Back-door intruders

Recent FCI investigations by Christiansen and co-workers have provided evidence that the MP series can diverge even in the case of single reference dominated systems when using extended basis sets. The authors investigated the Ne atom and found for A. = —0.82 an avoided crossing ( back door intruder... 

In Figure 14.4, we have illustrated the behaviour of the two-state model for two sets of parameters, which represent a back-door intruder dominated by high-order excitations (to the left) and a front-door intruder dominated by low-order excitations (to the right). The numerical values of the parameters were obtained from the Mpller-Plesset calculations discussed in Section 14.5.5. For the high-excitation back-door intruder, the parameters are yS — a = 12.32, S = —0.00034 and... 

In the plot corresponding to the back-door intruder, an avoided crossing is observed at z = —0.74. As expected from the smallness of the coupling, the energy difference (14.5.36) is a... 

Over the years, many techniques have been developed to improve the convergence rale of convergent sequences and to turn divergent sequences into convergent ones. We shall here consider one of the simpler approaches, analytic continuation [17], which enables us to remove the divergence caused by back-door intruders. 

We assume that the only intruder within the unit circle is a back-door intruder The perturbation expansion therefore converges for z < b1- In the method of analytic continuation, we choose a new point of expansion z closer to the physical state z = 1. We here take z to be a real... 

As an example of analytic continuation, consider the M0ller-Ple.sset calculation on the HF molecule at the equilibrium geometry in the aug-cc-pVDZ basis. As discussed in Section 14.5.4, this expansion is divergent with a back-door intruder at about z = —0.7. The expansion around z = 0.4 should be convergent for z = I since l — 0.4 < — 0.7 — 0.4. In Table 14.4, we have listed the convergent expansion for z = 1 around z = 0.4 as well as the divergent expansion around z = 0.0. 

Fig. 14.1. Points of degeneracy in the complex plane. The conjugate points (fz.fj) corre.spond to a front-door intruder and the points ( 4. 4) to a back-door ininider.

Father and son stared in blazing disbelief at the intruders, from Vasco to Zeno and back again. Vasco stepped aside with a flourish to give me the stage. The clerk tactfully scuttled out, closing the door. 

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