Moller-Plesset Perturbation Theory
Also known as: MP2, MP3, MP4
Möller-Plesset perturbation theory is a post-Hartree-Fock method that systematically corrects the HF reference by treating electron correlation as a perturbation. Introduced in 1934, MP theory provides increasingly accurate energy estimates (MP2, MP3, MP4, ...) by expanding the correlation energy in orders of perturbation.
Key highlights
- MP2 is affordable for systems with 50–100 atoms, vastly cheaper than CCSD.
- Systematic improvement in accuracy with increasing order (MP2 < MP3 < MP4).
- Well-established with reliable implementations across quantum chemistry packages.
- Good description of electron correlation for weakly-correlated systems.
- Generates predictable accuracy-cost tradeoff.
Intuition
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How it works
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When to use it
MP2 is the workhorse for including electron correlation in moderately sized molecules (< 100 atoms). MP3 and MP4 provide refinement but with steep computational cost increases. MP theory works best when the HF reference is a good starting point (closed-shell, weakly correlated systems).
Strengths & limitations
- MP2 is affordable for systems with 50–100 atoms, vastly cheaper than CCSD.
- Systematic improvement in accuracy with increasing order (MP2 < MP3 < MP4).
- Well-established with reliable implementations across quantum chemistry packages.
- Good description of electron correlation for weakly-correlated systems.
- Generates predictable accuracy-cost tradeoff.
- MP2 significantly overestimates correlation energy for some systems.
- Perturbation series may converge slowly for systems with strong correlation.
- MP3, MP4, and higher orders scale prohibitively (O(N^6) or worse).
- Poor for open-shell systems and charge-transfer excitations.
- Results sensitive to basis set quality; basis set errors can dominate.
Common pitfalls
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Applications
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Frequently asked
What is MP2 and why is it so popular?
MP2 is second-order Möller-Plesset perturbation theory, the lowest-order correction to HF that includes electron correlation. It is popular because it is relatively cheap (O(N^5) scaling) and gives surprisingly good accuracy for many molecules, often within 1–2% of experiment.
Why does the perturbation series sometimes diverge for MP?
For strongly correlated systems or when the HF reference is poor, higher-order terms in MP can grow instead of decay, causing divergence. This signals that perturbation theory is unsuitable; coupled cluster or multi-reference methods are better.
Is MP2 accurate for van der Waals interactions?
MP2 describes dispersion interactions reasonably well, better than DFT without explicit dispersion correction. However, DFT-D (with dispersion corrections) is often preferred for efficiency.
How much more expensive is MP3 compared to MP2?
MP3 is roughly 10–100 times more expensive than MP2 due to higher-order tensor contractions. For large molecules, MP3 is often prohibitive. MP2.5 (mixture of MP2 and MP3) is sometimes used as a compromise.
Can I use MP for excited states?
Standard MP2 (RMP2) is not reliable for excited states; results are often poor. Algebraic-diagrammatic construction (ADC) or equation-of-motion CC (EOM-CC) are preferred for excited state correlation.
Sources
- 1.Möller, C., Plesset, M. S. (1934). Note on an approximation treatment for many-electron systems. Physical Review, 46, 618–622.
- 2.Head-Gordon, M., Gomperts, R., Pople, J. A. (1994). Kohn-Sham density-functional theory applied to excited states of closed-shell molecules. Chemical Physics Letters, 153, 503–506.
- 3.Szabo, A., Ostlund, N. S. (2012). Modern Quantum Chemistry. Dover Publications.
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Cite this page
ScholarGate. (2026, June 3). Moller-Plesset Perturbation Theory. ScholarGate. https://scholargate.app/quantum-computing/moller-plesset-perturbation-theory