Zeff & SCF
From WikidChem
[edit]Zeff
Now we have finished the study of one-electron atoms. But how do we calculate the situation in which the atom has more than one electron? The very simplest way to take electron-electron repulsion into partial account while keeping the simplicity of the H-like atom, is to let other electrons partially "cancel" out the attraction of protons in the atomic nucleus. Orbitals near the nucleus would be particularly effective at "screening" the nuclear charge seen by electgrons in more remote orbitals. Generally s-orbitals, which have density at the nucleus should be less effectively screened than p- or d-orbitals which have no density at the nucleus. Adopting this approach, people attempted to calculate the effective Z of the nuclei for different orbital electrons, that would give reasonable approximations of orbital shape and energy. These Zeff charges can be used to estimate starting orbital shapes for SCF calculation.
[edit]Self-Consistent Field
Begin with two H-like orbitals for a single atom: each of them has one electron. How do you calculate their energies? SCF provides us a way to solve this problem.
First question: what do we need to calculate the Psi of an electron? The potential energy as a function of position. In this case of two electrons, while calculating the orbital of one of them, we can consider the cloud of the other electron as a source of the potential energy. Thus for electron 1, we can get a preliminary Psi function with the second one approximated as a fixed cloud. The first electron is then treated as a fixed cloud to provide potential energy for determining the orbital of the second electron.
(I have revised this far. The proprietors should pick up from here. Make sure you understand any terms you choose to use. - JMM)
Thus, we can get the density, so as to the energy field. In this way, we can start to consider the next step of the calculation. In the next step, we can use this enhanced potential energy field function to re calculate the Psi of the first electron. This approximation is better than before. After this, as you can imagine, a new circulation can be done. This process can be continued infinitely, but we would stop when the promotion of the precision of the result stop changing. However, the method "self-consistent" is named after the result->input->result "self-consistent" circulation.
Question: what can we get from this result? what is wrong? SCF will always give an energy value that is higher than the actual energy. This is because the calculation holds an electron static as a cloud, when in actuality it is moving in a way so as to avoid the other electron(s). This makes the actual energy lower than the calculated energy.
by a lower energy, we mean more negative, correct? MV
