Excited states calculated from Raman

H. How to calculate the excited state distortions from electronic spectra and/or raman intensities... 

The theoretical background which will be needed to calculate the excited state distortions from electronic and Raman spectra is discussed in this section. We will use the time-dependent theory because it provides both a powerful quantitative calculational method and an intuitive physical picture [42,46-50]. The method shows in a simple way the inter-relationship between Raman and electronic spectroscopy. It demonstrates that the intensity of a peak in a resonance Raman spectrum provides detailed information about the displacement of the excited state potential surface along the normal mode giving rise to the peak [42,48]. It can also be used to calculate distortions from the intensities of vibronic peaks in electronic spectra [49]. For harmonic oscillators, the time-dependent theory is mathematically equivalent to the familiar Franck-Condon calculation [48]. 

H. How to Calculate the Excited State Distortions from Electronic Spectra and/or Raman Intensities... 

An investigation of the overtone region 21 1 and 2v of CH4 by spontaneous Raman spectroscopy [231] did not allow a precise dermination of the position and rotational structure of these states, which are part of a tetradecad system. Through population of the excited state by stimulated Raman pumping and subsequent quasi-CW stimulated Raman spectroscopy, the difference band 2v — could be observed and analyzed recently [232]. Figure 25 shows the transitions from the ground state to P2 + P4 (top) which appear in this region, the additional spectrum of the difference band 2p — Pi (middle), and the theoretical spectrum calculated with the polyads model (bottom). 

Figure 3.7. Comparison of the ground state normal Raman spectra of DMABN obtained by experimental measurement (with 532 nm excitation in solid phase) and the spectrum obtained from a DFT B3-LYP/6-31G calculation, (from reference [30] - Reproduced by permission of the PCCP Owner Societies.)...

This expression for the complete overlap is Fourier transformed to give the electronic emission spectrum. In order to carry out the calculation it is necessary to know the frequencies and the displacements for all of the displaced normal modes. In addition, the energy difference between the minima of the two potential surfaces E0 and the damping r must be known. As will be discussed below, the frequencies and displacements can be experimentally determined from pre-resonance Raman spectroscopy, and the energy difference between the ground and excited states and the damping can be obtained from the electronic absorption spectrum and/or emission spectrum. 

Calculation of Excited State Distortions and Electronic Spectra from Raman Intensities... 

The electronic spectrum is calculated by using equations 3 and 5. The distortions used in these equations are determined from the pre-resonance Raman intensities by using equations 7 and 9. Both the vibrational frequencies of the normal modes and the displacements of the excited state potential surfaces along these normal modes are obtained from the pre-resonance Raman spectrum. 

Raman data were used. Excellent agreement between the experimental spectrum and the theoretical spectrum calculated from the 18 dimensional excited state potential surface is obtained. Interpretation of these results will be discussed below. 

Besides the sum-over-states and time-dependent models for the resonance Raman cross-section, other models can be used to calculate resonance Raman cross-sections, such as the transform and time correlator models. In the transform model, the resonance Raman cross-sections as a function of excitation energy, the excitation profiles, can be calculated from the absorption spectrum within the separable harmonic oscillator approximation directly by the following relationship [85-87]... 

The UV resonance Raman spectrum of thymine was revisited in 2007, with a slightly different approach, by Yarasi, et al. [119]. Here, the absolute UV resonance Raman cross-sections of thymine were measured and the time-dependent theory was used to experimentally determine the excited-state structural dynamics of thymine. The results indicated that the initial excited-state structural dynamics of thymine occurred along vibrational modes that are coincident with those expected from the observed photochemistry. The similarity in a DFT calculation of the photodimer transition state structure [29] with that predicted from the UV resonance Raman cross-sections demonstrates that combining experimental and computational techniques can be a powerful approach in elucidating the total excited-state dynamics, electronic and vibrational, of complex systems. 

What is remarkable is that all of these early measurements of the UV resonance Raman spectra of nucleic acid components involved computational and theoretical support to their experimental findings. For example, Spiro used CINDO calculations to determine the nature of the excited electronic states of the nucleotides [157], In the early and mid 1970 s, many researchers were also attempting to understand resonance Raman spectroscopy, the types of information it could provide, and a unifying theoretical framework to the intensities [147, 159-172], UV resonance Raman spectra provided some of the first experimental evidence to test the various theoretical models. Peticolas attempted to fit the observed experimental excitation profiles of AMP [156], UMP [151, 154] and CMP [152, 153] to the sum-over-states model for the resonance Raman cross-sections. From these simulations, they were able to obtain preliminary excited-state structural dynamics of the nucleobase chromophores of the nucleotides for UMP [151, 153, 158] and CMP [153], For AMP, the experimental excitation profiles were simulated with an A-term expression, but the excited-state structural changes were not obtained. Rather, the goal of that work was to identify the electronic transitions within the lowest-energy absorption band of adenine [156],... 

As 1 is a nonpolar symmetric top with symmetry, it should have no pure rotational spectrum, but it acquires a small dipole moment by partial isotopic substitution or through centrifugal distortion. In recent analyses of gas-phase data, rotational constants from earlier IR and Raman spectroscopic studies, and those for cyclopropane-1,1- /2 and for an excited state of the v, C—C stretching vibration were utilized Anharmonicity constants for the C—C and C—H bonds were determined in both works. It is the parameters, then from the equilibrium structure, that can be derived and compared from both the ED and the MW data by appropriate vibrational corrections. Variations due to different representations of molecular geometry are of the same magnitude as stated uncertainties. The parameters from experiment agree satisfactorily with the results of high-level theoretical calculations (Table 1). 

All the necessary excited-state parameters (frequencies, force constants, and equilibrium geometries) can be obtained from MO calculations or, in a few cases, from excited-state Raman measurements. The above rate expression, like the standard Marcus-Jortner equation, can be readily modified to include more than one vibrational mode. The difference between the two approximations should be most pronounced when h v — vpj > ksT and /i ri — vp > Aj. The second condition is more likely to be satisfied for electronic excitation transfer than for charge transfer. 

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