Electron correlation Mpller-Plesset perturbation theory

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... 

There is also a hierarchy of electron correlation procedures. The Hartree-Fock (HF) approximation neglects correlation of electrons with antiparallel spins. Increasing levels of accuracy of electron correlation treatment are achieved by Mpller-Plesset perturbation theory truncated at the second (MP2), third (MP3), or fourth (MP4) order. Further inclusion of electron correlation is achieved by methods such as quadratic configuration interaction with single, double, and (perturbatively calculated) triple excitations [QCISD(T)], and by the analogous coupled cluster theory [CCSD(T)] [8],... 

In ab initio methods the HER approximation is used for build-up of initial estimate for and which have to be further improved by methods of configurational interaction in the complete active space (CAS) [39], or by Mpller-Plesset perturbation theory (MPn) of order n, or by the coupled clusters [40,41] methods. In fact, any reasonable result within the ab initio QC requires at least minimal involvement of electron correlation. All the technical tricks invented to go beyond the HFR calculation scheme in terms of different forms of the trial wave function or various perturbative procedures represent in fact attempts to estimate somehow the second term of Eq. (5) - the cumulant % of the two-particle density matrix. 

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. 

In the G2 and G3 [10,11] theories, the Mpller-Plesset perturbation theories of the 2-nd and 4-th orders are used to estimate the consequences of extending orbital basis sets by including the diffuse and polarization functions. These attempts, however, do not allow one to eliminate a systematic error of about 6 millihartree per electronic pair, which, in the frame of the G2 and G3 theories, bears the pompous name of higher level correlation of unknown nature. These latter are parametrized in the form ... 

Chalasinski and Szczesniak have provided a means of decomposing the correlation contribution to the interaction energy into four separate terms. Their philosophy takes the electron exchange operator as a second perturbation in the spirit of many-body perturbation theory, with molecular interaction as the first perturbation in their intermolecular Mpller-Plesset perturbation theory (IMPPT). At the level of second order of the correlation operator, they obtain a number of separate terms. The first is the dispersion energy, e... 

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... 

They employed ab initio calculations such as the nth order many-fcody perturbation theory, abbreviated to MBPT(n), whose better known variant is the nth order Mpller-Plesset perturbation theory, MPn. The MBPT(n) procedure takes account of all the terms to a predetermined final order n for the electron correlation. In the coupled cluster (CC) theory, on the other hand, certain contributions from the MBPT formalism are summated for all orders... 

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. 

One of the original approximate methods is the wavefunction-theory-based Hartree-Fock (HF) method [40]. The HF method is a single determinant method that does not include any correlation interactions between the electrons, and as such has limited accuracy [41, 42]. Higher level wavefunction-based methods such as coupled cluster [43 5], configuration interaction [40,46,47], and complete active space [48-50] methods include multiple determinants to incorporate some of the electron-electron correlation. Methods based on perturbation theory, such as second order Mpller-Plesset perturbation theory [51], go beyond the HF method by perturbatively adding electron correlation. These correlated wavefunction-based methods have well-defined ways in which they approach the exact solution to the Schrodinger equation and thus have the potential to be extremely accurate, but this accuracy comes at a price [52]. 

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. ... 

The least expensive and conceptually simplest correlation treatment that can be applied to medium-size molecules is the second-order Mpller-Plesset perturbation theory (MP2), which is the most popular single-reference approach for the low-level treatment of electron correlation [21]. Higher order MP perturbation theory such as MP3 and MP4 are typically less useful in particular, results coming from MP3 level are inferior to MP2 because of the characteristically oscillatory convergence of perturbation theory. MP4, MP5, and MP6 offer some improvements, but the high computational costs required prevent their routine application [22]. 

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