| Møller–Plesset perturbation theory | |
|---|---|
| Name | Møller–Plesset perturbation theory |
| Field | Quantum chemistry |
| Introduced | 1930s |
| Author | Christian Møller and Milton S. Plesset |
Møller–Plesset perturbation theory
Møller–Plesset perturbation theory (commonly abbreviated MP) is a post‑Hartree–Fock perturbative method used to include electronic electron correlation energy by treating electron–electron interaction beyond the mean field as a perturbation. It is widely used in quantum chemistry and computational studies of molecular and condensed matter systems because it offers a systematic hierarchy of approximations (MP2, MP3, MP4, …) with clear links to many‑body perturbation theory and Rayleigh–Schrödinger perturbation theory. MP methods remain important for benchmarking and for balancing accuracy and computational cost in practical applications.
Møller–Plesset perturbation theory was introduced in seminal work by Christian Møller and Milton S. Plesset to apply Rayleigh–Schrödinger perturbation theory to electronic structure problems defined by the Hartree–Fock reference determinant. The approach emerged alongside parallel developments in many-body theory and perturbation theory used in nuclear and condensed matter physics, with subsequent formal refinements influenced by workers at institutions such as Harvard University, University of Copenhagen, and research groups associated with the development of computer programs like Gaussian and Molpro. MP theory played a central role in the post‑war expansion of computational quantum chemistry and in establishing standardized benchmarks for correlation methods.
The MP formalism partitions the electronic Hamiltonian H into a zeroth‑order Fock operator F (the sum of one‑electron terms and mean‑field potentials) and a perturbation V = H − F. Using the closed‑shell Slater determinant from a converged Hartree–Fock calculation as the reference, energy corrections E^(n) are computed via Rayleigh–Schrödinger perturbation theory expansions. The second‑order term (MP2) involves double excitations and two‑electron integrals over molecular orbitals, employing antisymmetrized Coulomb and exchange integrals (⟨ij|ab⟩). MP theory connects formally to Goldstone diagram expansions and to the coupled cluster hierarchy; MPn corrections can be viewed as truncations of the linked cluster theorem expansion and relate to diagrammatic many-body theory used in condensed matter physics.
The MP hierarchy denotes successive orders: MP2 (second order), MP3, MP4, and higher. MP2 is the most commonly used due to favorable cost and reasonable accuracy. Computational scaling grows steeply: canonical MP2 scales formally as O(N^5) with respect to system size N (basis functions), MP3 as O(N^6), and MP4 and beyond reach O(N^7) or worse. Reduced‑scaling and local correlation variants (e.g., Local MP2, density fitting / Resolution of the identity (RI‑MP2), and Cholesky decomposition) have been developed to lower prefactors and enable treatment of larger molecules. Implementation in electronic structure packages such as Psi4, ORCA, TURBOMOLE, and Q-Chem has broadened access to MP methods.
MP theory explicitly targets the correlation energy defined as the difference between the exact nonrelativistic energy and the Hartree–Fock energy. The first nonzero MP correction (MP2) typically recovers a large fraction of dynamic correlation for closed‑shell molecules and weakly correlated systems. MP methods do not change the reference determinant and therefore inherit limitations of the Hartree–Fock reference such as spin contamination in unrestricted form and failure in multireference situations. The relation between MP and Coupled cluster (e.g., CCSD(T)) methods is well studied: MP2 can often approximate correlation energies efficiently, while CC methods provide more robust size‑extensivity and higher accuracy for chemical energetics.
Accuracy of MP results depends strongly on basis set choice: correlation‑consistent basis sets (cc‑pVXZ) developed by David E. W. Dunning and augmented variants (aug‑cc‑pVXZ) are standard for systematic convergence studies. Basis set superposition error (BSSE) and extrapolation to the complete basis set (CBS) limit are typical concerns; counterpoise correction and two‑point extrapolation schemes are commonly used. For large systems, approximate MP2 with RI and local correlation reduces memory and disk demands. Scalar relativistic effects (via Douglas–Kroll–Hess or ZORA) and effective core potentials (ECPs) are sometimes incorporated when treating heavy elements.
MP methods are widely applied to compute binding energies, reaction barriers, intermolecular interactions (e.g., van der Waals forces), conformational energetics, and spectroscopic constants. MP2 is popular in studies of noncovalent complexes, organic reaction mechanisms, and as a stepping stone toward higher‑level composite methods like G3 theory or CBS methods. In materials science, MP2 and periodic MP variants have been adapted for lattice systems, surfaces, and adsorption studies, complementing density functional theory (DFT) where dispersion or weak correlation is critical. MP benchmarks contribute to datasets used by groups at NIST and academic consortia validating electronic structure methods.
MP methods can fail in systems with strong static correlation, near bond dissociation, or small HOMO–LUMO gaps, where the perturbation expansion is poorly convergent or divergent. MP3 and MP4 improvements are not guaranteed to improve results monotonically; oscillatory behavior and slow convergence have motivated alternative approaches such as coupled cluster theory (CCSD, CCSD(T)), multireference perturbation theories (e.g., CASPT2), and nonperturbative methods. Regularized and scaled MP2 variants (SCS‑MP2, SOS‑MP2, and orbital‑optimized MP2) have been developed to mitigate failures while retaining computational affordability. Ongoing research at universities and national labs seeks robust, efficient replacements that preserve the tradition of reliable, reproducible computational protocols in chemical and materials modeling.
Category:Quantum chemistry Category:Computational chemistry