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Preamble: Part 1


Main idea:

  • Each structure (geometry) has an associated unique energy - PES \(= f(R)\)
  • The changes between geometry are smooth, and so too is the PES
  • Can be very highly dimensional

Dimensionality/Degrees of freedom

  • Formally the system is \(3n\) dimensional (\(n=\)atoms)
  • Chemically speaking, the dimensionality is about relative dimensions so we use the formula \(3n-6\) where \(n>2\) (nonlinear molecules), just as in IR spectroscopy

Any PES that we can visualise is just a ⅔/4 dimensional “slice” of the whole multidimensional PES. This is useful for showing specific features of the landscape.