Subject: Summary: Definition of diffuse function?

From: Jerry C C Chan <[email-masked]>
Date: Tue, 12 Mar 1996 16:01:13 +0800 (HKT)

Dear Netters,

	I would like to express my gratitude to Jan and Cory for their 
responds to my question.  The original post is reproduced below:

	I am currently working with the TZV cobalt basis set developed by A. 
Schafer et.al. (JCP, 97 (1992) 2571.).  If the TZV basis set is uncontracted
from (842111/631/411) to (61121111111/3111111111/111111) and then 2
polarization p functions prepared by Wachters are added, I would like 
to know how I should label the new basis set? 

i.  (61121111111/311111111111*/111111)
i.  (61121111111/311111111111+*/111111)
ii. (61121111111/311111111111+*/111111+)

In the new basis set, the smallest exponents are 0.043402 and 0.3038145779
for p and d, respectively.  I think the answer depends on the definition of
diffuse function.  Could anybody please comment on this issue.  Thank you
very much. 

+++++++++++++++++++++++ 

 ... Diffuse functions is even less defined. It simply means: functions
which are diffuse, i.e., have small exponent. I understand, that it is
usually used to s and p functions, but in principle, you may have "diffuse
polarization" functions. What does it mean small exponent? Beats me...
Usually exponent is considered small if it is below 0.2, and "normal" when
it is above 0.7. In between, you are entering the "grey area" and it
probably depends on element. For carbon 0.3 is small exponent. For heavier
elements it is not necessarily small. So for cobalt, I am not sure. 

Also remember that term "diffuse" was really popularized in 1980's, so in
papers older than that, you may find diffuse called all sorts of names.

Sorry for confusing you, rather than giving straight answers, but I am
afraid, some of these terms are more artistic than scientific, since
construction of basis sets is a black art rather than science.

Jan
[email-masked]

+++++++++++++++++++++

I don't believe there is a systematic name for most of these basis sets,
but we were faced with a similar dilemna in naming basis sets from the
same paper. We wanted to use some basis sets that were included at thir
ftp site which were not (explicitly) mentioned in their paper, so we had
to come up with a label to describe them (See C. C. Pye et al., J. Mol. 
Struct. (Theochem), 307 (1994) 239 ). For the first row atoms, the SV, DZ
and TZ basis sets were already defined to be a particular contraction
pattern that was based on `common-sense' i.e. for carbon, of 1s2s2p
minimal configuration, the 511111/411 scheme implies (LOOSELY) that there
are 3 functions that describe mostly the 1s (511.../...), 3 functions that
describe mostly the 2s (...111/...), and 3 that describe the 2p
(....../411). What we called TQZ was when 4 functions described the 2p
set, the 1s and 2s still having (loosely) 3 functions each. Since these
are 'energy-optimized', the extra function is not really a diffuse or
polarization function. Similarly the QPZ set (61111111/51111) has 4
functions to describe each s shell (Quadruple) and 5 functions to describe
the p shell (Pentuple). 

If I had to describe your basis set:
Co 1s2s2p3s3p3d4s (minimal)
It is certainly at least TZ (in all shells). 1 missing s. The p-s are
between TZ and QZ, and the d shell is hextuple-zeta, so maybe call it
TsTQpHdZ or (more neatly) Ts-TQp-Hd-Z. For the extra functions you could use
this as the root name and (with the Wachters functions added), call it
Ts-TQp-Hd-Z(2p). In the end, WHAT you call it doesn't matter, as long as 
people know how you constructed the basis in order to be able to duplicate
the result.

-Cory
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