Automatic Generation of Auxiliary Functions
Automatically generated auxiliary function sets are provided in deMon2k
by means of the auxiliary function specification GENA, with , and
GENA*, with [133,156]. The GENA1 set possesses
only auxiliary functions and is usually used only for debugging. The
GENA sets consist of , , and Hermite Gaussian functions. In
addition, the GENA* also have and Hermite Gaussians. Because the
auxiliary functions are used to fit the electron density they are grouped
in , , and sets. The exponents are shared within each of
these sets [53,54]. Therefore, the auxiliary function notation
(3,2,2) describes 3 sets with a total of 3 functions, 2 sets
with a total of 20 functions and 2 sets with a total of 70
functions (see also 4.3.3). The range of exponents of all automatically
generated auxiliary functions is determined by the smallest,
,
and largest,
, primitive Gaussian exponent of the specified
orbital basis set. Therefore, the GENA and GENA* auxiliary function
sets differ for different orbital basis sets. The number of exponents
(auxiliary function sets) is given by:

(1) 
Here is 1, 2, 3, or 4 according to the index of the selected GENA
or GENA* set. The exponents are generated in almost eventempered form
(see details below) and split into , and, if a GENA* set is
specified, sets. The tightest (largest) exponents are assigned
to the sets, followed by the , and, if specified, sets.
The basic exponent from which the generation starts is defined as:

(2) 
In case ECPs or MCPs are used, equation (A..2) changes to:

(3) 
Furthermore, only and sets are generated on ECP and MCP
centers. From the two tightest , or set exponents,
and are generated according to the formulas:
The other or set exponents are generated according to the
eventempered progression:

(6) 
The exponent of the subsequent sets is also generated according
to the progression (A..6). Based on this exponent, the
exponents of the first two sets are calculated with the formulas
(A..4) and (A..5). The subsequent
set exponents are calculated again according to the eventempered
progression (A..6). In the same way, the set exponents
are calculated. In the case of elements, an extra diffuse auxiliary
function set is added.