CCL: The “philosophical cornerstone” of the Moller-Plesset perturbation theory



 Sent to CCL by: Grigoriy Zhurko [reg_zhurko^^^chemcraftprog.com]
 I am sorry if my post is too unusual for this list; if so, please suggest me
 some web forums where I can get answers to my question.
 It is known that the MP rows (MP2, MP3, MP4, etc) can converge both quickly and
 slowly, and for some cases (e.g. CeI4) they even diverge instead of converging.
 The first question is, whether this tendency becomes apparent for some molecules
 like CeI4 not only for the MP series, but also for other applications of
 perturbation theory. In other case, if we know that the MP series diverge for
 some molecule, can we predict that the CCSD(T) method gives worse results for
 this molecule in comparison to CCSD (at least the advantages of the CCSD(T)
 approach for this molecule are not as evident as for other ones).
 The second question is quite philosophic: what is the “mathematical
 cornerstone”, or “philosophical cornerstone” of the
 perturbation theory, and whether it can be shown with some simple samples. If
 yes, maybe this information will help us predict whether the MP rows will
 diverge for some molecule not yet investigated.
 I have asked this question on some web forums, and got some answers.
 Let’s consider the salvation of two equations:
 1)
 x+sin(x)=3000
 If we write the following:
 x=3000-sin(x)
 We can set x0=0 and get the following iterations:
 0
 3000
 2999,78081002572
 2999,5739029766
 2999,39713977695
 2999,26623684759
 2999,18383222963
 2999,13904100976
 This series converge after 40 iterations.
 2)
 6000=(x−1)(x−3000)+sin(x)
 We transform this equation into the following:
 x=(6000-sin(x))/(x-3000)+1
 Choosing x0=0 we get the following convergence:
 0
 -1
 -0,999613952344155
 -0,999614140048658
 -0,999614139957402
 -0,999614139957447
 -0,999614139957447
 -0,999614139957447
 So, this series converges within 6 iterations.
 Some people said that the second example illustrates the
 суть of the perturbation theory, while the first one
 does not. Some other people said that both these examples are not really
 attributed to the perturbation theory. Can you suggest your opinion?