Moller-Plesset theory , ground state

Ah initio methods are applicable to the widest variety of property calculations. Many typical organic molecules can now be modeled with ah initio methods, such as Flartree-Fock, density functional theory, and Moller Plesset perturbation theory. Organic molecule calculations are made easier by the fact that most organic molecules have singlet spin ground states. Organics are the systems for which sophisticated properties, such as NMR chemical shifts and nonlinear optical properties, can be calculated most accurately. 

Another way that additional configurations can be added to the the ground-state wave function is by the use of Moller-Plesset perturbation theory (MPPT). As it happens, a Hamiltonian operator constructed from a sum of Fock operators has as its set of solutions the HF single determinantal wave function and all other determinantal wave... 

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 ... 

Instantaneous correlation can be taken into account either by mixing ground state with excited state wavefunctions (configuration interaction and Moller-Plesset models) or by introducing explicitly approximate correction terms [density functional theory (DFT) models]. 

The total molecular energy of the ground state was estimated to be Ef P=-342.648 E [4, 5] the so far best theoretical value, E = -341.42843 Eh, resulted from a recent G2 calculation using a method that treats the electron correlation by Moller-Plesset perturbation theory (MP4) and quadratic configuration interaction (QCI) [6]. 

In an interesting, combined experimental and theoretical study Burgert et al. addressed an issue closely related to the non-scalable size effects of nanosystems Why do small anionic aluminum clusters (with some 10-20 atoms) act slower with O2 when the number of atoms in the aluminum cluster is odd than when it is even. For the theoretical calculations they used the Hartree-Fock method to which correlation effects were added via Moller-Plesset perturbation theory. Their interesting finding is that, since the ground state of O2 is a triplet state, spin is important. Thus, the interaction of O2 with AlW or Al rH depends critically on the spin of the AlW or Al rH anions. 

The Moller-Plesset second-order perturbation theory (MP/2) is comparatively simple because only matrix elements of the form Po v 0 ) need to be calculated, while in third order there are already matrix elements of type V 0 (as in a Cl calculation). There are many more of these matrix elements (even for an atomic basis of middle quality there are many more virtual than occupied bands) than those corresponding to excitations between the ground state and the different doubly excited states. 

Computational methods such as density functional theory (DFT) [1-3], Moller-Plesset perturbation theory (MP) [4, 5], and coupled-cluster (CC) theory [6-8] are common computational methods used to calculate ground state properties with quantum chemistry. These methods are black-box in the sense that the system can be analysed solely in terms of giving an input structure and a level of theory. When a problem is formulated, the choice of which method to choose comes down to a balance between levels of accuracy required versus computational expense. Even for ground state problems black-box methods may not be applicable in all cases. For example, in cases of near or actual degeneracy then any method based on a single determinant as a reference will be invalid. Such things are far more common when transition metals are involved. 

Ab initio calculations using the fourth-order Moller-Plesset perturbation theory (MP4(SDTQ)) were performed on HeN " in its ground (X IT) and excited states ( X ) which both were found to be covalently bound. HeN is metastable and dissociates via the exothermic charge-separation reactions HeN (X Il) He ( S) + N ( P) and HeN (" 2 ) He ( S) + N ( D). There is a barrier to dissociation of 201.7 kJ/mol for ground-state HeN. Other calculated data are [1] ... 

Calculations at the HF level and with the second-order Moller-Plesset perturbation theory (MP2) yielded a potential curve minimum for the species re = 1.415A, v = 774 cm at the HF level, re = 1.499 A, v = 455 cm at the MP2 level [1] the use of higher orders of the Moller-Plesset perturbation theory yielded a purely repulsive ground-state potential curve for NeN [1, 2]. 

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