Moller-Plesset perturbation theory equations

Theory. Usually we do not solve the fundamental equations directly. We use a theory, for example, Har-tree-Fock theory [3], Moller-Plesset perturbation theory [4], coupled-cluster theory [5], Kohn s [6, 7], Newton s [8], or Schlessinger s [9] variational principle for scattering amplitudes, the quasiclassical trajectory method [10], the trajectory surface hopping method [11], classical S-matrix theory [12], the close-coupling approximation... 

The heat of combustion (AcH) of dinitrobiuret (DNB) was determined experimentally using oxygen bomb calorimetry AcH(DNB) = 5195 200kjkg The standard heat of formation (AfH°) of DNB was obtained on the basis of quantum chemical computations at the electron-correlated ab initio MP2 (second order Moller-Plesset perturbation theory) level of theory using a correlation consistent double-zeta basis set (cc-pV-DZ) AfPf°(DNB) =- 353 kj mol - 1829 kj kg (Fig. 34). The detonation velocity (D) and detonation pressure (P) of DNB was calculated using the empirical equations by Kamlet and Jacobs D(DNB) = 8.66 mm xs P(DNB) = 33.9 GPa. 

In the Hartree-Fock equations explicit electron-electron interactions are neglected. To meet this drawback the Hartree-Fock approach has been upgraded by several so-called post-Hartree-Fock methods, as there are Moller-Plesset perturbation theory, configuration interaction, or the... 

The most simple and instructive way to study the main elements of F12 theory is to start with second-order Moller-Plesset perturbation theory, MP2. We will show in the following how the conventional, orbital-expansion based theory is supplemented by additional geminal functions and how the working equations change. We will then discuss how expensive many-electron integrals are avoided by reducing them to products of two-electron integrals, and finally, how F12 theory is transferred to second quantization, which in particular is required for the formulation of coupled-cluster theory with F12 terms. 

This initial guess may then be inserted on the right-hand sides of the equations and subsequently used to obtain new amplitudes. The process is continued until self-consistency is reached. For the special case in which canonical Hartree-Fock molecular orbitals are used, the Fock matrix is diagonal and the T2 amplitude approximation above is exactly the same as the first-order perturbed wave-function parameters derived from Moller-Plesset theory (cf. Eq. [212]). In that case, the Df and arrays contain the usual molecular orbital energies, and the initial guess for the T1 amplitudes vanishes. 

In this chapter we employ a special version of the second-order Moller-Plesset [13] perturbation theory (MP2/CA) which is especially useful in applications to closed-shell atoms. In this approach the first-order wave function consists of spinor-bitals and symmetry-adapted pair functions (SAFE). A detailed presentation of the MP2/CA method can be found in Ref. [14]. For sake of describing the nomenclature used, we repeat here the basic equations. 

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. 

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