Hartree-Fock model, zero-order Hamiltonian

Arrays in which the calculated energy components will be stored are set to zero, etotal will contain the total energy whilst etwo will contain the two-body component, iz = 1 corresponds to the Hartree-Fock model zero order hamiltonian, that is the Moller-Plesset expansion whereas iz = 2 identifies the shifted denominator scheme which uses the Epstein-Nesbet zero order hamiltonian. ediag will be used to store the diagonal components. These energies are stored in the common block ptres together with the orbital energy (eorb (60)). 

In the above expressions the iV-electron Hartree-Fock model hamiltonian, o, was used as a zero-order operator. This leads to the perturbation series of the type first discussed through second-order by Moller and Plesset.55 84 However, it is clear that any operator X obeying the relation... 

The zero-order Hamiltonian H0 corresponds to the Fock operator, whereas the fluctuation potential V represents the difference between the full, instantaneous two-electron potential and the averaged SCF potential of the Hartree-Fock model ... 

In the M0ller-Plesset formalism, a single-reference function is employed and the partition of the Hamiltonian into a reference or zero-order operator and a perturbation uses the Hartree-Fock model to define the reference. Third-order theory (mp3) and fourth-order theory (mp4) are computationally tractable. 

The use of M0ller-Plesset or Hartree-Fock model to label particular choices of zero-order Hamiltonian in many-body perturbation theory dates from the work of Pople et al. [2] and of Wilson and Silver [3]. In their original publication of 1934, MpUer and Plesset [4] did not recognize the many-body character of the theory in the modern (post-Brueckner) sense. 

While using (4.14) and exact wave functions. This supports the conclusion of Drake [83] that for electric dipole transitions, by considering the commutator of with the atomic Hamiltonian in the Pauli approximation, we obtain Qwith relativistic corrections of order v2/c2 (see (4.18)-(4.20)). However, for many-electron atoms and ions, one has to use approximate (e.g., Hartree-Fock) wave functions, and then this term gives non-zero contribution, conditioned by the inaccuracy of the model adopted. 

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