Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

6.2 Polyatomic molecules 139
6.2 Polyatomic molecules
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The potential energy becomes dependent of the different internal coordinates.
Question: How many internal coordinates (dimensions) do we need?
Answer:
• Total number of degrees of freedom of an -atomic molecule:
• for translational motion of center of gravity:
• for rotational motion around center of gravity
• resulting number of vibrational coordinates:
3 (6.5)
3 (6.6)
2 for linear molecules (6.7)
3 for nonlinear molecules (6.8)
— linear molecules:
— nonlinear molecules:
3 − 5 (6.9)
3 − 6 (6.10)
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3N − 6 dimensional potential energy hypersurface:
• The internal coordinates are described using the normal coordinates (vibrational
displacements).
• The potential energy function
( 1 2 3−6 ) (6.11)
is a hypersurface in a 3 − 6 (3 − 5) dimensional hyperspace. But we can plot
only in 2-D or 3-D space.