MOLPRO

46 BASIS SET EXTRAPOLATION 345
ECORR=variable
ECORRD=variable
Provide the correlation energies to be extrapolated in variable (a vector
with the same number of energies as basis sets are given)
Provide the Davidson corrected correlation energies to be extrapolated
in variable (a vector with the same number of energies as basis
sets are given). If both ECORR and ECORRD are given, both will be
extrapolated.
MINB=number First basis set to be used for extrapolation (default 1)
MAXB=number
NPR=number
NPC=number
XR=array
XC=array
PR=array
PC=array
Last basis set to be used for extrapolation (default number of basis
sets)
If given, the last NPR values are used for extrapolating the reference
energy. NPR must be smaller or equal to the number of basis sets.
If given, the last NPC values are used for extrapolating the reference
energy. NPC must be smaller or equal to the number of basis sets.
Provide a vector of exponents to be used for defining the extrapolation
functional for the reference energy when using the LX functional.
Provide a vector of exponents to be used for defining the extrapolation
functional for the correlation energy when using the LX functional.
Provide the constant p to be used for defining the extrapolation functional
for the reference energy.
Provide the constant p to be used for defining the extrapolation functional
for the correlation energy.
46.2 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.
Lx
LHx
E n = E CBS + A · (n + p) −x
E n = E CBS + A · (n + 1 2 )−x
LX
E n = E CBS + ∑ nx
i=1 A i · (n + p) −x(i)
EX1 E n = E CBS + A · exp(−C · n)
EX2 E n = E CBS + A · exp(−(n − 1)) + B · exp(−(n − 1) 2 )
KM
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 HF,n = E HF,CBS +A(n+1)·exp(−9 √ n). Use METHOD R=KM
for this.
The following example shows various possibilities for extrapolation: