Results of work at UMass Dartmouth with D. Goodson

Preliminary estimations
Generalized Feenberg transformations
   I. 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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References (bibTeX format)

Generalized Feenberg transformations: additional figures
   Error 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
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Location of singularities using [1,1,0] quadratic approximant
   I. [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
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Examples of Moller-Plesset perturbation theory, detailed study
   Table 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
Molecule - icon for Allen-dataAllen's data

Molecule - iconOlsen's data

Molecule - iconPSI package output

Calculations using MOLPRO quantum chemistry package
   On-line forms
   Pre-calculated examples
Analytical formula for large-order coefficients
   Coefficients of expansion of the model function
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List of results on Moller - Plesset perturbation theory worthwhile of mention
   Singularities 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
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Estimation of singularities of Moller - Plesset perturbation theory
   Estimation of radius of convergence from MP4
   Fitting to an eigenvalue of 2x2 matrix M0 + z M1
   [1, 1, 1] quadratic approximant
   Comparison of di erent methods
   Quadratic approximants of larger orders
   Quadratic approximants of the second kind
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