Moller-Plesset theorem

The SCF solution for a first-order, one-electron property is usually argued to be relatively accurate. The reason follows from the Moller-Plesset theorem. Earlier we found that the first correlation correction to Oq comes solely from double excitations, 0 + However, ( I>o 0 Ii / ) = 0... 

There sure other quantities that are related to expectation values other than that of the Hamiltonian e.g. dipole and higher multipole moments, spin densities, field gradients). Most of the operators that come into play here are one-electron operators, and the Moller-Plesset theorem states that their expectation values (like the electron density) are affected by correlation corrections to the wave function only to second order. As a consequence, correlation does not much influence these expectation values, except when the Hartree-Fock contribution is unusually small, so that a correlation correction may even determine the sign, as is the case for the dipole moment of CO >. 

These integrals will he non-zero only for double excitations, according to the Brillouin theorem. Third- and fourth-order Moller-Plesset calculations (MP3 and MP4) are also... 

It was seen in Section 5.3 that to determine the QP band structures of a polymeric chain one must use a size-consistent method to determine the major part of the correlation [many-body perturbation theory (MBPT) in the Moller-Plesset partitioning, coupled-cluster theory, etc.]. Suhai, in his QP band-structure calculation on polyacetylenes and polydiace-tylenes, used second-order (MP/2) Moller-Plesset MBPT. For polydiacetylenes he obtained 5.7 eV as first ionization potential (using the generalized Koopmans theorem) for the PTS structure (see Figure 8.1), in reasonable agreement with experiment (A = 5.5 0.1 while the HF value (the simple Koopmans theorem) is 6.8 eV.< > For the TCDU diacetylene structure the theoretical value is 5.0 eV (HF value, 6.2 eV). Unfortunately, there is no reliable experimental ionization-potential value available for the TCDU structure of polydiacetylene. 

The ionization potentials of NH2 in the a A state, Ej(vert) = 24.7 and Ej(ad) = 23.2 eV, were obtained using the 4th-order Moller-Plesset perturbation theory [44]. Semiempirical calculations are given in [8]. Additional Ej(vert) values of NHj(a Ai) were determined applying Koopman s theorem [28]. 

In non-variational approaches such as Moller-Plesset perturbation theory or coupled cluster methods the wavefunction is not at all variationally optimized. However, it is possible to choose ( o hi such a way that the Hellmann-Feynman theorem is fulfilled to a certain extent, while the transition expectation value in Eq. (9.88) still gives the energy. 

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