Helium atom ground state

For the helium atom ground state, which we shall later generalize to many election atoms and molecules. 

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. 

Here we overview our applications to the helium atom ground state. In the Hyller-aas coordinate defined by... 

PERTURBATION TREATMENT OF THE HELIUM-ATOM GROUND STATE... 

Section 9,3 Perturbation Treatment of the Helium-Atom Ground State 253... 

EXAMPLE Do an SCF calculation for the helium-atom ground state using a basis set of two Is STOs with orbital exponents = 1.45 and 2 = 2.91. [By trial and error, these have been found to be the optimum s to use for this basis set see C. Roetti and E. Clementi, J. Chem. Phys., 60, 4725 (1974).]... 

Now consider variation functions for the helium-atom ground state. If we used 4° [Eq. (9.49)] as the trial function, we would get the first-order perturbation result, -74.82 eV. To improve on this result, we introduce a variational parameter into (9.49). We try the normalized function... 

TABLE 5-1 Average Values for Energy Calculated from Helium Atom Ground State... 

The chemical reactivity that starts with Ar does not exist for He and Ne as, for example, in the case of the formation of diatomic fluorine ions [98]. In fact, in a review of the subject, Holloway and Hope [99] write that "The inert status for helium and neon remains unchallenged." Indeed, this is in accordance with the prediction that accompanied the introduction of the rough classification of atomic ground states in terms of Fermi-seas [7,26c, 45]. 

An application of the variation method to the lithium atom ground state uses an orbital wave function containing hydrogen-like orbitals with variable orbital exponents (effective nuclear charges) similar to that used with helium, except that different effective... 

Table 4 Atomic and molecular data (number of electrons in atomic valtmce shell, atomic chemical hardness jj, atomic ground-state energy Eg, interatomic homopolar binding length with respect to the first Bohr radius oq. along the specific physical and chemical bonding BEC energies) for hydrogen and helium toward assessing their BEC-bonding Lennard-Jones-type potential (181), all in atomic units...

Mainly for considerations of space, it has seemed desirable to limit the framework of the present review to the standard methods for treating correlation effects, namely the method of superposition of configurations, the method with correlated wave functions containing rij and the method using different orbitals for different spins. Historically these methods were developed together as different branches of the same tree, and, as useful tools for actual applications, they can all be traced back to the pioneering work of Hylleraas carried out in 1928-30 in connection with his study of the ground state of the helium atom. 

To test the accuracy and convenience of the method of superposition of configurations, the problem of the ground state of the helium atom has recently been reexamined by several authors. According to Hylleraas (1928), the total wave function may be expressed in the form... 

TABLE VI. Ground State of the Helium Atom Obtained by Superposition of Configurations ... 

Power Series Expansions and Formal Solutions (a) Helium Atom. If the method of superposition of configurations is based on the use of expansions in orthogonal sets, the method of correlated wave functions has so far been founded on power series expansions. The classical example is, of course, Hyl-leraas expansion (Eq. III.4) for the ground state of the He atom, which is a power series in the three variables... 

LennarD-Jones, J. E., and Pople, J. A., Phil. Mag. 43, 581, Ser. 7, The spatial correlation of electrons in atoms and molecules. I. Helium and similar two-electron systems in their ground states. Analysis of in-out effect and angular effect. 

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

Kinoshita, T., Phys. Rev. 105, 1490, Ground state of the helium atom. ... 

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