Helium atom orbitals

The intensity of shading at any point represents the magnitude of 1, i.e. the probability of finding the electron at that point. This may also be called a spherical charge-cloud . In helium, with two electrons, the picture is the same, but the two electrons must have opposite spins. These two electrons in helium are in a definite energy level and occupy an orbital in this case an atomic orbital. 

VV e now wish to establish the general functional form of possible wavefunctions for the two electrons in this pseudo helium atom. We will do so by considering first the spatial part of the u a efunction. We will show how to derive functional forms for the wavefunction in which the i change of electrons is independent of the electron labels and does not affect the electron density. The simplest approach is to assume that each wavefunction for the helium atom is the product of the individual one-electron solutions. As we have just seen, this implies that the total energy is equal to the sum of the one-electron orbital energies, which is not correct as ii ignores electron-electron repulsion. Nevertheless, it is a useful illustrative model. The wavefunction of the lowest energy state then has each of the two electrons in a Is orbital ... 

The final wavefunction stUl contains a large proportion of the Is orbital on the helium atom, but less than was obtained without the two-electron integrals. 

All of our orbitals have disappeared. How do we escape this terrible dilemma We insist that no two elections may have the same wave function. In the case of elections in spatially different orbitals, say. Is and 2s orbitals, there is no problem, but for the two elechons in the 1 s orbital of the helium atom, the space orbital is the same for both. Here we must recognize an extr a dimension of relativistic space-time... 

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... 

Turning to the orbital part of we consider the electrons in two different atomic orbitals Xa and x.b as, for example, in the 1x 2/) configuration of helium. There are two ways of placing electrons 1 and 2 in these orbitals giving wave functions Z (1)Z6(2) and Z (2)Z6(1) but, once again, we have to use, instead, the linear combinations... 

Figure 16-3D shows the simplified representation of the interaction of two helium atoms. This time each helium atom is crosshatched before the two atoms approach. This is to indicate there are already two electrons in the Is orbital. Our rule of orbital occupancy tells us that the Is orbital can contain only two electrons. Consequently, when the second helium atom approaches, its valence orbitals cannot overlap significantly. The helium atom valence electrons fill its valence orbitals, preventing it from approaching a second atom close enough to share electrons. The helium atom forms no chemical bonds. ... 

Each helium atom does have, of course, vacant 2s and 2p orbitals which extend farther out than the filled Is orbital. The electrons of the second helium atom can "overlap with these vacant orbitals. Since this overlap is at great distance, the resulting attractions are extremely small. This type of interaction presumably accounts for the attractions that cause helium to condense at very low temperatures. 

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. 

As an example we may calculate the energy of the helium atom in its normal state (24). Neglecting the interaction of the two electrons, each electron is in a hydrogen-like orbit, represented by equation 6 the eigenfunction of the whole atom is then lt, (1) (2), where (1) and (2) signify the first and the second electron. 

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 ). 

C08-0105. Write a brief explanation for each of the following (a) All three 2 p orbitals of a helium atom have identical energy, (b)... 

We have just explained that the wave equation for the helium atom cannot be solved exacdy because of the term involving l/r12. If the repulsion between two electrons prevents a wave equation from being solved, it should be clear that when there are more than two electrons the situation is worse. If there are three electrons present (as in the lithium atom) there will be repulsion terms involving l/r12, l/r13, and l/r23. Although there are a number of types of calculations that can be performed (particularly the self-consistent field calculations), they will not be described here. Fortunately, for some situations, it is not necessary to have an exact wave function that is obtained from the exact solution of a wave equation. In many cases, an approximate wave function is sufficient. The most commonly used approximate wave functions for one electron are those given by J. C. Slater, and they are known as Slater wave functions or Slater-type orbitals (usually referred to as STO orbitals). 

A ground-state helium atom has two paired electrons in the Is orbital (Is2). The electrons with paired spin occupy the lowest of the quantised orbitals shown below (the Pauli exclusion principle prohibits any two electrons within a given quantised orbital from having the same spin quantum number) ... 

Electronic excitation can promote one of the electrons in the Is orbital to an orbital of higher energy so that there is one electron in the Is orbital and one electron in a higher-energy orbital. Such excitation results in the formation of an excited-state helium atom. 

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