Configuration interaction beryllium atom

Under these conditions, the 3-RDM of the three lower states of the Beryllium atom and the two lower ones of the Water molecule were determined [48] by taking as initial data the 2-RDM obtained in a Full Configuration Interaction. In Table 4 some of these results are given and as can be seen they are very satisfactory. 

Let us now discuss the correlation effects on the atomic shell structure. We plot in Fig. 7 some of the described potentials for the case of the beryllium atom. The exact exchange-correlation potential v c is calculated from an accurate Cl (Configuration Interaction) density using the procedure described in [20]. The potentials Vx, and u" , are calculated within the optimized potential model (OPM) [21,40,41] and are probably very close to their exact values which can be obtained from the solution for of the OPM integral equation [21,40,41] by insertion of the exact Kohn-Sham orbitals instead of the OPM... 

Configuration interaction expansion coefficients for the approximate ground-state wavefunctions [ (l-s) of the beryllium atom for orbits [i] = 1,..., 4 and densities... 

To factor out basis set effects, we first compare in Table 24 full configuration interaction (FCI) excitation energies and dipole strengths (the values in parentheses) to those obtained with the TDA, RPA, ACISD, and EOM-CCSD approximations. Because FCI is a very expensive method, which has a factorial dependence on the number of electrons, we are restricted to a small system and present comparisons only for the beryllium atom and the CH" molecule." ... 

In Section III.E, EOM ionization potentials and electron affinities are compared with accurate configuration interaction (Cl) results for a number of atomic and molecular systems. The same one-electron basis sets are utilized in the EOM and Cl calculations, allowing for the separation of basis set errors from errors caused by approximations made in the solution of the EOM equation. EOM results are reported for various approximations including those for the extensive EOM theory developed in Section II. Section III.F presents results of excitation energy calculations for helium and beryllium to address a number of remaining difficult questions concerning the EOM method. 

Boys S F 1950 Electronic wave functions II. A calculation for the ground state of the beryllium atom Proc. R. Soc. A 201 125-37 Shavitt I 1977 The method of configuration interaction Modern Theoretical Chemistry vo 3, ed H F III Schaefer (New York Plenum) pp 189-275... 

Let us imagine that we want to calculate the interaction energy of two beryllium atoms, and that we decide that to describe the beryllium atom, we have to include not only the Ys 2s configuration, but also the doubly excited one, s 2p. In the case of beryllium, this is a very reasonable step, since both configurations have very close energies. Let us assume now that we calculate the wave function for two beryllium atoms. If we want this function to describe the system correctly, also at large interatomic distances, we have to make sure that the departing atoms have appropriate excitations at their disposition (i.e., in our case s 2p for each). To achieve this, we must incoiporate quadruple excitations into the method. ... 

---