Mpller-Plesset methods

Until the advent of density functional theory (Chapter 13), thinking centred around means of circumventing the two-electron integral transformation, or at least partially circumventing it. The Mpller-Plesset method is one of immense historical importance, and you might like to read the original paper. 

Things have moved on since the early papers given above. The development of Mpller-Plesset perturbation theory (Chapter 11) marked a turning point in treatments of electron correlation, and made such calculations feasible for molecules of moderate size. The Mpller-Plesset method is usually implemented up to MP4 but the convergence of the MPn series is sometimes unsatisfactory. The effect... 

The Mpller-Plesset (MP) treatment of electron correlation [84] is based on perturbation theory, a very general approach used in physics to treat complex systems [85] this particular approach was described by M0ller and Plesset in 1934 [86] and developed into a practical molecular computational method by Binkley and Pople [87] in 1975. The basic idea behind perturbation theory is that if we know how to treat a simple (often idealized) system then a more complex (and often more realistic) version of this system, if it is not too different, can be treated mathematically as an altered (perturbed) version of the simple one. Mpller-Plesset calculations are denoted as MP, MPPT (M0ller-Plesset perturbation theory) or MBPT (many-body perturbation theory) calculations. The derivation of the Mpller-Plesset method [88] is somewhat involved, and only the flavor of the approach will be given here. There is a hierarchy of MP energy levels MPO, MP1 (these first two designations are not actually used), MP2, etc., which successively account more thoroughly for interelectronic repulsion. 

The configuration interaction (Cl) treatment of electron correlation [83,95] is based on the simple idea that one can improve on the HF wavefunction, and hence energy, by adding on to the HF wavefunction terms that represent promotion of electrons from occupied to virtual MOs. The HF term and the additional terms each represent a particular electronic configuration, and the actual wavefunction and electronic structure of the system can be conceptualized as the result of the interaction of these configurations. This electron promotion, which makes it easier for electrons to avoid one another, is as we saw (Section 5.4.2) also the physical idea behind the Mpller-Plesset method the MP and Cl methods differ in their mathematical approaches. 

The second consideration in choosing a method is the level of electron correlation. A range of methods from no electron correlation (Hartree-Fock methods) to full configuration interaction is available however, the more extensive the electron correlation, the more computationally demanding the calculations become. Some electron correlation methods, such as the Mpller-Plesset method, can scale as N5 where N is the number of electrons.45 One can imagine that such methods become impractical for larger model systems. 

Recent Advances in Multireference Mpller-Plesset Method (AT. Hirao, K. Nakayama, T. Nakajima H. Nakano)... 

The Hartree—Fock model throws all its effort into obtaining the best possible one term expansion Do = 1, Dk = 0 for K > Q. The Configuration Interaction and Mpller—Plesset methods improve on this single-term model by... 

Several attempts have been made to extend the analytical energy derivative method also to the case of time-dependent perturbations. The pseudo-energy derivative (BED) method of Rice and Handy (1991), the quasi-energy derivative (QED) method of Sasagane, et al., (1993) and the time-dependent second-order Mpller-Plesset method... 

We have developed three hybrid approximations to the ECI wave function and energy CC2, CC3 and CCSD(T). The characteristics of these methods are summarized in Tables 14.6 and 14.7, where comparisons are made with the coupled-cluster and Mpller-Plesset methods. In Figure 14.10, we have, for the methods in Table 14.7, plotted the cc-pVDZ errors relative to FCI for the water molecule with bond lengths Rref and 2/ ref- The two plots represent situations where the Hartree-Fock dominance in the FCI wave function is strong (weight 0.941) and weak (weight 0.589). 

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