Subject: Re: CCL:MP4 || MP2

From: "Ernest Chamot" <[email-masked]>
Date: Fri, 30 Aug 96 10:37:38 EDT

Hi Alex,

I don't have a reference supporting your particular application:

>I have heard that it is 'OK' to use MP4 energyies from MP2 structures - IE
>MP4 energy hyper-planes are parrallel to MP2 ones.
>
>Does anyone know of a good paper to support this idea. . .

But your observation:

>. . . would that not
>suggest that mp2 energy differences are better than MP2 energies?

is absolutely correct, and important to remember in the general case, not
only for MP2 etc.  With few exceptions, systematic errors tend to cancel
within a given method, so that energy differences have less error than
absolute energies.  This is true for correlated and uncorrelated HF, DFT,
and semiempirical methods.

One "difference" that this isn't as useful for, is activation energies with
semiempirical methods.  Here you are looking at the difference between a
ground state and an excited state, so the errors aren't all systematic: they
tend to be different for excited state molecules than for ground state
molecules in semiempirical parameterizations.  Even here, though, if you
look at RELATIVE activation barriers (ie. the difference between energy
differences) you again get better accuracy due to cancellation of systematic
errors.  The use of isodesmic reactions to improve accuracy when calculating
thermodynamic data relies on this type of cancellation: when you are
comparing systems that are similar (in this case matching the bonding to
define similarity) systematic errors tend to cancel.

In the case of the shape of a potential surface, you are comparing VERY
similar systems (ie. the same molecule in different geometries) within any
local region.  So, unless you are mapping the surface all the way from a
ground state to a transition state, you get very good cancellation, and
therefore very parallel surfaces.  To my mind, this is sort of what's behind
G2 theory (much discussed on the CCL since you posted your note, I see): you
know the calculations you can afford to do are going to be offset from the
"truth", but to the extent that different calculations (size of basis set,
and degree of correlation) systematically differ from the "truth," you can
use them to estimate the "true" energy.

EC
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