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Moller-Plesset

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Moller-Plesset Perturbation Theory

Moller-Plesset perturbation theory is a post-SCF quantum chemistry method which adds dynamic electron correlation to improve upon SCF level wavefunctions. This method is a workhose of quantum chemistry as it has proved to be remarkably accurate considering its overall cost and is the basis for many theories built ontop of this result.

Included Reference Implementations

  • MP2.py: Second-order Moller-Plesset perturbation theory
  • DF-MP2.py: MP2 utilizing density-fitting to reduce its overall cost.
  • DF-MP2_NAF.py: DF-MP2 using natural auxiliary functions to reduce the DF tensor rank. Explicitly builds DF tensor.
  • sDF-MP2.py: Stochastic orbital MP2 utilizing density-fitting (sDF-MP2) to further reduce the computational cost of DF-MP2.
  • MP3.py: Third-order Moller-Plesset perturbation theory
  • MP3-SO.py: MP3 in spin-orbital formalism that simplifies the equations and provides contrast to the spin-summed version above.
  • MPn.py: An example on how to automate the contraction of higher order MP theory.
  • MP2_Gradient.py: Calculation of a nuclear gradient at the MP2 level of theory.
  • MP2_Hessian.py: Calculation of a nuclear hessian at the MP2 level of theory.
  • LT-MP2.py: Laplaced-transformed MP2 for a restricted reference.

References

  1. The original paper that started it all: "Note on an Approximation Treatment for Many-Electron Systems"
    • [Moller:1934:618] C. Møller and M. S. Plesset, Phys. Rev. 46, 618 (1934)
  2. The Laplace-transformation in MP theory: "Minimax approximation for the decomposition of energy denominators in Laplace-transformed Møller–Plesset perturbation theories"
    • [Takasuka:2008:044112] A. Takatsuka, T. Siichiro, and W. Hackbusch, J. Phys. Chem., 129, 044112 (2008)
  3. Equations used in reference implementations:
    • [Szabo:1996] A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Courier Corporation, 1996.
  4. sDF-MP2 reference:
    • [Takeshita:2017:4605] T.Y. Takeshita, W.A. de Jong, D. Neuhauser, R. Baer and E. Rabani, J. chem. Theory Comput. 13, 4605 (2017)
  5. Laplaced-transformed MP2 reference:
    • [Almlof:1991] J. Almlöf, Chem. Phys. Lett. 181, 319 (1991)