chemtools.cbs module

Module for Complete Basis Set (CBS) Extrapolations.

expo()[source]

CBS extrapolation formula by exponential Dunning-Feller relation.

\[E^{HF}(X) = E_{CBS} + a\cdot\exp(-bX)\]
Returns:
function object
exposqrt(twopoint=True)[source]

Three-point formula for extrapolating the HF reference energy [2].

[2]Karton, A., & Martin, J. M. L. (2006). Comment on: “Estimating the Hartree-Fock limit from finite basis set calculations” [Jensen F (2005) Theor Chem Acc 113:267]. Theoretical Chemistry Accounts, 115, 330–333. doi:10.1007/s00214-005-0028-6
\[E^{HF}(X) = E_{CBS} + a\cdot \exp(-b\sqrt{X})\]
Args:
twpoint : bool
A flag marking the use of two point extrapolation with b=9.0
Returns:
funtion object
exposum()[source]

Three point extrapolation through sum of exponentials expression

\[E(X) = E_{CBS} + a \cdot\exp(-(X-1)) + b\cdot\exp(-(X-1)^2)\]
extrapolate(x, energy, method, **kwargs)[source]

An interface for performing CBS extrapolations using various methods.

Args:
x : numpy.array
A vector of basis set cardinal numbers
energy : numpy.array
A vector of corresponding energies
method : str
Method/formula to use to perform the extrapolation
Kwargs:
Keyword arguments to be passed to the requested extrapolation function using the method argument
poly(p=0.0, z=3.0, twopoint=True)[source]

CBS extrapolation by polynomial relation.

\[E(X) = E_{CBS} + \sum_{i}a_{i}\cdot (X + P)^{-b_{i}}\]
Kwargs:
twpoint : bool
A flag for choosing the two point extrapolation
z : float or list of floats
Order of the polynomial, default=3.0
p : float
A parameter modifying the cardinal number, default=0.0
uste(method='CI')[source]

CBS extrapolation using uniform singlet and triplet pair extrapolation (USTE) scheme [1].

[1]Varandas, A. J. C. (2007). “Extrapolating to the one-electron basis-set limit in electronic structure calculations. The Journal of Chemical Physics, 126(24), 244105. doi:10.1063/1.2741259
Args:
x : int
Cardinal number of the basis set
e_cbs : float
Approximation to the energy value at the CBS limit
a : float
Empirical A3 parameter
method : str
One of: ci, cc
Returns:
function object