Diffuse functions are often added to basis sets using "even-tempered" exponents, or sometimes I have heard the phrase "even tempering".
In this paper by Jacek Koput, the author says "the customary even-tempered exponents were calculated in this work by multiplying the exponent of the outermost primitive function of a given angular symmetry in the valence basis set by a factor of 0.4."
The factor of 0.4 (or factors with a very similar value, such as 0.3) have been used in various other papers, but in my experience the factor is chosen without any detailed explanation. Is there any reason why the numerical factor should be specifically 0.4 (or similar)?