Rotational Constants. Geometrical Structure

A reduced Hamiltonian [2] was used [1] for the rotational and centrifugal distortion constants (see also pp. 146/7). The spin-rotation splitting was analyzed [1] by an expression y(N+V2) [3] with 7 = [Eaa - V2(Ebb Ecc)] K2/N(N +1) V2(Ebb + Ecc) (N = rotational angular momentum excluding electronic spin, K = projection of N on the symmetry axis of the corresponding near prolate top). 

A distance r(0-F) = 1.63A was inferred from force constants and from a comparison with O2F2 [7]. 

Bond lengths r(O-O) and r(O-F) and bond angle a(OOF) were also calculated by ab initio [8,13], CNDO [9], INDO [11, 12], and MINDO [10] methods. 

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Quantum chemical calculations are the most accurate theoretical methods available for studying the structures, energies, and elementary reactions of molecules. It is possible to determine the structure, energy, and geometrical parameters (i.e., vibrational frequencies, electronic states, and rotational constants) for reactants, transition states, and products of a chemical reaction. With this information,... 

The disadvantages of the two techniques, i.e. low resolution of closely spaced distances in ED and insufficient number of rotational constants for one isotopic species or introduction of systematic errors if data for different isotopic species are used in MW, can be avoided to some extent by joint analysis of ED intensities and rotational constants of a single isotopic species. This analysis occurs at the level of r°Jrz structures and the result is often called rav structure (average of both methods). In general, such joint analyses provide the most reliable geometric strcutures for free molecules. 

These spectroscopic methods with high resolution provide us with rotational constants, from which we may extract information on the geometric structures of molecules. The rotational constants are inversely proportional to the principal moments of inertia. In a rigid molecule, the three principal moments of inertia (two for a linear molecule) are defined such that... 

Theoretically, the interpretation of geometric parameters tends to be hedged by qualifications. Most directly, the constants of rotational analysis may be interpreted in terms of average moments of inertia as in microwave spectroscopy except that the data tend to be much less extensive. From rotational constants A, B, Cy are calculated structures which are effective averages over vibrational amplitudes in the level V. The level v is most often the zero-point level, and hence most of the sttuctures quoted in these tables are the so-called "ro-structures" (1.3.1). As in ground states, ro-structures differ rather little from "true" r -... 

Rotational Constants. Moments of Inertia. Geometric Structure... 

The following values of the bond distances r (in A), the bond angle a(OOF), and the dihedral angle 4> (see Fig. 2) were derived from the above rotational constants [1 ], see also [3]. The type of the respective geometric parameter ( substitution or effective ) has been added according to the tables [4] of molecular structures see also tables [5] of structural data. ... 

The geometrical parameters as determined in the electron diffraction analysis are shown in Table 7 The results appeared to be little sensitive to the changing conformational properties of the models. It was of great advantage that the 0...0 distance with great accuracy was available from the microwave spectra. Besides, in addition to the requirement of convergency in the least-squares refinement, an important criterion for any acceptable structure was the consistency with the rotational constants derived from the microwave spectra. It is stressed, however, that such a criterion was considered to a certain limit only. Discrepancies up to 2% were acceptable since the parameters were not corrected for the effects of the intramolecular motion, and, what may be even more important, the standard deviations were relatively large. 

This volume is made of four subvolume, each containing the geometric parameters determined in the gas phase either by an analysis of the rotational constants (and sometimes the vibrational constants) obtained from microwave, infrared, Raman, electronic and photoelectron spectroscopy or by an analysis of electron diffraction intensities. Most of the structures listed in the tables are for molecules in the electronic ground state, but structures for electronically excited states have also been included as far as they are available (see 1.5). 

The most accurate calculations of the mono- and dihydrated complexes of 2-pyridone have been performed at the MP2/6-31+G(d,p) level [102]. Aecording to these data the lowest energy monohydrated complex of the 2-pyridone molecule has the same type of the structure as in the case of the simplest prototypic molecules, i.e. the water molecule acts as a proton donor to the carbonyl oxygen and as a proton acceptor to amino group. The ealeulated geometrical parameters (Figure 4) are in excellent correspondence with the experimental data which were obtained from the rotationally resolved S]<- So fluorescence excitation spectrum [103]. They are also verified by the correspondence of the calculated rotational constants to ones measured experimentally. 

The rotational constants are a source of information on the geometrical structure of the molecule. By combining the rotational constants of a parent molecule (usually the main species) and isotopically substituted daughter molecules it is now possible to... 

Structure and dynamics of molecules includes the geometric structure (interatomic distances and angles) as well as vibrational frequencies, force constants (see Force Fields A General Discussion), barriers to internal rotation, ionization energies, dipole moments, etc. These are intrinsic molecular properties, independent of temperature and pressure. 

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