51.2 Extrapolation functionals

The extrapolation functional is chosen by a keyword with the METHOD, METHOD_R, and/or METHOD_C options. The default functional is L3. In the following, $n$ is the cardinal number of the basis set (e.g., 2 for VDZ, 3 for VTZ etc), and $x$ is an arbitrary number. $p$ is a constant given either by the PR or PC options (default $p=0$). X is a number or a vector given either by the XR or XC options (only for LX; $nx$ is the number of elements provided in X). $A$, $B$, $A_i$ are the fitting coefficients that are optioized by least-squares fits.

$E_{n} = E_{\tt CBS} + A \cdot (n+p)^{-x}$
$E_{n} = E_{\tt CBS} + A \cdot (n+\frac{1}{2})^{-x}$
$E_{n} = E_{\tt CBS} + \sum_{i=1}^{nx} A_i \cdot (n+p)^{-x(i)}$
$E_{n} =E_{\tt CBS}+A\cdot \exp(-C\cdot n)$
$E_{n} =E_{\tt CBS}+A\cdot \exp(-(n-1))+B\cdot\exp(-(n-1)^2)$
Two-point formula for extrapolating the HF reference energy, as proposed by A. Karton and J. M. L. Martin, Theor. Chem. Acc. 115, 330 (2006): $E_{\rm HF,n}=E_{\rm HF,CBS} +A (n+1)\cdot \exp(-9 \sqrt{n})$. Use METHOD_R=KM for this.

The following example shows various possibilities for extrapolation:


The second example shows extrapolations of MRCI energies. In this case both the MRCI and the MRCI+Q energies are extrapolated.


molpro@molpro.net 2019-06-19