Moller-Plesset models

One approach is to construct a more flexible description of electron motions in terms of a combination of Hartree-Fock descriptions for ground and excited states. Configuration interaction (Cl) and Moller-Plesset (MP) models are two of the most commonly used models of this type. The so-called second-order Moller-Plesset model (MP2) is the most practical and widely employed. It generally provides excellent descriptions of equilibrium geometries and conformations, as well as thermochemistry, including the thermochemistry of reactions where bonds are broken and formed. Discussion is provided in Section n. 

This chapter reviews models based on quantum mechanics starting from the Schrodinger equation. Hartree-Fock models are addressed first, followed by models which account for electron correlation, with focus on density functional models, configuration interaction models and Moller-Plesset models. All-electron basis sets and pseudopotentials for use with Hartree-Fock and correlated models are described. Semi-empirical models are introduced next, followed by a discussion of models for solvation. 

Size consistency is a more important attribute than variational, and because of this, Moller-Plesset models are generally preferred over configuration interaction models. 

Basis sets for use in practical Hartree-Fock, density functional, Moller-Plesset and configuration interaction calculations make use of Gaussian-type functions. Gaussian functions are closely related to exponential functions, which are of the form of exact solutions to the one-electron hydrogen atom, and comprise a polynomial in the Cartesian coordinates (x, y, z) followed by an exponential in r. Several series of Gaussian basis sets now have received widespread use and are thoroughly documented. A summary of all electron basis sets available in Spartan is provided in Table 3-1. Except for STO-3G and 3 -21G, any of these basis sets can be supplemented with additional polarization functions and/or with diffuse functions. It should be noted that minimal (STO-3G) and split-valence (3-2IG) basis sets, which lack polarization functions, are unsuitable for use with correlated models, in particular density functional, configuration interaction and Moller-Plesset models. Discussion is provided in Section II. 

Ab Initio Models. The general term used to describe methods seeking approximate solutions to the many-electron Schrodinger Equation, but which do not involve empirical parameters. Ab initio models include Hartree-Fock Models, Moller-Plesset Models and Density Functional Models. 

Correlated Models. Models which take implicit or explicit account of the Correlation of electron motions. Moller-Plesset Models, Configuration Interaction Models and Density Functional Models... 

Models terminated to a given order, e.g., the MP2 energy is the energy of the second-order Moller-Plesset Model (or MP2). 

Moller-Plesset Models. Methods which partially account for Electron Correlation by way of the perturbation theory of Moller and Plesset. 

MP2 Model. A Moller-Plesset Model terminated to be second order in the energy. 

Size Consistent. Methods for which the total error in the calculated energy is more or less proportional to the (molecular) size. Hartree-Fock and Moller-Plesset models are size consistent, while Density Functional Models, (limited) Configuration Interaction Models and Semi-Empirical Models are not size consistent. 

Variational. Methods for which the calculated energy represents an upper bound to the exact (experimental) energy. Hartree-Fock and Configuration Interaction Models are variational while Moller-Plesset Models, Density Functional Models and Semi-Empirical Models are not variational. 

Instantaneous correlation can be taken into account either by mixing ground state with excited state wavefunctions (configuration interaction and Moller-Plesset models) or by introducing explicitly approximate correction terms [density functional theory (DFT) models]. 

---