M0ller-Plesset perturbation theory first-order

Figure 1. Hierarchial diagram of the BAC-MP4 method for determining thermochemical properties of molecules. First, a Hartree-Fock calculation provides the molecular geometries and frequencies. Fourth-order M0ller-Plesset perturbation theory (MP4) provides the ab initio electronic energy to which bond-additivity corrections (BAC) are then added to obtain chemical bond energies. Finally, statistical mechanics calculations are used to determine the enthalpy, entropy, and free energy of the molecule.

For second-order many body or M0ller-Plesset perturbation theory (MBPT2 or MP2 see M0ller-Plesset Perturbation Theory), the first-order wavefunction, I l, can be written as... 

In M0ller-Plesset theory, first-order perturbation theory does not improve on the HF energy because the zeroth-order Hamiltonian is not itself the HF Hamiltonian. However, first-order perturbation theory can be useful for estimating energetic effects associated with operators that extend the HF Hamiltonian. Typical examples of such terms include the mass-velocity and one-electron Darwin corrections that arise in relativistic quantum mechanics. It is fairly difficult to self-consistently optimize wavefunctions for systems where these tenns are explicitly included in the Hamiltonian, but an estimate of their energetic contributions may be had from simple first-order perturbation theory, since that energy is computed simply by taking the expectation values of the operators over the much more easily obtained HF wave functions. 

We employed Hartree-Fock (HF) method for the geometry optimizations and the JT potential calculation. Radom has reviewed computational studies on various molecular anions that includes only first raw elements [21], It has been concluded that reliable structural predictions may be made from single-determinant MO calculations with double-zeta basis sets. Furthermore, we applied second-order M0ller-Plesset (MP2) perturbation theory for the optimized geometries with HF... 

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