Mpller Plesset perturbation theory properties

The accurate calculation of these molecular properties requires the use of ab initio methods, which have increased enormously in accuracy and efficiency in the last three decades. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Mpller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster (CC) theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become the method of choice since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

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. ... 

In this chapter we wiU finally follow the third approach, which means that we abandon the perturbation-theory approach all together and go back to the definitions of the properties as derivatives of the energy in the presence of the perturbation. We will illustrate with a few examples how this approach can be appfied to approximate expressions for the energy in the presence of both static as well as time-dependent perturbations. However, the presentation will be very brief and restricted to Mpller-Plesset perturbation theory and coupled cluster energies as nothing new is obtained for variational methods compared to the response theory approaches in Chapters 10 and 11. 

Integrals of Electron Repulsion Molecular Magnetic Properties Mpller-Plesset Perturbation Theory NMR Chemical Shift Computation Ab Initio Nonadiabatic Derivative Couplings Normal Modes Reaction Path Following Spectroscopy Computational Methods Time-dependent Multi-configurational Hartree Method Transition Structure Optimization Techniques. 

SM calculations are broadly based on either the (i) Hartree-Fock method (ii) Post-Hartree-Fock methods like the Mpller-Plesset level of theory (MP), configuration interaction (Cl), complete active space self-consistent field (CASSCF), coupled cluster singles and doubles (CCSD) or (iii) methods based on DFT [24-27]. Since the inclusion of electron correlation is vital to obtain an accurate description of nearly all the calculated properties, it is desirable that SM calculations are carried out at either the second-order Mpller-Plesset (MP2) or the coupled cluster with single, double, and perturbative triple substitutions (CCSD(T)) levels using basis sets composed of both diffuse and polarization functions. 

Considering these two drawbacks, the use of Density Functional Theory (DFT) within its Kohn-Sham (KS) formulation is very appealing First, because the cost of a KS-DFT calculation is at most of the same order of magnitude as a Hartree-Fock one, whereas most of the description of electron correlation is taken into account, it is substantially less expensive than traditional correlated techniques. Moreover, most order n methods which are presently under development are all built on the DFT framework. Indeed, in a number of systematic validation studies , DFT has been shown successfully predicting various molecular properties, often giving results of quality comparable to or better than second order Mpller-Plesset (MP2) perturbation theory. It appears more and more evident that the use of DFT techniques could lead to reliable theoretical evaluation of ionization potentials. Moreover, the obtention of new exchange-correlation (XC) functionals is still under development, and one can expect that ionization potentials will be calculated more accurately in a close future. 

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