Ground state helium energy

Figure J Helium ground state energy computed by two different methods. The Rivelino and Vianna calculations [108] vs the results of reference [117] considered here as the exact ones.

Figure 5 Helium ground state energy as a function of distance D between the nucleus and the spherical box centre obtained by means of two basis sets four s orbitals for the first, and four s plus one p(z) for the second.

To go further, we turn to so-called all-order methods. We start by considering relativistic calculations of type carried out by Lindroth [38] and Blundell et al. [39], which account for all possible single and double excitations of the ground-state helium HF wave function. These calculations have the potential of giving an exact helium ground-state energy. 

Putting Z = 2, we get as our approximation to the helium ground-state energy - 21/ 6fe /ao = -(729/256)2(13. 4 eV) = -77.48 eV, as compared with the true value of -79.01 eV. Use of i instead of Z has reduced the error from 5.3% to 1.9%. In accord with the variation theorem, the true ground-state energy is less than the variational integral. 

Wilets, L., and Cherry, I. J., Phys. Rev. 103, 112, Lower bound to the ground state energy and mass polarization in helium-like atoms. ... 

In this section we examine the ground-state energy of the helium atom by means of both perturbation theory and the variation method. We may then compare the accuracy of the two procedures. 

Table 9.1. Ground-state energy of the helium atom...

Figure 4-1 Convergence of the correlation energy for the helium ground state with the number N of pair natural orbitals.

Figure 18 Variation of the ground state energy of helium-like ions agai nst the Debye parameter. The lowermost curve is for He and the uppermost curve is for Ar16+ Reprinted with permission from [192] 2002, Springer Science + Business Media...

Before the individual parts of this function are discussed, the energy eigenvalue will be considered. The ground state energy g of the helium atom is just the energy value for double-ionization which can be determined accurately by several different kinds of experiments. Before the experimental value can be compared with the calculated one, some small corrections (for the reduced mass effect, mass polarization, relativistic effects, Lamb shift) are necessary which, for simplicity, are... 

The result of such a calculation for Pls(r) of helium and how it compares with the hydrogenic case are shown in Fig. 7.6, and the differences can be seen clearly. For the total energy of the helium ground state the HF approach yields Eg = — 2.862 au. This is rather close to the experimental value, Eg(exp.) =... 

Table 3. Convergence study for the ground state energy of helium, using a triple basis set (in atomic units). R(fl) is the ratio of successive differences between the tabulated energies...

Abstract. With an eye on the high accuracy ( 10 MHz) evaluation of the ionization energy from the helium atom ground state, a complete set of order ma6 operators is built. This set is gauge and regularization scheme independent and can be used for an immediate calculation with a wave function of the helium ground state. 

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