Moller second-order

Moller-Plesset theory at second order, third order, etc. 

To obtain an improvement on the Hartree-Fock energy it is therefore necessary to use Moller-Plesset perturbation theory to at least second order. This level of theory is referred to as MP2 and involves the integral J dr. The higher-order wavefunction g is... 

Correlation can be added as a perturbation from the Hartree-Fock wave function. This is called Moller-Plesset perturbation theory. In mapping the HF wave function onto a perturbation theory formulation, HF becomes a hrst-order perturbation. Thus, a minimal amount of correlation is added by using the second-order MP2 method. Third-order (MP3) and fourth-order (MP4) calculations are also common. The accuracy of an MP4 calculation is roughly equivalent to the accuracy of a CISD calculation. MP5 and higher calculations are seldom done due to the high computational cost (A time complexity or worse). 

Molecular frequencies depend on the second derivative of the energy with respect to the nuclear positions. Analytic second derivatives are available for the Hartree-Fock (HF keyword). Density Functional Theory (primarily the B3LYP keyword in this book), second-order Moller-Plesset (MP2 keyword) and CASSCF (CASSCF keyword) theoretical procedures. Numeric second derivatives—which are much more time consuming—are available for other methods. 

MP2 second-order Moller-Plesset perturbation theory... 

Table4.4 Spectroscopic properties for Au2 q= -1,0, + 1) using ab-initio (Hartree Fock, HF, second-order Moller-Plesset, MP2, and coupled cluster, CCSD(T)) and DFT (local spin-density approximation, LSDA, Perdew-Wang CCA, PW91, and Becke three-parameter Lee-Yang-Parr functional, B3LYP) methods at the RPPA level of theory.

CC) methods, which have largely superseded Cl methods, in the limit can also be used to give exact solutions but again with same prohibitive cost as full Cl. As with Cl, CC methods are often truncated, most commonly to CCSD (N cost), but as before these can still only be applied to systems of modest size. Finally, Moller-Plesset (MP) perturbation theory, which is usually used to second order (MP2 has a cost), is more computationally accessible but does not provide as robust results. 

Its first term, Emp2, has exactly the same functional form as the conventional second order Moller-Plesset correlation contribution (MP2). However, in Eqs (4 7 4.8) the ( )9 represent KS orbitals, which experience the multiplicative KS potential (2 7), rather... 

Table 2 Correlation energies of the neon isoelectronic series Comparison ofE 2 1- (4-6), with the corresponding second order Moller-Plesset (MP2) [30], RLDA [16] andPW91-GGA [8] results. In addition, AHF 1- is compared With the difference IaE, Eq. (4.9), between RHF [60] and x-only ROPM [16]...

The total correlation energy, as obtained from a second-order Moller-Plesset (MP2) [71] calculation, can easily be split into parallel- and antiparallel-spin contributions. The MP2 correlation energy 2 is given by [81]... 

Klopper, W., Samson, C.C.M. Explicitly correlated second-order Moller-Plesset methods with auxiliary basis sets. J. Chem. Phys. 2002,116, 6397-410. 

Ten-no, S. New implementation of second-order Moller-Plesset perturbation theory with an analytic Slater-type geminal. J. Chem. Phys. 2007, 126, 014108. 

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