Moller-Plesset perturbation theory zero-order Hamiltonian

Moller-Plesset perturbation theory (MPPT) aims to recover the correlation error incurred in Ilartree- Fock theory for the ground state whose zero-order description is ,. The Moller-Plesset zero-order Hamiltonian is the sum of Fock operators, and the zero-order wave functions are determinantal wave functions constructed from HF MOs. Thus the zero-order energies are simply the appropriate sums of MO energies. The perturbation is defined as the difference between the sum of Fock operators and the exact Hamiltonian ... 

The Moller-Plesset method uses perturbation theory to correct for the electron correlation in a many-electron system. The Moller-Plesset method has the advantage that it is a computationally faster approach than Cl computations however, the disadvantage is that it is not Variational. A non-Variational result is not, in general, an upper bound of the trae ground-state energy. In the MoUer-Plesset method, the zero-order Hamiltonian is defined as the sum of all the N one-electron Hartree-Fock Hamiltonians, H", as given in Equation 9-30. 

For single reference perturbation theory, there is a choice of reference hamil-the Moller-Plesset and Epstein-Nesbet zero-order hamiltonians were two choices considered in the early literature (see, for example, Ref. 54). 

The theoretical description of any many body system is usually approached in two distinct stages. First, the solution of some independent particle model yielding a set of quasi-particles, or dressed particles, which are then used to formulate a systematic scheme for describing the corrections to the model. Perturbation theory, when developed with respect to a suitable reference model, affords the most systematic approach to the correlation problem which today, because it is non-iterative and, therefore, computationally very efficient, forms the basis of the most widely used approaches in contemporary electronic structure calculations, particularly when developed with respect to a Moller-Plesset zero order Hamiltonian. 

The Moller-Plesset (MP) perturbation theory [13] is based on the zero-order Hamiltonian of the form ... 

Hamiltonian proposed by Muller and Plesset gives rise to a very successful and efficient method to treat electron correlation effects in systems that can be described by a single reference wave function. However, for a multireference wave function the Moller-Plesset division can no longer be made and an alternative choice of B(0> is needed. One such scheme is the Complete Active Space See-ond-Order Perturbation Theory (CASPT2) developed by Anderson and Roos [3, 4], We will briefly resume the most important definitions of the theory one is referred to the original articles for a more extensive description of the method. The reference wave function is a CASSCF wave function that accounts for the largest part of the non-dynamical electron correlation. The zeroth-order Hamiltonian is defined as follows and reduces to the Moller-Plesset operator in the limit of zero active orbitals ... 

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