Moller-Plesset perturbation theory energy

To obtain an improvement on the Hartree-Fock energy it is therefore necessary to use Moller-Plesset perturbation theory to at least second order. This level of theory is referred to as MP2 and involves the integral J dr. The higher-order wavefunction g is... 

MP4 4 Order Moller-Plesset Perturbation Theory (including Singles, Doubles, Triples and Quadruples by default) Energies only... 

Thus, the value of E the first perturbation to the Hartree-Fock energy, will always be negative. Lowering the energy is what the exact correction should do, although the Moller-Plesset perturbation theory correction is capable of overcorrecting it, since it is not variational (and higher order corrections may be positive). 

Higher level calculations, based on higher orders of Moller-Plesset perturbation theory, can also be performed, albeit with the consumption of much more computer time. For example, an MP4SDTQ calculation uses fourth-order Moller-Plesset perturbation theory, includes excitations through quadruples, and gives better energies than MP2 does. 

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 ... 

We state without further derivation that the electronic energy corrected to second order in Moller-Plesset perturbation theory, mp2 is... 

The matrix f in (4 66) can be chosen such that the matrix elements of H represent orbital energy differences in the spirit of Moller-Plesset perturbation theory. A suitable choice is then ... 

G2(MP2) theory is a variation of G2 theory that uses reduced orders of Moller-Plesset perturbation theory.76 In this theory the basis set extension corrections of G2 theory in steps 4a, 4b, and 4d are replaced by a single correction obtained at the MP2 level with the 6-311+G(3df,2p) basis set, A (+3df,2p), as given by step 4 (d) in Table 4. The total G2(MP2) energy is thus given by... 

A variation of G2 theory that uses reduced orders of Moller-Plesset perturbation theory in combination with a smaller basis set for the quadratic configuration correction is G2(MP2,SVP) theory.77 78 The SVP refers to the split-valence plus polarization basis, 6-31G(d), used in this QCISD(T) correction. In this theory the final energy is given by... 

Table 6 displays some bonding energies for CI2-, as calculated at the D-BOVB level and at other theoretical levels, including Hartree-Fock and Moller-Plesset perturbation theory. Unlike the F2 case, the Moller-Plesset series converges well around the values of 24-25 kcal/mol which can be taken as references for the bonding energy in this basis set. 

Using a single determinant to derive the Hartree-Fock wavefunction does not take into account the correlation between electrons of different spins. If the wavefunction is described by a linear combination of determinants, then configuration interaction is incorporated. Another method to model correlation energy involves Moller-Plesset perturbation theory. A more detailed description of this may be found in Ref. 41. 

One of the inherent problems with ab initio calculations is that they do not take full account of electron correlation, which arises from electrons keeping away from the vicinity of other electrons. This can make a significant contribution to the energy and is especially significant for accurate calculations of reaction energies and bond dissociation. One early method used for adding the effects of electron correlation to the Hartree-Fock method incorporated Moller-Plesset perturbation theory and led to methods labeled MP2, MP3, MP4, etc. 

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