Mpller-Plesset perturbation theory correlation effects

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... 

Instead, practical methods involve a subset of possible Slater determinants, especially those in which two electrons are moved from the orbitals they occupy in the HF wavefunction into empty orbitals. These doubly excited determinants provide a description of the physical effect missing in HF theory, correlation between the motions of different electrons. Single and triple excitations are also included in some correlated ab initio methods. Different methods use different techniques to decide which determinants to include, and all these methods are computationally more expensive than HF theory, in some cases considerably more. Single-reference correlated methods start from the HF wavefunction and include various excited determinants. Important methods in inorganic chemistry include Mpller-Plesset perturbation theory (MP2), coupled cluster theory with single and double excitations (CCSD), and a modified form of CCSD that also accounts approximately for triple excitations, CCSD(T). 

An ab initio version of the Mpller-Plesset perturbation theory within the DPCM solvation approach was introduced years ago by Olivares et al. [26] following the above intuitive considerations based on the fact that the electron correlation which modifies both the HF solute charge distribution and the solvent reaction potential depending on it can be back-modified by the solvent. To decouple these combined effects the authors introduced three alternative schemes ... 

In this section, we briefly discuss some of the electronic structure methods which have been used in the calculations of the PE functions which are discussed in the following sections. There are variety of ab initio electronic structure methods which can be used for the calculation of the PE surface of the electronic ground state. Most widely used are Hartree-Fock (HF) based methods. In this approach, the electronic wavefunction of a closed-shell system is described by a determinant composed of restricted one-electron spin orbitals. The unrestricted HF (UHF) method can handle also open-shell electronic systems. The limitation of HF based methods is that they do not account for electron correlation effects. For the electronic ground state of closed-shell systems, electron correlation effects can be accounted for relatively easily by second-order Mpller-Plesset perturbation theory (MP2). In modern implementations of MP2, linear scaling with the size of the system has been achieved. It is thus possible to treat quite large molecules and clusters at this level of theory. 

Two general groups of methodologies are used to solve the Schrodinger equation in combination with cluster models, the Hartree-Fock (HF) approach and related methods to include correlation effects like Mpller-Plesset perturbation theory (MP2) or configuration interaction (Cl) [58,59] and the Density Functional Theory (DFT) approach [59,60]. 

The dimers of Be, Mg and Ca are very weakly bound by the electron correlation effects, at the self-consistent field (SCF) level they are not stable. The binding energy of alkaline earth dimers is only 2-4 times larger than that in Kr2 and Xe2 dimers. Thus, alkaline dimers can be attributed to the van der Waals molecules. The situation is changed in many-atom clusters, even in trimers (Table II). This is evidently a manifestation of the many-body effects. The crucial role of the 3-body forces in the stabilization of the Be clusters was revealed at the SCF level previously [3-5], and more recently was established at the Mpller-Plesset perturbation theory level up to the fourth order (MP4) [6,7]. The study of binding in the Ben clusters [8-10] reveals that the 3-body exchange forces are attractive and give an important contribution to... 

Finally, algorithms have been developed which incorporate electron correlation effects explicitly in wave function based band theory for crystalline solids [16, 17]. These algorithms construct the many-electron Hamiltonian matrix for a periodic system by extracting the matrix elements from calculations on finite embedded clusters. In this way the incorporation of correlation effects leads to many-electron energy bands, not only associated with hole states and added-electron states but also with excited states. More recently, Pisani and co-workers [18] introduced a post-Hartree-Fock program based on periodic local second order Mpller-Plesset perturbation theory. 

It is well known that Hartree-Fock (HF) theory not only has been proven to be quite suitable for calculations of ground state (GS) properties of electronic systems, but has also served as a starting point to develop many-parti-cle approaches which deal with electronic correlation, like perturbation theory, configuration interaction methods and so on (see e.g., [1]). Therefore, a large number of sophisticated computational approaches have been developed for the description of the ground states based on the HF approximation. One of the most popular computational tools in quantum chemistry for GS calculations is based on the effectiveness of the HF approximation and the computational advantages of the widely used many-body Mpller-Plesset perturbation theory (MPPT) for correlation effects. We designate this scheme as HF + MPPT, here after denoted HF -f- MP2. ... 

As noted above, the theoretical challenges to be overcome include the validation of existing theories as well as the development of new theories. One of the surprises in electronic structure theory in the 1990s was the finding that Mpller-Plesset perturbation theory, the most widely used means to include electron correlation effects, does not lead to a convergent perturbation expansion series. This... 

The first such method has been explored by Foresman et al. [1], who have called the method CIS-MP2 as it adds electron correlation effects to CIS in a similar way as the second-order Mpller-Plesset perturbation (MP2) theory [56] does in the ground state. The MP2 correlation correction to the HF total energy is evaluated by using the formula... 

The use of low-order perturbation theory is probably the cheapest and conceptually simplest method for including correlation effects in a quantum-chemical calculation while maintaining a minimum of formal rigor. In particular, Mpller-Plesset perturbation expansions to various orders (commonly denoted MPn) have seen widespread use. For our purposes it is sufficient to discuss only the MP2 expansion, which is the lowest order that contributes beyond the mean-field approximation. 

As usual, the Hartree-Fock model can be corrected with perturbation theory (e.g., the Mpller-Plesset [MP] method29) and/or variational techniques (e.g., the configuration-interaction [Cl] method30) to account for electron-correlation effects. The electron density p(r) = N f P 2 d3 2... d3r can generally be expressed as... 

Prior to stretching C-S bond, we optimized the geometry of the anionic Me-S-Me molecule and parent neutral molecule at the unrestricted second-order Mpller-Plesset (UMP2) perturbation level of theory (in order to take into account the effect of electron correlation) with aug-cc-pVDZ basis sets [9]. We also... 

We have above discussed the CASSCF method and how we can choose the active space. We noted that this choice was closely connected to the method we use to compute the effects of dynamic correlation, in this case the CASPT2 method. The development of this approach was inspired by the success of the Mpller-Plesset second order perturbation theory (MP2), which has been used for a long time to treat electron correlation for ground states, where the reference function is a single determinant. It was assumed that such an approach would be even more effective with the more accurate CASSCF reference function. A first attempt was made soon... 

The perturbation approach originally proposed by Mpller and Plesset [26] (MP method) provides a simpler and less time-consuming scheme for computing the electron correlation effect. Within this scheme, the full Cl Hamiltonian is treated as a perturbed Hamiltonian and the energy and the wavefunction are expanded in power series following the Rayleigh-Schrodinger perturbation theory. 

MC approaches [30] involve the optimization of molecular orbitals within a restricted subspace of electronic occupations provided such active space is appropriately chosen, they allow for an accurate description of static electron correlation effects. Dynamical correlation effects can also be introduced either at the perturbation theory level [complete active space with second-order perturbation theory (CASPT2), and multireference Mpller-Plesset (MR-MP2) methods] [31] or via configuration interaction (MR-CI). 

---