11.8 Primitive set definition

Default basis sets given using one-line `BASIS`
commands or `DEFAULT` directives in a basis block
can be overwritten by explicit specifications of basis functions (type, exponents, contraction coefficients).

A group of basis functions is defined by a data card specifying a set of primitive gaussians, optionally followed by one or more cards specifying particular contractions of primitives to be included in the final basis (see section 11.9 for specification of contractions).

If an individual basis function type (, , , etc.) is specified for an atom, it is required that all other types are also defined, i.e., as soon as an explicit definition of a basis function for an atom is given, all defaults are erased for this atom.

There are four different input forms for basis functions, as explained below under a) to d). In case that
options (e.g. `SCALE`, `NPRIM`) are specified, they can be given in any order,
but no value without option key must be given after an option.

In all four cases *type* defines the angular symmetry (`S, P, D, F, G, H,` or `I`).
*type* can include several types, e.g., `SPD` or `DF` (this usually makes sense
only with default library contractions or no contractions).
The basis is loaded for all atoms with tag name *atom* in the geometry input.
If *atom* is an integer, it refers to a z-matrix row.

a) Library basis sets:

*type,atom,name,scale2,nprim*;

or

*type,atom,name*,[`SCALE=`*scale*`SCALE2=`*scale2*],[`NPRIM=`*nprim*`DELETE=`*ndel*];

Load basis named *name* from the
library

If *scale* or *scale2* is
present, all exponents are scaled by *scale* or *scale**2*, respectively.
If *nprim* is
specified, the first *nprim* exponents only are taken from the
library. If
*nprim* is negative or *ndel* is given, the last
() basis functions from the
library
set
are deleted. Associated with the library basis may be a set of default contraction
coefficients which may be accessed in subsequent contraction cards. *type*
can include several types, e.g., `SPD` or `DF`. This usually makes sense
only with default contractions, i.e., such cards should be followed only by “`C`” without any other specifications for contractions.

b) Explicit basis input:

*type,atom,exp1,exp2,**expn;expn+1,*;

General specification of exponents; continuation onto subsequent cards (separated by semicolon) is permitted as shown (the first card can hold up to 19 exponents, each following card 20 exponents).

The exponents (and other numerical parameters described below such as numbers of functions, and contraction coefficients) can be given as general input expressions, possibly involving variables. It is important to note, however, that these expressions are evaluated typically just once, at the same time as the complete basis set is parsed. This generally happens the first time that the basis set is required, perhaps before the first SCF calculation can be done. If the variables on which the basis depends are altered, this will not be noticed by the program, and the new basis set will not be used for subsequent stages of the computation. If, however, a new basis block is presented in the input, then the program marks as outdated any quantities such as integrals that have been calculated with the old basis set; subsequent job steps will then use the new basis.

c) Even tempered basis sets:

*type,atom*,`EVEN`,*nprim,ratio,centre,dratio*

or

*type,atom*,`EVEN`,`NPRIM=`*nprim*,[`RATIO=`*ratio*],[`CENTRE=`*centre*],[`DRATIO=`*dratio*]

Generates a generalized
even tempered set of functions.
The number of functions is specified by nprim,
their geometric mean by centre,
the mean ratio of successive exponents by ratio,
and the variation of this ratio, , by dratio.
If *centre* is not given,
the previous basis of the same type is extended by diffuse functions. If in
this case *ratio* is not given, is determined from the exponents of the last
two function of the previous basis. If this is not possible, the
default is adopted.
(the default) specifies a true even-tempered set, but otherwise
the ratio between successive
exponents changes linearly; the exponents are given explicitly by

**Example 1**`SP,1,VTZ;C;SP,1,EVEN,1;`

generates the generally contracted and triple-zeta basis sets for atom 1 and extends these by one diffuse function.**Example 2**`SPD,1,VTZ,DELETE=1;C;`

SP,1,EVEN,NPRIM=2,RATIO=2.5;

generates the generally contracted , triple-zeta basis sets for atom 1. Two energy optimized -functions of Dunning are included. The last and functions are deleted and replaced by two even tempered functions with ratio 2.5.

d) 3-term tempered basis sets:

*type,atom*,`EVEN3`,*nprim,, , *

Generates a 3-parameter set of *nprim* functions with exponents
given by

e) Regular even tempered basis sets:

*type,atom*,`EVENR`,*nprim,aa,ap,bb,bp*

Generates an even tempered set of *nprim* functions according to the
“regular” prescription described in
M W Schmidt and K Ruedenberg, J. Chem. Phys. 71 (1970) 3951.
If any of the parameters
*aa, ap, bb, bp*
is zero or omitted, the values are taken from table III of the above.

f) Even tempered basis set with confined progression:

*type,atom*,`EVENP`,*nprim,,,*

Generates an even tempered basis set with *nprim* functions
and a maximal exponent given by *. The progression (ratio)
between the first and second exponent is adjusted using parameter **
and the progression between the last but one and the last exponent
is adjusted with parameter **. In between the progression
is linearly interpolated. The explicit values of the progression factors
are given by:
*

*
*

so that for and for which limits the progression factors in between these two values and enables unconstrained basis set optimisations. For the progression has a factor of about 2.

*type,atom*,`EVENP2`,*nprim,,,,*

Generalises confined progression tempered basis sets by a third paramter (now ) which defines the progression as above in the centre. The ratio factors are then determined by interpolating between and .

molpro@molpro.net 2019-03-24