packaging-extrapolation 1.0.0

Extrapolation methods for complete basis sets

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packaging-extrapolation Manual

About

• This package contains partial extrapolation methods in quantum chemistry.
• This package is written using the extrapolation method proposed in the literature. Extrapolation to the CBS limit can be done by entering two successive energies.

Quickly Use

• Please use the pip command to install: pip install packaging_extrapolation or python3 -m pip install packaging_extrapolation
• Please make sure the package is the latest: pip install --upgrade packaging_extrapolation
• After installation, test the example in src/packaging_extrapolation/examples/examples_energy.py to see if you get results.
  • Extrapolation Method Calls: python examples_energy.py -m "Klopper_1986" -xe -76.0411795 -ye -76.0603284 -low 2 -high 3 -a 4.25
  • -m: extrapolation method name.
  • -xe: energy for E(X).
  • -ye: energy for E(Y).
  • -low: cardinal number for X.
  • -high: cardinal number for Y.
  • -a: extrapolation parameter alpha/beta.

Ten Extrapolation Schemes

Method	Two-point From	Name	Reference
Klopper-1986	$E_{CBS}=\frac{E(Y)e^{-α\sqrt{X}}-E(X)e^{-α\sqrt{Y}}}{e^{-α\sqrt{X}}-e^{-α\sqrt{Y}}}$	Klopper_1986	https://doi.org/10.1016/0166-1280(86)80068-9
Feller-1992	$E_{CBS}=\frac{E(Y)e^{-αX}-E(X)e^{-αY}}{e^{-αX}-e^{-αY}}$	Feller_1992	https://doi.org/10.1063/1.462652
Truhlar-1998 (Hartree-Fock)	$E_{CBS}=\frac{E(Y)X^{-\alpha}-E(X)Y^{-\alpha}}{X^{-\alpha}-Y^{-\alpha}}$	Truhlar_1998	https://doi.org/10.1016/S0009-2614(98)00866-5
Jensen-2001	$E_{CBS}=\frac{E(Y)(X+1)e^{-α\sqrt{X}}-E(X)(Y+1))e^{-α\sqrt{Y}}}{(X+1)e^{-α\sqrt{X}}-(Y+1)e^{-α\sqrt{Y}}}$	Jensen_2001	https://doi.org/10.1063/1.1413524
Schwenke-2005	$E_{CBS}=[E(Y)-E(X)]\alpha+E(X)$	Schwenke_2005	https://doi.org/10.1063/1.1824880
Martin-1996	$E_{CBS}=\frac{E(Y)(X+1/2)^{-\beta}-E(X)(Y+1/2)^{-\beta}}{(X+1/2)^{-\beta}-(Y+1/2)^{-\beta}}$	Martin_1996	https://doi.org/10.1016/0009-2614(96)00898-6
Truhlar-1998 (Correlation)	$E_{CBS}=\frac{E(Y)X^{-\beta}-E(X)Y^{-\beta}}{X^{-\beta}-Y^{-\beta}}$	Truhlar_1998	https://doi.org/10.1016/S0009-2614(98)00866-5
Huh-2003	$E_{CBS}=\frac{E(Y)(X+\beta)^{-3}-E(X)(Y+\beta)^{-3}}{(X+\beta)^{-3}-(Y+\beta)^{-3}}$	HuhLee_2003	https://doi.org/10.1063/1.1534091
Bakowies-2007	$E_{CBS}=\frac{E(Y)(X+1)^{-\beta}-E(X)(Y+1)^{-\beta}}{(X+1)^{-\beta}-(Y+1)^{-\beta}}$	Bkw_2007	https://doi.org/10.1063/1.2749516
OAN(C)	$E_{CBS}=\frac{3^3E(Y)-\beta^3E(X)}{3^3-\beta^3}$	OAN_C	https://doi.org/10.1002/jcc.23896

Another Use

• If you need to calculate the extrapolation energy of more systems, please refer to the following examples:

from packaging_extrapolation import UtilTools
from packaging_extrapolation.Extrapolation import FitMethod
import pandas as pd
import numpy as np

"""
Calculate more systems.
"""

if __name__ == "__main__":
    # Input file.
    data = pd.read_csv('../data/hf.CSV')

    model = FitMethod()
    method_name = 'Klopper_1986'
    x_energy_list, y_energy_list = data['aug-cc-pvdz'], data['aug-cc-pvtz']
    low_card, high_card, alpha = 2, 3, 4.25
    result = UtilTools.train_alpha(model=model,
                                   method=method_name,
                                   x_energy_list=x_energy_list,
                                   y_energy_list=y_energy_list,
                                   alpha=alpha)
    print(result)
    df = pd.DataFrame()
    df['CBS Energy'] = result
    # Output file.
    df.to_csv('CBS_Energy.csv', index=False)

• The input file should be in .csv format and have the following content:

mol,aug-cc-pvdz,aug-cc-pvtz,aug-cc-pvqz,aug-cc-pv5z,aug-cc-pv6z
HCN,-92.8880397,-92.9100033,-92.915489,-92.9166367,-92.9167832
HCO,-113.2672513,-113.2947633,-113.3022304,-113.3039105,-113.3041055
HNO,-129.8114596,-129.8401888,-129.8486338,-129.8505396,-129.8507611
HO2,-150.2024221,-150.239531,-150.2495353,-150.2520093,-150.2522722
N2O,-183.7105405,-183.7530387,-183.7649319,-183.7675527,-183.7678624
NH2,-55.5749363,-55.5878344,-55.5911626,-55.5919484,-55.5920423
NH3,-56.1972947,-56.2127423,-56.2164646,-56.217354,-56.2174645
NO2,-204.0664514,-204.1137363,-204.1275371,-204.1305865,-204.1309424

Functions
UtilTools.calc_MAD(y_true, y_pred): Calculate the Mean Absolute Deviation (kcal/mol).
UtilTools.calc_max_MAD(y_true, y_pred): Calculate the Maximum Absolute Deviation (kcal/mol).
UtilTools.calc_min_MAD(y_true, y_pred): Calculate the Minimum Absolute Deviation (kcal/mol).
UtilTools.calc_RMSE(y_true, y_pred): Calculate the Root Mean Square Deviation (kcal/mol).
UtilTools.calc_MSD(y_true, y_pred): Calculate the Mean Square Deviation (kcal/mol).
UtilTools.calc_MaxPosMAD(y_true, y_pred): Calculate the Maximum Positive Deviation (kcal/mol).
UtilTools.train_alpha(*, model, method, x_energy_list, y_energy_list, alpha, low_card, high_card): Calculate extrapolated energy.