Keyword ECPS

This keyword specifies the effective core potentials (ECPS).
Options:

$<$ECP$>$

The ECP string $<$ECP$>$ defines the global effective core potentials. If absent, an all-electron calculation is assumed by default.

Usage of the keyword ECPS is very similar to that for the keyword BASIS (Section 4.3.1). Different ECPs can be assigned to individual atoms by the atomic symbol (e.g. Au1) or to atom groups by the element symbol (e.g. Au). The global ECP is used for all atoms which are not specified explicitly. If the keyword ECPS is not specified for an atom but the substring "ECP" is present in the basis set definition of the keyword BASIS, then an ECP of the same name will be assigned automatically to the atom. The assignment of the ECP by atomic symbols, element symbols, and global ECPS definition possesses the hierarchy (highest to lowest):

$<$atomic symbol$>$
$<$element symbol$>$
$<$global ECPS$>$
$<$basis set name$>$

Thus, any ECPS definition for an atom can be overridden by the explicit assignment of the ECP using the atomic symbol. For example the following ECPS definition

 
 ECPS (ECP|SD)
 Au   (ECP19|SD)
 Au1  (ECP1|SD)

assigns the one-electron ECP denoted by (ECP1|SD) to the atom Au1, the 19-electron ECP denoted by (ECP19|SD) to all other gold atoms, and the globally defined (ECP|SD) ECP to any other atom in the input. The file ECPS contains the ECPs from Stuttgart-Dresden [148] and from Los Alamos National Laboratory [131] in the deMon2k format [158]. Figures 7 and 8 give an overview of the effective core potentials available in the ECPS file of deMon2k [159]. All default ECPs that are obtained by the specification of the ECP acronym alone, without an explicit valence electron number, e.g. (ECP$\vert$SD), (QECP$\vert$SD), (RECP$\vert$SD), (ECP$\vert$LANL2DZ) and (QECP$\vert$LANL2DZ), refer to the ground state configuration of the corresponding element. If an ECP for an excited state is selected, e.g. for lanthanides or actinides, the tight-binding guess generation may fail. In such cases please switch to a core start density by using GUESS CORE (see 4.5.5 for further details).

Figure 7: Stuttgart-Dresden ECPs (top), RECPs (middle) and QECPs (bottom) that are available in the ECPS file of deMon2k.

Figure 8: Los Alamos National Laboratory ECPs (top) and QECPs (bottom) that are available in the ECPS file of deMon2k.

Specifying only the keyword ECPS and not specifying a corresponding valence basis set leads to a situation in which the default all-electron DZVP basis set is used in combination with the defined effective core potential. Therefore, it is handy to define the effective core potential and the corresponding basis set at the same time with the keyword BASIS. Then the keyword ECPS should be used only to define an effective core potential different from the one automatically defined by the specified basis set. In the following example,

 
 BASIS (ECP|SD)
 Au    (ECP19|SD)
 Au1   (ECP1|SD)
 ECPS       
 Cu   (RECP|SD)

the relativistic (RECP$\vert$SD) is used for copper atoms in combination with the corresponding non-relativistic valence basis set. For more elaborate inputs, it is important to note that explicit effective core potential definitions from the ECPS keyword will override implicit effective core potentials specified from the BASIS keyword. Take this input sequence as an example.

 
 BASIS (ECP|SD)
 Au    (ECP19|SD)
 Au1   (ECP1|SD)
 ECPS (RECP|SD)

Here the effective core potential assigned by the keyword ECPS will override all definitions of the effective core potential by the BASIS keyword. Also, the effective core potentials can be specified directly in the input file using the format

 
 ECPS
 SYMBOL Read ELECTRONS
 N  L  K
    EXPONENT  COEFFICIENT
       :          :
    EXPONENT  COEFFICIENT

where SYMBOL can be an element or atomic symbol, ELECTRONS is an integer number specifying the number of valence electrons, N denotes the radial power of the operator, L the angular momentum of the effective potential, and K the contraction degree. The exponents and contraction coefficients are listed in free format under the ECP block definition line, one line for each Gaussian (EXPONENT and COEFFICIENT). The following example shows a user-defined ECP input for gold in the Au(H$_2$O)$_2^+$ cation:

 CHARGE 1
 BASIS (DZVP)
 Au (AUG-CC-PVTZ-PP)
 ECPS       
 Au Read 19
  0  0   2
  13.2051000000      426.7098400000
   6.6025500000       35.9388240000
  0  1   2
  10.4520200000      261.1610230000
   5.2260100000       26.6262840000
  0  2   2
   7.8511000000      124.7568310000
   3.9255500000       15.7722600000
  0  3   2
   4.7898000000       30.5684750000
   2.3949100000        5.1837740000
  0  4   1
   1.0000000000        0.0000000000
 AUXIS (GEN-A2*)
 PRINT BASIS ECPS
 #
 GEOMETRY CARTESIAN ANGSTROM
 AU       0.000000   -0.004153    0.000033     79   196.966540
 O        2.088157    0.052069   -0.041878      8    15.999400
 O       -2.088163    0.052040    0.041551      8    15.999400
 H        2.507511   -0.813975   -0.228354      1     1.007940
 H       -2.507532   -0.814141    0.227289      1     1.007940
 H        2.490319    0.393274    0.784571      1     1.007940
 H       -2.490152    0.393861   -0.784705      1     1.007940

Calculation of the basis set superposition error (BSSE) using the counterpoise correction [160] when ECP atoms are involved requires special consideration because of the ECP projectors. If the ECP-carrying atom represents a ghost atom in the BSSE calculation, then the effective core potential must be disabled but the valence basis set must still be defined and used. The following input sequence describes this situation for the gold atom in AuF.

 ECPS
 Au (NONE)
 BASIS (DZVP)
 Au (RECP|SD)
 #
 GUESS CORE
 #
 GEOMETRY ZMATRIX
 Au             0
 F  Au 1.936660

Thus, the result of this calculation is the BSSE corrected energy for the F atom in AuF. Please note the use of the CORE start density for this atomic calculation. On the other hand, if the BSSE for the ECP-carrying atom is to be calculated, no modification of the effective core potential should be made. The following input can be used to calculate the BSSE corrected energy of the Au atom in AuF:

 BASIS (DZVP)
 Au (RECP|SD)
 #
 GUESS CORE
 #
 GEOMETRY ZMATRIX
 Au
 F  Au 1.936660 0

Example on page of the deMon2k Tutorial shows an input for BSSE calculations involving more than one ECP center. For accurate energy derivatives in ECP calculations, extended grids are often necessary. Therefore, we recommend the use of GRID FINE or equivalent GRID options (see 4.3.6) if ECPs are specified. This is particularly important for heavier elements.