Stabilization graph

Figure 3. Stabilization graph for model problem of Equation 15 with the basis of Equation 16. Reproduced with permission from Ref. 37, copyright 1983, North Holland.

Figure 3 A typical fragment of the stabilization graph for the 3D nonrotated HCO system calculated using 100 values of the box size. The resonance at the energy E = 1994.47 cm 1 can be easily noted due to the flat avoided-crossings region.

Figure 8.3 Stabilization graph of a meta-stable state for a van der Waals complex (BaCic and Simons, 1982).

Assume that the initial wave packet P(O) is not a superposition state but an individual resonance state. The energy E and wave function / for the resonance could be determined by performing a stabilization graph calculation as described above. If the initial wave-packet is i] , Eq. (8.10) becomes the same as (8.2), that is. 

To understand these methods, first consider the underlying physics of the avoided crossings in the stabilization graphs. These arise due to the interaction... 

One possible analytic continuation procedure is as follows.Since the data plotted in the stabilization graphs are +( /), one can express the three unknown functions H2(v), and V t]) as polynomials whose coefficients... 

The advantage of the exponent stabilization method is that all necessary calculations can be performed using standard quantum chemistry codes, without modification. This makes such calculations readily accessible to the average chemist, and in addition various levels of theory can be brought to bear to compute the E t]) stabilization curves. That said, the procedure is somewhat more complicated as compared to ordinary bound-state quantum chemistry calculations, because multiple states of M must be calculated, the stabilization graphs must be fit to analytic functions in the avoided crossing region(s), and finally these functions must be analytically continued and stationary points located... 

R. F. Frey and J. Simons,/. Chem. Phys., 84, 4462-4469 (1986). Resonance State Energies and Lifetimes via Analytic Continuation of Stabilization Graphs. 

M. Guerra,/. Phys. Chem., 94, 8542-8547 (1990). Boxing Procedure for Estimating Shape Resonance Energies from Stabilization Graphs with the MSXa Method. 

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