Møller–Plesset perturbation theory

Møller–Plesset perturbation theory
Name	Møller–Plesset perturbation theory
Caption	Diagrammatic illustration of correlation energy corrections
Field	Theoretical chemistry
Introduced	1934
Developers	Christian Møller; Milton S. Plesset
Notable works	"Note on an Approximation Treatment for Many-Electron Systems"

Møller–Plesset perturbation theory Møller–Plesset perturbation theory is a post-Hartree–Fock electronic-structure method that introduces systematic corrections to a single-determinant reference wavefunction, originally proposed by Christian Møller and Milton S. Plesset. It connects to foundational work by Douglas Hartree and Vladimir Fock while influencing later developments associated with John Pople, Walter Kohn, and Martin Karplus. The method underpins many computational studies performed with software from companies and institutions such as Gaussian, Inc., IBM Research, and the Fritz Haber Institute.

Introduction

MP theory was formulated to correct the mean-field description provided by Hartree and Fock, incorporating electron correlation via Rayleigh–Schrödinger perturbation theory as framed by Wolfgang Pauli and Erwin Schrödinger. The original MP2 level links conceptually to the configuration interaction work of John Lennard-Jones and to coupled cluster approaches advanced by Izaak Bloch and Josef Paldus, while MP3 and higher orders were explored in follow-up studies by Pople and Bartlett. Historical context includes contemporary advances at institutions like the University of Copenhagen and Princeton University where many-body perturbation techniques were contrasted with contemporaneous approaches from the Cavendish Laboratory and Bell Labs.

Theoretical Foundation

At its core MP uses an antisymmetrized product reference determinant from Hartree–Fock theory, building on Fock's operator mathematics and Koopmans' theorem employed by Tjalling Koopmans. The unperturbed Hamiltonian is the sum of Fock one-electron operators; the perturbation is the difference between the full electronic Hamiltonian and this sum, a perspective that relates to the many-body formulations of Lev Landau and John Bardeen. Energy corrections are obtained order-by-order via Rayleigh–Schrödinger formulas and diagrammatically interpretable through techniques used by Murray Gell-Mann and Freeman Dyson. MP2 energy is expressible using two-electron integrals over molecular orbitals as in work by Per-Olov Löwdin, and the convergence properties echo discussions by Richard Feynman and Julian Schwinger regarding perturbative series in quantum electrodynamics. Theoretical comparisons often cite coupled cluster theory by Rodney Bartlett and Jürgen Hirshfeld and density functional approximations formulated by Pierre Hohenberg and Walter Kohn.

Computational Implementation

Practical MP calculations rely on molecular integral evaluation and orbital transformations developed in computational toolchains from John Pople’s Gaussian program and the GAMESS project associated with Mark Gordon. Efficient algorithms leverage direct integral techniques introduced by Peter Pulay and Chirlian Frenkel, and integral screening strategies tracing to Boys and Handy, while parallel implementations are influenced by developments at Lawrence Livermore National Laboratory and Sandia National Laboratories. Basis set choices reference families by Fritz Haber Institute alumni and chemists such as John D. Dunning and Frank Jensen; implementation details draw from matrix diagonalization methods advanced by Gene Golub and Walter Kahan. Memory and disk management strategies for MP4 and higher orders were refined in collaboration with developers of NWChem and MOLPRO at the Max Planck Institutes and École Normale Supérieure.

Variants and Extensions

Beyond canonical MPn, many variants exist: spin-component-scaled MP2 developed in follow-on studies by Grimme and co-workers, orbital-optimized MP2 related to work by Werner Heisenberg and Per-Olov Löwdin, and scaled opposite-spin corrections introduced by Szabo and Ostlund. Local correlation embodiments, inspired by the locality ideas of Nevill Mott and Philip Anderson, include local MP2 schemes promoted by Fritz Weigend and Frank Neese. Multi-reference perturbation theories, connecting to the complete active space methods of Bertrand Halperin and Roald Hoffmann, extend MP concepts into regimes examined by Roos and Malmqvist. Diagrammatic resummations tie to parquet equations studied by Nikolay Bogoliubov and Lev Keldysh; perturbative corrections are hybridized with density functional approximations in frameworks influenced by John Perdew and Axel Becke.

Applications and Limitations

MP methods, particularly MP2, are widely used for thermochemistry, reaction barriers, and noncovalent interactions in studies performed at national laboratories like Los Alamos and academic centers including MIT and Caltech. MP2 frequently competes with coupled cluster singles and doubles (CCSD) results from groups such as Bartlett’s, yet it exhibits limitations: slow convergence toward full configuration interaction as discussed by Pople and inadequacy for strongly correlated systems emphasized in works by Philip Anderson and Steven White. Pathological cases include bond dissociation and transition-metal complexes studied by Roald Hoffmann and Christopher Cramer, where multi-reference character or near-degeneracy invalidate low-order perturbation. Remedies often reference methods developed at institutions like the Weizmann Institute and ETH Zurich, combining multi-reference approaches or explicitly correlated F12 corrections by Werner and Valeev.

Numerical Examples and Benchmarks

Benchmarking suites for MP methods often draw on datasets compiled by groups led by Karton, Martin, and Truhlar, and comparison studies use reference data from Computational Chemistry Comparison and Benchmark studies coordinated by leaders at NIST and the University of Georgia. Typical MP2 errors relative to higher-level CCSD(T) benchmarks reported by Pople and Head-Gordon are systematic for reaction energies and noncovalent complexes but vary with basis set families such as Dunning’s correlation-consistent sets and Pople-style split-valence sets. Performance maps visualized in community benchmarks from the Royal Society of Chemistry and ACS meetings illustrate where MP2 provides cost-effective accuracy versus where coupled cluster or multi-reference methods are required, as demonstrated in studies by Schaefer and Bartlett.

Category:Theoretical chemistry