Angular and radial geometry

As alluded to above, the superposition method, typified by the AOM, overcomes many of the problems of the global scheme and is discussed in detail in Chapter 2.52. Flf is constructed as a superposition of contributions from individual M L bonds which explicitly separates the angular and radial parts. The former is implicit in the geometry so that the AOM energy parameters focus... 

In this section, we discuss the observed geometries, both angular (the relative orientation of the components B and XY in space) and radial (the distance between B and XY at the observed orientation) of complexes B XY. 

Attention will be paid to the systematic relationship of the geometries of B- XY to those of hydrogen-bonded complexes in the corresponding series B- HX, especially for angular geometries, which are dealt with in detail in Sects. 3.1, 3.2 and 3.3. Radial geometries are treated only in summary (Sect. 3.4) here, but a detailed analysis is available in [19]. 

Table 2. Energies (eV) and geometrical (R(A), 9(°)) parameters for the D3h — C3v transition of AsF3 and AsBr3 (in parentheses), calculated when taking only variations of rr and ra, respectively, into account, and when optimizing both, the radial and angular geometry (upper index m)...

Pr and Pr are the radial momenta conjugate to R and r, respectively UC and uv are the translational and vibrational reduced masses t and j are the orbital and rotational angular momenta and V Is the full potential energy function V depends on the three variables R, r and Y where y Is the angle between R and r such that y 0 for linear COH geometries In the lOS treatment, the quantities t,j and y are taken to be parameters, with I chosen In the usual way (from 0 to < In the quantum calculations and 0 to imax classical calculations with... 

For characterizing a dipolar molecule in its electronic ground state, few methods are more instructive than pulsed-nozzle Fourier-trans-form microwave spectroscopy (32). As illustrated schematically in Fig. 5, a short pulse of microwave radiation directed at the gas pulse excites a rotational transition in the species of interest subsequently the rotationally excited molecules reemit radiation, which is detected. This technique provides a remarkably sensitive probe for transients, the properties of which can be specified with all the precision and detail peculiar to rotational spectroscopy only microseconds after their production. In relation to a weakly bound adduct A --B formed by two molecular reagents A and B, for example, we may draw on the rotational spectrum to determine such salient molecular properties as symmetry, radial and angular geometry, the intermolecular stretching force constant and internal dynamics, the electric charge distribution, and the electric dipole and quadrupole moments of A -B (see Table I). 

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