Bond angles geometric relationship between

For systems of more than two atoms, the vibrations can be symmetrical or asymmetrical about the centre. If there is no change in the angle between any of the bonds and the plane defined by the remaining atoms, they are classified as in plane . The opposite case is known as out of plane vibrations. Depending on the geometric relationship between the transition moment for a specific vibrational mode and the symmetry axis for the mode, vibrational modes may be further classified as parallel or perpendicular. 

The relationship between two bond vectors can be represmted using a distance, two angles and a torsion indicated (top). To derive the data for the database all possible pairs ofexocyclic vectors are considered and ur geometric parameters calculated. 

The key observation is that there is a systematic relationship between the geometrical parameters defining the reaction . When the Y-M bond is lengthened (Ar) under the various influences of a particular crystal and molecular environment, the rest of the tetrahedral structure (YMX angle, M-X bond length, r,) responds in a standard, predictable, way. [See, for example, the correlation shown in Fig. 5, which is discussed also by Dunitz (1979).] This must represent, in the particular circumstances, the most favourable, i.e. the minimum energy, pathway for the structural change... 

A 3D geometric search is then performed to look for relationships between features in a molecule. The initial 2D pattern search takes into account only the composition of the molecule, such as atom types and bond types. The 3D portion is only concerned with the geometric relations between the features (e.g., distance, angle, exclusive van der Waals volume, overlapping van der Waals volume, and constraints). A 3D search makes use of the coordinates stored in the database for determining whether constraints are satisfied. 

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