Modulated perturbation theory for molecular interactions. III. Variational calculations of the second‐order energy for the ground state of H2+

1977 ◽  
Vol 66 (8) ◽  
pp. 3742-3744 ◽  
Author(s):  
V. Magnasco ◽  
G. Figari ◽  
M. Battezzati
Keyword(s):  
Perturbation Theory ◽  
Molecular Interactions ◽  
Ground State ◽  
Second Order ◽  
Order Energy ◽  
Variational Calculations

Pertubation Theory About Self-Consistent Field Solution in One-Dimensional Hubbard Model

2003 ◽  
Vol 17 (18n20) ◽  
pp. 3363-3366 ◽  
Author(s):  
A. N. Kocharian ◽  
C. Yang ◽  
Y. L. Chiang
Keyword(s):  
Perturbation Theory ◽  
Hubbard Model ◽  
Electron Concentration ◽  
Ground State ◽  
Second Order ◽  
Electron Interaction ◽  
Field Solution ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

The accurate analytical and numerical calculations of the electronic band structure and ground state properties of strongly correlated electrons within the Hubbard model are performed by constructing convergent perturbation theory for general interaction strength and electron concentration. We test the developed perturbation approach about mean field solution in the extreme conditions of one dimensionality for entire parameter space of electron interaction U/t and electron concentration n. The many-body perturbation formalism up two second order about the generalized self-consistent field (GSCF) Hamiltonian goes beyond the range of applicability of standard perturbation theory by incorporating systematically the effect of the random-phase-type perturbation techniques and controlled expansion of the energy functional for general U/t and n. The second order perturbation correction vanishes at small and large U/t limit and performed calculations of the ground state energy show a next to the perfect numerical agreement with the Bethe-ansatz results.

Relativistic many-body perturbation theory using discrete basis expansion method: accurate representation of second-order energy of Xe atom with contracted well-tempered Gaussian basis set

1992 ◽  
Vol 70 (2) ◽  
pp. 399-403 ◽  
Author(s):  
Yasuyuki Ishikawa
Keyword(s):  
Perturbation Theory ◽  
Second Order ◽  
Basis Set ◽  
Basis Sets ◽  
Compact Representation ◽  
Many Body ◽  
Gaussian Basis Sets ◽  
Gaussian Type ◽  
Order Energy ◽  
Many Body Perturbation Theory

Relativistic many-body perturbation theory calculations on Xe have been performed with basis sets of well-tempered Gaussian-type functions of Huzinaga and Klobukowski. The well-tempered Gaussian-type functions were used in both contracted and uncontracted form. The contracted Gaussian basis sets used in the relativistic many-body study are designed to retain flexibility for correlated calculations both in the core and the valence region. They reproduce second-order energy corrections computed with uncontracted Gaussian basis sets to an accuracy of greater than 99%. A compact representation of the relativistic wave functions in terms of contracted well-tempered Gaussian functions used in the present study provides a useful means of curtailing integral storage requirements and the time needed for correlated calculations, while still retaining high accuracy in relativistic electron correlation effects. Keywords: Dirac–Fock, relativistic many-body perturbation theory, well-tempered Gaussian basis, xenon.

Third-order energy for the ground state of three-electron atoms inZ-dependent perturbation theory

1977 ◽  
Vol 15 (2) ◽  
pp. 444-448 ◽  
Author(s):  
Yat Yan Yung ◽  
Frank C. Sanders ◽  
Robert E. Knight
Keyword(s):  
Perturbation Theory ◽  
Ground State ◽  
Third Order ◽  
Order Energy
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