Special invariance properties of [ N +1/ N ] Padé approximants in Rayleigh-Schrödinger perturbation theory II. Molecular interaction energies

1982 ◽  
Vol 383 (1785) ◽  
pp. 477-483 ◽  
Keyword(s):  
Potential Energy ◽  
Padé Approximants ◽  
Potential Energy Curves ◽  
Pade Approximants ◽  
Invariance Properties ◽  
Curves And Surfaces ◽  
Molecular Potential ◽  
Diatomic Systems ◽  
Molecular Potential Energy ◽  
Schrödinger Perturbation

The use of Padé approximants in the calculation of molecular potential energy curves and surfaces is discussed. It is shown that [ N + 1/ N ] Padé approximants to the interaction energy are more useful than [ N + 1/ N ] Padé approximants to the total energy when complete potential energy curves and surfaces are being calculated. Illustrative calculations are presented for some four-electron diatomic systems. Long-range behaviour of Padé approximants to potential energy curves is considered.

Non-non-crossings in molecular potential energy curves

1976 ◽  
Vol 40 (3) ◽  
pp. 437-440 ◽  
Author(s):  
G.J. Hatton ◽  
W.L. Lichten ◽  
N. Ostrove
Keyword(s):  
Potential Energy ◽  
Potential Energy Curves ◽  
Molecular Potential ◽  
Molecular Potential Energy

Special invariance properties of the [ N +1/ N ] Padé approximants in Rayleigh-Schrödinger perturbation theory

1977 ◽  
Vol 356 (1686) ◽  
pp. 363-374 ◽  
Keyword(s):  
Perturbation Theory ◽  
Padé Approximants ◽  
Electronic Energy ◽  
Zero Order ◽  
Expansion Parameter ◽  
Pade Approximants ◽  
Invariance Properties ◽  
Change Of Scale ◽  
Shift Of Origin ◽  
Schrödinger Perturbation

Padé approximants to the electronic energy of atoms and molecules are investigated by using the expansion parameter of Rayleigh-Schrödinger perturbation theory as a formal variable. These problems are characterized by the fact that the exact Hamiltonian is known and, although the Hamiltonian is split into a zero order and a perturbing part, the exact Hamiltonian is recovered when the expansion parameter equals unity. The present study shows that for these problems the sequence of [ N +1/ N ] Padé approximants is special in that, when the expansion parameter is set equal to unity, the numerical value of each of these approximants is invariant to two modifications in the zero-order Hamiltonian; namely, a change of scale and a shift of origin in the zero-order energy spectrum. This suggests that it is the essence of the exact Hamiltonian which produces the final energy result, rather than the arbitrary scaling of the unperturbed Hamiltonian. This formalism is particularly appropriate for ab initio perturbative calculations, where the variational principle cannot be used to determine optimal values for the scale and shift parameters.

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