Normal coordinate autocorrelation

Figure 3 shows the absolute values of the autocorrelation functions for three different offsets AQ, defining three different initial positions for 4> on the final state potential energy surface in Figure 2. The slope of the potential surface at the initial position determines the decrease of the autocorrelation function from its initial value of 1, and it depends on the offset AQ between the minima of the potentials along the normal coordinate in Figures 1 and 2. For an offset AQ of zero, the center of the wavepacket (f> encounters a flat potential surface. No decrease of the absolute value of the autocorrelation is expected with time, as the overlap remains 1 at all times. The slow decrease seen for the solid line in Figure 3 is therefore caused by the damping factor F and the calculated spectrum is narrow. For an offset AQ of 1, the decrease at short times is faster, due to the nonzero slope of the potential surface at Q = l, and the calculated spectrum shows a large overall bandwidth. This trend is even more pronounced for the larger offset Ag = 3, the...

The autocorrelation function of this vector is readily found as an expression based on the autocorrelation function of the normal coordinates, Eq. 55,... 

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