Moller-Plesset perturbation theory limitations

Ab initio correlated or so-called post Hartree-Fock methods provide a proper description of dispersion forces. Unfortunately, these methods are computationally limited to systems with few atoms. Only few CCSD(T) calculations of very small ionic liquid systems were reported so far. Second-order Moller Plesset perturbation theory (MP2) might be also a suitable ab initio method to study ionic liquids. Recent developments have made this approach available for systems with hundreds of atoms. However, calculations of medium sized ionic liquid systems need still enormous computational resources. Thus, MP2 and similar approaches seem to be limited to static quantum chemical calculations and are still too expensive for ab initio molecular dynamics simulations over an appropriate system size and time frame. 

The performance of the unrestricted Moller-Plesset theory is perhaps somewhat surprising even though the unrestricted theory performs well in the dissociation limit, its performatKe in the intermediate region is altogether unsatisfactory. Thus, the hump apparent in the coupled-cluster dissociation curve in Figure 5.18 is now much more prominent and persists even at the MP4 level. In addition, a kink has appeared where the restricted and unrestricted curves separate. Clearly, unrestricted M0ller-Plesset perturbation theory does not provide a uniform description of the dissociation process and does not appear to be an appropriate tool for the study of such processes. 

CC) methods, which have largely superseded Cl methods, in the limit can also be used to give exact solutions but again with same prohibitive cost as full Cl.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. 

Hamiltonian proposed by Muller and Plesset gives rise to a very successful and efficient method to treat electron correlation effects in systems that can be described by a single reference wave function. However, for a multireference wave function the Moller-Plesset division can no longer be made and an alternative choice of B(0> is needed. One such scheme is the Complete Active Space See-ond-Order Perturbation Theory (CASPT2) developed by Anderson and Roos [3, 4], We will briefly resume the most important definitions of the theory one is referred to the original articles for a more extensive description of the method. The reference wave function is a CASSCF wave function that accounts for the largest part of the non-dynamical electron correlation. The zeroth-order Hamiltonian is defined as follows and reduces to the Moller-Plesset operator in the limit of zero active orbitals ... 

It has been shown that the reaction path from the pyran to the most stable open form involved a two-step mechanism through a cis open form (Figure 1). The first step of this mechanism (transition state TS1) is the rate-limiting step, with a barrier of 138 kJmol-1 at the Hartree-Fock 6-31G(d) level, corrected to 92kJmol-1 with Moller-Plesset second-order perturbation theory. This value is in agreement with experimental measurements of the activation energy of the ring... 

Ab initio calculated geometrical parameters depend on the kind of applied basis sets (which is the main variable when using an ab initio computer programme like, for example, Pople s GAUSSIAN 90 ) and on the kind of calculational procedure The so-called Hartree-Fock limit is the theoretically best result obtainable with a single determinant MO basis. Because of the different weighting of inter-electron repulsion between electron pairs of like and unlike spin, Hartree-Fock calculations are in error. They may be improved by the use of configuration interaction methods (Cl) or by the use of perturbation theory, like the Moller-Plesset treatment of second, third or fourth order (MP2, MP3 or MP4). 

Two relevant topics have been ignored completely in this short chapter the treatment of electron correlation with more sophisticated methods than DFT (that remains unsatisfactory from many points of view) and the related subject of excited states. Wave function-based methods for the calculation of electron correlation, like the perturbative Moller-Plesset (MP) expansion or the coupled cluster approximation, have registered an impressive advancement in the molecular context. The computational cost increases with the molecular size (as the fifth power in the most favorable cases), especially for molecules with low symmetry. That increase was the main disadvantage of these electron correlation methods, and it limited their application to tiny molecules. This scaling problem has been improved dramatically by modern reformulation of the theory by localized molecular orbitals, and now a much more favorable scaling is possible with the appropriate approximations. Linear scaling with such low prefactors has been achieved with MP schemes that the... 

What is of more practical interest here is that HF descriptions of the dimer cannot give a DIS term. This may be recovered by introducing Cl descriptions of the system. The simpler Cl description, now largely used in routine calculations on molecules and molecular aggregates, is called MP2. This acronym means that use has been made of a specialized version of file perturbation theory (called Moller-Plesset) limited to second order to determine the expansion coefficients. 

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