Restricted Mpller-Plesset methods

Perturbative approximation methods are usually based on the Mpller-Plesset (MP) perturbation theory for correcting the HF wavefunction. Energetic corrections may be calculated to second (MP2), third (MP3), or higher order. As usual, the open- versus closed-shell character of the wavefunction can be specified by an appropriate prefix, such as ROMP2 or UMP2 for restricted open-shell or unrestricted MP2, respectively. 

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. 

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). 

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. 

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