Non-analytical Systems

For systems more complicated than the harmonic oscillator, it is almost never possible to write down analytical expressions for the position and momentum components of the phase space trajectory as a function of time. However, if we approximate Eqs. (3.10) and (3.12) as 

In a typical (classical) molecular system, the fastest motion is bond vibration which, for a heavy-atom-hydrogen bond has a period of about 10 s. Thus, for a system containing such bonds, an integration time step At should not much exceed 0.1 fs. This rather short time 

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