Mpller-Plesset perturbation theory configuration interaction

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],... 

The calculations are not all at exactly the same bond length R. The basis set is indicated after the slash in the method. R, L, C, and T are basis sets of Slater-type functions. The aug-cc-pVDZ and aug-cc-pVTZ basis sets [360] are composed of Gaussian functions. SCF stands for self-consistent-field MC, for multiconfiguration FO, for first-order Cl, for configuration interaction MR, for multireference MPn, for nth-order Mpller-Plesset perturbation theory and SDQ, for singles, doubles, and quadruples. 

The Section on More Quantitive Aspects of Electronic Structure Calculations introduces many of the computational chemistry methods that are used to quantitatively evaluate molecular orbital and configuration mixing amplitudes. The Hartree-Fock self-consistent field (SCF), configuration interaction (Cl), multiconfigurational SCF (MCSCF), many-body and Mpller-Plesset perturbation theories,... 

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. 

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]. 

Figure 1 Angular variation of components of the two-body interaction energy in (HF)3 in a planar Cii, configuration. SCF components are labeled as follows ES = electrostatic, EX = exchange, def = deformation energy (AE - - ES - EX). The dispersion energy 6cjisp ° computed by perturbation theory is denoted disp. The curve representing the complete two-body interaction through third-order Mpller-Plesset perturbation theory is labeled as full. All terms have been computed in the dimer-centered basis set. (Data taken from ref. 120.)...

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. ... 

Basis Sets Correlation Consistent Sets Configuration Interaction Coupled-cluster Theory Density Functional Applications Density Functional Theory Applications to Transition Metal Problems G2 Theory Integrals of Electron Repulsion Integrals Overlap Linear Scaling Methods for Electronic Structure Calculations Localized MO SCF Methods Mpller-Plesset Perturbation Theory Monte Carlo Quantum Methods for Electronic Structure Numerical Hartree-Fock Methods for Molecules Pseudospectral Methods in Ab Initio Quantum Chemistry Self-consistent Reaction Field Methods Symmetry in Hartree-Fock Theory. 

Configuration Interaction PCI-X and Applications Coupled-cluster Theory Density Functional Applications Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Mpller-Plesset Perturbation Theory Self-consistent Reaction Field Methods Spin Contamination Transition Metal Chemistry Transition Metals Applications. 

Carbenes A Testing Ground for Electronic Structure Methods Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Mpller-Plesset Perturbation Theory Natural Orbitals Transition State Theory Unimolecu-lar Reaction Dynamics. 

An in-depth description of the theoretical basis of these methodologies as well as other computational techniques can be found in Refs. [5,8]. The dynamic correlation energy can be efficiently recovered by using the Cl (configurational interaction), Mpller-Plesset perturbation theory (MP ), and coupled cluster (CC) methods, whereas multireference Cl methods such as complete active space self-consistent field (CASSCF) allow an adequate description of the static correlations. 

The difference between the Hartree-Fock energy and the exact solution of the Schrodinger equation (Figure 60), the so-called correlation energy, can be calculated approximately within the Hartree-Fock theory by the configuration interaction method (Cl) or by a perturbation theoretical approach (Mpller-Plesset perturbation calculation wth order, MPn). Within a Cl calculation the wave function is composed of a linear combination of different Slater determinants. Excited-state Slater determinants are then generated by exciting electrons from the filled SCF orbitals to the virtual ones ... 

Accounting for relativistic effects in computational organotin studies becomes complicated, because Hartree-Fock (HF), density functional theory (DFT), and post-HF methods such as n-th order Mpller-Plesset perturbation (MPn), coupled cluster (CC), and quadratic configuration interaction (QCI) methods are non-relativistic. Relativistic effects can be incorporated in quantum chemical methods with Dirac-Hartree-Fock theory, which is based on the four-component Dirac equation. " Unformnately the four-component Flamiltonian in the all-electron relativistic Dirac-Fock method makes calculations time consuming, with calculations becoming 100 times more expensive. The four-component Dirac equation can be approximated by a two-component form, as seen in the Douglas-Kroll (DK) Hamiltonian or by the zero-order regular approximation To address the electron cor-... 

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... 

---