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WIREs Comput Mol Sci
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Møller–Plesset perturbation theory: from small molecule methods to methods for thousands of atoms

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Abstract The development of Møller–Plesset perturbation theory (MPPT) has seen four different periods in almost 80 years. In the first 40 years (period 1), MPPT was largely ignored because the focus of quantum chemists was on variational methods. After the development of many‐body perturbation theory by theoretical physicists in the 1950s and 1960s, a second 20‐year long period started, during which MPn methods up to order n = 6 were developed and computer‐programed. In the late 1980s and in the 1990s (period 3), shortcomings of MPPT became obvious, especially the sometimes erratic or even divergent behavior of the MPn series. The physical usefulness of MPPT was questioned and it was suggested to abandon the theory. Since the 1990s (period 4), the focus of method development work has been almost exclusively on MP2. A wealth of techniques and approaches has been put forward to convert MP2 from a O(M5) computational problem into a low‐order or linear‐scaling task that can handle molecules with thousands of atoms. In addition, the accuracy of MP2 has been systematically improved by introducing spin scaling, dispersion corrections, orbital optimization, or explicit correlation. The coming years will see a continuously strong development in MPPT that will have an essential impact on other quantum chemical methods. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 509–530 DOI: 10.1002/wcms.58 This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

Schematic representation of model space and orthogonal space , projection operators and , and the relationship between exact wavefunction Ψ (equal to the perturbed wavefunction), unperturbed wavefunction Ψ (0), and correlation function χ. The consequences of intermediate normalization are indicated.

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The complex plane of the strength parameter z switching on the perturbation represented by . Unperturbed (model) system and perturbed (real) system are located at z = 0 and z=1, respectively. Singularities (poles) of two MPn series are schematically indicated by balls. For the right one, the radius of convergence Rc is larger than 1 and accordingly the MPn series is converging. In the other case, Rc < 1 and the MPn series is diverging (see text).

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Typical oscillatory behavior of calculated MPn response properties on the order n.

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Average MPn correlation energies given in percent of the FCI correlation energy for 14 class A and 19 class B examples.21

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Schematic representation of matrix elements and the substitution functions that make a contribution at MPn (n= 2, 3, 4, 5, 6). denotes the perturbation operator, 0 the reference Φ (0), S Φ ia, D Φ ijab, T Φijkabc, Q Φijklabcd, P Φ ijklmabcde, and H Φ ijklmnabcdef.

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Electronic Structure Theory > Ab Initio Electronic Structure Methods

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