stretching vibration at 1620 cm-1 was registered instead. 

Figure 2.2 Spectrum of states of the one-dimensional anharmonic oscillator, N = 6.

One can see that these represent the eigenvalues of two local anharmonic oscillators. The spectrum of Eq. (4.21) when the two oscillators are identical, as in H20, where they represent the stretching of the O-H bonds, is shown in Figure 4.1. 

Figure 4.1 Spectrum of two coupled local anharmonic oscillators. Note the inherent degeneracies in the spectrum.

The spectrum corresponding to Eq. (4.27) is shown in Figure 4.2. One can see that this represents the usual spectrum of two normal anharmonic coupled oscillators. 

Figure 4.2 Spectrum of two normal coupled anharmonic oscillators. Note how the different levels are almost equispaced.

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