Keyword AUXIS

This keyword specifies the auxiliary function set.
$<$Auxis$>$ The auxiliary function set string $<$Auxis$>$ defines the global auxiliary function set. If this option is absent, the GEN-A2 auxiliary function set is used by default.
Similar to the orbital basis set options, the auxiliary function sets can also be assigned to individual atoms by the atomic symbol or to atom groups by the element symbol in the keyword block of AUXIS. The syntax and hierarchy of these assignments is analogous to the orbital basis set assignments (see 4.3.1). For C$_2$H$_4$ (see input in 4.1.1) the following auxiliary function definition

 C     (GEN-A2*)
 C1    (GEN-A2)

assigns a GEN-A2 auxiliary function set to atom C1, a GEN-A2* auxiliary function set to the other carbon and the A2 auxiliary function set to all other atoms. The AUXIS file of deMon contains only the A2 auxiliary function set. The other auxiliary function sets used above (GEN-A2 and GEN-A2*) are generated automatically [133,156] according to the procedure described in Appendix A. The GEN-An+ ($n=2,3,4$) auxiliary function sets are particular for the variational fitting of Fock exchange. They have a set structure as the corresponding GEN-An* auxiliary function sets but without the angular momentum index augmentation to $f$ and $g$ Hermite Gaussians during the SCF iterations. Instead, this augmentation is only performed post-SCF for the final Fock energy calculation. Thus, the computational demand for the GEN-An+ auxiliary function set during the SCF is close to that of GEN-An, whereas the final (non-variational) energy is close to GEN-An*. Just as with the orbital basis sets, auxiliary function sets can also be specified directly in the input file using the format:

  :       :

Here LMAX denotes the maximum angular momentum quantum number of the auxiliary function subset and EXPONENT the exponent which is shared [53,54] by all functions in that subset. Thus an auxiliary function subset with ${\tt LMAX} = 2$ contains ten functions, namely one $s$, three $p$ and six (Cartesian) $d$ functions. In deMon2k, these functions are primitive Hermite Gaussians [51,157] of the form (without normalization):

{\bar{a}}({\bf r}) = {\left (
{\partial \over {\partial A...
... \right )}^{\bar{a}_z} \,
e^{- \beta ({\bf r} - {\bf A})^2}%
\end{displaymath} (7)

In the following we extend the previous example of a user-defined basis set input for an oxygen molecule with a user-defined auxiliary function set input:

 Multiplicity 3
 VxcType Basis BLYP
 Mixing 0.4
 Geometry Z-Matrix
 O  O  r
 r  1.207
 O Read
 1    0    2
 49.98097100        0.4301280000
 8.896588000        0.6789140000
 2    0    2
 1.945237000        0.4947200000E-01
 0.493363000        0.9637820000
 2    1    2
 1.945237000        0.5115410000
 0.493363000        0.6128200000
 O Read
 0  100.0
 0   25.0
 2    5.0
 2    1.0

The auxiliary function set in this example consists of two $s$ and two $d$ sets. Together these comprise 22 auxiliary functions (1+3+6 from each $d$ set and 1 from each $s$ set).