Subject: collation of responses on ab initio/first principles

From: "Joerg-Ruediger Hill" <[email-masked]>
Date: Thu, 29 Nov 2001 09:15:41 +0100

> I was not so much interested in the origin of the term ab initio but
> of course the answers are interesting.  My real aim was to discover
> whether there is an intended subtle shift in meaning in using "first
> principles" rather than ab initio.  None of the responses indicate
> that this might be so.

In my understanding there has always been that subtle shift in meaning
you talk about and others seem to think the same:
"The appealing feature of the LDA approach is that it treats both exchange
and correlation effects on an equal footing and requires only to solve
one-particle equations with a local effective potential. Its limitation
is that the exact potential is not available and one is forced to work
with expressions transferred from simple model systems. This brings an
empirical element in such calculations, although they avoid adjustable
parameters. Therefore, a clear distinction in terminology seems desireable
between the exact-exchange 'HF plus electron correlation' approach on the
one hand and the LDA or LSD-based approaches on the other hand. The former
are known as 'ab initio' methods, while for the latter the terminus 'first
principle' method is widely accepted. Perhaps it is better to be more
specific and refer directly to the 'density functional' (DF) or to the
'local (spin) density approximation' (LDA, LSD)." J. Sauer, Chem. Rev.
(1989), 89, 199.

> Also, I was particularly interested in the posting from Per Ola
> Norrby who discusses how basis sets are constructed in a
> semi-empirical manner especially regarding expansion coefficients and
> contraction.  I would be interested in learning more about this
> aspect and/or references to where it is discussed in the literature.
>
>> It's not always realised  that what is called "ab initio" incorporates
>> many empirical parameters.  For example, a standard HF/6-31G* calculation
>> would be called "ab initio", but all the exponents and contraction
>> coefficients in the basis set were selected by fitting to
>> experimental data!  That's one of the main reasons for the success of
>> the Pople basis sets, they have been fit to real data, thus they are
>> good at reproducing real data.  The effect, of course, is that the
>> basis set incorporates systematical errors that to a large extent
>> cancels the systematical errors in HF ...

Basis sets are NOT constructed in a "semi-empirical manner" or "fitted
to experimental data". Basis sets are obtained by performing electronic
structure calculations (Hartree-Fock, MP2, DFT - the method the basis set
is to be used with) usually for atoms but sometimes for molecules while
varying the exponents of the basis functions and the expansion coefficients
until the minimum energy has been found. Basis sets obtained for Hartree-
Fock are often transferred to other electronic structure methods which
usually gives good results. See e.g.:
- basics, including the derivation of Pople's basis sets
S. Huzinaga, Computer Physics Reports (1985), 2, 279
- more recent developments in basis sets for Hartree-Fock
A. Schäfer, H. Horn and R. Ahlrichs, J. Chem. Phys. (1992), 97, 2571
- basis sets for DFT
N. Godbout, D. R. Salahub, J. Andzelm and E. Wimmer, Can J. Chem. (1992), 70,
560

You might also want to read about the work of T. H. Dunning, Jr. concerning
correlation-consistent basis sets.

Jörg-Rüdiger Hill

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