Potential energy distribution normal-mode frequencies

TABLE 10. Vibrational frequencies (cm-1), infrared intensities, normal modes and potential energy distribution of the anilino radical (C6H5N"H). Values obtained from scaled UB3LYP/6-311 + + G(3df,2p) calculations... 

Frequencies in cm", infrared absortivities in parentheses, in km/mol. Our mode description is based on potential energy distribution over symmetry coordinates. We have indicated significant minor contributions in square brackets. In some cases two coordinates contribute almost equally to the normal modes accordingly, two numbers are indicated for these modes. [49] The experimental frequencies were obtained from solid state measurements therefore the lower frequency values are to be regarded as only approximate. Revised assignments, see text. The 1191 (Ei) and 1189 ( ])cm" observed frequencies are not assigned to fundamentals. 

Also, our normal coordinate analysis revealed that the Cr-CO-, ring-Cr-C-and the C-Cr-C-bending coordinates are strongly coupled in E symmetry. In AI symmetry, the C-Cr-C umbrella opening mode is coupled with the Cr-C-O parallel bend. For details of the assignments the reader is referred to Table 12, in which we also included mode descriptions based on the criterion of potential energy distribution. The frequency related to the B2U C-C stretching vibration is overestimated, as it is for free benzene and for BzaCr. 

The differences between the results of this and previous studies underline the importance of a proper representation of the skeletal modes. On the basis of our normal-coordinate analysis with the complete force field, the contribution of the skeletal coordinates in those frequencies that exhibit shifts is not more than 5% in terms of the potential energy distribution. This contribution is far too small to... 

The most relevant experimental and calculated frequencies along with the potential energy distribution (FED) are displayed in Table 14.2. Due to the extended 7t electronic system, the FED shows a high degree of coupling between most of the normal modes. 

Table 14.2. Some Relevant Observed and Calculated Frequencies and Approximate Potential Energy Distribution (PED) for the Normal Modes of Hexaazacyclophane...

Kg. 6 The W-H normal modes of the DFT optimized CpW(dhpe)H3 with their frequency, intensity (A, 10 L mor cm , and potential energy distribution (in %, major components are in bold italic). The Cp- and P-bonded H atoms and ethylene backbone have been omitted for clarity. Negative sign means antisymmetric stretch. Adapted with permission from ref 30. Copyright 2008 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim. 

Hence, for a normal mode of frequency V, one has for the general case where no defined assignment has been given a mixing of the symmetry coordinates which can be "measured" by various methods (e.g., PED = potential energy distribution). 

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