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	View last extended version TeX source file of last version First version Second corrected version 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	View figures TeX file
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	View text TeX file
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	Allen's data Olsen's data PSI package output
Calculations using MOLPRO quantum chemistry package    On-line forms    Pre-calculated examples	Run MOLPRO
Analytical formula for large-order coefficients    Coefficients of expansion of the model function	View text TeX file
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	View text TeX file
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 dierent methods    Quadratic approximants of larger orders    Quadratic approximants of the second kind	View text TeX file

More Unpublished reports

Pictures of UMassD in winter

Designed by A. Sergeev.