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

*From*: Grigoriy Zhurko <reg_zhurko*o*chemcraftprog.com>
*Subject*: CCL: The “philosophical cornerstone” of the
Moller-Plesset perturbation theory
*Date*: Thu, 31 Jan 2019 22:09:01 +0400

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?