[Wien] Completeness of the basis set

[Stefaan Cottenier]

> it maybe a crazy question, but I would like to know if there is some 
> kind of measure of the completeness of the basis set? 
>  
> I can find measures of the orthogonality - but they are also rather 
> easy  to do, but if I want to "converge" the basis set, I would like 
> to know  if there is any way to determine how well converged it is, 
> or would I have to infer it from the changes to the total energy? 
 
Maybe an ingenious mathematical criterion exists for this -- I don't 
know -- but intuitively it looks like this is an impossible question. 
In an ideal world, your total energy will always decrease if you 
increase the basis set, however large the basis might be already. 
Therefore, what you call "complete" will depend on the precision in 
total energy that is relevant for you. 
 
In real life, you will anyway run into problems with overcompleteness 
if you work with too large basis sets (total energy can increase again, 
due to numerical problems). 
 
More generally, I think you can watch any property (and not just the 
total energy): if the properties you are interested in are converged 
(again, what you call "converged" depends on the accuracy you require) 
with respect to the basis set, then this basis set is "complete" for 
your particular purpose. 
 
Because always "completeness" depends on the required precision, I 
would be surprized if a general mathematical criterion could ever exist 
for it. 
 
Stefaan