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Second-order many-body perturbation theory: an eternal frontier
So Hirata1, Xiao He, Matthew R Hermes
1Department of Chemistry, University of Illinois at Urbana-Champaign , 600 South Mathews Avenue, Urbana, Illinois 61801, United States.
The Journal of Physical Chemistry. A
|December 17, 2013
Summary
Second-order many-body perturbation theory (MBPT(2)) provides a foundation for quantum chemistry calculations. Recent advances include finite-temperature extensions, stochastic evaluations, and applications to vibrational energies.
Area of Science:
- Quantum Chemistry
- Theoretical Physics
- Computational Science
Background:
- Second-order many-body perturbation theory (MBPT(2)) is a fundamental method for approximating solutions to the Schrödinger equation.
- It serves as a benchmark for developing new theoretical approaches and computational algorithms.
- MBPT(2) is known for properties like size consistency and describing dispersion interactions.
Purpose of the Study:
- To introduce the foundational concepts of MBPT(2) from multiple theoretical perspectives.
- To survey recent significant advancements in MBPT(2) methodology and application.
- To highlight the utility of MBPT(2) in addressing complex quantum mechanical problems.
Main Methods:
- Exposition of Rayleigh-Schrödinger perturbation theory and many-body Green's function theory.
- Application of Feynman-Goldstone diagrams for theoretical visualization.
- Development of finite-temperature extensions and stochastic Monte Carlo evaluations.
Main Results:
- A finite-temperature extension of MBPT(2) resolving the Kohn-Luttinger conundrum.
- Stochastic evaluation of correlation and self-energies using Laplace-transformed Monte Carlo integration.
- Extension of MBPT(2) to anharmonic vibrational energies and transition frequencies.
Conclusions:
- MBPT(2) remains a versatile and crucial tool in theoretical chemistry and physics.
- Recent theoretical and computational developments have expanded its applicability.
- The presented advances offer new avenues for accurate quantum mechanical simulations.
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