Ground state energy of helium

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...

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...

The angular integrals in Eqs. (79) and (80) can performed analytically, and the equations solved iteratively. The value of the energy obtained in the iteration is approximately the same as the energy obtained from n -order perturbation theory. In Table 6 we show how the iteration solution to Eqs. (79-80) converges to the exact ground-state energy of helium [43]. 

Contributions to the ground-state energy of helium in an iterative solution to the all-order equations. Units a.u. 

Figure 2. Ratio test for expansion coefficients of the ground state energy of helium (solid curve) and the ground state energy of the hydrogen atom (dotted curve).

Figure 5. Poles (x) and zeros (o) of the [12/13] Fade approximant for the ground state energy of helium.

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...

The energy of the three separated particles on the right side of Eq (8.1) is, by definition, zero. Therefore the ground-state energy of the helium atom is given by () = -(l + h) = -79.02 cV = -2.90372 hartrees. We will attempt to reproduce this value, as closely as po.ssiblc, by theoretical analysis. 

Having reviewed the results for the critical behavior of the ground-state energy of the helium isoelectronic sequence, we may now consider other excited states. The ground state is symmetric under electronic exchange and has a natural parity, which means that its parity = (— l/1 (— l/2 is equal... 

Calculation of the ground state energy of the helium atom is a critical case as well because it is the first example of correlation energy, the difference between the Hartree-Fock energy and the exact value. The energy required to remove one electron from a neutral He atom is the first ionization potential... 

Then the ground state energies of the confined helium atom are given by... 

Table 9 Ground state energy of the helium atom confined by an impenetrable spherical box of radius R obtained by ten Seldam and de Groot [99]. Distances and energies are given in bohrs and hartrees, respectively...

Figure 5.4b The output of each iteration to self-consistency for the Clementi double-zeta Slater basis calculation of the ground state energy of the helium atom and the final converged result of the worksheet hfs in fig5-4.xls. Further iterations lead to no improvement of the results and the energy of the helium atom is found to be 2.86167 a.u.

Figure 5.10 Determination of the best ground state energy for helium by varying the independent coefficient of the split-basis linear combination from the sto-4g) Gaussian set of Table 5.1. The energy of helium is found to be —2.85516 Hartree for the coefficients of equation 5.40 equal 0.51380 and 0.59189. The orbital energy, is, is calculated to be —0.91412 Hartree and compares well with Huzinaga s result. Table 5.2.

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