packaging-extrapolation 1.0.4

Extrapolation methods for complete basis sets

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packaging-extrapolation Manual

About

• This package contains partial extrapolation methods in quantum chemistry, written using the extrapolation method proposed in the literature. Extrapolation to the CBS limit can be done by entering two successive energies.
• Additionally, the web calculator is availble at the internet: https://xizaokaiz-1324489885.cos.ap-shanghai.myqcloud.com/homepage.html
• If you found this site useful for your work please cite it as: Xi, Z.; Ding, Y.; Tian, X. Building a New Platform for Significantly Improving Performance of Hartree–Fock and CCSD(T) Correlation Energy Based on Two-Point Complete Basis Set Extrapolation Schemes. J. Phys. Chem. A 2024, 128 (18), 3742–3749. https://doi.org/10.1021/acs.jpca.4c01712

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.

Tow-Point 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')

    # Extrapolation model.
    model = FitMethod()
    # The E(X) and E(Y).
    x_energy_list, y_energy_list = data['aug-cc-pvdz'], data['aug-cc-pvtz']
    # Using Klopper-1986 method and alpha=4.25, extrapolate to the CBS limit at the AV {D, T}Z basis set pair.
    low_card, high_card, alpha, method_name = 2, 3, 4.25, 'Klopper_1986'
    result = UtilTools.train_alpha(model=model,
                                   method=method_name,
                                   x_energy_list=x_energy_list,
                                   y_energy_list=y_energy_list,
                                   low_card=low_card,
                                   high_card=high_card,
                                   alpha=alpha)
    for i in range(len(result)):
        print(result[i], 'Eh')
    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
HCN,-92.8880397,-92.9100033
HCO,-113.2672513,-113.2947633
HNO,-129.8114596,-129.8401888
HO2,-150.2024221,-150.239531
N2O,-183.7105405,-183.7530387
NH2,-55.5749363,-55.5878344
NH3,-56.1972947,-56.2127423
NO2,-204.0664514,-204.1137363

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.
UtilLog.extract_energy(input_path, output_path): Extracting energy from many log files.
UtilLog.train_all(*, model, method, x_energy_list, y_energy_list, low_card, high_card, limit_list, init_guess=0.001, temp='RMSD') : Optimizing extrapolation parameters with RMSD or MAD.