Preliminary estimations | |
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Generalized Feenberg transformationsI. Reformulation of Feenberg transformation II. Relationship between Feenberg transformation and conformal mapping of variables III. Generalization with two parameters IV. Moller - Plesset perturbation series Fig. 1. Coefficients of Moller - Plesset perturbation theory Fig. 2. Accuracy of algebraic approximants versus number of coeefficients Fig. 3. Error as a function of the parameter lambda and locations of singularities Fig. 4. Error and positions of singularities as a function of lambda1 of generalized Feenberg transformation for "cc4BH" series |
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Generalized Feenberg transformations: additional figuresError of quadratic approximants for a model function with two square-root singularities Branch point locations of the [1/0, 1] quadratic approximant for the model function Using the conformal mapping g(z) to move one of singularities as far as possible from the origin Using Feenberg transformation to modify analytic structure of the function associated with a perturbation series Radius of convergence of Feenberg transformation of the MP perturbation series of E(z) with a branch point in the negative half-plane and a pair of branch points in the positive half-plane. Modelling the MP perturbation series E(z) by the ground-state eigenvalue of the matrix M0 + z M1 Summation of the series for the model function (a big table) Location of two singularities of the Feenberg transformation of series for the model function | View figures |

Location of singularities using [1,1,0] quadratic approximantI. [1,1,0] quadratic approximant II. Example of estimation of singularities Fig. 1. Using quadratic approximant [1, 1, 0] to estimate singularities of the model problem Fig. 2. The same as Figure 1 but for the augmented Moller - Plesset perturbation series for HF molecule | View text |

Examples of Moller-Plesset perturbation theory, detailed studyTable of coefficients and partial sums Semilogarithmic plot of coefficients Plot of scaled coefficients Convergence of summation approximants Singularities of approximants in complex plane Table of singularities with their weights Plot of the energy function found by summation of the series Known inaccuracies | Allen's data |

Calculations using MOLPRO quantum chemistry packageOn-line forms Pre-calculated examples |
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Analytical formula for large-order coefficientsCoefficients of expansion of the model function | View text |

List of results on Moller - Plesset perturbation theory worthwhile of mentionSingularities at negative axis A negative real singularity and a pair of complex-conjugate singularities in positive half plane Moller - Plesset perturbation theory for Ar atom | View text |

Estimation of singularities of Moller - Plesset perturbation theoryEstimation of radius of convergence from MP4 Fitting to an eigenvalue of 2x2 matrix M _{0} + z M^{1}[1, 1, 1] quadratic approximant Comparison of dierent methods Quadratic approximants of larger orders Quadratic approximants of the second kind | View text |

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