Ground states of Beryllium

Table 3 lists results for the ground state of beryllium with a HY-CI basis[45]. This Table also contains Cl and MCHF calculations for comparison. 

For some cases like the 5i/2 ground state of beryllium the ls 2s and ls 2p configurations strongly interact and both should therefore be included in the model space. Furthermore a wave operator is introduced which generates the exact wave function from the model function V o according to... 

Explain whether the following could be a valid symmetrized spin wavefunction for the ls 2s ground state of beryllium ... 

Boys S F 1950 Eleetronie wave funetions II. A ealeulation for the ground state of the beryllium atom Proc. R. See. A 201 125-37 Shavitt I 1977 The method of eonfiguration interaetion Modern Theoretical Chemistry vo 3, ed H F III Sehaefer (New York Plenum) pp 189-275... 

Boys, S. F., Proc. Roy. Soc Londno) A201, 125, Electronic wave functions. II. A calculation for the ground state of the beryllium atom." a. 

While from the energy point of view, the correlation effects seem to be overestimated, the RDAf s are particularly satisfactory. Thus, when comparing the 2-RDAf s obtained with these approximations for the ground state of the Beryllium atom with the corresponding FCI one, the standard deviations are 0.00208236 and 0.00208338 for the MPS and IP respectivelyFor this state, which has a dominant four electron configuration of the type, 1122 >, the more important errors, which nevertheless can be considered small, are given in table 2. 

An analysis of the values taken by the different elements of the correlation matrices was recently reported [15] for the ground state of the Beryllium atom. This analysis suggested that the contributions of the 1 -, 2- and 3-body correlation effects differed according to the kind of orbitals involved in a given element. In particular, the highest occupied homo) and lowest empty (lumo) orbital of the HF configuration seemed to play an important role. 

Figure 2. Lowest eigenvalue of the 2-RDM and the 2-HRDM matrices at each iteration of the MZ purification procedure for the ground state of the beryllium atom.

Polymerization of the beryllium hydride molecule. Ground state of the beryllium hydride (BeFl2, Bc2Fl4, and Be3H6) systems have been studies by the... 

Fock (HF) one. This property is exploited (Sect. 4) for obtaining an equation in which both the correlation energy and the correlation matrices appear explicitly. These correlation matrices are defined here as the difference between a FCI-RDM and the corresponding UF-RDM. By applying the arguments given in [19] the exact structure of these correlation matrices can be expressed in terms of the 1 -RDM and of the first order transition RDM s. A calculation of the ground state of the beryllium atom illustrates the formalism. 

We can now predict the electron configurations and orbital diagrams for the ground state of lithium, which has three electrons, and beryllium, which has four electrons ... 

K. Jug and D. N. Nanda, Theor. Chim. Acta, 57, 131 (1980). SINDOI. 111. Application to Ground States of Molecules Containing Fluorine, Boron, Beryllium, and Lithium. 

Another manifestation of the reciprocity of densities in r- and p-space is provided by Fig. 19.2. It shows the radial electron number density D r) = Aiir pir) and radial momentum density /(p) = Aitp nip) for the ground state of the beryllium atom calculated within the Hartree-Fock model in which the Be ground state has a ls 2s configuration. Both densities show a peak arising from the Is core electrons and another from the 2s valence electrons. However, the origin of the peaks is reversed. The sharp,... 

What are the allowed transitions from the ground states of (a) a beryllium atom and (b) a boron atom ... 

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