Ground state energy beryllium

An impressive success of the lEPA is its prediction of the ground state energy of the beryllium atom. The spin-orbital pair correlation energies obtained by... 

Alternative methods are based on the pioneering work of Hylleraas ([1928], [1964]). In these cases orbitals do not form the starting point, not even in zero order. Instead, the troublesome inter-electronic terms appear explicitly in the expression for the atomic wavefunction. However the Hylleraas methods become mathematically very cumbersome as the number of electrons in the atom increases, and they have not been very successfully applied in atoms beyond beryllium, which has only four electrons. Interestingly, one recent survey of ab initio calculations on the beryllium atom showed that the Hylleraas method in fact produced the closest agreement with the experimentally determined ground state atomic energy (Froese-Fischer [1977]). 

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. 

Divalent beryllium honds through two equivalent sp, or (Sgonal, hybrids. The appropriate ionization energy therefore is not that of ground state beryllium, ls2 2. hut an average of those energies necessary to remove electrons from the promoted, valence state ... 

The main dijfference between a linear H3 system and beryllium hydride, BeH2, which is a linear molecule, is that the central atom now contributes two valence electrons and four atomic orbitals the 2s orbital, which is doubly occupied in an isolated ground state Be atom (configuration Is, 2s ), and the three 2p orbitals which are empty in Be but lie not too far above 2s in energy. Graphically, we have ... 

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. 

El.30 Frontier orbitals of Be Recall from Section 1.9(c) Electron affinity, that the frontier orbitals are the highest occupied and the lowest unoccupied orbitals of a chemical species (atom, molecule, or ion). Since the ground-state electron configuration of a beryllium atom is ls 2s , the frontier orbitals are the 2s orbital (highest occupied) and three 2p orbitals (lowest unoccupied). Note that there can be more than two frontier orbitals if either the highest occupied and/or lowest unoccupied energy levels are degenerate. In the case of beryllium we have four frontier orbitals (one 2s and three 2p). 

The rules of perturbation theory associated with the relativistic no-pair Hamiltonian are identical to the well-known rules of nonrelativistic many-body perturbation theory, except for the restriction to positive-energy states. The nonrelativistic rules are explained in great detail, for example, in Lindgren and Morrison [30]. Let us start with a closed-shell system such as helium or beryllium in its ground state, and choose the background potential to be the Hartree-Fock potential. Expanding the energy in powers of V) as... 

The Be ( a) Li" reaction has been much used for exciting the states of Li and the 0.48 MeV and 4.62 MeV states have been seen with moderate bombarding energies and possibly the 7.65 MeV state with 14 MeV deuterons . The angular distribution for the ground state group is isotropic for deuterons of energy from 0.3 to 0.7 MeV , and the correlation between the alpha particles to the first excited and the subsequent radiation is isotropic . This confirms the spin J = for the first excited state of Li . The alpha particle spectrum in the bombardment of beryllium by deuterons includes a continuous distribution of particles from the three body process Be (< 2a) H . 

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