Zero of energy used in MECI

Zero of energy used in the Multi Electron Configuration Interaction

The energy of the system after all the electronic terms arising from the electrons of the M.O.s involved in the starting configuration are removed is a useful quantity. Removal of these terms lowers the orbital energies thus:

$\begin{displaymath}\epsilon_{ii}^+ = \epsilon_{ii} -\sum_{j=B}^A(J_{ij}-K_{ij})O_j^g. \end{displaymath}$

The arbitrary zero of energy in a MECI calculation is the starting ground state, without any correction for errors introduced by the use of fractional occupancies. In order to calculate the energy of the various configurations, the energy of the vacuum state (i.e., the state resulting from removal of the electrons used in the C.I.) needs to be evaluated. This energy is given by:

$\begin{displaymath}GSE=E_g^+ = - \sum_{i=B}^A2\epsilon_{ii}^+O_i^g+J_{ii}(O_i^g)^2+ \sum_{i=B}^A\sum_{j=B}^{i-1}2(2J_{ij}-K_{ij})O_i^gO_j^g \end{displaymath}$

(Within the MECI routine, GSE refers to E_g⁺.)

By redefining the system so that those filled M.O.s which are not used in the MECI are considered part of an unpolarizable core, the new energy levels ε_i^- can be identified with the one-electron energies H_ii and the total electronic energy E_r of any microstate is set equal to the sum of the energy of the electrons considered in the microstate plus E_g⁺.