Helium atom, configurations

Example The electron configuration for Be is Is lsfi but we write [He]2s where [He] is equivalent to all the electron orbitals in the helium atom. The Letters, s, p, d, and f designate the shape of the orbitals and the superscript gives the number of electrons in that orbital. 

A hydrogen atom (Z = 1) has one electron a helium atom (Z = 2) has two The single electron of hydrogen occupies a Is orbital as do the two electrons of helium We write their electron configurations as... 

The analogy is even closer when the situation in oxygen is compared with that in excited configurations of the helium atom summarized in Equations (7.28) and (7.29). According to the Pauli principle for electrons the total wave function must be antisymmetric to electron exchange. 

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... 

A neutral helium atom has two electrons. To write the ground-state electron configuration of He, we apply the aufbau principle. One unique set of quantum numbers is assigned to each electron, moving from the most stable orbital upward until all electrons have been assigned. The most stable orbital is always ly( = l,/ = 0, JW/ = 0 ). 

For hydrogen, the notation Is1 is used, where the superscript denotes a single electron in the Is state. Because an electron can have a spin quantum number of +1/2 or -1/2, two electrons having opposite spins can occupy the Is state. The helium atom, having two electrons, has the configuration Is2 with the electrons having spins of +1/2 and —1/2. 

In the lowest excited-state helium atom there are two possible spin configurations ... 

Fig. 13.4 Logarithm of error(Eh) in the configuration interaction energy for the ground state of the helium atom as a function of maximum orbital quantum number, L, of the one-electron basis functions. The data were obtained in an...

Atoms and ions with noble-gaS electron configurations have usually been described as having spherical symmetiy. For some considerations this description is satisfactory for others, however, it is advantageous to consider the atoms or ions to have a shape other than spherical—the helium atom can be described as deformed to a prolate ellipsoid of revolution, and the neon atom and other noble-gas atoms as deformed to a shape with cubic symmetry. 

The molecule He, is unknown since the number of antibonding electrons (2) is equal to the number of bonding electrons (2) and the net bond order is zero. With no bond energy14 to overcome the dispersive tendencies of entropy, two helium atoms in a "molecule will not remain together but fly apart. If it existed, molecular helium would have the electron configuration ... 

Exercise 6-1 Write the ground-state configuration for a helium atom with two unpaired electrons (He ) that is in accord with the Pauli principle. Give your reasoning. 

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