Examples of Electron Correlation Effects

In this section we will illustrate the calculation of electromagnetic properties taking the electric dipole moment jl Eq. (4.40) in Table 13.1, the static electric dipole polarizability a Eq. (4.52) in Table 13.2, the absolute nuclear magnetic shielding constant a Eq. (5.67) in Table 13.3 and the indirect nuclear spin-spin coupling constants J 

75) in Tables 13.4 to 13.6 as examples. The emphasis is here on the comparison of some of the methods introduced in Chapters 10 to 12 and in particular on the effect of electron correlation, meaning the difference in the results obtained with methods based on the Hartree-Fock wavefunction, like SCF linear response (section 11.2) or RPA (section 10.3) and CHF (section 11.1) on one side and with methods based on multiconfigurational (sections 10.4 and 11.2), Mpller-Plesset (sections 10.3 and 12.2) or coupled cluster wavefunctions (sections 10.3, 11.4 and 12.2) on the other side. Only results for small molecules are discussed here. 

In Table 13.1 some results for the electric dipole moment (Packer et al., 1994) of the hydrogen halides, HX, and methyl halides, CH3X, are shown. They are calculated with the SCF density matrix, Eq. (9.112),with the unrelaxed second-order (MP2) density matrix in Eqs. (9.116)-(9.118) and with the relaxed second-order (MP2) density matrix in Eq. (12.5). The results for the dipole moments are clearly improved by the second-order correction to the MP density matrix. However, no clear trend is observable for the comparison of the relaxed and unrelaxed MP2 density matrix. Correlation at this level reduces the dipole moments on average by 9%. The root-mean-square percentage deviation of the unrelaxed MP2 results from the experimental equilibrium geometry values is 3.6% with a maximum and minimum deviation of 5.0% and -1.4%, respectively. 

4 Indirect Nuclear Spin-Spin Coupling Constants 

Astrand et al., 1999 Jaszunski and Ruud, 2001) a slightly different basis set and nuclear geometry were employed than in the other calculations. However, this has no effect on the conclusions of the comparison. 

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