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Singularities of Møller-Plesset energy functions
Alexey V Sergeev1, David Z Goodson
1Department of Chemistry and Biochemistry, University of Massachusetts Dartmouth, North Dartmouth, Massachusetts 02747, USA.
The Journal of Chemical Physics
|March 11, 2006
Summary
The convergence of Møller-Plesset (MP) perturbation series depends on energy singularities. Analyzing these singularities provides benchmarks for MP4 and aids in developing new summation methods.
Area of Science:
- Quantum Chemistry
- Computational Chemistry
- Theoretical Chemistry
Background:
- Møller-Plesset (MP) perturbation theory is a widely used method in quantum chemistry for approximating molecular energies.
- The convergence of MP perturbation series can be problematic, especially for systems with strong electron correlation.
- Understanding the factors governing MP series convergence is crucial for accurate electronic structure calculations.
Purpose of the Study:
- To investigate the singularity structure of the Møller-Plesset energy as a function of the perturbation parameter.
- To determine the locations and types of these singularities for various atomic and molecular systems.
- To establish benchmarks for evaluating the convergence of low-order MP methods and for developing improved summation techniques.
Main Methods:
- High-order Møller-Plesset perturbation series were computed for selected atoms and small molecules.
- Quadratic approximant analysis was employed to determine the location of singularities in the energy as a function of the perturbation parameter.
- The computed singularity structures were compared with theoretical predictions based on functional analysis of the Schrödinger equation.
Main Results:
- Singularity locations for the Møller-Plesset energy were determined for a range of atoms and small molecules.
- The analysis revealed specific patterns and types of singularities governing the convergence behavior.
- The results confirmed qualitative predictions derived from the functional analysis of the Schrödinger equation.
Conclusions:
- The singularity structure of the energy is the primary determinant of Møller-Plesset perturbation series convergence.
- The identified singularity locations serve as valuable benchmarks for assessing the reliability of low-order MP calculations (e.g., MP4).
- These findings facilitate the development and validation of novel summation methods designed to accurately model the singularity structure and improve series convergence.
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