## 19.8 Basis set extrapolation

Basis set extrapolation can be carried out for correlation consistent basis sets using

EXTRAPOLATE,BASIS=basislist,options

where basislist is a list of at least two basis sets separated by colons, e.g. AVTZ:AVQZ:AV5Z. Some extrapolation types need three or more basis sets, others only two. The default is to use extrapolation of the correlation energies, and in this case two subsequent basis sets and the corresponding energies are needed. The default is not to extrapolate the reference (HF) energies; the value obtained with the largest basis set is taken as reference energy for the CBS estimate. However, extrapolation of the reference is also possible by specifying the METHOD_R option.

The simplest way to perform extraplations for standard methods like MP2 or CCSD(T) is to use, e.g.

```***,H2O
memory,32,m
gthresh,energy=1.d-8

r =   0.9572 ang, theta =  104.52
geometry={O;
H1,O,r;
H2,O,r,H1,theta}

basis=avtz
hf
ccsd(t)
extrapolate,basis=avqz:av5z

table,basissets,energr,energy-energr,energy
```

This will perform the first calculation with AVTZ basis, and then compute the estimated basis set limit using the AVQZ and AV5Z basis sets. The correlation energy obtained in the calculation that is performed immediately before the extrapolate command will be extrapolated (in this case the CCSD(T) energy), and the necessary sequence of calculations [here HF;CCSD(T)] will be automatically carried out. Unless otherwise specified (see below), the Hartree-Fock energy is taken from the largest basis set and not extrapolated.

The resulting energies are returned in variables ENERGR (reference energies), ENERGY (total energies), and ENERGD (Davidson corrected energy if available); the corresponding basis sets are returned in variable BASISSETS. The results can be printed, e.g., in a table as shown above, or used otherwise. The above input produces the table

``` BASIS       EHF           ECORR          ETOT
AVQZ    -76.06600082   -0.29758099   -76.36358181
AV5Z    -76.06732050   -0.30297495   -76.37029545
CBS     -76.06732050   -0.30863418   -76.37595468
```

The extrapolated total energy is also returned in variable ECBS (ECBSD for Davidson corrected energy if available).

In order to extrapolate the HF energy as well (for example using Karton-Martin extrapolation), one can modify the input as follows:

extrapolate,basis=avqz:av5z,method_r=km

This yields

``` BASIS           EREF            ECORR           ETOT
AVQZ        -76.06600082     -0.29758099    -76.36358181
AV5Z        -76.06732050     -0.30297495    -76.37029545
CBS         -76.06754138     -0.30863418    -76.37617556
```

Alternatively, one can do the energy calculations manually and pass the energies to be extrapolated to extrapolate via variables. This is more flexible and allows to carry out different extrapolations with the same energies.

For example:

```***,H2O
memory,32,m
gthresh,energy=1.d-8  !energy convergence threshold

r =   0.9572 ang, theta =  104.52
geometry={O;
H1,O,r;
H2,O,r,H1,theta}

basis=vqz
hf
ccsd(t)
eref(1)=energr  !VQZ reference (HF) energy
etot(1)=energy  !VQZ ccsd(t) total energy

basis=v5z
hf
ccsd(t)
eref(2)=energr  !V5Z reference (HF) energy
etot(2)=energy  !V5Z ccsd(t) total energy

text,extrapolate total energy:
extrapolate,basis=vqz:v5z,etot=etot

text,extrapolate correlation energy only:
extrapolate,basis=vqz:v5z,etot=etot,eref=eref

text,extrapolate reference and correlation energies separately:
extrapolate,basis=vqz:v5z,etot=etot,eref=eref,method_r=km
```

This yields

For extrapolation of the total energy:

``` BASIS           ENERGY
VQZ         -76.35979334
V5Z         -76.36904020
CBS         -76.37874183
```

For extrapolation of the correlation energy only:

``` BASIS           EREF            ECORR           ETOT
VQZ         -76.06483534     -0.29495800    -76.35979334
V5Z         -76.06709083     -0.30194937    -76.36904020
CBS         -76.06709083     -0.30928458    -76.37637541
```

For separate extrapolation of reference and correlation energies:

``` BASIS           EREF            ECORR           ETOT
VQZ         -76.06483534     -0.29495800    -76.35979334
V5Z         -76.06709083     -0.30194937    -76.36904020
CBS         -76.06746834     -0.30928458    -76.37675292
```

molpro@molpro.net 2018-12-15