Scheme and Its Check

In variational methods, the interaction energy is not calculated directly even if the M0ller-Plesset perturbation theory is used. We have to calculate the interaction energy at all calculation levels as a difference 

All calculations in Ref. [22] were performed utilizing the Gaussian-98 code [30]. The potential energy scan was performed by means of the Mqller-Plesset perturbation theory up to the fourth order (MP4) in the frozen core approximation. The electronic density distribution was studied within the population analysis scheme based on the natural bond orbitals [31,32], A population analysis was performed for the SCF density and MP4(SDQ) generalized density determined applying the Z-vector concept [33]. 

We tested the quality of the calculations [22] by applying several different approaches. Firstly, the calculations were compared with Mqller-Plesset calculations with no frozen core, Is2 frozen, and ls22s22p6 frozen core electrons for Be, Mg, and Ca clusters, respectively. The inclusion of more electron in the correlation energy calculations slightly lowers two- as well as three-body 

In Table II the results of our calculations [22] of the equilibrium geometry and binding energy together with the published data are presented. A comparison with literature data indicates a quite satisfactory agreement. The values of the binding energy for the trimers Be3 and Mg3 are very close to the best estimations in Ref. [18]. 

In order to check the convergence of the MP perturbation series, the perturbation contributions e P to the interaction energy in each order have to be calculated  

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